Centre for Discrete Mathematics and Theoretical Computer Science Minimal Deterministic Inco

中山大学本科教学大纲Undergraduate Course Syllabus学院（系）：数据科学与计算机学院School (Department)：School of Data and Computer Science课程名称：离散数学基础Course Title：Discrete Mathematics二〇二〇年离散数学教学大纲Course Syllabus: Discreate Mathematics（编写日期：2020 年12 月）(Date: 19/12/2020)一、课程基本说明I. Basic Information二、课程基本内容 II. Course Content（一）课程内容i. Course Content1、逻辑与证明（22学时） Logic and Proofs (22 hours)1.1 命题逻辑的语法和语义(4学时) Propositional Logic (4 hours)命题的概念、命题逻辑联结词和复合命题，命题的真值表和命题运算的优先级，自然语言命题的符号化Propositional Logic, logic operators (negation, conjunction, disjunction, implication, bicondition), compound propositions, truth table, translating sentences into logic expressions1.2 命题公式等值演算(2学时) Logical Equivalences (2 hours)命题之间的关系、逻辑等值和逻辑蕴含，基本等值式，等值演算Logical equivalence, basic laws of logical equivalences, constructing new logical equivalences1.3 命题逻辑的推理理论（2学时）论断模式，论断的有效性及其证明，推理规则，命题逻辑中的基本推理规则（假言推理、假言易位、假言三段论、析取三段论、附加律、化简律、合取律）,构造推理有效性的形式证明方法Argument forms, validity of arguments, inference rules, formal proofs1.4 谓词逻辑的语法和语义 (4学时) Predicates and Quantifiers (4 hours)命题逻辑的局限，个体与谓词、量词、全程量词与存在量词，自由变量与约束变量，谓词公式的真值，带量词的自然语言命题的符号化Limitations of propositional logic, individuals and predicates, quantifiers, the universal quantification and conjunction, the existential quantification and disjunction, free variables and bound variables, logic equivalences involving quantifiers, translating sentences into quantified expressions.1.4 谓词公式等值演算(2学时) Nested Quantifiers (2 hours)谓词公式之间的逻辑蕴含与逻辑等值，带嵌套量词的自然语言命题的符号化，嵌套量词与逻辑等值Understanding statements involving nested quantifiers, the order of quantifiers, translating sentences into logical expressions involving nested quantifiers, logical equivalences involving nested quantifiers.1.5谓词逻辑的推理规则和有效推理(4学时) Rules of Inference (4 hours)证明的基本含和证明的形式结构，带量词公式的推理规则（全程量词实例化、全程量词一般化、存在量词实例化、存在量词一般化），证明的构造Arguments, argument forms, validity of arguments, rules of inference for propositional logic (modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, addition, simplication, conjunction), using rules of inference to build arguments, rules of inference for quantified statements (universal instantiation, universal generalization, existential instantiation, existential generalization)1.6 数学证明简介(2学时) Introduction to Proofs (2 hours)数学证明的相关术语、直接证明、通过逆反命题证明、反证法、证明中常见的错误Terminology of proofs, direct proofs, proof by contraposition, proof by contradiction, mistakes in proofs1.7 数学证明方法与策略初步(2学时) Proof Methods and Strategy (2 hours)穷举法、分情况证明、存在命题的证明、证明策略（前向与后向推理）Exhaustive proof, proof by cases, existence proofs, proof strategies (forward and backward reasoning)2、集合、函数和关系（18学时）Sets, Functions and Relations(18 hours)2.1 集合及其运算(3学时) Sets (3 hours)集合与元素、集合的表示、集合相等、文氏图、子集、幂集、笛卡尔积Set and its elements, set representations, set identities, Venn diagrams, subsets, power sets, Cartesian products.集合基本运算（并、交、补）、广义并与广义交、集合基本恒等式Unions, intersections, differences, complements, generalized unions and intersections, basic laws for set identities.2.2函数(3学时) Functions (3 hours)函数的定义、域和共域、像和原像、函数相等、单函数与满函数、函数逆与函数复合、函数图像Functions, domains and codomains, images and pre-images, function identity, one-to-one and onto functions, inverse functions and compositions of functions.2.3. 集合的基数（1学时）集合等势、有穷集、无穷集、可数集和不可数集Set equinumerous, finite set, infinite set, countable set, uncountable set.2.4 集合的归纳定义、归纳法和递归（3学时）Inductive sets, inductions and recursions (3 hours)自然数的归纳定义，自然数上的归纳法和递归函数；数学归纳法（第一数学归纳法）及应用举例、强归纳法（第二数学归纳法）及应用举例；集合一般归纳定义模式、结构归纳法和递归函数。

