COUNTING THE LOCAL FIELDS IN SG THEORY.
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二项式系数公式大全The binomial coefficient formula is a fundamental concept in combinatorics, algebra, and probability theory. It is used to calculate the number of ways to choose a subset of items from a larger set, and it has numerous applications in various fields of mathematics and science. The formula is often denoted by "n choose k" or "C(n, k)", and it represents the number of ways to choose k elements from a set of n distinct elements without regard to the order in which they are chosen.The binomial coefficient formula can be expressed in several different ways, depending on the context in whichit is being used. One of the most common forms of the formula is given by the expression C(n, k) = n! / (k! (n - k)!), where "n!" denotes the factorial of n, which is the product of all positive integers up to n. This formula is derived from the principle of counting the number of ways to choose k elements from n without replacement, and it is widely used in combinatorics and probability theory.Another important form of the binomial coefficient formula is the Pascal's triangle, which provides a visual representation of the coefficients for each combination of n and k. The triangle is constructed by starting with the number 1 at the top, and then adding the two numbers above each number to obtain the value for the next row. The coefficients in Pascal's triangle can be used to quickly determine the value of C(n, k) for any given n and k, and they have applications in various areas of mathematics and computer science.In addition to its applications in combinatorics and probability theory, the binomial coefficient formula also has important connections to algebra and calculus. For example, the coefficients in the expansion of a binomial expression, such as (a + b)^n, can be calculated using the binomial coefficient formula, and they represent the coefficients of the terms in the expansion. This connection between the binomial coefficient formula and binomial expressions is a fundamental concept in algebra, and it is used in various areas of mathematics and engineering.Furthermore, the binomial coefficient formula has applications in the field of statistics, where it is used to calculate the probabilities of various events in a given sample space. For example, in the context of a binomial distribution, the formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, each with the same probability of success. This application of the binomial coefficient formula is important in statistical inference and hypothesis testing, and it has practical implications in fields such as economics, biology, and psychology.In conclusion, the binomial coefficient formula is a fundamental concept in mathematics and science, with applications in combinatorics, algebra, probability theory, and statistics. It represents the number of ways to choose a subset of items from a larger set, and it can be expressed in various forms, such as the factorial formula and Pascal's triangle. The formula has important connections to algebra and calculus, and it is used in various areas of mathematics, engineering, and computerscience. Its applications in statistics and probability theory have practical implications in fields such as economics, biology, and psychology, making it a versatile and essential tool in mathematical modeling and analysis.。
课下天天练(三十八)40分阅读提分练姓名班级考号时间:40分钟阅读(共两节,总分值40分)第一节(共15小题;每题2分,总分值30分)阅读以下短文,从每题所给的A、B、C和D四个选项中,选出最正确选项。
A[2022•长春高三质量监测]Los Angeles public schools take three weeks off during the holidays, leaving working parents in need of camps for their kids. Here's a list of terrific Winter Camps in Los Angeles to choose from.Act One Theatre CampA new online camp which brings the exciting world of theatres straight to your living room! Join us for a dynamic and interactive theatre experience where our campers get the opportunity to enjoy the fun, creativity and laughter of the theatre world. Each and every day they'll participate in acting, singing, dancing, movie-making, and stage design. All of them lead up to a professionally produced Big Show for the whole family to watch online! From the shy wallflower to the class clown: All levels of experiences are welcomed!Available Dates: Dec. 21-23 and Dec. 28-31Atwater Photo CampIn addition to Photo Camp. APC is offering Editing Camp. Learning how to edit with Lightroom & Photoshop will not only take your images to the next level, but it will also vastly improve the way you shoot. Join us!Available Dates: Dee. 28-31 and Jan. 5-8 for both Photo Camp and Editing CampCamp WildfolkJoin us in person for Wide-Open SpacesWinter Camp in a beautiful outdoor setting in Valley Village. We're outdoors, and all ready to make some wonderful memories for our kids. Games, Science, Nature Exploration, Robotics, Art, and more, 1 st-5th grade. Very few spaces remain!Available Dates: Dec. 21-24 and Jan. 4-8Sender One LAXLooking fbr something fun and health-conscious to do for your child this season? Sign up for our 3-day rock climbing camp! Activities include rope climbing, games, zip lines, king swings, and Sender City. Space is limited, so register early! Morning and afternoon sessions are available.Available Dates: Dec. 21-23 and Dec. 28-301.What is special about Act One Theatre Camp?A.It is a camp intended only for beginners.B.It is an in-person camp held in a theatre.C.It presents kids with a big TV show for fun.D.It offers kids various kinds of theatre experiences.2.Which will a boy choose if he wants to look for a five-day winter camp in January?A.Act One Theatre Camp.B.Camp Wildfolk.C.Sender One LAX.D.Atwater Photo Camp.3.What do the four winter camps have in common?A.They are held in Los Angeles.B.They are online winter camps.C.They are open to students of all ages.D.They are available every day in December.B[2022•广东七校联考]When you feel thankful for things you've received or something that has happened, that's gratitude. Gratitude is how you relate to others, when you see yourself in connection with things larger than yourself.Last year, I felt compelled (强迫的)to bake cookies for complete strangers to say “thank you”. However, what occurred later changed my view about it. One day, I had to call 999 because I found my partner unconscious on the floor. Within minutes, a police car and an ambulance arrived, filled with first responders who took my partner away to the nearest hospital, where he received the critical care he needed.A week later, still impressed by the kindness of the strangers, I wrote (hank-you notes to those helpful first responders and baked for them. It was a small gesture with a big impact...When I dropped off still-warm cookies a( (he police and the fire station, they thanked me for delivering gifts. Thanking me? All I'd done was baking, however, they'd saved a life.I drove away feeling light and happy, partly because I'd done a good deed, but mostly because I was amazed that there are great people who do life-saving work and expect nothing in return.Laler、I realized (hat my nalural high mighl have been more (han whal it sccmed. Sharing thoughts of gratitude and performing acts of kindness can boost your mood. Gratitude really does have an impact on happiness, which increases life satisfaction. I am the one who indeed benefits from expressing thanks. Then why not thank others?4.Whal changed the author's view last year?A.The stranger's gifts.B.The doctors' critical care.C.His partner's thank-you notes.D.The police's thanks for his cookies.5.Which word can describe the author's feeling in Paragraph 3?A. Proud.B. Doubtful.C. Unexpected.D. Relieved.6.What does the underlined sentence in Paragraph 5 suggest?A.The author was extremely excited.B.The author couldn't control himself.C.The author looked taller than before.D.The author thought highly of the nature.7.Which of the following may the author agree with?A.You reap what you sow.B.Roses given, fragrance in hand.C. Where there's a will, there's a way.D. With a grateful heart, life will be better.c[2022•重庆高三质量抽测]There are breathing robots versed in "thousands of years of Buddhist breathing techniques“ that claim to soothe you to sleep. Then there are weighted blankets that press around 10% of your body weight down as you take a nap. And there are apps, such as supermodel NataliaVbdianova's Loona, designed to create a “sleepscape” by combining visual and aural storytelling with relaxation-based activities such as colouring in. These are just some of the products at the heart of the “sleep aid revolution”.Sleep occupies almost as much of the national conversation as weather-how much, when, how deep it is—and we are more than prepared to spend our money on more, and better, shut-eye.In the past 12 months, sales of sleep-related products have soared. At John Lewis, silk pillowcase sales have increased by 533%. At weighted blankets company Mela, sales are up by 250%, while at Holland & Barrett sales of products in the sleep and relaxation category have grown by over 30% year on year. "Sleep” is the third most common unique search term for visitors to Neal's Yard Remedies' site.But there are some dissenting voices. "The sleep aid industry steps in with claims that we're not sleeping because it's time for a new mattress, and offers us products to enable sleep, " says Darian Leader, author of Why Can't We Sleep?” However, v he points out, “ what wc arc seeing is a depoliticizing of sleep-ignore the socioeconomic burdens and internal pain that people face and see lack of sleep as a separate problem with a ' separate solution'.”The growing interest isn't limited to those suffering from diagnosable sleep issues—sleep has become a pillar of the wellness market and tracking it has become another symptom of the rise of the quantified self, a movement that sees people tracking their every step.Sleep expert Dr. Neil Stanley distrusts the market: "It is a trick to scare everybody because nobody's going to make any money if you just go around saying it's common sense, and you know how to sleep.”While rebutting any scientific evidence for many of the products, he admits that anything—a silk pillowcase, camomile tea, yoga or listening to Pink Floyd really loudly—could, in theory, help.But, he says, many are overlooking the simple things. 4k You need three things fbr a good night's sleep: a bedroom that's comfortable, a relaxed body and a quiet mind...you need to make space in your life fbr sleep.”8.What does the underlined word “dissenting” probably mean?A. Approving.B. Opposed.C. Indifferent.D. Pessimistic.9.What message does Darian Leader intend to convey in Paragraph 4?A. A sleep problem is mainly caused by lack of a good mattress.B.Social and psychological factors should be taken into account.C.Social and psychological factors are more important than the physical setting.D.Manufacturers trick people into buying those sleep-related products.10.What can wc infer from the passage?A.Sleep-related products meet a mixed reception among customers.B.Only people with sleep problems need sleep-related products.C.There is a trend (hat more people monitor (heir sleep situation.D.Darian and Dr. Neil hold contradictory opinions towards sleep-related products.11.Why does Dr. Neil Stanley say the words in the last paragraph?A.To give a warning.B.To provide a comment.C.To express a concern.D.To make a suggestion.D[2021 •普通高等学校招生全国统一考试]The average bear, it seems, is getting ever smarter. First,it turned out that at least one can use a comb. Now it appears that some can count, too.Jennifer Vbnk, of Oakland University, in Michigan, and Michael Beran, from Georgia State University, set three American black bears the task of distinguishing between numerically larger and smaller groups of dots (点)on a computer screen. In return for a food reward one bear, Brutus, would touch the more heavily dotted pattern with his nose. The others, Bella and Dusty, would touch the screen with (heir claws (爪).As the researchers report in Animal Behaviour, the bears did best with patterns where the coloured dots did not move and where more of them also took up a larger coloured area. This could be explained by the bears' distinguishing the different areas of colour rather than truly counting the dots. However, the three bears managed to pick out the bigger number of dots even in pairs of patterns where fewer dots took up a larger area.Moving patterns, where each dot followed its own path around the screen, were more of a challenge. But Brutus, least, was not defeated. He seemed to be counting mobile dots even when the scientists tried to mislead him by moving the total coloured area of the dots at the same time.It is not entirely surprising that bears should have a high degree of intelligence. They face a lot of challenges when trying to get food. They arc, however, always alone, and so do not have the complex social systems that contribute to animal smarts. Perhaps, then, their maths skill develops because they cannot count on their friends for help.12.What (ask did the scientists sei fbr the three bears?A.Distinguishing different dot patterns.B.Figuring out different colours of dots.C.Putting the dots into differently coloured groups.D.Picking out the group with a larger number of dots.13.For the bears, the task was easier when.A.the coloured dots were moving slowlyB.the dot patterns were regular in shapeC.the dots followed a path on the screenD.more dots covered a larger coloured area14.What may explain the bears' high degree of intelligence?A.They learn skills from other animals.B.They face life challenges on their own.C.They feed on a diverse range of food.D.They have complex social networks.15.What can be a suitable title for the text?A.Bears Taught to Distinguish ColoursB.New Evidence of Bear Intelligence Was FoundC.Three Bears Learned How to CountD.The Smartest American Black Bear Brutus第二节(共5小题;每题2分,总分值10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最正确选项。