Do The MathAligns to 21stCentury CommunityLearning Centers CriteriaScholastic EducationPage 1 of 8The purpose of the 21st Century Community Learning Centers (21st CCLC) program is to create community learning center s that provide academic enrichment opportunities for children, particularly students who attend high-poverty and low-performing schools, to meet State andlocal student standards in core academic subjects, to offer students a broad array of enrichment activities that can complement their regular academic programs, and to offer literacy and othereducational services to the families of participating children. The following chart details how Do The Math can support the development of a 21st CCLC program. The criteria are drawn from the federal 21st Century Community Learning Centers Non-Regulatory Guidance .Key Criteria for 21stCCLC ProgramsDo The Math1. Activities that provide remedialeducation and academicenrichment to improve academic achievementFocusing on numbers and operations—the cornerstone of elementary math education—Do The Math helps students in grades 2-8 build a solid foundation in computation, number sense, and problem solving for immediate and long-term learning. The program addresses the diverse needs of all students. Incorporating research-based instructional strategies to specifically meet the needs of students who struggle with math, the program helps students to gain necessary conceptual understanding of addition, subtraction, multiplication, division, and fractions.Do The Math consists of 12 modules that target addition and subtraction, multiplication, division, and fractions. Each module includes a series of thirty, 30-minute step-by-step lessons. The proven instructional strategies include:Well organized, manageable lessons that help studentsbuild a solid foundation of understandingExplicit, intentional instruction based on teaching forunderstandingMultiple strategies used for developing concepts andskillsFour-phase pedagogy built on gradual release thatprepares students for individual successStudent interaction that deepens the connectionsstudents make to the skills and strategiesMotivating practice that provides students theopportunity to strengthen and extend their learningVocabulary instruction that helps students developeffective communication and understanding about mathOngoing assessment that allows teachers todifferentiate instruction21st CCLC Programs2. Activities for limited Englishproficient students thatemphasize language skills andacademic achievement Do The Math is an intervention program for Grades 2-8 that can be used with any core math curriculum. The program is intended to help struggling students catch up and keep up with grade-level math skills and standards by helping students develop number sense, computation, and problem solving skills. The twelve modules target Addition & Subtraction, Multiplication, Division, and Fractions.English-Language LearnersDo the Math is designed to grant maximum access and success for English-Language Learners, with an emphasis on language development, the incorporation of visual representations and directions, and consistency across all instructional routines.The four-phase gradual release model prepares students for individual success and ensures that they are prepared to complete their work independently.Routines are will established so English-Language Learners can focus on the content and not the process of the assignment.Numerous structured opportunities for students to engage in meaningful conversations about math are embedded throughout the program to support intentional vocabulary and language development, while increasing access to content. Working in pairs allows for English-Language Learners to speak in their first language in order to understand the task at hand before practicing articulating their solution in English when they share with the larger group.“Built-in-Differentiation” notes on each planner page summarize for teachers some of the important key practices use din each lesson that support English-Language Learners.Visual tools, such as visual representations of mathematical concepts, visual directions in the student WorkSpace, visual representations of manipulatives, and the visual connections to mathematics in children’s literature all support students who second language is English.Math vocabulary is explicitly taught using a consistent routine. Every lesson includes a sidebar that highlights the key math and academic vocabulary used in each lesson along with the Spanish translation of each word or phrase. Language Development boxes provide further explanation and additional support.21st CCLC Programs3. Activities involvingtelecommunications andtechnology education programs The Do The Math Interactive Whiteboard Tools provide all the demonstration tools and WorkSpace pages that teachers need to teach the lesson in the program. The easy-to-use tools work on all interactive whiteboards and are designed to use with large groups of students or with the whole class. Students can easily view the Do The Math Interactive Whiteboard Tools no matter where they are sitting in the classroom. While the tools do not replace the hands-on manipulatives, teachers can use them in a similar way on a whiteboard.4. Activities to promote parentalinvolvement and family literacy Do The Math offers a Community Newsletter, available in English and Spanish that is sent home after every fifth lesson. Through this ongoing communication, parents are informed of the topics and concepts that have been presented in the classroom. The newsletter also includes suggested activities and practice games for students to try at home. In addition, teachers can share WorkSpace pages and assessment results with parents.5. Programs that provide assistanceto students who have been truant,suspended, or expelled to allowthe students to improve theiracademic achievement In Do The Math explicit instruction utilizes scaffolded content and is designed to support students’ learning as they see visual models, connect those models and concepts to their mathematical representations, and while they learn appropriate mathematical and academic language. Do The Math lessons engage students with concepts and skills using concrete manipulative materials, games that reinforce and provide practice, selected children’s literature that provides a context for mathematical concepts and skills, and visual representations to help students represent their thinking.21st CCLC Programs6. Programs and activities thatfollow principles of effectivenessby being based on:Assessment of objective data regarding need for before-and after-school programs Established set ofperformance measures aimedat ensuring the availability ofhigh-quality academicenrichment opportunities If appropriate, scientificallybased research that providesevidence that the program oractivity will help studentsmeet state and localachievement standards The most recent National Assessment of Education Progress (NAEP) data indicates that two-thirds of students are scoring at or below basic as measured by the NAEP Mathematics test. Furthermore, the gap in performance between AYP subgroups continues and in some grade levels widens significantly. Do The Math is a research-based math intervention program designed to support students who are struggling with elementary arithmetic. The program was developed to address the growing national concern regarding mathematics performance as evidenced by the NAEP results.The National Mathematics Advisory Panel’s Final Report (2008) states that to “prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills.” With a focus on Number and Operations, the cornerstone of elementary Math education and a critical foundation of Algebra, Do The Math supports students in building a strong foundation in computation, number sense, and problem solving. Do The Math is based on these eight proven instructional strategies—scaffolded content, explicit instruction, multiple strategies, gradual release, student interaction, meaningful practice, systematic vocabulary and language development, and effective assessment and differentiation.Do The Math—Arithmetic Intervention by Marilyn Burns,A Summary of the Research provides specificinformation regarding the research foundation for the program.Do The Math includes processes and materials that scientifically-based research has shown to be effective in increasing academic achievement. The program, which reflects National Council of Mathematics (NCTM) standards, teaches essential Numbers and Operations math skills that integrate with a core math curriculum. Step-by-step lessons help students develop understanding, learn skills, see relationships, and make connections. Students develop the skills they need to compute with accuracy and efficiency, the number sense they need to reason, and the ability to apply their skills and reasoning to solve problems. Learning experiences link concepts and skills to their mathematical representations and language.(Continued)21st CCLC ProgramsPrograms and activities that follow principles of effectiveness Continued A four-phase pedagogy built on gradual release prepares students for individual success.1. Phase One—The teacher models and records themathematical representation on the board.2. Phase Two—The teacher models again, now elicitingresponses from students, and again records on theboard.3. Phase Three—Students work in pairs to do themathematics and then the teacher, once again, recordson the board.4. Phase Four—Students work independently, monitoredand supported by the teacher.Multiple strategies for developing concepts and skills support student learning. Lessons engage students with each concept and skill in several ways, deepening their mathematics knowledge. Manipulative materials provide students concrete experiences with abstract ideas. Games offer engaging situations where mathematical understandings and skills are reinforced. Children’s literature provides a springboard for instruction. Contexts make abstract mathematical ideas accessible.7. The eligible entity has experienceor promise of success in providingeducational and related activitiesthat will complement and enhancethe academic performance,achievement, and positive youthdevelopment of the students. Do The Math was developed in collaboration with schools across the country and represents Marilyn Burns’ and her professional development company’s, Math Solutions, life work regarding the tools teachers need to be effective and the foundation in math that students need to be successful. From 2005 to 2006, Marilyn and a team of Math Solutions Master Classroom Teachers spent over two years drafting, testing, debating, and refining the lessons in the program within classrooms across the country. In 2007-2008, Scholastic published Do The Math and entered into several partnerships with large districts to document the efficacy of the program.Over the course of the spring of 2008 (from January 30th-June 15th), research was conducted on the implementation and impact of Do The Math in six schools in New York City. Scholastic partnered with the New York City Department of Education (NY DOE) to select schools where the city’s diverse student population would be represented and where the program could be implemented with fidelity. Half were general education elementary schools, and half were within District 75 schools, a district that serves students with special needs. In whole class or small groups, students were instructed using one or two of the Do The Math multiplication modules.(Continued21st CCLC ProgramsThe eligible entity has experience or promise of success in providing educational and related activities that will complement and enhance the academic performance, achievement, and positive youth development of the students.Continued) The Do The Math research study reveals positive results for students who struggle with elementary math, as well as for the schools and teachers that are working with them. The four-month-long study showed that diverse populations of students in grades three through six who received instruction in one of the Multiplication modules (either A or B), including students with special needs, English-Language Learners, and General Elementary school students identified as at-risk, made statistically significant gains on the program’s End-of-Module Assessment, and acquired the key math vocabulary presented in the program. In addition, it showed that students’ confidence in themselves as math learners improved from the time when they began the program until they finished it.The Do The Math—Math Intervention in New York City Schools Impact Study is available upon request.8. To sustain a quality program, staffdelivering academic support andenrichment services should beprovided ongoing training andlearning opportunities. Do the Math offers a variety of professional development solutions:Do The Math Implementation TrainingThis half-day training helps teachers to successfully get started using the program in their classrooms. They will learn how to effectively use the program, including:Navigating the program materials and exploring how they address current issues in math interventionExperiencing the pace of a Do The Math module with tips for implementing instructional strategiesAssessing student progress and learning how to differentiate instructionReviewing ongoing math professional development opportunitiesEmbedded Professional DevelopmentThe Teacher Guide provided for each module of the program provides step-by-step teaching instructions, clear models, modified scripting, and guidance for monitoring student progress. Supporting Instruction, Language Development, and Mathematical Background boxes at point-of-use provide professional information that helps prevent learning, and well as teaching stumbling blocks.21st CCLC Programs9. Academic activities are alignedwith the school’s curriculum in thecore subject areas. Do The Math focuses on the most essential topics in Number and Operations, all of which are sequenced, paced appropriately, and presented in ways that are accessible for struggling students. Unlike most textbooks, which cover a broad range of topics and treat all equally, Do The Math focuses on core concepts and skills that are essential to long-term success. Do The Math consists of twelve modules that cover addition, subtraction, multiplication, division, and fractions. Students receive instruction in the topic that aligns to their grade level, their performance, or the goals of their Individualized Education Plans (IEPs).10. Program was developed and willbe carried out in activecollaboration with the schools thestudents attend. Do The Math provides various opportunities for teachers to collect and use data to inform and target their instruction in order to meet all of their students’ diverse needs. Teachers record students’ progress monitoring results on a copy of the Objectives Tracker found at the back of each module’s Teacher Guide. The tracker is provided so that teachers may document students’ progress at meeting each module objective by recording the date when the student consistently performed the objective with accuracy. Students complete a Beginning-of-Module Assessment as a pre-module snapshot of what they know. Upon completion of the module, administering the End-of-Module Assessment provides the teacher with documentation for mathematical growth in skill and understanding demonstrated by each student.11. The program includes a plan forhow the community learningcenter will continue after fundingunder this part ends. Do The Math can be integrated with funds from state, local, and other sources. The federal funding programs for which it qualifies include:Title IA—Improving Basic ProgramsTitle IA—Supplemental Educational ServicesTitle III—English Language Acquisition21st Century Community Learning CentersIDEA, Part BIDEA, Response to Intervention12. The program or activity shallundergo a periodic evaluation toassess its progress towardachieving its goal of providinghigh-quality opportunities foracademic enrichment. Do the Math has a Beginning-of-Module Assessment for each of its twelve modules. The Beginning-of-Module Assessment, administered prior to instruction, is given to students that the teacher has identified as needing instruction on that particular topic. The assessment will reveal what students know in regard to the topic content for that module. The first few questions on the assessment will inform whether the student has the prerequisite skills for that module. If not, the student will need additional support before beginning that module.(Continued)21st CCLC ProgramsThe program or activity shall undergo a periodic evaluation to assess its progress toward achieving its goal of providing high-quality opportunities for academic enrichment.Continued Additional support may mean moving the student into another module. Each module also includes an End-of-Module Assessment with questions similar to the Beginning-of-Module Assessment so that the teacher can measure student growth.Do the Math also includes several periodic assessments that check student progress and help teachers adjust instruction accordingly. Progress monitoring in the form ofa written formative assessment occurs after every fifth lesson so teachers can quickly identify and provide immediate support. During every fifth lesson, students independently complete a written assessment which mirrors what they have been working on in the previous four lessons. Teachers then use the results to select and implement the suggestions for differentiation included in the program and make decisions about targeting instruction according to each student’s needs.Formative Assessment through daily observations is built into the program so students receive the proper attention and differentiation required to enable them to develop conceptual understanding and skills successfully. Supporting instruction boxes appear frequently to highlight opportunities for teachers to observe student understanding and provide additional support.。

Canadian Intermediate Mathematics Contest NOTE:1.Please read the instructions on the front cover of this booklet.2.Write solutions in the answer booklet provided.3.It is expected that all calculations and answers will be expressed as exact numbers such as 4π,2+√7,etc.,rather than as 12.566...or4.646....4.While calculators may be used for numerical calculations,other mathematical steps must be shown and justified in your written solutions and specific marks may be allocated for these steps.For example,while your calculator might be able to find the x -intercepts of the graph of an equation like y =x 3−x ,you should show the algebraic steps that you used to find these numbers,rather than simply writing these numbers down.5.Diagrams are not drawn to scale.They are intended as aids only.6.No student may write both the Canadian Senior Mathematics Contest and the Canadian Intermediate Mathematics Contest in the same year.PART AFor each question in Part A,full marks will be given for a correct answer which is placed in the box.Part marks will be awarded only if relevant work is shown in the space provided in the answer booklet.1.There are 200people at the beach,and 65%of these people are children.If 40%of the children are swimming,how many children are swimming?2.If x +2y =14and y =3,what is the value of 2x +3y ?3.In the diagram,ABCD is a rectangle with points Pand Q on AD so that AB =AP =P Q =QD .Also,point R is on DC with DR =RC .If BC =24,whatis the area of P QR ?A B CD P Q R 4.At a given time,the depth of snow in Kingston is 12.1cm and the depth of snow in Hamilton is 18.6cm.Over the next thirteen hours,it snows at a constant rate of2.6cm per hour in Kingston and at a constant rate of x cm per hour in Hamilton.At the end of these thirteen hours,the depth of snow in Kingston is the same as the depth of snow in Hamilton.What is the value of x ?5.Scott stacks golfballs to make a pyramid.The first layer,or base,of the pyramid is a square of golfballs and rests on a flat table.Each golfball,above the first layer,rests in a pocket formed by four golfballs in the layer below (as shown in Figure 1).Each layer,including the first layer,is completely filled.For example,golfballs can be stacked into a pyramid with 3levels,as shown in Figure 2.The four triangular faces of the pyramid in Figure 2include a total of exactly 13different golfballs.Scott makes a pyramid in which the four triangular faces include a total of exactly 145different golfballs.How many layers does this pyramid have?Figure 1Figure 26.A positive integer is a prime number if it is greater than1and has no positive divisorsother than1and itself.For example,the number5is a prime number because its only two positive divisors are1and5.The integer43797satisfies the following conditions:•each pair of neighbouring digits(read from left to right)forms a two-digit primenumber,and•all of the prime numbers formed by these pairs are different,because43,37,79,and97are all different prime numbers.There are many integers with more thanfive digits that satisfy both of these conditions.What is the largest positive integer that satisfies both of these conditions?PART BFor each question in Part B,your solution must be well organized and contain words of explanation or justification.Marks are awarded for completeness,clarity,and style of presentation.A correct solution,poorly presented,will not earn full marks.1.(a)Determine the average of the six integers22,23,23,25,26,31.(b)The average of the three numbers y+7,2y−9,8y+6is27.What is the valueof y?(c)Four positive integers,not necessarily different and each less than100,have anaverage of94.Determine,with explanation,the minimum possible value forone of these integers.2.(a)In the diagram, P QR is right-angled at R.If P Q=25and RQ=24,determine the perimeterand area of P QR.PQR(b)In the diagram, ABC is right-angled at C withAB=c,AC=b,and BC=a.Also, ABC has perimeter144and area504.Determine all possible values of c.(You may use the facts that,for any numbers x and y, (x+y)2=x2+2xy+y2and(x−y)2=x2−2xy+y2.)AB C ab cCanadian Intermediate Mathematics Contest(English)20143.Vicky starts with a list(a,b,c,d)of four digits.Each digit is0,1,2,or3.Vickyenters the list into a machine to produce a new list(w,x,y,z).In the new list,w is the number of0s in the original list,while x,y and z are the numbers of1s,2s and3s,respectively,in the original list.For example,if Vicky enters(1,3,0,1),the machine produces(1,2,0,1).(a)What does the machine produce when Vicky enters(2,3,3,0)?(b)Vicky enters(a,b,c,d)and the machine produces the identical list(a,b,c,d).Determine all possible values of b+2c+3d.(c)Determine all possible lists(a,b,c,d)with the property that when Vicky enters(a,b,c,d),the machine produces the identical list(a,b,c,d).(d)Vicky buys a new machine into which she can enter a list of ten digits.Eachdigit is0,1,2,3,4,5,6,7,8,or9.The machine produces a new list whoseentries are,in order,the numbers of0s,1s,2s,3s,4s,5s,6s,7s,8s,and9s inthe original list.Determine all possible lists,L,of ten digits with the propertythat when Vicky enters L,the machine produces the identical list L.。

国外数学期刊英汉对照作者:admin 日期:2009-06-17字体大小: 小中大Advances in Applied Mathematics 应用数学Advances in Applied Probability 应用概率论进展Advances in Computational Mathematics 计算数学进展Advances in Mathematics 数学进展Algebra Colloquium 代数学讨论会Algebras and Representation Theory 代数和表示理论American Mathem atical Monthly 美国数学月刊American Statistician 美国统计员Annals of Applied Probability 应用概率论年报Annals of Global Analysis and Geometry 整体分析与几何学年报Annals of Mathematics and Artificial Intelligence 人工智能论题年报Annals of Operations Research 运筹学研究年报Annals of Probability 概率论年报Annals of Pure and Applied Logic 抽象和应用逻辑年报Annals of Statistics 统计学年报Annals of The Institute of Statistical Mathematics 统计数学学会年报Applicable Algebra in Engineering Communication and Computing 代数在工程通信与计算中的应用Applied and Computational Harmonic Analysis 调和分析应用和计算Applied Categorical Structures 应用范畴结构Applied Mathematics and Computation 应用数学与计算Applied Mathematics and Optimization 应用数学与最优化Applied Mathematics Letters 应用数学快报Archive for History of Exact Sciences 科学史档案Archive for Mathem atical Logic 数理逻辑档案Archive for Rational Mechanics and Analysis 理性力学和分析档案Archives of Computational Methods in Engineering 工程计算方法档案Asymptotic Analysis 渐近线分析Autonomous Robots 机器人British Journal of Mathematical & Statistical Psychology 英国数学与统计心理学杂志Bulletin of The American Mathematical Society 美国数学会快报Bulletin of the London Mathematical Society 伦敦数学会快报Calculus of Variations and Partial Differential Equations 变分法与偏微分方程Combinatorics Probability & Computing 组合概率与计算Combustion Theory and Modeling 燃烧理论建模Communications in Algebra 代数通讯Communications in Contemporary Mathematics 当代数学通讯Communications in Mathematical Physics 数学物理学通讯Communications in Partial Differential Equations 偏微分方程通讯Communications in Statistics-Simulation and Computation 统计通讯–模拟与计算Communications on Pure and Applied Mathematics 纯数学与应用数学通讯Computational Geometry-Theory and Applications 计算几何- 理论与应用Computational Optimization and Applications 优化计算与应用Computational Statistics & Data Analysis 统计计算与数据分析Computer Aided Geometric Design 计算机辅助几何设计Computer Physics Communications 计算机物理通讯Computers & Mathematics with Applications 计算机与数学应用Computers & Operations Research 计算机与运筹学研究Concurrent Engineering-Research and Applications 共点工程- 研究与应用Conformal Geometry and Dynamics 投影几何与力学Decision Support Systems 决策支持系统Designs Codes and Cryptography 编码设计与密码系统Differential Geom etry and Its Applications 微分几何及其应用Discrete and Continuous Dynamical Systems 离散与连续动力系统Discrete Applied Mathematics 应用离散数学Discrete Computational Geometry 离散计算几何学Discrete Event Dynamic Systems-Theory and Applications 离散事件动态系统- 理论和应用Discrete Mathematics 离散数学Educational and Psychological Measurement 教育与心理测量方法Engineering Analysis with Boundary Elem ents 工程边界元素分析Ergodic Theory and Dynamical System s 遍历理论和动力系统European Journal of Applied Mathematics 欧洲应用数学杂志European Journal of Combinatorics 欧洲组合数学杂志European Journal of Operational Research 欧洲运筹学杂志Experimental Mathematics 实验数学Expert Systems with Applications 专家系统应用Finite Fields and Their Applications 有限域及其应用Foundations of Computational Mathematics 计算数学基础Fuzzy Sets and Systems 模糊集与模糊系统Glasgow Mathematical Journal 英国格拉斯哥数学杂志Graphs and Combinatorics 图论与组合数学IEEE Robotics & Automation Magazine IEEE机器人与自动化杂志IEEE Transactions on Robotics and Automation IEEE机器人与自动化学报IMA Journal of Applied Mathem atics IMA应用数学学报IMA Journal of Mathem atics Applied in Medicine and Biology IMA数学在医药与生物中的应用杂志IMA Journal of Numerical Analysis IMA数值分析学报Information and Computation 信息与计算Insurance Mathematics & Economics 保险数学和经济学International Journal for Numerical Methods in Engineering 国际工程数值方法杂志International Journal of Algebra and Computation 国际代数和计算杂志International Journal of Computational Geometry & Applications 国际计算几何应用杂志International Journal of Computer Integrated Manufacturing 国际计算机集成制造业国际杂志International Journal of Game Theory 国际对策论国际杂志International Journal of Mathematics 国际数学杂志International Journal of Production Research 国际研究成果杂志International Journal of Robotics Research 国际机器人研究杂志International Journal of Systems Science 国际系统科学杂志International Statistical Review 国际统计评论Inverse Problems 反比问题Journal of Algebra 代数学报Journal of Algebraic Combinatorics 代数组合数学学报Journal of Algebraic Geometry 代数几何学报Journal of Algorithm s 算法学报Journal of Applied Mathematics and Mechanics 数学应用与力学学报Journal of Applied Probability 应用概率杂志Journal of Approximation Theory 近似值理论杂志Journal of Combinatorial Optimization 组合最优化学报Journal of Combinatorial Theory Series B 组合理论学报B辑Journal of Combinatorial Theory Series A 组合理论学报A辑Journal of Computational Acoustics 声学计算杂志Journal of Computational Analysis and Applications 计算分析与应用学报Journal of Computational and Applied Mathematics 计算与应用数学杂志Journal of Computational Biology 生物计算杂志Journal of Computational Mathematics 计算数学学报Journal of Computational Neuroscience 神经系统计算杂志Journal of Computational Neuroscience 神经系统计算杂志Journal of Differential Equations 微分方程组学报Journal of Econom etrics 计量经济学会会刊Journal of Engineering Mathematics 工程数学学报Journal of Functional Analysis 泛函分析学报Journal of Geometry and Physics 几何学和物理学学报Journal of Global Optimization 整体优化学报Journal of Graph Theory 图论理论学报Journal of Group Theory 群论理论学报Journal of Lie Theory 展开理论杂志Journal of Mathematical Analysis and Applications 数学分析和应用学报Journal of Mathematical Biology 数学生物学杂志Journal of Mathematical Economics 数学经济学学报Journal of Mathematical Imaging and Vision 成像和视觉数学学报Journal of Mathematical Physics 数学物理学的杂志Journal of Mathematical Psychology 数学心理学杂志Journal of Multivariate Analysis 多变量分析杂志Journal of Nonlinear Science 非线性数学学报Journal of Number Theory 数论学报Journal of Operations Management 操作管理杂志Journal of Pure and Applied Algebra 纯代数与应用代数学学报Journal of Statistical Planning and Inference 统计规划和推论杂志Journal of Symbolic Computation 符号计算学报Journal of the American Mathematical Society 美国数学会杂志Journal of the London Mathematical Society-Second Series 伦敦数学会杂志- 第二辑Journal of the Royal Statistical Society Series B-Statistical Methodology 皇家学会系列杂志B 辑-统计方法学Journal of The Royal Statistical Society Series C-Applied Statistics 皇家学会系列杂志C - 应用统计Journal of Theoretical Probability 概率理论杂志K-Theory K-理论Lecture Notes in Economics and Mathematical Systems 经济学和数学体系讲座Lecture Notes on Mathematics 数学讲座Letters in Mathematical Physics 数学物理学通讯Linear Algebra and Its Applications 线性代数及其应用Mathematical Biosciences 数理生物学Mathematical Finance 数理财金学Mathematical Geology 数理地质学Mathematical Intelligencer 数学情报Mathematical Logic Quarterly 数理逻辑学报Mathematical Methods in the Applied Sciences 数学应用学科Mathematical Methods of Operations Research 运筹学研究Mathematical Models & Methods in Applied Sciences 数学模拟与应用方法Mathematical Physics Electronic J 数学物理电子杂志Mathematical Proceedings of the Society 数学学会学报Mathematical Programming 数学规划Mathematical Social Sciences 数学社会科学Mathematics and Computers in Simulation 数学与电脑模拟Mathematics and Mechanics of Solids 数学与固体力学Mathematics Archives 数学档案库Mathematics Magazine 数学杂志Mathematics of Computation 计算数学Mathematics of Control Signals and Systems 控制信号系统数学Memoirs of the American Mathematical Society 美国数学会备忘录Modem Logic 现代逻辑学Nonlinear Analysis-Theory Methods & Applications 非线性分析- 理论与应用Nonlinearity 非线性特性Notices 短评Numerical Algorithms 数字算法Numerical Methods for Partial Differential Equations 偏微分方程式数值方法Oxford Bulletin of Economics and Statistics 牛津大学经济与统计快报Potential Analysis 位势分析Proceedings of the American Mathem atical Society 美国数学会会议录Proceedings of the London Mathematical Society 伦敦数学会会议录Proceedings of the Royal Society of Edinburgh Section A-Mathem atics 英国爱丁堡皇家学会会议录A分册数学Quarterly Journal of Mathematics 数学季刊Quarterly Journal of Mechanics and Applied Mathematics 数学与应用数学季刊Quarterly of Applied Mathematics 应用数学季刊Queueing Systems 排列系统Random Structures and Algorithms 随机结构与算法Reports on Mathematical Physics 数学物理学报告Representation Theory 表示法理论Robotics and Autonomous Systems 机器人技术和自动系统Rocky Mountain Journal of Mathematics 数学难题学报Set-Valued Analysis 精点分析Statistical Papers 统计学论文Statistics & Probability Letters 统计和概率通讯Statistics and Computing 统计和计算Stochastic Analysis and Applications 随机分析和应用Stochastic Environm ental Research and Risk Assessm ent 随机环境论研究和风险评估Stochastic Processes and Their Applications 随机过程及其应用Studies in Applied Mathematics 应用数学研究The College Mathematics Journal 大学数学杂志The Electronic Journal of Combinatorics 组合数学电子期刊Theory of Computing Systems 计算方法理论Theory of Probability and Its Applications 概率理论及其应用程序理论Topology 拓扑学Topology and Its Applications 拓扑学及其应用Transactions of the American Mathematical Society 美国数学会学报Applied Numerical Mathematics《应用数值数学》荷兰Annales Scientifiques de l'École Normale Supérieure《高等师范学校科学纪事》法国Applied and Computational Harmonic Analysis《应用和计算谐波分析》美国Applied Stochastic Models in Business and Industry《商业与工业应用随机模型》英国Acta Applicandae Mathematicae 《应用数学学报》荷兰Advances in Computational Mathematics《计算数学进展》荷兰Annals of Mathematics and Artificial Intelligence《数学与人工智能纪事》荷兰Annals of Operations Research《运筹学纪事》荷兰Annals of the Institute of Statistical Mathematics《统计数理研究所纪事》日本。