你想做工作者还是劳役者英语作文全文共3篇示例,供读者参考篇1Do You Want to Be a Worker or a Slave Laborer?As a student about to enter the workforce, I often find myself pondering the fundamental question - do I want to be a worker who finds fulfillment in their career, or a slave laborer who merely toils away for a paycheck? This dichotomy is one that has profound implications on our quality of life, mental well-being, and overall trajectory in this world.To be a worker, in its truest sense, is to engage in purposeful and meaningful labor that aligns with our values, interests, and aspirations. It is a state of being where we don't merely sell our time and effort for financial compensation, but rather, we invest our talents and passion into something greater than ourselves. A worker derives a sense of pride, accomplishment, andself-actualization from their endeavors, as they contribute to the betterment of society or the advancement of a cause they believe in.On the other hand, a slave laborer is one who has resigned themselves to a life of drudgery, where their work holds little to no personal significance beyond the acquisition of a paycheck. They trudge through each day, performing tasks that neither stimulate their minds nor ignite their souls, merely going through the motions to survive. This existence is akin to a slow, soul-crushing death, where the individual's potential withers away, and their inherent creativity and zest for life are gradually extinguished.The consequences of embracing the role of a slave laborer are far-reaching and deeply troubling. Firstly, it breeds a profound sense of dissatisfaction and disillusionment, as one's dreams and aspirations are sacrificed at the altar of mere subsistence. This internal conflict can manifest in various forms, such as depression, anxiety, and a general lack of motivation, ultimately impacting not only the individual's mental health but also their interpersonal relationships and overall well-being.Moreover, slave labor perpetuates a vicious cycle of mediocrity, where individuals settle for the bare minimum, never striving to reach their full potential or contribute substantially to the world around them. This stagnation stifles innovation, creativity, and progress, as society becomes mired in a sea ofdisengaged and apathetic individuals who have lost touch with their inherent drive to excel and leave a lasting impact.Conversely, embracing the role of a worker opens up a world of possibilities and personal fulfillment. When we align our labor with our passions and values, we unlock a wellspring of motivation, dedication, and resilience that propels us forward, even in the face of adversity. Our work becomes an extension of our identity, a source of pride and accomplishment that transcends mere financial compensation.Furthermore, being a worker fosters a sense of purpose and contribution to something greater than ourselves. We become agents of change, actively shaping the world around us through our efforts and leaving a lasting legacy that inspires future generations. This notion of leaving a positive impact is a powerful motivator that imbues our lives with meaning and significance, elevating us beyond the confines of mere survival.Additionally, the intrinsic rewards of being a worker extend far beyond personal satisfaction. By cultivating a workforce of engaged and passionate individuals, we create a ripple effect that benefits society as a whole. Innovation thrives, productivity soars, and collective progress is accelerated, as each workercontributes their unique talents and perspectives to the greater good.However, it is important to acknowledge that the path of the worker is not without its challenges. Pursuing a career that aligns with our deepest values and aspirations often requires sacrifices, such as navigating competitive job markets, enduring periods of financial instability, or even relocating to pursue opportunities that align with our goals. It demands unwavering determination, resilience, and a willingness to step outside our comfort zones in pursuit of something greater.Yet, these challenges should not be viewed as deterrents but rather as opportunities for personal growth and character development. The journey of the worker is one of continuous learning, adaptation, and self-discovery, as we navigate the ever-changing landscapes of our chosen fields, constantly refining our skills and expanding our horizons.Ultimately, the choice between being a worker or a slave laborer is a deeply personal one that each individual must grapple with. It is a decision that has far-reaching implications, not only for our own well-being but also for the advancement of society as a whole. As students poised to embark on our respective career paths, we must carefully examine ourmotivations, aspirations, and values, and make a conscious choice to embrace the path that resonates most deeply with our souls.For those who choose to be workers, the road ahead may be arduous, but the rewards are immeasurable. We will find fulfillment in our labor, contribute to the greater good, and leave a lasting legacy that inspires generations to come. Our work will become an expression of our humanity, a testament to our ability to shape our destinies and make a meaningful impact on the world around us.On the other hand, those who resign themselves to the role of slave laborers risk surrendering their dreams, stifling their potential, and resigning themselves to a life of quiet desperation. They may find temporary solace in the security of a paycheck, but at what cost? The price of sacrificing one's passions and aspirations is a steep one, often leading to a hollowness within that no amount of material wealth can fill.As for me, the choice is clear – I aspire to be a worker, an individual who finds purpose and meaning in their labor, and who contributes to the betterment of society through their efforts. I refuse to be a mere cog in the machine, exchanging my time and energy for a paycheck devoid of personal significance.My goal is to align my career with my values, to pursue work that ignites my passion and allows me to leave a lasting impact on the world.The path ahead may be fraught with challenges and uncertainties, but I embrace them wholeheartedly. For it is through these trials that I will forge my character, refine my skills, and cultivate the resilience necessary to thrive as a worker in this ever-changing world. I am determined to be an agent of change, a catalyst for progress, and a beacon of inspiration for those who follow in my footsteps.In the end, the choice between being a worker or a slave laborer is not merely a matter of profession but a fundamental decision that shapes the trajectory of our lives. It is a choice that reverberates through the fabric of society, impacting not only our personal well-being but also the collective progress of humanity. Let us choose wisely, for in our hands lies the power to shape our destinies and leave an indelible mark on the world around us.篇2Do You Want to be a Worker or a Laborer?As students, we're constantly being asked what we want to be when we grow up. Teachers, parents, even random adults at family gatherings seem to have an obsession with knowing the career path we plan to pursue. And while I understand theirwell-meaning intentions, I can't help but feel like the way this question is phrased is a bit misguided. Because at the end of the day, aren't we all just workers or laborers?Now, before you jump to any conclusions, let me explain what I mean by those terms. To me, a worker is someone who finds fulfillment and purpose in their work. They approach their job with passion, creativity, and a drive to constantly improve and grow. A laborer, on the other hand, is someone who views their job as simply a means to an end – a way to earn a paycheck and little else.I know what you're thinking: "Of course I want to be a worker! Who in their right mind would choose to be a laborer?" And you'd be right, in theory. But the sad reality is that far too many people end up settling for a life of labor, even if that wasn't their original intention.Think about it – how many people do you know who absolutely dread going to work each day? Who constantly complain about their job, their boss, their coworkers, or theirworkload? Who live for the weekends and vacations, counting down the days until their next break from the daily grind? These are the people who have resigned themselves to the life of a laborer, whether they realize it or not.And let's be honest, it's easy to see why. The path of the worker is a difficult one, fraught with challenges and obstacles. It requires a level of passion, dedication, and perseverance that many simply don't possess. It's far easier to clock in, do the bare minimum, and clock out, content with the knowledge that you've earned your paycheck for the day.But is that really living? Is that the kind of life you want for yourself?Personally, I can't imagine anything more soul-crushing than spending the majority of my waking hours doing something I despise, simply because it pays the bills. Life is too short, and too precious, to waste it in such a way.Now, I'm not saying that being a worker is easy. In fact, it's quite the opposite. It requires a level of self-awareness,self-motivation, and self-discipline that can be incredibly difficult to cultivate and maintain. It means constantly pushing yourself outside of your comfort zone, taking on new challenges, and embracing failure as a learning opportunity.It also means being willing to make sacrifices – sacrifices of time, energy, and sometimes even financial security, at least篇3Do You Want to be a Worker or a Slave?As students, we've all dreamed about our future careers and what we want to do with our lives after graduation. Well, now it's time to make a crucial decision – do we want to be workers or slaves? I know that might sound a bit extreme, but hear me out.Being a worker means having autonomy, dignity, and the ability to find fulfillment in what you do. It means pursuing a career path that aligns with your talents, interests, and values. When you're a worker, you have a voice, and your contributions are valued. You're not just a cog in a machine, but an integral part of something greater.On the other hand, being a slave is the antithesis of that. It's about being trapped in a job that sucks the life out of you, where you're treated like a disposable commodity, and your dreams and aspirations are crushed by the relentless pursuit of profit and productivity. As slaves, we're expected to mindlessly follow orders, suppress our individuality, and sacrifice our well-being for the benefit of our corporate overlords.Now, I know what you're thinking – "Woah, that's a bit heavy, isn't it?" But let's be real here, the line between being a worker and a slave is becoming increasingly blurred in today's world. With the rise of the gig economy, zero-hour contracts, and the normalization of unpaid internships, many of us are already teetering on the edge of modern-day slavery without even realizing it.Don't get me wrong; I'm not saying that all jobs are inherently evil or that we should all quit and become beach bums (although that does sound pretty appealing sometimes). What I'm saying is that we need to be mindful of the choices we make and the environments we choose to work in.Think about it – how many times have you heard horror stories about toxic workplaces, abusive bosses, andsoul-crushing corporate cultures? How many people do you know who dread going to work every morning, counting down the days until retirement or their next vacation? Is that really what we want for ourselves?Of course, not all jobs are created equal, and there will always be aspects of work that we might find less than enjoyable. But there's a big difference between having a healthy work-life balance and being treated like a disposable resource.So, what can we do to ensure that we become workers and not slaves? First and foremost, we need to be honest with ourselves about our priorities and values. What kind of work environment do we thrive in? What are our non-negotiable boundaries? What kind of company culture aligns with our ethics and beliefs?Once we have a clear understanding of what we want, we need to be proactive and do our research. Look into potential employers, read reviews from current and former employees, and don't be afraid to ask tough questions during the interview process. Remember, you're not just being evaluated – you're evaluating them too.It's also important to advocate for ourselves and know our worth. Don't settle for less than you deserve, and don't be afraid to negotiate for better working conditions, fair compensation, and opportunities for growth and development.But it's not just about finding the right job – it's also about cultivating the right mindset. We need to reject the toxic notion that our self-worth is tied to our productivity or our ability to sacrifice ourselves for the sake of our careers. We are human beings, not machines, and our well-being should always come first.Ultimately, the choice between being a worker or a slave comes down to one fundamental question: do we want to live our lives on our own terms, or do we want to surrender our autonomy and dignity to the whims of others?For me, the answer is clear – I want to be a worker, not a slave. I want to wake up every morning with a sense of purpose and fulfillment, knowing that my contributions are valued and that I'm part of something greater than myself. I want to work in an environment that nurtures my growth and enables me to reach my full potential.But more importantly, I want to live a life that is true to my values and my beliefs. I want to be able to look back on my career and know that I made a positive impact on the world, not just a profit for some faceless corporation.So, my fellow students, as we approach the next chapter of our lives, let's make a pact – let's vow to be workers, not slaves. Let's refuse to settle for less than we deserve and let's continue to fight for a world where everyone has the opportunity to find fulfillment and meaning in their work.Because at the end of the day, our careers are not just a means to an end – they are an expression of who we are and what we stand for. And if we're not careful, we might just findourselves trapped in a life that we never wanted, sacrificing our dreams and our humanity for the sake of someone else's bottom line.The choice is ours, my friends. Worker or slave? The decision is yours to make.。