The University of SydneyFaculties of Arts,Economics,Education,Engineering and ScienceMATH2969:Discrete Mathematics and Graph Theory(Advanced)Paper1:Discrete MathematicsPRACTICE EXAM FOR REVISION ONLYLecturer:Anthony HendersonTime allowed:11hours2This booklet contains4pages.1.In this question,your numerical answers need not be evaluated.One of the highest-profile athletics events at this year’s Olympic Games will be the 100m sprint for men.Suppose there are128athletes who enter,8of whom will make it through to thefinal.(a)Suppose that there are7change-rooms available for the128athletes.Explainwhy there must be a change-room used by at least19athletes.(b)The change-room cleaner only cares about how many athletes use each room,not who they are–however,he does distinguish between the7rooms.Fromhis point of view,how many possible allocations of athletes to the change-rooms are there in which no rooms go unused?(c)In thefirst round of the event,the entrants must be split into16heats,eachwith8athletes.Suppose that it doesn’t matter to the athletes which of the16heats they are put into,just who is in the same heat with them.Howmany different allocations of athletes to heats are there?(d)Suppose6of the128entrants werefinalists in the last Olympics.How manyof the allocations of athletes to heats have the property that these6specialathletes are all in different heats?Explain your answer.(e)The outcome of the event,as it will be recorded in the history books,consistsof the following information:the name of the gold medallist,the name ofthe silver medallist,the name of the bronze medallist,and then the namesof the other5finalists in alphabetical order.Given the list of128entrants,how many possible outcomes are there?(f)How many of the outcomes counted in the previous part have the propertythat at least two of the6special athletes win a medal?(3+2+2+3+2+2=14marks) 2.(a)Recall that the Lucas sequence is defined by the initial conditions L0=2,L1=1,and the recurrence relation L n=L n−1+L n−2for n≥2.Prove byinduction thatL n+2L n=L2n+1+5(−1)n,for all n≥0.(b)Give the rest of this definition:“The characteristic polynomial of the homo-geneous linear recurrence relation a n=ra n−1+sa n−2,n≥2,is...”.(c)Suppose that this characteristic polynomial has distinct rootsλ1andλ2.Explain why the sequence a n=C1λn1+C2λn2satisfies the recurrence relation,for any constants C1and C2.(d)Continuing with the assumption of distinct roots,prove the converse:thatevery sequence a n which satisfies a n=ra n−1+sa n−2for n≥2has the forma n=C1λn1+C2λn2for some constants C1and C2.(e)Using the characteristic polynomial of the recurrence relation for the Lucasnumbers,derive a closed formula for L n.3.(a)Give the rest of this definition:“The generating function A (z )of a sequencea 0,a 1,a 2,···is ...”.(b)Suppose the generating function of the sequence a 0,a 1,a 2,···is A (z ),andthat s n ,for any n ≥0,is defined by the rule s n =a 0+a 1+a 2+···+a n .Prove that the generating function of the sequence s 0,s 1,s 2,···is A (z )1−z .(Explain carefully what facts you are using.)(c)Find a formula for the generating function A (z )of the sequence defined bythe initial conditions a 0=a 1=a 2=1and the recurrence relationa n =1n (a n −1+a n −2+a n −3),for n ≥3.(d)Using the generating function,or any other valid method,solve the recur-rence relationa n =4a n −1−3a n −2+n,for n ≥2,with the initial conditions a 0=1,a 1=−1/4.(2+3+4+5=14marks)4.(a)Complete this definition:“If X is a set with n elements,and n 1,n 2,···,n kare nonnegative integers such that n 1+n 2+···+n k =n ,then the multinomial coefficient n n 1,n 2,···,n k is the number of ...”.(b)State the formula for n n 1,n 2,···,n k in terms of factorials.(c)Is it always true that n n 1,n 2,···,n k ≤k n ?Explain your answer.(d)Assuming that ∞ n =0(n +1)z n =1(1−z )2,find a formula for ∞ n =0 n +21,1,n z n .(Explain your argument carefully.)(e)By expressing (a +b )2n as (a 2+2ab +b 2)n and expanding this via the Multi-nomial Theorem,prove the following equation for all nonnegative integers m,n such that m ≤n :2n m = m 2 n 1=02m −2n 1 n n 1,m −2n 1,n −m +n 1 .5.Let f (n )and g (n )be two functions of a nonnegative integer variable such thatlim n →∞f (n )=lim n →∞g (n )=∞.Recall that f (n ) g (n )means that there exist positive constants C,D,N such thatC ≤f (n )g (n )≤D,for all n ≥N.(a)Is it always true that if g (n )is defined by g (n )=f (n )+f (n −1)+···+f (0),then g (n ) f (n )?Explain your answer.(b)Give the rest of this definition:“We say that f (n )grows at a slower ratethan g (n ),the notation for which is f (n )≺g (n ),if ...”.(c)Prove that 3n ≺n !.(d)An integer k ≥2is said to be composite if there is some integer d suchthat 2≤d ≤ √k and k/d is an integer.Here is a recursive algorithm (not necessarily a good one),called COMP(n ),which outputs the number of composite k such that 2≤k ≤n .The steps are:1.If n =1,return the answer 0and stop.2.(To arrive here,we must have n ≥2.)For each integer d such that 2≤d ≤ √n ,divide n by d .The results of these divisions tell youwhether n is composite or not.e COMP(n −1)to find the number of composite k with 2≤k ≤n −1.4.If n was found to be composite in Step 2,add one to the answer of Step 3;otherwise leave it unchanged.Return this as the answer.For any n ≥1,let d n be the number of divisions which are carried out in COMP(n ).Find a recurrence relation for d n ,and unravel it to give a non-closed formula for d n .(e)Hence prove that d n n 3/2.(3+2+3+3+3=14marks)。

外国文学作选读Selected Reading of Foreign Literature现代企业管理概论Introduction to Modern Enterprise Managerment电力电子技术课设计Power Electronics Technology Design计算机动画设计3D Animation Design中国革命史China’s Revolutionary History中国社会主义建设China Socialist Construction集散控制DCS Distributed Control计算机控制实现技术Computer Control Realization Technology计算机网络与通讯Computer Network and CommunicationERP/WEB应用开发Application ＆ Development of ERP/WEB数据仓库与挖掘Data Warehouse and Data Mining物流及供应链管理Substance and Supply Chain Management成功心理与潜能开发Success Psychology & Potential Development信息安全技术Technology of Information Security图像通信Image Communication金属材料及热加工Engineering Materials & Thermo-processing机械原理课程设计Course Design for Principles of Machine机械设计课程设计Course Design for Mechanical Design机电系统课程设计Course Design for Mechanical and Electrical System 创新成果Creative Achievements课外教育Extracurricular education。

Canadian Intermediate Mathematics Contest NOTE:1.Please read the instructions on the front cover of this booklet.2.Write solutions in the answer booklet provided.3.Express calculations and answers as exact numbers such as π+1and √2,etc.,rather than as4.14...or 1.41...,except where otherwise indicated.4.While calculators may be used for numerical calculations,other mathematical steps must be shown and justified in your written solutions and specific marks may be allocated for these steps.For example,while your calculator might be able to find the x -intercepts of the graph of an equation like y =x 3−x ,you should show the algebraic steps that you used to find these numbers,rather than simply writing these numbers down.5.Diagrams are not drawn to scale.They are intended as aids only.6.No studentmay write both the Canadian Senior Mathematics Contest and the Canadian Intermediate Mathematics Contest in the same year.PART AFor each question in Part A,full marks will be given for a correct answer which is placed in the box.Part marks will be awarded only if relevant work is shown in the space provided in the answer booklet.1.Stephanie has 1000eggs to pack into cartons of 12eggs.While packingthe eggs,she breaks n eggs.The unbroken eggs completely fill a collection of cartons with no eggs left over.If n <12,what is the value of n ?2.In the diagram,ABCD is a square with side length 4.Points P ,Q ,R ,and S are the midpoints of the sides ofthe square,as shown.What is the area of the shadedregion?3.In the diagram,line segments AB ,CD and EF parallel,and points A and E lie on CG and respectively.If ∠GAB =100◦,∠CEF =30◦,∠ACE =x ◦,what is the value of x ?H4.If 12x =4y +2,determine the value of the expression 6y −18x +7.5.Determine the largest positive integer n with n <500for which 6048(28n )is a perfect cube (that is,it is equal to m 3for some positive integer m ).6.A total of2015tickets,numbered1,2,3,4,...,2014,2015,are placed in an emptybag.Alfie removes ticket a from the bag.Bernice then removes ticket b from the bag.Finally,Charlie removes ticket c from the bag.They notice that a<b<c and a+b+c=2018.In how many ways could this happen?PART BFor each question in Part B,your solution must be well organized and contain words of explanation or justification.Marks are awarded for completeness,clarity,and style of presentation.A correct solution,poorly presented,will not earn full marks.1.At Cornthwaite H.S.,many students enroll in an after-school arts program.Theprogram offers a drama class and a music class.Each student enrolled in the program is in one class or both classes.(a)This year,41students are in the drama class and28students are in the musicclass.If15students are in both classes,how many students are enrolled in theprogram?(b)In2014,a total of80students enrolled in the program.If3x−5students werein the drama class,6x+13students were in the music class,and x studentswere in both classes,determine the value of x.(c)In2013,half of the students in the drama class were in both classes and one-quarter of the students in the music class were in both classes.A total ofN students enrolled in the program in2013.If N is between91and99,inclusive,determine the value of N.2.Alistair,Conrad,Emma,and Salma compete in a three-sport race.They each swim2km,then bike40km,andfinally run10km.Also,they each switch instantly from swimming to biking and from biking to running.(a)Emma has completed113of the total distance of the race.How many kilometershas she travelled?(b)Conrad began the race at8:00a.m.and completed the swimming portion in30minutes.Conrad biked12times as fast as he swam,and ran3times as fast as he swam.At what time did hefinish the race?(c)Alistair and Salma also began the race at8:00a.m.Alistairfinished theswimming portion in36minutes,and then biked at28km/h.Salmafinished the swimming portion in30minutes,and then biked at24km/h.Alistair passed Salma during the bike portion.At what time did Alistair pass Salma?2015Canadian Intermediate Mathematics Contest (English)3.Heron’s Formula says that if a triangle has side lengths a ,b and c ,then its area equals s (s −a )(s −b )(s −c ),where s =12(a +b +c )is called the semi-perimeter ofthe triangle.A B Ca b c(a)In the diagram, ABC has side lengthsAB =20,BC =99,and AC =101.If his the perpendicular distance from A toBC ,determine the value of h .A BC 9910120h (b)In the diagram,trapezoid P QRS hasP S parallel to QR .Also,P Q =7,QR =40,RS =15,and P S =20.Ifx is the distance between parallel sidesP S and QR ,determine the value of x .(c)The triangle with side lengths 3,4and 5has the following five properties:•its side lengths are integers,•the lengths of its two shortest sides differ by one,•the length of its longest side and the semi-perimeter differ by one,•its area is an integer,and •its perimeter is less than 200.Determine all triangles that have thesefive properties.。

全球数学网址大全数理逻辑、数学理论AILAhttp://www.disi.unige.it/aila/eindex.html意大利逻辑及其应用协会的主页，包括意大利数理逻辑领域的相关内容。

Algebra and Logic/title.cgi?2110《代数与逻辑》，《西伯利亚代数与逻辑期刊》的翻译版，荷兰的Kluwer学术出版社提供其在线服务。

alt.math.undergrad-Math Forum/epigone/alt.math.undergradMsth Forum上的大学生和研究生数学论坛,提供档案文件、论题等信息。

Annals of Pure and Applied Logic/~dmjones/hbp/apal/《纯逻辑与应用逻辑学年鉴》，麻省理工大学计算理论小组主页提供其过刊的浏览，荷兰的Elservier出版社提供其电子刊的在线服务。

Archive for Mathematical Logichttp://link.springer.de/link/service/journ...00153/index.htm《数学逻辑档案》，属于德国Springer出版公司在线电子期刊的一种。

Aristotle and the Paradoxes of Logic-Gilbert Voeten/nilog/files/arist...adoxes_of_l.htm亚里士多德及其逻辑理论研究。

BLC/~exr/blc/不列颠逻辑研讨会的主页，包括数学逻辑的相关研究，如相关网站及电子期刊。

Books:Professional&Technical:Professional Science: /exec/obidos/tg/brows...3600008-7001844浏览亚马逊网上专业和技术店中的数学畅销书，提供应用范畴，混沌与系统化；几何与拓扑；数学分析；数学物理学；数字规律；纯数学；数学变换等领域，包括数理逻辑方面的畅销书的在线预览。