循环计数英语Circular CountingCounting is a fundamental mathematical concept that is essential for understanding and navigating the world around us. From a young age, we learn to count objects, quantify quantities, and track the passage of time. However, as we delve deeper into the realm of mathematics, we encounter a more sophisticated form of counting –circular counting.Circular counting, also known as cyclical counting or modular arithmetic, is a method of enumeration where the numbers wrap around, forming a continuous loop. Unlike the linear counting we are accustomed to, where numbers increase or decrease in a straight line, circular counting operates on a cyclical framework, where the sequence repeats itself at regular intervals.One of the most common examples of circular counting is the 24-hour clock. As the day progresses, the hours cycle from 1 to 12, and then back to 1 again. This circular pattern continues throughout the day, allowing us to keep track of time in a continuous and intuitive manner. Similarly, the days of the week and the months of the yearalso follow a circular pattern, with the sequence repeating itself year after year.The concept of circular counting extends far beyond the practical applications of timekeeping. In mathematics, circular counting is fundamental to the study of modular arithmetic, which has numerous applications in computer science, cryptography, and number theory.In modular arithmetic, numbers are represented in a circular fashion, with the remainder of a division operation determining the position of the number within the cycle. For example, in modular arithmetic with a base of 7, the numbers 1, 8, 15, and 22 are all equivalent, as they all have the same remainder when divided by 7. This circular structure allows for the efficient manipulation and analysis of numbers, making it a powerful tool in various mathematical and computational domains.One of the key advantages of circular counting is its ability to simplify complex problems and facilitate efficient calculations. When working with large numbers or repetitive sequences, circular counting can provide a more compact and intuitive representation, allowing for easier pattern recognition and problem-solving.Moreover, circular counting has important applications in variousfields, such as coding theory, where it is used to detect and correct errors in digital transmissions. In digital signal processing, circular counting is employed to efficiently handle the wrapping around of phase angles in periodic signals.Beyond its mathematical and technical applications, circular counting also holds cultural and historical significance. Many ancient civilizations, such as the Babylonians, Egyptians, and Mayans, developed circular counting systems based on the movements of celestial bodies, reflecting their deep understanding and reverence for the cyclical nature of the universe.In conclusion, circular counting is a fascinating and versatile aspect of mathematics that extends far beyond the simple act of enumerating objects. It represents a deeper understanding of patterns, symmetry, and the cyclical nature of the world around us. By embracing the principles of circular counting, we can unlock new perspectives, solve complex problems, and gain a more holistic appreciation for the beauty and complexity of the mathematical world.。
两集合容斥原理公式证明Two-set inclusion-exclusion principle is a fundamental concept in combinatorics and probability theory that provides a way to count the elements in the union of two sets, while avoiding the overcounting of elements that are in the intersection of the sets.两集合容斥原理是组合数学和概率论中的一个基本概念,它提供了一种计算两个集合的并集中元素数量的方法,同时避免了计算重复的交集中的元素。
The principle is based on the idea that the total number of elements in the union of two sets can be calculated by summing the number of elements in each set separately, and then subtracting the number of elements in the intersection of the sets.这个原理的基本思想是,两个集合的并集中元素的总数可以通过分别计算每个集合中的元素数,然后减去集合的交集中的元素数来计算。
To prove this principle mathematically, we can start by defining two sets A and B, and then consider the cardinality of the union of the two sets, denoted by A ∪ B.为了在数学上证明这个原理,我们可以先定义两个集合 A 和 B,然后考虑这两个集合的并集的基数,记为A ∪ B。
小学英语(人教版)三年级下册Unit 6 How many? Part C Story timePeriod 4 Counting in a race【设计意图】同桌练习操练本话轮,为最后整体表演故事打下基础。
9. Do the dubbing(TW)Tips for dubbing: 1.Nobooks; 2. Keep pace withactions; 3. Have emotion【设计意图】由于在前面的环节中已经进行了听音跟读,所以不设置整体听音跟读,学生分角色对整个故事做配音,为最后整体表演故事打下基础。
Summary(TW)T: Today we have learn this interesting story. And we know we should be well prepared before anything. Who won today? Let’s count the apples. Team A, how many apples do you have? What about Team B? So who won? Team... Congrats! You can say...? Ss: I won.【设计意图】总结今天所学的故事和故事教给我们的道理。
将评价总结,数数两个组的摘了多少苹果,呼应本课主题apple-picking race,体现“课堂既是教材”的理念。
学生课堂活动Activity 1 Guessing game1.学生结合图片读教师的介绍,猜测教师的幸运数字,猜一个数字,教师就缩小范围,快速缩小到幸运数字18。
学生回顾老师的一段介绍,发现教师最喜欢的水果是蕴藏其中的apple。
导入到今天故事的学习中。
2.学生和教师一起数仿真苹果,并了解分组竞赛机制。
Activity 2 Look and say学生看图,教师呈现大量的苹果,猜测Zoom可能会说什么。
Discrete Mathematics and Its Applications, 8th Edition:Teaching PlanDiscrete Mathematics and Its Applications by Kenneth H. Rosen is a popular textbook for undergraduate students studying computer science, mathematics, engineering, and related fields. This teaching plan outlines a semester-long course based on the eighth edition of the book. The course is designed to introduce students to the fundamental concepts of discrete mathematics and their applications in computer science and other areas.Course OverviewThe course is divided into two parts: Foundations and Applications. The Foundations portion of the course introduces students to the basics of logic, set theory, relations, functions, and graphs. The Applications portion of the course covers combinatorics, discrete probability, mathematical induction, recursion, and algorithmic thinking. Throughout the course, we will explore real-worldapplications of these concepts and their relevance to computer science.Learning ObjectivesBy the end of the course, students should be able to: •Apply logic and set theory to solve problems in computer science.•Understand and analyze relations and functions, and use them to solve problems.•Represent and manipulate graphs and trees, and comprehend their use in modeling and solving problems.•Solve combinatorics problems and apply them to real-world scenarios.•Understand and apply mathematical induction to prove theorems.•Understand and apply the concept of recursion, including recursive algorithms.•Develop algorithmic thinking skills, including analyzing problem requirements and designing algorithms.TextbookDiscrete Mathematics and Its Applications, 8th Edition by Kenneth H. Rosen will serve as the primary text for the course. This textbook is a comprehensive and well-written introduction to discrete mathematics. It contns numerousexamples, problems, and mathematically rigorous proofs to support student learning.Course OutlinePart I: FoundationsChapter 1: The Foundations: Logic and ProofsThis chapter introduces students to the basics of mathematical language and logic. Topics include propositional logic, the different types of statements, and understanding proof techniques.Chapter 2: Basic Structures: Sets, Functions, Sequences, and SumsThis chapter is focused on set theory and its applications in computer science. Topics include set operations and properties, functions and their properties, sequences, and summations.Chapter 3: The Fundamentals: Algorithms, the Integers, and MatricesThis chapter covers the basics of algorithms, their classifications, performance analysis, and the use of recurrence relations. Also, students will be introduced tothe integers, divisibility and gcd, prime numbers, and matrices.Chapter 4: Induction and RecursionThis chapter explores mathematical induction, strong induction, and structural induction, as well as recursion and recursive algorithms.Chapter 5: CountingThis chapter introduces combinatorics, exploring permutations, combinations, and the binomial coefficients. Applications of these methods are presented in probability concepts.Chapter 6: Discrete ProbabilityThis chapter covers the fundamentals of probability theory and its applications in computer science. Topics include sample spaces and probability functions.Part II: ApplicationsChapter 7: Advanced Counting TechniquesThis chapter explores advanced counting techniques for solving combinatorial problems, including With Repetition and Generating Functions.Chapter 8: RelationsThe chapter introduces the concept of relations andpresents examples of relations, properties of relations, closure and matrix representation, and others.Chapter 9: GraphsThe chapter introduces the concept of graphs, including properties of graphs, graph colorings, Kruskal’s and Prim’s algorithms, network models, and the shortest path problem.Chapter 10: TreesThis chapter explores the concept of trees, spanning trees, rooted trees, binary trees, and traversal algorithms.Chapter 11: Boolean AlgebraThis chapter covers Boolean Algebra and Quine-McCluskey algorithms as common tools in digital circuitry synthesis.Chapter 12: Modeling ComputationThe final chapter covers models of computation andexplores the relationship between automata, formal languages, and complexity theory.AssessmentStudent understanding of course material will be evaluated through a combination of assignments, quizzes, mid-term and final examinations. Homework assignments will be given weekly or biweekly, and quizzes will be administered every two to three weeks. The final exam will be comprehensive and will cover all the topics of the course. Additionally, students will be expected to participate actively in class and online discussions.ConclusionDiscrete Mathematics and Its Applications is an essential course for students pursuing a degree in computer science, mathematics, or engineering. The course covers foundational topics in discrete mathematics in a comprehensive and engaging format, emphasizing real-world applications in computer science. It is hoped that this teaching plan will help students gn a deeper understanding and appreciation of this fascinating field.。
本次翻译练习的难度比较大,文章出自北京师范大学研究生英语阅读与翻译课程所用的授课材料,作者布洛诺夫斯基是英国著名的数学家和散文家,剑桥大学数学博士。
这篇文章从科学发展史的角度出发,论述的问题主要是科学并不排斥想象力和创造力。
因此标题翻译成“科学理性的本质”或“科学推理的本质”是比较恰当的。
要翻译好这篇文章不仅应在在宏观的层面牢牢把握文章的主旨,也需要从微观的角度考虑作者使用的语言在语法和修辞上的特点,这样才能在理解的基础上恰当的表达。
当然,这篇文章相对于大家目前的英语水平,在理解和表达两个方面都具有不小的挑战性。
下面通过对这次翻译比较好的赵新平同学作业的点评,来分段落说一说这篇文章究竟有哪些细节部分需要注意,以及相应的翻译策略。
1What is the insight in which the scientist tries to see into nature? Can it indeed be called either imaginative or creative? To the literary man the question may seem merely silly. He has been taught that science is a large collection of facts; and if this is true, then the only seeing which scientists need to do is, he supposes, seeing the facts. He pictures them, the colorless professionals of science, going off to work in the morning into the universe in a neutral, unexposed state. They then expose themselves like a photographic plate. And then in the darkroom or laboratory they develop the image, so that suddenly and startlingly it appears, printed in capital letters, as a new formula for atomic energy.原译:什么是洞察力?科学家一直试图弄清它的本质。
概率统计英语English:Probability and statistics are two closely related branches of mathematics that deal with the study of uncertainty and the analysis of data. Probability focuses on the study of random events and the likelihood of their occurrence. It involves understanding the principles and rules that govern the measurement and interpretation of probabilities. Statistics, on the other hand, involves the collection, analysis, interpretation, presentation, and organization of data. It provides methods and techniques for summarizing and making inferences from data, and it plays a crucial role in decision-making, forecasting, and scientific research.In probability, the concept of probability is expressed as a number between 0 and 1, where 0 represents an event that is impossible (has no chance of occurring) and 1 represents an event that is certain (will definitely occur). The probability of an event can be determined using different approaches such as classical probability, where probabilities are based on counting equally likely outcomes, orsubjective probability, which relies on personal judgment or experience. Probability theory allows us to calculate the likelihood of multiple events happening together, known as joint probability, or the likelihood of an event given that another event has already occurred, known as conditional probability.Statistics, on the other hand, involves the collection, analysis, interpretation, presentation, and organization of data. It encompasses various techniques for summarizing and describing data, including measures of central tendency (such as mean, median, and mode) and measures of dispersion (such as variance and standard deviation). Additionally, it provides methods for making inferences about the population based on a sample, such as hypothesis testing and confidence intervals. Inferential statistics is crucial for generalizing findings from a sample to a larger population and making predictions or drawing conclusions based on the data.Probability and statistics are used in various fields such as finance, engineering, medicine, social sciences, and natural sciences. They enable us to analyze and understand uncertain events, make informed decisions based on available data, and quantify thelikelihood of certain outcomes. By studying probability and statistics, we can gain valuable insights into the world around us and make more accurate predictions and informed choices.中文翻译:概率和统计是数学的两个紧密相关的分支,涉及到不确定性的研究和数据的分析。
高一英语科学探索方向多元单选题50题及答案1.Scientists carry out experiments to _____.A.prove a theoryB.create a theoryC.doubt a theoryD.ignore a theory答案:A。
解析:科学家进行实验的目的是为了证明一个理论。
选项B“create a theory”是创建理论,通常不是通过实验直接创建。
选项C“doubt a theory”是怀疑理论,实验不是为了单纯怀疑。
选项D“ignore a theory”是忽视理论,与实验目的不符。
2.The first step in a scientific experiment is to _____.A.collect dataB.form a hypothesisC.analyze resultsD.publish findings答案:B。
解析:科学实验的第一步是形成一个假设。
选项A“collect data”是收集数据,在形成假设之后进行。
选项C“analyze results”是分析结果,在收集数据之后。
选项D“publish findings”是发表发现,是实验的最后一步。
3.In an experiment, the variable that is changed by the scientist is called _____.A.independent variableB.dependent variableC.control variableD.constant variable答案:A。
解析:在实验中,由科学家改变的变量被称为自变量。
选项B“dependent variable”是因变量,是随着自变量的变化而变化的变量。
选项C“control variable”是控制变量,保持不变以确保实验的准确性。
选项D“constant variable”是常量变量,也是保持不变的变量。
Journal of Literature and Art Studies, August 2019, Vol. 9, No. 8, 852-855doi: 10.17265/2159-5836/2019.08.006Feminism in The Story of an Hour From the Perspective of SpatialNarrativeWANG XuCollege of Foreign Languages, Zhoukou Normal University, Zhoukou, China, 466001The Story of an Hour is a short story written by Kate Chopin, an American realistic novelist, at the end of the 19thcentury. There are three spaces in the novel, the room, the house and space outside the window. Each one containscertain characters, actions, emotions and even ideology. This paper tries to analyze its Feministic significance ofthe novel from the perspective of space narration.Keywords: The Story of an Hour, Spatial Narrative, FeminismClassical narratology focuses on the study of stories and discourses in fiction at the time level. Until 1978, Chartman, first put forward the concepts of story space and discourse space. He pointed out that the latitude ofstory events is temporal, while the existence in story space, characters, and environment are spatial. Chatman’sview inherits the traditional narrative theory that narration belongs to the art of time, but he puts forward the space All Rights Reserved.latitude from the story level, and puts the almost marginalized space background of traditional novel into thetheoretical research field as an existence. He believes that story space refers to the place or place where eventsoccur. Discourse space is the place or environment where the narrative action takes place. Structuralist narratorsgenerally believe that story space has important structural significance in narrative works. In addition toproviding the necessary place for the characters to move, story space is also an important way to show thecharacters’psychological activities, shape the characters’ images, and reveal the addresses of the works. In orderto discuss these aspects, it is necessary to deal with the observation and description of story space. As far as therelationship between the perspective of characters and the space of stories is concerned, what is usuallyemphasized is the space in the eyes of characters. In this sense, we say that the space of narrative works is alwaysfilled with many meanings beyond the space. It can be said that the use of character perspective to show the storyspace can make objective environment space to show the observer’s psychological activities, and thepsychological space closely related to the ideological value. This technique helps novelists to shape the image ofthe characters and reveal the theme of the work at the same time.In the 19th century, America was imprisoned by patriarchal ideology, so women were oppressed in all aspects of politics, economy, society, and psychology. Women’s will and ideas were regarded as insignificant.Women should become “angels” or “virgins” in family, and sacrifice all their wishes and take husbands andchildren as the center of life. However, Kate Chopin, as a pioneer of American Feminism, deviated from theWANG Xu, MA, Lecturer, College of Foreign Languages, Zhoukou Normal University, Zhoukou, China.FEMINISM IN THE STORY OF AN HOUR FROM THE PERSPECTIVE OF SPATIAL NARRATIVE853patriarchal ideology and created some short stories which were considered unruly and immoral at that time. TheStory of an Hour is one of her representative short novels. The physical space in the novel is not only an objectivegeographical location, but also a container carrying time, characters, actions, speech, psychological activities,values and ideology in it. The physical space, whether intentionally or accidentally observed by the character,reflects the character’s judgment and choice more or less.The Relationship Between Focalization and Space in The Story of an HourThere is little description of the house, but we can see from the fragmentary introduction that the whole house has at least two floors. Mrs. Mallard has her own room upstairs, with a comfortable, wide rocking armchairnear the window. She usually rests here, not only eliminating physical exhaustion, but also enjoying therelaxation into the depths of her heart. Through the window, she could see the vast square, the vibrant green trees,the free flying birds, the blue sky, and the white clouds; she could hear the salesmen, the chirping birds, and thedistant songs; she could smell the sweet smell of the drizzle outside the window. The author does not directlyintroduce Mrs. Mallard’s family background, but through Mrs. Mallard’s perspective (vision, hearing, smell),indirectly reflects that Mrs. Mallard’s life is superior, because the house is located in an excellent environment.She is the hostess of a middle-class family. In addition, the focalization must have the subjective thought andemotional projection of the observer. In the sad mood of the bereaved husband, why is she joyful and clear toobserve the scenery, sound and smell presented by human vision, hearing, and smell? We know that the mood ofthe observer can affect the cognition of the objective things, that is, the objective things carry the inner world ofthe observers. However, the objective things in the novel are without the slightest melancholy atmosphere, but All Rights Reserved.relaxed and joyful. Obviously, the inner world of the hostess still has hidden thoughts to be excavated. This kindof dramatic irony (the difference between what the reader thinks and the content of the text) will arouse thereaders’ curiosity and interest in reading.The following psychological description of Mrs. Mallard in the room highlights her desire for freedom and self-identity. In this limited space, the focalization is extended to psychological perception, from outside to inside.The physical space of the room is as rich as the contents of the container. All of this is done through thefocalization of the characters. The implied author hides outside the text, and there is almost no explanation of thewriter. The description of the scenery outside the window in the former text has foreshadowed the heroine’sdifferent inner world and paved the way for the following text. At first, the heroine’s yearning for freedom madeher very frightened. She could not clearly define freedom. She felt freedom everywhere, in the sky, in the voice,in the scenery, in the color, even full of any corner of her life. When the desire for freedom began to emerge in hermind, she tried to suppress it, but in turn it became more and more intense. Until the heart emerged three words,“free, free, free”, again and again to call her to grasp the chance of freedom, pulse accelerated, blood was boiling,and the whole body and mind had been greatly relaxed. She named this joy evil pleasure. There is also a dramaticirony below, that is, through the heroine’s perspective, reflecting her husband’s constant attention and love to herevery day, but the heroine hardly loves her husband, or the number of love is very small. The latter part gives anexplanation. It turned out that the Mr. Mallard’s love was only out of selfishness, regardless of his wife’s realthoughts. Mrs. Mallard wanted to find her identity and live for herself. She believed that it was a crime to imposeone’s will on others, whether the intension is cruel or good. The heroine’s ideology finally really awakened, and854FEMINISM IN THE STORY OF AN HOUR FROM THE PERSPECTIVE OF SPATIAL NARRATIVE she realized that what she wanted was self-affirmation and confidence. So when the voice of her sister begging toopen the door appeared outside the room, no one knew that the protagnist was actually drinking the nectar of lifethrough the window. Her thoughts were galloping. In the years to come, no matter summer, autumn, or winter,any time belongs to her. She sighed how long her life had been without her identity before, and then she prayedthat the days of freedom would be longer.The Relationship Between Theme and Space in The Story of an HourThe core space of the novel is the upstair bedroom which symbolizes the protagnist’s psychological space.The author does not narrates much about this physical place, only a comfortable and spacious rocking chair andan open window. We can vaguely see that the protagnist’s living conditions are superior, but in this private spaceonly one window opens to the outside world, where there are blue sky, white clouds, fresh air after rain, distantsongs, and countless sparrows, showing the vitality of a new life in spring. The whole house represents apatriarchal family, and her husband watched her with loving eyes all the time. The husband’s so-called lovinggaze is only a manifestation of love for himself, or just a male gaze, that is to say, satisfying the partner’sappearance or character conforms to the social and cultural norms. She is young, white, serene, obedient, weak,and has heart trouble, who needs to be protected by others. In the family, she is just like a comfortable rockingchair. It is only an object or a materialized existence. Her husband has never realized the wishes and expectationsof his wife. Therefore, such feelings are selfish and oppressive “love” of women. Putting women on the high shelf,like the Virgin Mary, is actually the worship and maintenance of the image of female “family angel” under thepatriarchal norms, fundamentally in order to safeguard the rights and interests of men. It was not surprising that All Rights Reserved.she admitted that she had loved him, not often, sometimes. Although the protagnist has been waiting for freedomand longing for freedom, she has never lived for herself. The centre of her life is her husband. The oppression andfatigue under the patriarchal will are surrounded in life and make women breathless all the time.It is impossible for her relatives and friends to understand her real state and needs including her sister and her friend Rechards. She did not allow anyone else to enter the room, suggesting that she was estranged from thesurrounding society, that the outside world did not understand her, and that she did not allow others to enter herinner world. Her sister told her husband’s death half-covertly in intermittent words to prevent her from having aheart attack. In their minds, the heroine was a weak traditional woman. When her husband died, she would losethe support of her life. Most women would feel sad and be at a loss. She cried bitterly in her sister’s arms at thevery beginning. However later, her sister begged outside the door trying to persuade her not to do silly things.Richard tried to hide her husband when he came home, so as not to stimulate a series of heart trouble, whichstrengthens the vulnerable image of women in ordinary people’s minds.Although the protagnist’s longing for freedom lasted for a long time in her heart, she was at a loss. From the beginning, she felt abandoned and sobbed. Finally, she saw the scenery outside the window. Her voice forfreedom grew louder and more frequent. She was frightened at first and did not know what this thing was. Later,she tried to suppress the idea, wondered if it was evil, and finally felt relaxed and warm in body and mind. Atsister’s repeated requests, she opened the door and came downstairs like the goddess of victory. She grabbedsister’s wrist as if it was someone else, not herself, who was injured. However, before she could stand firm, herhusband came back. It was too late. She died of despair or the destruction of a new life, rather than the sudden joyFEMINISM IN THE STORY OF AN HOUR FROM THE PERSPECTIVE OF SPATIAL NARRATIVE855that everyone thought. We can see that for the lady, the space of the room carries all her fantasies and hopes, andin fact symbolizes her psychological space. In her short stream of consciousness, which lasted only an hour, allhappiness suddenly came and all went away in a hurry. Do not mention the society represented by going out ofthe window. She had just come downstairs, but she had not yet stood firm. All the fantasies have been shattered.In that patriarchal society and soul, hope can only exist in imagination, limited by space (the room) and time(only an hour). We cannot help thinking that even if the woman has no heart disease, when her husband cameback, her heart would also turn to dust. Even if it was not subject to the ideological imprisonment of husbands, thesociety in which they lived would always permeate the ideology of oppression of women.ConclusionIn short, the novel revolves around Mrs. Mallard’s psychological reaction after she learned that her husband had “died” in an accident. In her stream of consciousness, the novel reveals that patriarchal ideology in 19thcentury American society is pervasive everywhere and everytime. The three physical spaces in the article: thehouse, the upstair bedroom, the square and the sky outside the window, respectively symbolize the patriarchalfamily, women and society. Room represents men’s respect and praise for women and their high admiration. Infact, the patriarchal society represses, regulates, and restricts women. Women have no freedom both of body andmind, without personal will. Men love angels and virgin who abide by social rules, not women who exist asnatural persons. Room represents women’s private psychological space from another aspect, which is enclosednarrow, full of fantasy, unrealistic, and once out of fantasy, will fall into despair and even spiritual death. Womenthemselves are also seriously persecuted and influenced by patriarchal ideology. They are ideologically All Rights Reserved.internalized, doubtful, and self-confident. Room also indicates that women are incompatible with the surroundingsocial environment. Women prevent society from entering their hearts, and the social environment cannotunderstand women. People take it for granted that women should be weak and helpless and need to be protected.In fact, they depreciate the value of women’s existence and strengthen the way of thinking attached to men.Paradoxically, room is a part of the house. Room has its own special emotional, psychological and evenideological meaning. It is unreal to exist independently of the house, because women were oppressed andconfined in that time of patriarchal society. Women could have new ideas and the will of persuing freedom andindividuality, but it was ardious for them to seperate from the bondage of time and space. That is why the title ofthe novel first published in 1894 is The Dream of an Hour, which just show the protagnist’s an hour’s dream. Theauthor also deeply regrets that women’s independence and equality in the society at that time was mirage, like acastle in the air, nihility, fleeting.ReferencesLuo, T. (1994). The dilemma and self-help of modern American women. Study of Foreign Literature, 158-162.Shen, D. (2015). Western narratology: Classics and post-classics. Beijing: Peking University Press.Tyso, L. (2014). Practical guide to contemporary critical theory. (G. X. Zhao et al., Trans.). Beijing: Foreign Language Teaching and Research Press.Wang, Q. (2008). Study of irony and symbolic art in Tempest. Appreciation of Famous Works, 103-106.Zhu, H. (1983).Short stories by American female writers. Beijing: China Social Sciences Press.。