Abbreviations of Names of SerialsThis list gives the form of references used in Mathematical Reviews(MR).The abbreviation is followed by the complete title,the place of publication and other pertinent information.∗not previously listed E available electronically §journal reviewed cover-to-cover V videocassette series †monographic series¶bibliographic journal∗Abh.Braunschw.Wiss.Ges.Abhandlungen derBraunschweigischen Wissenschaftlichen Gesellschaft.J.Cramer Verlag,Braunschweig.(Formerly Abh.Braunschweig.Wiss.Ges.)Abh.Braunschweig.Wiss.Ges.Abhandlungen derBraunschweigischen Wissenschaftlichen Gesellschaft.Goltze,G¨o ttingen.(Continued as Abh.Braunschw.Wiss.Ges.)§Abh.Math.Sem.Univ.Hamburg Abhandlungen aus dem Mathematischen Seminar der Universit¨a t Hamburg.Vandenhoeck&Ruprecht,G¨o ttingen.ISSN0025-5858.†Abh.Math.-Naturwiss.Kl.Akad.Wiss.Lit.Mainz Abhandlungen der Mathematisch-NaturwissenschaftlichenKlasse.Akademie der Wissenschaften und der Literaturin Mainz.[Transactions of the Mathematical-ScientificSection.Academy of Sciences and Literature in Mainz]Steiner,Stuttgart.ISSN0002-2993.§Abstr.Appl.Anal.Abstract and Applied Analysis.Mancorp,Tampa,FL.ISSN1085-3375.¶Abstracts Amer.Math.Soc.Abstracts of Papers Presented to the American Mathematical Society.Amer.Math.Soc.,Providence,RI.ISSN0192-5857.Acad.Roy.Belg.Bull.Cl.Sci.(6)Acad´e mie Royale deBelgique.Bulletin de la Classe des Sciences.6e S´e rie.Acad.Roy.Belgique,Brussels.ISSN0001-4141.Acad.Roy.Belg.Cl.Sci.M´e m.Collect.8o(3)Acad´e mieRoyale de Belgique.Classe des Sciences.M´e moires.Collection in-8o.3e S´e rie.Acad.Roy.Belgique,Brussels.ISSN0365-0936.Acad.Serbe Sci.Arts Glas Acad´e mie Serbe des Scienceset des Arts.Glas.Classe des Sciences Naturelles etMath´e matiques.Srpska Akad.Nauk.i Umetnost.,Belgrade.ISSN0374-7956.†Acc`e s Sci.Acc`e s Sciences.[Access to Sciences]De Boeck Univ.,Brussels.§E ACM J.Exp.Algorithmics The ACM Journal ofExperimental Algorithmics.ACM,New York.ISSN1084-6654.E ACM Trans.Math.Software Association for ComputingMachinery.Transactions on Mathematical Software.ACM,New York.ISSN0098-3500.∗§Acta Acad.Paedagog.Agriensis Sect.Mat.(N.S.)Acta Academiae Paedagogicae Agriensis.Nova Series.SectioMatematicae.Eszterh´a zy K´a roly Coll.,Eger.∗§Acta Anal.Funct.Appl.Acta Analysis Functionalis Applicata.AAFA.Yingyong Fanhanfenxi Xuebao.SciencePress,Beijing.ISSN1009-1327.§E Acta Appl.Math.Acta Applicandae Mathematicae.An International Survey Journal on Applying Mathematics andMathematical Applications.Kluwer Acad.Publ.,Dordrecht.ISSN0167-8019.§Acta Arith.Acta Arithmetica.Polish Acad.Sci.,Warsaw.ISSN0065-1036.Acta Astronom.Sinica Acta Astronomica Sinica.TianwenXuebao.Kexue Chubanshe(Science Press),Beijing.(Translated in Chinese Astronom.Astrophys.)ISSN0001-5245.Acta Astrophys.Sinica Acta Astrophysica Sinica.TiantiWuli Xuebao.Kexue Chubanshe(Science Press),Beijing.(Translated in Chinese Astronom.Astrophys.)ISSN0253-2379.Acta Automat.Sinica Acta Automatica Sinica.ZidonghuaXuebao.Kexue Chubanshe(Science Press),Beijing.ISSN0254-4156.Acta Cienc.Indica Math.Acta Ciencia Indica.Mathematics.Pragati Prakashan,Meerut.ISSN0970-0455.Acta Cient.Venezolana Acta Cient´ıfica Venezolana.Asociaci´o n Venezolana para el Avance de la Ciencia.Asoc.Venezolana Avance Cien.,Caracas.ISSN0001-5504.Acta Comment.Univ.Tartu.Math.Acta etCommentationes Universitatis Tartuensis de Mathematica.Univ.Tartu,Fac.Math.,Tartu.ISSN1406-2283.E Acta Cryst.Sect.A Acta Crystallographica.Section A:Foundations of Crystallography.Munksgaard,Copenhagen.ISSN0108-7673.§Acta Cybernet.Acta Cybernetica.J´o zsef Attila Univ.Szeged,Szeged.ISSN0324-721X.Acta Hist.Leopold.Acta Historica Leopoldina.DeutscheAkad.Naturforscher Leopoldina,Halle an der Saale.ISSN0001-5857.§E Acta Inform.Acta Informatica.Springer,Heidelberg.ISSN0001-5903.§Acta Math.Acta Mathematica.Inst.Mittag-Leffler, Djursholm.ISSN0001-5962.§E Acta Math.Acad.Paedagog.Nyh´a zi.(N.S.)Acta Mathematica.Academiae Paedagogicae Ny´ıregyh´a ziensis.New Series.Bessenyei Gy¨o rgy Coll.,Ny´ıregyh´a za.ISSN0866-0182.§Acta Math.Appl.Sinica Acta Mathematicae Applicatae Sinica.Yingyong Shuxue Xuebao.Kexue Chubanshe(Science Press),Beijing.ISSN0254-3079.§Acta Math.Appl.Sinica(English Ser.)Acta Mathematicae Applicatae Sinica.English Series.Yingyong ShuxueXuebao.Science Press,Beijing.ISSN0168-9673.§E Acta Math.Hungar.Acta Mathematica Hungarica.Akad.Kiad´o,Budapest.ISSN0236-5294.§Acta rm.Univ.Ostraviensis Acta Mathematica et Informatica Universitatis Ostraviensis.Univ.Ostrava,Ostrava.ISSN1211-4774.§Acta Math.Sci.(Chinese)Acta Mathematica Scientia.Series A.Shuxue Wuli Xuebao.Chinese Edition.KexueChubanshe(Science Press),Beijing.(See also Acta Math.Sci.(English Ed.))ISSN1003-3998.§Acta Math.Sci.(English Ed.)Acta Mathematica Scientia.Series B.English Edition.Shuxue Wuli Xuebao.SciencePress,Beijing.(See also Acta Math.Sci.(Chinese))ISSN0252-9602.§E Acta Math.Sin.(Engl.Ser.)Acta Mathematica Sinica.English Series.Springer,Heidelberg.ISSN1000-9574.§Acta Math.Sinica Acta Mathematica Sinica.Chinese Math.Soc.,Acta Math.Sinica m.,Beijing.ISSN0583-1431.§E Acta enian.(N.S.)Acta Mathematica Universitatis Comenianae.New enius Univ.Press,Bratislava.ISSN0862-9544.§Acta Math.Vietnam.Acta Mathematica Vietnamica.Nat.Center Natur.Sci.Tech.,Hanoi.ISSN0251-4184.∗Acta Mech.Sin.Engl.Ser.Acta Mechanica Sinica.English Series.The Chinese Society of Theoretical and AppliedMechanics.Chinese J.Mech.Press,Beijing.(FormerlyActa Mech.Sinica(English Ed.))ISSN0567-7718.Acta Mech.Sinica(Beijing)Acta Mechanica Sinica.LixueXuebao.Chinese J.Mech.Press,Beijing.(See also ActaMech.Sinica(English Ed.))ISSN0459-1879.Acta Mech.Sinica(English Ed.)Acta Mechanica Sinica.English Edition.Lixue Xuebao.Kexue Chubanshe(SciencePress),Beijing.(Continued as Acta Mech.Sin.Engl.Ser.)(See also Acta Mech.Sinica(Beijing))ISSN0567-7718.∗Acta Mech.Solida Sin.Acta Mechanica Solida Sinica.Chinese Journal of Solid Mechanics.Huazhong Univ.Sci.Tech.,Wuhan.ISSN0894-9166.†Acta Numer.Acta Numerica.Cambridge Univ.Press, Cambridge.ISSN0962-4929.Acta Phys.Polon.B Jagellonian University.Institute ofPhysics and Polish Physical Society.Acta Physica PolonicaB.Jagellonian Univ.,Krak´o w.ISSN0587-4254.Acta Phys.Sinica Acta Physica Sinica.Wuli Xuebao.Chinese Phys.Soc.,Beijing.ISSN1000-3290.Acta put.Manage.Eng.Ser.Acta Polytechnica Scandinavica.Mathematics,Computingand Management in Engineering Series.Finn.Acad.Tech.,Espoo.ISSN1238-9803.§Acta Sci.Math.(Szeged)Acta Universitatis Szegediensis.Acta Scientiarum Mathematicarum.Univ.Szeged,Szeged.ISSN0001-6969.Acta Sci.Natur.Univ.Jilin.Acta Scientiarum NaturaliumUniversitatis Jilinensis.Jilin Daxue.Ziran Kexue Xuebao.Jilin University.Natural Sciences Journal.Jilin Univ.Nat.Sci.J.,Editor.Dept.,Changchun.ISSN0529-0279.Acta Sci.Natur.Univ.Norm.Hunan.Acta ScientiarumNaturalium Universitatis Normalis Hunanensis.HunanShifan Daxue Ziran Kexue Xuebao.J.Hunan Norm.Univ.,Editor.Dept.,Changsha.ISSN1000-2537.Acta Sci.Natur.Univ.Pekinensis See Beijing DaxueXuebao Ziran Kexue BanActa Sci.Natur.Univ.Sunyatseni Acta ScientiarumNaturalium Universitatis Sunyatseni.Zhongshan DaxueXuebao.Ziran Kexue Ban.Journal of Sun Yatsen University.Natural Sciences.J.Zhongshan Univ.,Editor.Dept.,Guangzhou.ISSN0529-6579.Acta Tech.CSA V Acta Technica CSA V.Acad.Sci.CzechRepub.,Prague.ISSN0001-7043.§Acta Univ.Carolin.Math.Phys.Acta Universitatis Carolinae.Mathematica et Physica.Karolinum,Prague.ISSN0001-7140.§Acta Univ.Lodz.Folia Math.Acta UniversitatisLodziensis.Folia Mathematica.Wydawn.Uniw.Ł´o dzkiego,Ł´o d´z.ISSN0208-6204.Acta Univ.Lodz.Folia Philos.Acta UniversitatisLodziensis.Folia Philosophica.Wydawn.Uniw.Ł´o dzkiego,Ł´o d´z.ISSN0208-6107.∗§Acta Univ.M.Belii Ser.Math.Acta Universitatis Matthiae Belii.Natural Science Series.Series Mathematics.MatejBel Univ.,Bansk´a Bystrica.(Formerly Acta Univ.MathaeiBelii Nat.Sci.Ser.Ser.Math.)§Acta Univ.Mathaei Belii Nat.Sci.Ser.Ser.Math.Matej Bel University.Acta.Natural Science Series.Series Mathematics.Matej Bel Univ.,Bansk´a Bystrica.(Continued as Acta Univ.M.Belii Ser.Math.)Acta Univ.Oulu.Ser.A Sci.Rerum Natur.ActaUniversitatis Ouluensis.Series A.Scientiae RerumNaturalium.Univ.Oulu,Oulu.ISSN0355-3191.§Acta Univ.Palack.Olomuc.Fac.Rerum Natur.Math.Acta Universitatis Palackianae Olomucensis.Facultas Rerum Naturalium.Mathematica.ISSN0231-9721.†Acta Univ.Ups.Stud.Philos.Ups.Acta Universitatis Upsaliensis.Studia Philosophica Upsaliensia.Uppsala Univ., Uppsala.ISSN0585-5497.†Acta Univ.Upsaliensis Skr.Uppsala Univ.C Organ.Hist.Acta Universitatis Upsaliensis.Skrifter r¨o randeUppsala anisation och Historia.[ActaUniversitatis Upsaliensis.Publications concerning Uppsalaanization and History]Uppsala Univ.,Uppsala.ISSN0502-7454.