组合数学英语Combinatorial MathematicsCombinatorial mathematics is a branch of mathematics that deals with the study of discrete structures and their properties. It is a field that has a wide range of applications in various areas, including computer science, cryptography, and operations research. The fundamental concepts of combinatorial mathematics include permutations, combinations, and probability.Permutations are the different ways in which a set of objects can be arranged in a specific order. For instance, if we have three letters, A, B, and C, the permutations of these letters would be ABC, ACB, BAC, BCA, CAB, and CBA. Permutations are often used in problems related to scheduling, coding, and counting the number of possible outcomes in a particular scenario.Combinations, on the other hand, are the different ways in which a set of objects can be chosen without regard to order. For example, if we have four letters, A, B, C, and D, the combinations of these letters taken two at a time would be AB, AC, AD, BC, BD, and CD. Combinations are commonly used in problems related to probability,voting, and resource allocation.Probability is the measure of the likelihood of an event occurring. In combinatorial mathematics, probability is often calculated using the concepts of permutations and combinations. For instance, if we have a deck of 52 playing cards and we want to calculate the probability of drawing a specific card, we can use the concept of combinations to determine the number of possible outcomes and the number of favorable outcomes.One of the most important applications of combinatorial mathematics is in the field of computer science. Algorithms and data structures, which are the fundamental building blocks of computer programs, often rely on the principles of combinatorial mathematics. For example, the design of efficient sorting algorithms, such as quicksort and merge sort, involves the use of permutations and combinations to optimize the performance of the algorithm.Another important application of combinatorial mathematics is in cryptography. Cryptographic systems often rely on the principles of permutations and combinations to ensure the security of the system. For instance, the RSA algorithm, which is one of the most widely used public-key cryptographic systems, uses the concept of prime factorization, which is closely related to the principles of combinatorial mathematics.In operations research, combinatorial mathematics is used to solve optimization problems, such as the traveling salesman problem and the knapsack problem. These problems involve finding the optimal solution from a set of possible solutions, and the principles of combinatorial mathematics are used to efficiently search the solution space.In addition to these practical applications, combinatorial mathematics also has a rich theoretical foundation. Combinatorists, who are researchers in the field of combinatorial mathematics, have developed a wide range of mathematical tools and techniques to study the properties of discrete structures. These include the use of generating functions, recurrence relations, and graph theory.One of the most active areas of research in combinatorial mathematics is the study of enumerative combinatorics, which deals with the counting of discrete structures. Enumerative combinatorics has applications in areas such as computer science, biology, and physics, and has led to the development of many powerful mathematical techniques, such as the inclusion-exclusion principle and the Polya enumeration theorem.Another important area of research in combinatorial mathematics is the study of extremal combinatorics, which deals with the study ofthe maximum or minimum size of certain discrete structures. This area of research has applications in areas such as graph theory, coding theory, and the study of social networks.Overall, combinatorial mathematics is a rich and diverse field of study that has a wide range of practical applications. Its principles are fundamental to many areas of science and technology, and it continues to be an active area of research and exploration.。
关于数字的英语单元整体小主题Unit Theme: NumbersNumbers are an essential part of our daily lives, from counting money to telling time, and from measuring ingredients for a recipe to understanding statistics. Let's explore the world of numbers and their significance in various aspects of our lives.数字是我们日常生活中不可或缺的一部分,从数钱到报时,从测量食谱配料到理解统计数据,数字在我们生活的各个方面都具有重要意义。
让我们一起探索数字的世界,以及它们在我们生活的各个方面的重要性。
1. Counting and Basic OperationsIn mathematics, counting is the process of determining the number of elements in a set. It is one of the earliest mathematical activities that children learn. Basic operations such as addition, subtraction, multiplication, and division are fundamental to understanding numbers and their relationships.在数学中,计数是确定集合中元素数量的过程。
这是孩子们学习的最早期的数学活动之一。
加法、减法、乘法和除法等基本运算对于理解数字及其关系至关重要。
2. Number SystemsDifferent cultures and civilizations have developed their own number systems throughout history. The most commonly used number system today is the decimal system, which is based on powers of 10. However, other number systems like the binary system (base 2) and the hexadecimal system (base 16) are used in computer science and digital electronics.不同的文化和文明在历史上发展了各自的数字系统。
英语专业八级考试TEM-8阅读理解练习册(1)(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的,邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地,仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫,蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地,假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库,蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的,灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池,残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的,意外的B. adventitious外加的,偶然的C. catastrophicD. precarious不稳定的,危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽,幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上,病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12.Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令,法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果,影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的,时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的,磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风,狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取,攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。
Practice Test #1 Reading Comprehension(18 Essays, 61 Questions)Essay #1. 019 (21201-!-item-!-188;#058&00019-00)During the nineteenth century, occupational information about women that was provided by the United States census--a population count conducted each decade--became more detailed and precise in response to social changes. Through 1840, simple enumeration by household mirrored a home-based agricultural economy and hierarchical social order: the head of the household (presumed male or absent) was specified by name, whereas other household members were only indicated by the total number of persons counted in various categories, including occupational categories. Like farms, most enterprises were family-run, so that the census measured economic activity as an attribute of the entire household, rather than of individuals.The 1850 census, partly responding to antislavery and women's rights movements, initiated the collection of specific information about each individual in a household. Not until 1870 was occupational information analyzed by gender: the census superintendent reported 1.8 million women employed outside the home in "gainful and reputable occupations." In addition, he arbitrarily attributed to each family one woman "keeping house." Overlap between the two groups was not calculated until 1890, when the rapid entry of women into the paid labor force and social issues arising from industrialization were causing women's advocates and women statisticians to press for more thorough and accurate accounting of women's occupations and wages.Question #1. 019-01 (21247-!-item-!-188;#058&000019-01)The primary purpose of the passage is to(A) explain and critique the methods used by early statisticians(B) compare and contrast a historical situation with a current-day one(C) describe and explain a historical change(D) discuss historical opposition to an established institution(E) trace the origin of a contemporary controversyQuestion #2. 019-02 (21293-!-item-!-188;#058&000019-02)Each of the following aspects of nineteenth-century United States censuses is mentioned in the passage EXCEPT the(A) year in which data on occupations began to be analyzed by gender(B) year in which specific information began to be collected on individuals in addition to the head of the household(C) year in which overlap between women employed outside the home and women keeping house was first calculated(D) way in which the 1890 census measured women's income levels and educational backgrounds(E) way in which household members were counted in the 1840 censusQuestion #3. 019-04 (21339-!-item-!-188;#058&000019-04)The passage suggests which of the following about the "women's advocates and women statisticians" mentioned in the highlighted text?(A) They wanted to call attention to the lack of pay for women who worked in the home.(B) They believed that previous census information was inadequate and did not reflect certaineconomic changes in the United States.(C) They had begun to press for changes in census-taking methods as part of their participation in the antislavery movement.(D) They thought that census statistics about women would be more accurate if more women were employed as census officials.(E) They had conducted independent studies that disputed the official statistics provided by previous United States censuses.Essay #2. 066 (21346-!-item-!-188;#058&00066-00)The general density dependence model can be applied to explain the founding of specialist firms (those attempting to serve a narrow target market). According to this model, specialist foundings hinge on the interplay between legitimation and competitive forces, both of which are functions of the density (total number) of firms in a particular specialist population. Legitimation occurs as a new type of firm moves from being viewed as unfamiliar to being viewed as a natural way to organize.At low density levels, each founding increases legitimation, reducing barriers to entry and easing subsequent foundings. Competition occurs because the resources that firms seek--customers, suppliers, and employees--are limited, but as long as density is low relative to plentiful resources, the addition of another firm has a negligible impact on the intensity of competition. At high density levels, however, competitive effects outweigh legitimation effects, discouraging foundings. The more numerous the competitors, the fiercer the competition will be and the smaller will be the incentive for new firms to enter the field.While several studies have found a significant correspondence between the density dependence model and actual patterns of foundings, other studies have found patterns not consistent with the model. A possible explanation for this inconsistency is that legitimation and competitive forces transcend national boundaries, while studies typically restrict their analysis to the national level. Thus a national-level analysis can understate the true legitimation and competitive forces as well as the number of foundings in an industry that is internationally integrated. Many industries are or are becoming international, and since media and information easily cross national borders, so should legitimation and its effects on overseas foundings. For example, if a type of firm becomes established in the United States, that information transcends borders, reduces uncertainties, and helps foundings of that type of firm in other countries. Even within national contexts, studies have found more support for the density dependence model when they employ broader geographic units of analysis--for example, finding that the model's operation is seen more clearly at the state and national levels than at city levels.Question #4. 066-02 (21392-!-item-!-188;#058&000066-02)According to the passage, which of the following may account for the inconsistency between the general density dependence model and the evidence provided by certain studies of foundings?(A) Such studies have overemphasized the impact of preexisting firms on the establishment of new firms.(B) Such studies have not focused strongly enough on the role of competition among newly established firms operating at the city and state levels.(C) Such studies fail to differentiate among specialist firms with regard to the degree to which they deviate from familiar forms of organization.(D) Such studies have not taken into account the fact that many industries are internationally integrated.(E) Such studies have neglected to investigate firms that attempt to serve only a narrow target market.Question #5. 066-04 (21438-!-item-!-188;#058&000066-04)In the second paragraph, the author is primarily concerned with(A) noting various exceptions to a certain general finding(B) examining the impact of one type of industry on another(C) proposing a possible explanation for an inconsistency(D) providing specific examples of a particular phenomenon(E) defending the validity of a particular study's conclusionsQuestion #6. 066-06 (21484-!-item-!-188;#058&000066-06)The passage suggests that when a population of specialist firms reaches a high density level, which of the following is likely to occur?(A) Foundings will decline despite legitimation that has occurred in these industries.(B) Increasing competition will encourage many firms to broaden their target market.(C) Competition for resources will become stabilized and thus foundings will be encouraged.(D) Many customers will abandon their loyalty to older firms as more innovative firms enter the market.(E) Firms will begin to cross national borders in an attempt to gain a competitive advantage. Question #7. 066-08 (21530-!-item-!-188;#058&000066-08)The primary purpose of the passage is to(A) question the validity of an economic model(B) point out some inconsistencies within an economic model(C) outline an economic model and suggest revisions to it(D) describe an economic model and provide specific examples to illustrate its use(E) explain why an economic model remains valid despite inconsistent research resultsEssay #3. 075 (21535-!-item-!-188;#058&00075-00)In its 1903 decision in the case of Lone Wolf v. Hitchcock, the United States Supreme Court rejected the efforts of three Native American tribes to prevent the opening of tribal lands to non-Indian settlement without tribal consent. In his study of the Lone Wolf case, Blue Clark properly emphasizes the Court's assertion of a virtually unlimited unilateral power of Congress (the House of Representatives and the Senate) over Native American affairs. But he fails to note the decision's more far-reaching impact: shortly after Lone Wolf, the federal government totally abandoned negotiation and execution of formal written agreements with Indian tribes as a prerequisite for the implementation of federal Indian policy. Many commentators believe that this change had already occurred in 1871 when--following a dispute between the House and the Senate over which chamber should enjoy primacy in Indian affairs--Congress abolished the making of treaties with Native American tribes. But in reality the federal government continued to negotiate formal tribal agreements past the turn of the century, treating these documents not as treaties with sovereign nations requiring ratification by the Senate but simply as legislation to be passed by both houses of Congress. The Lone Wolf decision ended this era of formal negotiation and finally did away with what had increasingly become the empty formality of obtaining tribal consent.Question #8. 075-03 (21581-!-item-!-188;#058&000075-03)According to the passage, the congressional action of 1871 had which of the following effects?(A) Native American tribal agreements were treated as legislation that had to be passed by both houses of Congress.(B) The number of formal agreements negotiated between the federal government and Native American tribes decreased.(C) The procedures for congressional approval and implementation of federal Indian policy were made more precise.(D) It became more difficult for Congress to exercise unilateral authority over Native American affairs.(E) The role of Congress in the ratification of treaties with sovereign nations was eventually undermined.Question #9. 075-06 (21627-!-item-!-188;#058&000075-06)According to the passage, which of the following resulted from the Lone Wolf decision?(A) The Supreme Court took on a greater role in Native American affairs.(B) Native American tribes lost their legal standing as sovereign nations in their dealings with the federal government, but their ownership of tribal lands was confirmed.(C) The federal government no longer needed to conclude a formal agreement with a Native American tribe in order to carry out policy decisions that affected the tribe.(D) The federal government began to appropriate tribal lands for distribution to non-Indian settlers.(E) Native American tribes were no longer able to challenge congressional actions by appealing to the Supreme Court.Question #10. 075-07 (21673-!-item-!-188;#058&000075-07)The author of the passage is primarily concerned with(A) identifying similarities in two different theories(B) evaluating a work of scholarship(C) analyzing the significance of a historical event(D) debunking a revisionist interpretation(E) exploring the relationship between law and social realityEssay #4. 094 (21680-!-item-!-188;#058&00094-00)Some historians contend that conditions in the United States during the Second World War gave rise to a dynamic wartime alliance between trade unions and the African American community, an alliance that advanced the cause of civil rights. They conclude that the postwar demise of this vital alliance constituted a lost opportunity for the civil rights movement that followed the war. Other scholars, however, have portrayed organized labor as defending all along the relatively privileged position of White workers relative to African American workers. Clearly, these two perspectives are not easily reconcilable, but the historical reality is not reducible to one or the other.Unions faced a choice between either maintaining the prewar status quo or promoting a more inclusive approach that sought for all members the right to participate in the internal affairs of unions, access to skilled and high-paying positions within the occupational hierarchy, and protection against management's arbitrary authority in the workplace. While union representatives often voiced this inclusive ideal, in practice unions far more often favored entrenched interests. The accelerating development of the civil rights movement following the Second World War exacerbated the unions'dilemma, forcing trade unionists to confront contradictions in their own practices.Question #11. 094-01 (21726-!-item-!-188;#058&000094-01)The "unions' dilemma" mentioned in the highlighted text can best be described as the question of whether or not to(A) pressure management to create more skilled and high-paying positions(B) fight for greater union participation in management decisions(C) include minority workers in their membership(D) extend full rights and benefits to all their members(E) emphasize the recruitment of new members over serving the needs of current members Question #12. 094-02 (21772-!-item-!-188;#058&000094-02)According to the passage, the historians mentioned in the first highlighted portion of text and the scholars mentioned in the second highlighted portion disagree about the(A) contribution made by organized labor to the war effort during the Second World War(B) issues that union members considered most important during the Second World War(C) relationship between unions and African Americans during the Second World War(D) effect of the Second World War on the influence of unions in the workplace(E) extent to which African Americans benefited from social and political changes following the Second World WarQuestion #13. 094-06 (21818-!-item-!-188;#058&000094-06)The passage is primarily concerned with(A) providing a context within which to evaluate opposing viewpoints about a historical phenomenon(B) identifying a flawed assumption underlying one interpretation of a historical phenomenon(C) assessing the merits and weaknesses of a controversial theory about a historical phenomenon(D) discussing the historical importance of the development of a wartime alliance(E) evaluating evidence used to support a particular interpretation of a historical phenomenonEssay #5. 118 (21825-!-item-!-188;#058&00118-00)Historians have identified two dominant currents in the Russian women's movement of the late tsarist period. "Bourgeois" feminism, so called by its more radical opponents, emphasized "individualist" feminist goals such as access to education, career opportunities, and legal equality. "Socialist" feminists, by contrast, emphasized class, rather than gender, as the principal source of women's inequality and oppression, and socialist revolution, not legal reform, as the only road to emancipation and equality.However, despite antagonism between bourgeois feminists and socialist feminists, the two movements shared certain underlying beliefs. Both regarded paid labor as the principal means by which women might attain emancipation: participation in the workplace and economic self-sufficiency, they believed, would make women socially useful and therefore deserving of equality with men. Both groups also recognized the enormous difficulties women faced when they combined paid labor with motherhood. In fact, at the First All-Russian Women's Congress in 1908, most participants advocated maternity insurance and paid maternity leave, although the intense hostility between some socialists and bourgeois feminists at the Congress made it difficult for them to recognize these areas ofagreement. Finally, socialist feminists and most bourgeois feminists concurred in subordinating women's emancipation to what they considered the more important goal of liberating the entire Russian population from political oppression, economic backwardness, and social injustice.Question #14. 118-03 (21871-!-item-!-188;#058&000118-03)The passage suggests that socialists within the Russian women's movement and most bourgeois feminists believed that in Russia(A) women would not achieve economic equality until they had political representation within the government(B) the achievement of larger political aims should take precedence over the achievement of women's rights(C) the emancipation of women would ultimately bring about the liberation of the entire Russian population from political oppression(D) women's oppression was more rooted in economic inequality than was the case in other countries(E) the women's movement was more ideologically divided than were women's movements in other countriesQuestion #15. 118-05 (21917-!-item-!-188;#058&000118-05)The passage is primarily concerned with(A) identifying points of agreement between two groups(B) advocating one approach to social reform over another(C) contrasting two approaches to solving a political problem(D) arguing that the views espoused by one political group were more radical than those espoused by another group(E) criticizing historians for overlooking similarities between the views espoused by two superficially dissimilar groupsQuestion #16. 118-06 (21963-!-item-!-188;#058&000118-06)According to the passage, Russian socialists within the women's movement and most bourgeois feminists disagreed about which of the following?(A) Whether legal reform was central to the achievement of feminist goals(B) Whether paid employment was important for the achievement of equality(C) Whether maternity insurance was desirable for working mothers(D) Whether working mothers faced obstacles(E) Whether women's emancipation should be subordinated to the liberation of the Russian population Essay #6. 145 (21972-!-item-!-188;#058&00145-00)Colonial historian David Allen's intensive study of five communities in seventeenth-century Massachusetts is a model of meticulous scholarship on the detailed microcosmic level, and is convincing up to a point. Allen suggests that much more coherence and direct continuity existed between English and colonial agricultural practices and administrative organization than other historians have suggested. However, he overstates his case with the declaration that he has proved "the remarkable extent to which diversity in New England local institutions was directly imitative of regional differences in the mother country."Such an assertion ignores critical differences between seventeenth-century England and New England. First, England was overcrowded and land-hungry; New England was sparsely populated andlabor-hungry. Second, England suffered the normal European rate of mortality; New England, especially in the first generation of English colonists, was virtually free from infectious diseases. Third, England had an all-embracing state church; in New England membership in a church was restricted to the elect. Fourth, a high proportion of English villagers lived under paternalistic resident squires; no such class existed in New England. By narrowing his focus to village institutions and ignoring these critical differences, which studies by Greven, Demos, and Lockridge have shown to be so important, Allen has created a somewhat distorted picture of reality.Allen's work is a rather extreme example of the "country community" school of seventeenth-century English history whose intemperate excesses in removing all national issues from the history of that period have been exposed by Professor Clive Holmes. What conclusion can be drawn, for example, from Allen's discovery that Puritan clergy who had come to the colonies from East Anglia wereone-third to one-half as likely to return to England by 1660 as were Puritan ministers from western and northern England? We are not told in what way, if at all, this discovery illuminates historical understanding. Studies of local history have enormously expanded our horizons, but it is a mistake for their authors to conclude that village institutions are all that mattered, simply because their functions are all that the records of village institutions reveal.Question #17. 145-03 (22018-!-item-!-188;#058&000145-03)According to the passage, which of the following was true of most villages in seventeenth-century England?(A) The resident squire had significant authority.(B) Church members were selected on the basis of their social status within the community.(C) Low population density restricted agricultural and economic growth.(D) There was little diversity in local institutions from one region to another.