†Actualit´e s Math.Actualit´e s Math´e matiques.[Current Mathematical Topics]Hermann,Paris.†Actualit´e s Sci.Indust.Actualit´e s Scientifiques etIndustrielles.[Current Scientific and Industrial Topics]Hermann,Paris.†Adapt.Learn.Syst.Signal mun.Control Adaptive and Learning Systems for Signal Processing,Communications,and Control.Wiley,New York.Adv.Appl.Clifford Algebras Advances in Applied Clifford Algebras.Univ.Nac.Aut´o noma M´e xico,M´e xico.ISSN0188-7009.†Adv.Appl.Mech.Advances in Applied Mechanics.Academic Press,Boston,MA.ISSN0065-2165.∗†Adv.Astron.Astrophys.Advances in Astronomy andAstrophysics.Gordon and Breach,Amsterdam.ISSN1025-8206.†Adv.Book Class.Advanced Book Classics.Perseus, Reading,MA.†Adv.Bound.Elem.Ser.Advances in Boundary Elements put.Mech.,Southampton.(Continued as Int.Ser.Adv.Bound.Elem.)ISSN1368-258X.†Adv.Chem.Phys.Advances in Chemical Physics.Wiley, New York.†put.Econom.Advances in Computational Economics.Kluwer Acad.Publ.,Dordrecht.§E put.Math.Advances in ComputationalMathematics.Baltzer,Bussum.ISSN1019-7168.†put.Sci.Advances in Computing Science.Springer,Vienna.ISSN1433-0113.∗†Adv.Des.Control Advances in Design and Control.SIAM, Philadelphia,PA.§Adv.Differential Equations Advances in Differential Equations.Khayyam,Athens,OH.ISSN1079-9389.†Adv.Discrete Math.Appl.Advances in DiscreteMathematics and Applications.Gordon and Breach,Amsterdam.ISSN1028-3129.†Adv.Fluid Mech.Advances in Fluid put.Mech.,Southampton.ISSN1353-808X.†Adv.Fuzzy Systems Appl.Theory Advances in Fuzzy Systems—Applications and Theory.World Sci.Publishing,River Edge,NJ.§E Adv.in Appl.Math.Advances in Applied Mathematics.Academic Press,Orlando,FL.ISSN0196-8858.§Adv.in Appl.Probab.Advances in Applied Probability.Appl.Probab.Trust,Sheffield.ISSN0001-8678.∗†Adv.Ind.Control Advances in Industrial Control.Springer, London.†Adv.Lectures Math.Advanced Lectures in Mathematics.Vieweg,Braunschweig.ISSN0932-7134.§E Adv.Math.Advances in Mathematics.Academic Press, Orlando,FL.ISSN0001-8708.§Adv.Math.(China)Advances in Mathematics(China).Shuxue Jinzhan.Peking Univ.Press,Beijing.ISSN1000-0917.†Adv.Math.Econ.Advances in Mathematical Economics.Springer,Tokyo.†Adv.Math.Sci.Advances in the Mathematical Sciences.Amer.Math.Soc.,Providence,RI.§Adv.Math.Sci.Appl.Advances in Mathematical Sciences and Applications.An International Journal.Gakk¯o tosho,Tokyo.ISSN1343-4373.§Adv.Nonlinear Var.Inequal.Advances in Nonlinear Variational Inequalities.An International Journal.Internat.Publ.,Orlando,FL.ISSN1092-910X.†Adv.Numer.Math.Advances in Numerical Mathematics.Teubner,Stuttgart.†Adv.Partial Differ.Equ.Advances in Partial Differential Equations.Wiley-VCH,Berlin.†Adv.Partial Differential Equations Advances in Partial Differential Equations.Akademie Verlag,Berlin.†Adv.Ser.Dynam.Systems Advanced Series in Dynamical Systems.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Math.Phys.Advanced Series in Mathematical Physics.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Math.Sci.Eng.Advanced Series in Mathematical Science and Engineering.World Fed.Publ.,Atlanta,GA.†Adv.Ser.Neurosci.Advanced Series in Neuroscience.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Nonlinear Dynam.Advanced Series in Nonlinear Dynamics.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Stat.Sci.Appl.Probab.Advanced Series on Statistical Science&Applied Probability.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Theoret.Phys.Sci.Advanced Series onTheoretical Physical Science.World Sci.Publishing,RiverEdge,NJ.∗†Adv.Soft Comput.Advances in Soft Computing.Physica, Heidelberg.†Adv.Spat.Sci.Advances in Spatial Science.Springer, Berlin.†Adv.Stud.Contemp.Math.Advanced Studies inContemporary Mathematics.Gordon and Breach,New York.∗§Adv.Stud.Contemp.Math.(Pusan)Advanced Studies in Contemporary Mathematics(Pusan).Adv.Stud.Contemp.Math.,m.,Saga.ISSN1229-3067.†Adv.Stud.Pure Math.Advanced Studies in PureMathematics.Kinokuniya,Tokyo.†Adv.Textb.Control Signal Process.Advanced Textbooks in Control and Signal Processing.Springer,London.∗†Adv.Texts Phys.Advanced Texts in Physics.Springer,Berlin.ISSN1439-2674.§E Adv.Theor.Math.Phys.Advances in Theoretical and Mathematical Physics.Internat.Press,Cambridge,MA.ISSN1095-0761.†Adv.Theory put.Math.Advances in the Theory of Computation and Computational Mathematics.Nova Sci.Publ.,Commack,NY.†Adv.Top.Math.Advanced Topics in Mathematics.PWN, Warsaw.§E Aequationes Math.Aequationes Mathematicae.Birkh¨a user,Basel.ISSN0001-9054.§Afrika Mat.(3)Afrika Matematika.Journal of the African Mathematical Union.Journal de l’Union Math´e matiqueAfricaine.S´e rie3.Union Math.Africaine,Caluire.†Agr´e g.Math.Agr´e gation de Math´e matiques.Masson,Paris.AI Commun.AI Communications.The European Journal onArtificial Intelligence.IOS,Amsterdam.ISSN0921-7126.†AIAA Ed.Ser.AIAA Education Series.AIAA,Washington, DC.†AIP Conf.Proc.AIP Conference Proceedings.Amer.Inst.Phys.,New York.ISSN0094-243X.†AIP Ser.Modern Acoust.Signal Process.AIP Series in Modern Acoustics and Signal Processing.Amer.Inst.Phys.,New York.†AKP Class.AKP Classics.A K Peters,Wellesley,MA.∗†Al-Furq¯a n Islam.Herit.Found.Publ.Al-Furq¯a n Islamic Heritage Foundation Publication.Al-Furq¯a n Islam.Herit.Found.,London.†Albion Math.Appl.Ser.Albion Mathematics&Applications Series.Albion,Chichester.§E Algebr.Represent.Theory Algebras and Representation Theory.Kluwer Acad.Publ.,Dordrecht.ISSN1386-923X.Algebra and Logic Algebra and Logic.Consultants Bureau,New York.(Translation of Algebra Log.and Algebra iLogika)ISSN0002-5232.†Algebra Ber.Algebra Berichte.[Algebra Reports]Fischer, Munich.ISSN0942-1270.§E Algebra Colloq.Algebra Colloquium.Springer,Singapore.ISSN1005-3867.§Algebra i Analiz Rossi˘ıskaya Akademiya Nauk.Algebrai Analiz.“Nauka”S.-Peterburg.Otdel.,St.Petersburg.(Translated in St.Petersburg Math.J.)ISSN0234-0852.§Algebra i Logika Sibirski˘ıFond Algebry i Logiki.Algebrai Logika.Izdat.NII Mat.-Inform.Osnov Obuch.NGU,Novosibirsk.(Continued as Algebra Log.)(Translatedin Algebra and Logic)ISSN0373-9252.∗§Algebra Log.Algebra i Logika.Institut Diskretno˘ıMatematiki i Informatiki.Sib.Fond Algebry Log.,Novosibirsk.(Formerly Algebra i Logika)(Translatedin Algebra and Logic)ISSN0373-9252.†Algebra Logic Appl.Algebra,Logic and Applications.Gordon and Breach,Amsterdam.ISSN1041-5394.§E Algebra Universalis Algebra Universalis.Univ.Manitoba, Winnipeg,MB.ISSN0002-5240.§Algebras Groups Geom.Algebras,Groups and Geometries.Hadronic Press,Palm Harbor,FL.ISSN0741-9937.§E Algorithmica Algorithmica.An International Journal in Computer Science.Springer,New York.ISSN0178-4617.†Algorithms Combin.Algorithms and Combinatorics.Springer,Berlin.ISSN0937-5511.†Algorithms Comput.Math.Algorithms and Computation in Mathematics.Springer,Berlin.ISSN1431-1550.§Aligarh Bull.Math.The Aligarh Bulletin of Mathematics.Aligarh Muslim Univ.,Aligarh.Aligarh J.Statist.The Aligarh Journal of Statistics.AligarhMuslim Univ.,Aligarh.ISSN0971-0388.§pok Alkalmazott Matematikai Lapok.Magyar Tudom´a nyos Akad.,Budapest.ISSN0133-3399.∗Allg.Stat.Arch.Allgemeines Statistisches Archiv.AStA.Journal of the German Statistical Society.Physica,Heidelberg.ISSN0002-6018.†´Alxebra´Alxebra.[Algebra]Univ.Santiago deCompostela,Santiago de Compostela.†Am.Univ.Stud.Ser.IX Hist.American University Studies.Series IX:ng,New York.ISSN0740-0462.∗§E AMA Algebra Montp.Announc.AMA.AlgebraMontpellier Announcements.AMA Algebra Montp.Announc.,Montpellier.§E Amer.J.Math.American Journal of Mathematics.Johns Hopkins Univ.Press,Baltimore,MD.ISSN0002-9327.Amer.J.Math.Management Sci.American Journal ofMathematical and Management Sciences.Amer.Sci.Press,Syracuse,NY.ISSN0196-6324.E Amer.J.Phys.American Journal of Physics.Amer.Assoc.Phys.Teach.,College Park,MD.ISSN0002-9505.Amer.Math.Monthly The American MathematicalMonthly.Math.Assoc.America,Washington,DC.ISSN0002-9890.†Amer.Math.Soc.Colloq.Publ.American Mathematical Society Colloquium Publications.Amer.Math.Soc.,Providence,RI.ISSN0065-9258.†Amer.Math.Soc.Transl.Ser.2American Mathematical Society Translations,Series2.Amer.Math.Soc.,Providence,RI.(Selected translations of Russian language publications Tr.St.-Peterbg.Mat.Obshch.)ISSN0065-9290.E Amer.Statist.The American Statistician.Amer.Statist.Assoc.,Alexandria,V A.ISSN0003-1305.†Amer.Univ.Stud.Ser.V Philos.American University Studies.Series V:ng,New York.ISSN0739-6392.†AMS Progr.Math.Lecture Ser.AMS Progress in Mathematics Lecture Series.Amer.Math.Soc.,Providence,RI.†AMS Short Course Lecture Notes AMS Short Course Lecture Notes.Amer.Math.Soc.,Providence,RI.†AMS-MAA Joint Lecture Ser.AMS-MAA Joint Lecture Series.Amer.Math.Soc.,Providence,RI.