(E) National events had little impact on local customs and administrative organization.Question #18. 145-05 (22064-!-item-!-188;#058&000145-05)The passage suggests that Professor Clive Holmes would most likely agree with which of the following statements?(A) An understanding of seventeenth-century English local institutions requires a consideration of national issues.(B) The "country community" school of seventeenth-century English history distorts historical evidence in order to establish continuity between old and new institutions.(C) Most historians distort reality by focusing on national concerns to the exclusion of local concerns.(D) National issues are best understood from the perspective of those at the local level.(E) Local histories of seventeenth-century English villages have contributed little to the understanding of village life.Question #19. 145-07 (22110-!-item-!-188;#058&000145-07)It can be inferred from the passage that the author of the passage considers Allen's "discovery" (see highlighted text) to be(A) already known to earlier historians(B) based on a logical fallacy(C) improbable but nevertheless convincing(D) an unexplained, isolated fact(E) a new, insightful observationQuestion #20. 145-08 (22156-!-item-!-188;#058&000145-08)The author of the passage is primarily concerned with(A) substantiating a claim about a historical event(B) reconciling two opposing ideas about a historical era(C) disputing evidence a scholar uses to substantiate a claim about a historical event(D) analyzing two approaches to scholarly research and evaluating their methodologies(E) criticizing a particular study and the approach to historical scholarship it representsEssay #7. 146 (22165-!-item-!-188;#058&00146-00)The United States government has a long-standing policy of using federal funds to keep small business viable. The Small Business Act of 1953 authorized the Small Business Administration (SBA) to enter into contracts with government agencies having procurement powers and to arrange for fulfillment of these contracts by awarding subcontracts to small businesses. In the mid-1960's, during the war on poverty years, Congress hoped to encourage minority entrepreneurs by directing such funding to minority businesses. At first this funding was directed toward minority entrepreneurs with very low incomes. A 1967 amendment to the Economic Opportunity Act directed the SBA to pay special attention to minority-owned businesses located in urban or rural areas characterized by high proportions of unemployed or low-income individuals. Since then, the answer given to the fundamental question of who the recipients should be--the most economically disadvantaged or those with the best prospects for business success--has changed, and the social goals of the programs have shifted, resulting in policy changes.The first shift occurred during the early 1970's. While the goal of assisting the economically disadvantaged entrepreneur remained, a new goal emerged: to remedy the effects of past discrimination. In fact, in 1970 the SBA explicitly stated that their main goal was to increase the number of minority-owned businesses. At the time, minorities constituted seventeen percent of the nation's population, but only four percent of the nation's self-employed. This ownership gap was held to be the result of past discrimination. Increasing the number of minority-owned firms was seen as a way to remedy this problem. In that context, providing funding to minority entrepreneurs in middle- and high-income brackets seemed justified.In the late 1970's, the goals of minority-business funding programs shifted again. At the Minority Business Development Agency, for example, the goal of increasing numbers of minority-owned firms was supplanted by the goal of creating and assisting more minority-owned substantive firms with future growth potential. Assisting manufacturers or wholesalers became far more important than assisting small service businesses. Minority-business funding programs were now justified as instruments for economic development, particularly for creating jobs in minority communities of high unemployment.Question #21. 146-01 (22211-!-item-!-188;#058&000146-01)The primary purpose of the passage is to(A) discuss historical changes in a government policy(B) describe the role of Congress in regulating the work of the SBA(C) contrast types of funding sources used by minority businesses(D) correct a misconception about minority entrepreneurship(E) advocate an alternative approach to funding minority entrepreneursQuestion #22. 146-05 (22257-!-item-!-188;#058&000146-05)It can be inferred that the "ownership gap" (see highlighted text) would be narrowed if which of the following were to occur?(A) Minority entrepreneurs received a percentage of government contracts equal to that received by nonminority entrepreneurs.(B) Middle- and high-income minority entrepreneurs gave more assistance to their low-income counterparts in the business community.(C) Minority entrepreneurs hired a percentage of minority employees equal to the percentage of minority residents in their own communities.(D) The percentage of self-employed minority persons rose to more than ten percent of allself-employed persons.(E) Seventeen percent of all persons employed in small businesses were self-employed.Question #23. 146-06 (22303-!-item-!-188;#058&000146-06)According to the passage, in 1970 funding to minority entrepreneurs focused primarily on which of the following?(A) Alleviating chronic unemployment in urban areas(B) Narrowing the ownership gap(C) Assisting minority-owned businesses with growth potential(D) Awarding subcontracts to businesses that encouraged community development(E) Targeting the most economically disadvantaged minority-owned businessesQuestion #24. 146-09 (22349-!-item-!-188;#058&000146-09)Which of the following best describes the function of the second paragraph in the passage as a whole?(A) It narrows the scope of the topic introduced in the first paragraph.(B) It presents an example of the type of change discussed in the first paragraph.(C) It cites the most striking instance of historical change in a particular government policy.(D) It explains the rationale for the creation of the government agency whose operations are discussed in the first paragraph.(E) It presents the results of policies adopted by the federal government.Essay #8. 147 (22358-!-item-!-188;#058&00147-00)In terrestrial environments, gravity places special demands on the cardiovascular systems of animals. Gravitational pressure can cause blood to pool in the lower regions of the body, making it difficult to circulate blood to critical organs such as the brain. Terrestrial snakes, in particular, exhibit adaptations that aid in circulating blood against the force of gravity.The problem confronting terrestrial snakes is best illustrated by what happens to sea snakes when removed from their supportive medium. Because the vertical pressure gradients within the blood vessels are counteracted by similar pressure gradients in the surrounding water, the distribution of blood throughout the body of sea snakes remains about the same regardless of their orientation in space, provided they remain in the ocean. When removed from the water and tilted at various angles。
离散数学英文书籍Discrete mathematics is a vital field of study that encompasses a wide range of mathematical concepts and techniques. It is a fundamental branch of mathematics that has numerous applications in various areas, including computer science, engineering, and operations research. The study of discrete mathematics involves the analysis of discrete, or non-continuous, mathematical structures and the relationships between them.One of the key aspects of discrete mathematics is the study of sets, which are collections of distinct objects. Sets can be used to represent a wide range of mathematical concepts, from numbers and symbols to more complex entities such as functions and relations. The study of sets and their properties, including set operations such as union, intersection, and complement, is an essential component of discrete mathematics.Another important aspect of discrete mathematics is the study of logic, which involves the analysis of the validity and truthfulness of statements. This includes the study of propositional logic, predicate logic, and Boolean algebra, which are used to represent and manipulate logical statements in a formal and rigorous manner.Combinatorics, the study of the enumeration, combination, and permutation of discrete structures, is also a crucial component of discrete mathematics. This field encompasses topics such as counting techniques, graph theory, and the analysis of algorithms, which are essential for understanding and solving a wide range of practical problems.Discrete mathematics also includes the study of number theory, which deals with the properties of integers and their relationships. This includes topics such as divisibility, prime numbers, and modular arithmetic, which have applications in cryptography, computer science, and other fields.In addition to these core topics, discrete mathematics also encompasses a wide range of other areas, such as recurrence relations, generating functions, and discrete probability theory. These topics are essential for understanding and analyzing complex systems and algorithms, and have numerous applications in fields such as computer science, engineering, and economics.One of the key benefits of studying discrete mathematics is the development of critical thinking and problem-solving skills. The rigorous and logical nature of the subject requires students to analyze problems, identify relevant information, and develop creativesolutions. This skill set is highly valued in a wide range of professional and academic settings, and is essential for success in fields such as computer science, engineering, and operations research.Another important aspect of discrete mathematics is its emphasis on mathematical proofs. The study of discrete mathematics involves the development and analysis of mathematical proofs, which are essential for understanding the underlying principles and relationships that govern discrete structures. This focus on proof-based reasoning is a valuable skill that is highly sought after in many academic and professional fields.Overall, the study of discrete mathematics is a highly valuable and important field of study that has numerous applications in a wide range of disciplines. Whether you are interested in computer science, engineering, operations research, or any other field that involves the analysis of discrete structures, the study of discrete mathematics is an essential component of your educational and professional development.。
Discrete Mathematics and Its Applications: Teaching Plan for6th EditionBackgroundDiscrete Mathematics is a foundational subject forcomputer science and mathematics. It covers a wide range of topics, including logic, set theory, algorithms, graph theory, and combinatorics. As a result, students who understand Discrete Mathematics are better prepared for further studyand for solving problems in a variety of fields.The sixth edition of Discrete Mathematics and Its Applications by Kenneth H. Rosen is a widely-used textbookfor students studying Discrete Mathematics. This teachingplan is designed for instructors teaching a course using this text.Course GoalsThe primary goal of this course is for students to develop an understanding of Discrete Mathematics and its applications. This will be achieved through the following objectives: •Develop an understanding of the fundamental concepts of Discrete Mathematics, including logic, settheory, counting, and graph theory.•Learn how to apply these concepts to solve problems in computer science and other areas.•Develop skills in problem-solving and logical reasoning.•Explore further applications of DiscreteMathematics in a variety of fields.Teaching PlanTextbook and ResourcesThe primary textbook for this course will be Discrete Mathematics and Its Applications (6th edition) by Kenneth H. Rosen. In addition to the textbook, there are several resources that can be used to enhance student learning, including:•Online lectures and tutorials•Problem sets and exercises•Supplemental reading materials and videos Course Outline1.Introduction to Discrete Mathematics•Overview of topics covered in the course•Introduction to sets and functions•Basic logic and proof techniques2.Propositional Logic•Propositions and truth values•Logical connectives and truth tables •Logical equivalences and implications3.Predicate Logic•Quantifiers and predicates•Universal and existential quantification •Validity and satisfiability4.Set Theory•Basic concepts and notation•Set operations and Venn diagrams •Applications to counting and probabilitybinatorics•Permutations and combinations•The Pigeonhole Principle and its applications •Binomial coefficients and Pascal’s triangle 6.Relations and Functions•Relations and their properties •Equivalence relations and partitioning •Functions and their properties7.Graph Theory•Basic concepts and notation•Graph representations and connectivity•Planar graphs and Euler’s formula8.Trees•Tree properties and traversal algorithms•Spanning trees and minimum weight trees•Applications to network optimization9.Boolean Algebra and Boolean Functions•Boolean algebra and its laws•Boolean functions and their representations•Applications to digital logic and circuit design Evaluation and GradingStudents will be evaluated based on their performance on the following components:•Homework assignments (30%)•Midterm exam (30%)•Final exam (40%)Homework assignments will consist of problem sets and exercises that reinforce the concepts covered in class. The mid-term exam will cover material from the first half of the course, while the final exam will cover all material from the course.ConclusionDiscrete Mathematics is a fundamental subject for computer science and mathematics, and the sixth edition of Discrete Mathematics and Its Applications is a widely-used textbookfor students studying this subject. This teaching plan is designed to help instructors teach this subject effectively and achieve the course objectives outlined above.。
1.The celebrated theory is still the source of great controversy.2.I thought a good architectural structure should be useful, durable and beautiful.3. A group meeting will be held tomorrow in the library conference room.4. A person’s educational level is closely associated with their social and economicbackground.5.We can all meet at my office after the lecture.6.All industries are a system of inputs, processes, outputs and feedback.7.Economic development needs to be supported by the government.8.All students are expected to attend ten lab sessions per semester.9.Leaving valuable possessions unattended in public place is risky.10.T he toughest part of postgraduate education is funding.11.M ost scientists believe that climate change threatens the lives on earth.12.A lthough sustainable development is not easy, it is an unavoidable responsibility.13.A nimals raised in captivity behave differently than their wild counterparts.14.S tudents will develop confidence in their ability to think critically.15.C ertain scientific principles must be learned verbally or by logical deduction.16.C linical placements in nursing prepare students for professional practice.17.D espite their differences, all forms of life share certain characteristics.18.E conomic problems caused a big rise in unemployment.19.H e landed a job in a very prestigious law firm.20.I t was hard to anticipate how all the different characters would react.21.W e are researching the most significant challenges we are facing in our society today.22.L ibrary reference desks hold a lot of materials on academic history.23.M ost university teaching takes place in lectures and seminars.24.O bservers waited nervously and with bated breath for the concert.25.O rganizational failure is considered from various perspectives in academic literature.26.T he university theater group will be performing in the concert hall.27.P ackaging is very important to attract the attention of a buyer.28.P lease check the information on the website for the opening times.29.R adio is a popular form of entertainment throughout the world.30.R emember, the prestigious election of student membership has strict eligibility criteria.31.R eview all your sources before drawing any definitive conclusions.32.T he supposed benefit of space exploration has been frequently questioned.33.T he speaker began by giving an outline of her presentation.34.S he has made a significant contribution to the field of chemistry.35.S ome departments have their own special book collections.36.S ome students find that true of false questions are harder than short answer questions.37.S tatistical results should be expressed in different ways depending on the circumstances.38.S tudent requiring an extension should apply sooner rather later.39.S tudent concession cards can be obtained by completing an application form.40.A bar chart provides a useful means of data comparison.41.T he archeologist’s new discoveries stand out in previously overlooked foundations.42.T he business policy seminar includes an internship with a local firm.43.T he cafeteria features soup, salads, sandwiches, fish and chicken.44.T he designers will complete the plan later today.45.T he island is located at the south end of the bay.46.T he key difference between courses is the kind of assessment.47.T he library holds a substantial collection of materials on the economic history.48.T he paper challenged many previously accepted theories.49.T he railway makes long-distance travel possible for everyone.50.T he results of the study underscored the importance of early detection.51.T he teacher asked the group to commence the task.52.T he theme of the instrumental work exhibits more of a demure compositional style.53.S afety glasses should be worn while doing experiments in the lab.54.T he visiting speaker used to be a lecturer in this department.55.T here is clearly a need for further research in this filed.56.T his class will look at the structure of an essay.57.O ur laboratory equipment is provided free of charge.58.T raveling by boat on the river is not possible in winter.59.I t will be extremely beneficial to work together.60.T his project is divided into four main sections.61.U niversity fees are expected to increase next year.62.A ll students are expected to participate in all class activities.63.W e can work together to achieve higher educational standards.64.Y ou will need to purchase an academic gown fore the commencement.65.Y our lowest quiz grade has been omitted from the calculations.66.S peak to your tutor if you require further assistance.67.E ducation and training provide important skills for the labor force.68.F arming methods across the world have greatly developed recently.69.F ind out how to get resources before your research.70.G lobal connections thrived in academic communities, thanks to social media.71.S everal candidates are qualified as the greatest scientists of all time.72.S tudents are advised that the lecture today has been canceled.73.T here are opportunities to receive grants in most artistic fields.74.T here is a welcome party for all new students for each term.75.T his course considerably emphasizes critical thinking skills.76.T hose who are considering a career in marketing should attend the talk.77.O ur curriculum covers different aspects of the subject.78.D ifferent factors affect the freezing time of water.79.A ll lectures and learning materials can be found on the internet.80.N ew credit cards will soon use fingerprint technology.81.S tatistics is crucial branch of mathematics.82.C ollaboration between departments is a feature of successful companies.83.G eography is generally divided into two main branches, human and physical.84.H e was constantly looking for ways to bring industry and agriculture closer together.85.L aw is beneficial to investors by protecting their rights and avoiding any improper actionsin the market.86.M aking mistakes is fine as long as learn from them.87.M any graduates of journalism can get jobs in the communications field.88.T his course provides the opportunity to get valuable industry experience.89.T he ability to work with fellow students cannot be stressed enough.90.A rcheologists discovered tools and other artifacts near the ancient tomb.91.E ssays and assignments are spread out across the academic year.92.C ontinuing students will be sent the necessary application forms.93.C alculators may not be used during the examination.94.T he elective course introduces engineering students to construction practices andconcepts.95.T he economy is now showing the first sign of recovery.96.T he site is designed to be highly interactive.97.U niversity departments carefully monitored articles and other publications by faculty.98.Y ou should submit your term papers to the general office.99.S cientists were unsure when the early men first left Africa.100.The printers automatically print on both sides of each page.101.Some vocational courses at institutions are funded by private enterprises.102.This book can be borrowed for a maximum of one week.103.Blue whales are the largest mammals that have ever lived.104.His appointment to the Minister of Culture is seen as a demotion.105.It takes a long time to walk to university.106.As student union members, you can influence and change our university.107.Many food crops require large amounts of water and fertilizer.108.Classical mechanics is sometimes considered as a branch of applied mathematics. 109.This advanced course requires a basic knowledge of economic theory.110.New materials and techniques are changing the style of modern architecture. 111.Sea levels are expected to rise during the next century.rmation technology has changed the way we study today.113.The very basic feature of computing would be counting and calculating.114.There is an accounting assignment for finance students.115.Linguistics is the scientific study and analysis of language.116.Philosophy uses logic and reasons to analyze human experiences.117.Field trips are an important part of geography courses.118.Practical experiments are an essential part of the chemistry course.119.People have been dependent on using phones in their everyday life.120.The digital camera has some advantages over traditional film.121.The university provides great leisure facilities for students and staff.122.Students must attend the safety instruction course before entering the engineering workshop.123.Undergraduates may pursue their specific interests within certificate programs. 124.Air pollution is a serious problem all over the world.125.The commissioner will apportion the funds among all the authorities.126.These three separate research resources are not enough for this assessment. 127.New media journalism is an exciting field of study.128.The extent of advertising to children is very much open to dabate.129.The key witnesses to the event have conflicting recollections.130.Many universities are continuously expanding the postgraduate education online learning resources.131.The very basic definition of computing would be counting and calculating.132.You will write poetry and plays as well as scientific papers.133.The economic predictions turned out to be incorrect.134.Summer school programs allow some students to accelerate their studies.135.Please click on the logo above to enter the site.136.The untapped potential of using sun rays is phenomenal.137.Students are encouraged to think carefully about their accommodation needs. 138.You will study two core and three optional modules.139.Peer review is an essential part of scientific methods.140.The north campus car park could be closed on Sunday.141.We aim to develop a partnership with the government and financial institutions. 142.Lecture outlines are available on the college board and the internal website. 143.The study center in the library has all the latest technologies.144.This course places considerable emphasis on critical thinking skills.145.The poster of this play is hung in the largest lecture theater.146. A typical part of the course involves the study of society.147.Banks charge interest on the money they lent to customers.148.You will be tested by continuous assessments and examinations.149.When launching a product, researching and marketing are very crucial.150.Scientists have found all parts of society today.151.Novelists write about things that they know about.152.Physics is the key subject to understanding the world and the universe.153.Practical experience is a vital part of legal training.154.The new camera can identify your eyes and focus on them.155.Recession triggers exciting creativity and high rates of public wisdom.156.Students will focus on reporting news on changing the media world.157.The lecture today will cover all the main reasons for global warming.158.There resources are not enough for this assessment.159.T he other book isn’t thorough, but it’s more insightful.160.Many businesses near the campus offer student discounts.161.The director of the gallery was grateful for the anonymous donation.162.Studies showed three is a positive correlation between the two variables. 163.You should have awareness of how the business operates globally.164.Art is an expression of creative skills and imagination.165.Humans use symbolic language to communicate plans and contentions. 166.Building trust is not something that can be achieved overnight.167.We have sophisticated ways to study brain actions.168.The dance department stages elaborated performances each semester. 169.An architect is required to have problem-solving skills and an eye for design. 170.Mathematics can be applied to various disciplines.171.The lecture will take place in the main hall.172.Student representatives will be visiting the classes with voting forms. 173.The article exhibits the leisure habits of teenagers in rural areas.174.To take this course, students should have basic economic knowledge. 175.Read the first section before the next meeting.176.Background music can help students concentrate on their studies.177.Most penguins live in the Southern Atlantic Sea.178.Keep your audience in your mind when writing an essay.179.Studying philosophy can help learners think in new ways.180.The university will seek a colossal renovation to the plain empty theater. 181. A wide range of courses covered different aspects in this subject.182.University fees are a key factor when choosing a course.183.Scientists learned through observations and the analysis of human behavior. 184.Crime rates are high because the police phones are difficult to call.185.It is not always possible to find patterns in data.186.Understanding ancient poetry is efficient for the project.187.The subject was complex and difficult to answer.188.In his lifetime, he composed a large number of works.189.Joining the societies is a great way to meet new people.190.Students must present a valid identification to enroll in this course.191.The lecturer intended to promote a series of thoughts and discussions.192.The guidelines are due to be undated shortly.193.Journalists need to work with a range of technologies.194.The instant av ailability of information has radically changed people’s lives.195.Universities across the United Kingdom welcome applications from all new students. 196.We have to reduce the use of plastic materials.197.Americans have progressively defined the process of plant growth and reproductive development int quantitative terms.198.Newspapers across the country have been reporting stories of the president. 199.Students must clean their hands before attending the engineering workshop. 200.Speak to your tutor if you require further research.201.Remember to bring calculators to class next week.202.During that time, people had large families as insurance against some children loss. 203.Medical researchers have focused on different causes of diseases and treatment. 204.The college operates a system of continuous assessments.205.Online courses enable people to improve their skills while employed.206.I looked into my closet for something to wear, but I want to find a new favorite.。