†AMS/IP Stud.Adv.Math.AMS/IP Studies in Advanced Mathematics.Amer.Math.Soc.,Providence,RI.ISSN1089-3288.E An.Acad.Brasil.Ciˆe nc.Anais da Academia Brasileira deCiˆe ncias.Acad.Brasil.Ciˆe nc.,Rio de Janeiro.ISSN0001-3765.†An.F´ıs.Monogr.Anales de F´ısica.Monograf´ıas.[Annals of Physics.Monographs]CIEMAT,Madrid.§An.S¸tiint¸.Univ.Al.I.Cuza Ias¸i Inform.(N.S.)Analele S¸tiint¸ifice ale Universit˘a t¸ii“Al.I.Cuza”din Ias¸i.Informatic˘a.Serie Nou˘a.Ed.Univ.“Al.I.Cuza”,Ias¸i.ISSN1224-2268.§An.S¸tiint¸.Univ.Al.I.Cuza Ias¸i.Mat.(N.S.)Analele S¸tiint¸ifice ale Universit˘a tii“Al.I.Cuza”din Ias¸i.SerieNou˘a.Matematic˘a.Univ.Al.I.Cuza,Ias¸i.ISSN1221-8421.§An.S¸tiint¸.Univ.Ovidius Constant¸a Ser.Mat.Universit˘a t¸ii “Ovidius”Constant¸a.Analele S¸tiint¸ifice.Seria Matematic˘a.“Ovidius”Univ.Press,Constant¸a.ISSN1223-723X.§An.Univ.Bucures¸ti Mat.Analele Universit˘a t¸ii Bucures¸ti.Matematic˘a.Univ.Bucharest,Bucharest.ISSN1013-4123.An.Univ.Craiova rm.Analele Universitˇa t¸iidin Craiova.Seria Matematic˘a-Informatic˘a.Univ.Craiova,Craiova.ISSN1223-6934.∗§An.Univ.Oradea Fasc.Mat.Analele Universit˘a t¸ii din Oradea.Fascicola Matematica.Univ.Oradea,Oradea.ISSN1221-1265.§An.Univ.Timis¸oara Ser.Mat.-Inform.Universit˘a t¸ii din Timis¸oara.Analele.Seria Matematic˘a-Informatic˘a.Univ.Timis¸oara,Timis¸oara.ISSN1224-970X.An.Univ.Timis¸oara Ser.S¸tiint¸.Fiz.Analele Universit˘a t¸iidin Timis¸oara.Seria S¸tiint¸e Fizice.Univ.Vest Timis¸oara,Timis¸oara.†Anal.Appl.Analysis and its Applications.IOS,Amsterdam.ISSN1345-4240.§E Anal.Math.Analysis Mathematica.Akad.Kiad´o,Budapest.ISSN0133-3852.†Anal.Methods Spec.Funct.Analytical Methods and Special Functions.Gordon and Breach,Amsterdam.ISSN1027-0264.†Anal.Modern.Apl.Analiz˘a Modern˘a s¸i Aplicat¸ii.[Modern Analysis and Applications]Ed.Acad.Romˆa ne,Bucharest.§Analysis(Munich)Analysis.International Mathematical Journal of Analysis and its Applications.Oldenbourg,Munich.ISSN0174-4747.E Analysis(Oxford)Analysis.Blackwell,Oxford.ISSN0003-2638.†Angew.Statist.¨Okonom.Angewandte Statistik und¨Okonometrie.[Applied Statistics and Econometrics]Vandenhoeck&Ruprecht,G¨o ttingen.§E Ann.Acad.Sci.Fenn.Math.Annales AcademiæScientiarium Fennicæ.Mathematica.Acad.Sci.Fennica,Helsinki.ISSN1239-629X.§Ann.Acad.Sci.Fenn.Math.Diss.AcademiæScientiarum Fennicæ.Annales.Mathematica.Dissertationes.Acad.Sci.Fennica,Helsinki.ISSN1239-6303.§E Ann.Appl.Probab.The Annals of Applied Probability.Inst.Math.Statist.,Hayward,CA.ISSN1050-5164.§E b.Annals of Combinatorics.Springer,Singapore.(Continued as b.)ISSN0218-0006.∗§E b.Annals of Combinatorics.Birkh¨a user,Basel.(Formerly b.)ISSN0218-0006.§Ann.Differential Equations Annals of DifferentialEquations.Weifen Fangcheng Niankan.Fuzhou Univ.,Fuzhou.ISSN1002-0942.†Ann.Discrete Math.Annals of Discrete Mathematics.North-Holland,Amsterdam.Ann.´Econom.Statist.Annales d’´Economie et deStatistique.Inst.Nat.Statist.´Etud.´Econom.,Amiens.ISSN0769-489X.§Ann.Fac.Sci.Toulouse Math.(6)Annales de la Facult´e des Sciences de Toulouse.Math´e matiques.S´e rie6.Univ.Paul Sabatier,Toulouse.ISSN0240-2963.†Ann.Fac.Sci.Univ.Kinshasa Annales de la Facult´e des Sciences.Universit´e de Kinshasa.[Annals of the Facultyof Science.University of Kinshasa]Presses Univ.Kinshasa,Kinshasa.Ann.Fond.Louis de Broglie Fondation Louis de Broglie.Annales.Fond.Louis de Broglie,Paris.ISSN0182-4295.§E Ann.Global Anal.Geom.Annals of Global Analysis and Geometry.Kluwer Acad.Publ.,Dordrecht.ISSN0232-704X.∗E Ann.Henri Poincar´e Annales Henri Poincar´e.A Journal of Theoretical and Mathematical Physics.Birkh¨a user,Basel.(Merged from Ann.Inst.H.Poincar´e Phys.Th´e or.and Helv.Phys.Acta)ISSN1424-0637.∗Ann.I.S.U.P.Annales de l’I.S.U.P..Univ.Paris,Inst.Stat., Paris.§E Ann.Inst.Fourier(Grenoble)Universit´e de Grenoble.Annales de l’Institut Fourier.Univ.Grenoble I,Saint-Martin-d’H`e res.ISSN0373-0956.§E Ann.Inst.H.Poincar´e Anal.Non Lin´e aire Annales de l’Institut Henri Poincar´e.Analyse Non Lin´e aire.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0294-1449.Ann.Inst.H.Poincar´e Phys.Th´e or.Annales de l’InstitutHenri Poincar´e.Physique Th´e orique.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.(Merged into Ann.HenriPoincar´e)ISSN0246-0211.§E Ann.Inst.H.Poincar´e Probab.Statist.Annales de l’Institut Henri Poincar´e.Probabilit´e s et Statistiques.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0246-0203.E Ann.Inst.Statist.Math.Annals of the Institute ofStatistical Mathematics.Kluwer Acad.Publ.,Norwell,MA.ISSN0020-3157.†Ann.Internat.Soc.Dynam.Games Annals of the International Society of Dynamic Games.Birkh¨a userBoston,Boston,MA.†Ann.Israel Phys.Soc.Annals of the Israel Physical Society.IOP,Bristol.ISSN0309-8710.Ann.Japan Assoc.Philos.Sci.Annals of the JapanAssociation for Philosophy of Science.Japan Assoc.Philos.Sci.,Tokyo.ISSN0453-0691.§Ann.Mat.Pura Appl.(4)Annali di Matematica Pura ed Applicata.Serie Quarta.Zanichelli,Bologna.ISSN0003-4622.E Ann.Math.Artificial Intelligence Annals of Mathematicsand Artificial Intelligence.Baltzer,Bussum.ISSN1012-2443.§Ann.Math.Blaise Pascal Annales Math´e matiques Blaise Pascal.Univ.Blaise Pascal,Lab.Math.Pures Appl.,Aubi`e re.ISSN1259-1734.§Ann.Math.Sil.Annales Mathematicae Silesianae.Wydawn.Uniw.´Sl‘askiego,Katowice.(See also Pr.Nauk.Uniw.´Sl.Katow.)ISSN0860-2107.†Ann.New York Acad.Sci.Annals of the New York Academy of Sciences.New York Acad.Sci.,New York.ISSN0077-8923.§E Ann.of Math.(2)Annals of Mathematics.Second Series.Princeton Univ.Press,Princeton,NJ.ISSN0003-486X.†Ann.of Math.Stud.Annals of Mathematics Studies.Princeton Univ.Press,Princeton,NJ.E Ann.of Sci.Annals of Science.Taylor&Francis,London.ISSN0003-3790.E Ann.Oper.Res.Annals of Operations Research.Baltzer,Bussum.ISSN0254-5330.E Ann.Phys.(8)Annalen der Physik(8).Wiley-VCH,Berlin.ISSN0003-3804.E Ann.Physics Annals of Physics.Academic Press,Orlando,FL.ISSN0003-4916.§Ann.Polon.Math.Annales Polonici Mathematici.Polish Acad.Sci.,Warsaw.ISSN0066-2216.§Ann.Probab.The Annals of Probability.Inst.Math.Statist., Bethesda,MD.ISSN0091-1798.§E Ann.Pure Appl.Logic Annals of Pure and Applied Logic.North-Holland,Amsterdam.ISSN0168-0072.§E Ann.Sci.´Ecole Norm.Sup.(4)Annales Scientifiques de l’´Ecole Normale Sup´e rieure.Quatri`e me S´e rie.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0012-9593.§Ann.Sci.Math.Qu´e bec Annales des SciencesMath´e matiques du Qu´e bec.Groupe Cherch.Sci.Math.,Montreal,QC.ISSN0707-9109.§Ann.Scuola Norm.Sup.Pisa Cl.Sci.(4)Annali della Scuola Normale Superiore di Pisa.Classe di Scienze.SerieIV.Scuola Norm.Sup.,Pisa.§Ann.Statist.The Annals of Statistics.Inst.Math.Statist., Hayward,CA.ISSN0090-5364.§Ann.Univ.Ferrara Sez.VII(N.S.)Annali dell’Universit`a di Ferrara.Nuova Serie.Sezione VII.Scienze Matematiche.Univ.Ferrara,Ferrara.§Ann.Univ.Mariae Curie-Skłodowska Sect.A Annales Universitatis Mariae Curie-Skłodowska.Sectio A.Mathematica.Uniw.Marii Curie-Skłodowskiej,Lublin.ISSN0365-1029.Ann.Univ.Sarav.Ser.Math.Annales UniversitatisSaraviensis.Series Mathematicae.Univ.Saarlandes,Saarbr¨u cken.ISSN0933-8268.§Ann.Univ.Sci.Budapest.E¨o tv¨o s Sect.Math.Annales Universitatis Scientiarum Budapestinensis de RolandoE¨o tv¨o s Nominatae.Sectio Mathematica.E¨o tv¨o s Lor´a ndUniv.,Budapest.ISSN0524-9007.§put.AnnalesUniversitatis Scientiarum Budapestinensis de RolandoE¨o tv¨o s Nominatae.Sectio Computatorica.E¨o tv¨o s Lor´a ndUniv.,Budapest.ISSN0138-9491.†Annu.Rev.Fluid Mech.Annual Review of FluidMechanics.Annual Reviews,Palo Alto,CA.ISSN0066-4189.Annuaire Univ.Sofia rm.Godishnik naSofi˘ıskiya Universitet“Sv.Kliment Okhridski”.Fakultetpo Matematika i Informatika.Annuaire de l’Universit´e deSofia“St.Kliment Ohridski”.Facult´e de Math´e matiques etInformatique.Presses Univ.“St.Kliment Ohridski”,Sofia.ISSN0205-0808.Annuaire Univ.Sofia Fac.Phys.Godishnik na Sofi˘ıskiyaUniversitet“Sv.Kliment Okhridski”.Fizicheski Fakultet.Annuaire de l’Universit´e de Sofia“St.Kliment Ohridski”.Facult´e de Physique.Presses Univ.“St.Kliment Ohridski”,Sofia.ISSN0584-0279.†Anu.Filol.Univ.Barc.Anuari de Filologia(Universitat de Barcelona).[Philology Yearbook(University ofBarcelona)]Univ.Barcelona,Barcelona.†Anwend.orientier.Stat.Anwendungsorientierte Statistik.[Applications-Oriented Statistics]Lang,Frankfurt am Main.ISSN1431-7982.Anz.¨Osterreich.Akad.Wiss.Math.-Natur.Kl.¨Osterreichische Akademie der Wissenschaften.Mathematisch-Naturwissenschaftliche Klasse.Anzeiger.¨Osterreich.Akad.Wissensch.,Vienna.∗§E ANZIAM J.The ANZIAM Journal.The Australian& New Zealand Industrial and Applied Mathematics Journal.Austral.Math.Soc.,Canberra.(Formerly J.Austral.Math.Soc.Ser.B)ISSN0334-2700.†Aportaciones Mat.Aportaciones Matem´a ticas.[Mathematical Contributions]Soc.Mat.Mexicana,M´e xico.†Aportaciones un.Aportaciones Matem´a ticas: Comunicaciones.[Mathematical Contributions:Communications]Soc.Mat.Mexicana,M´e xico.∗†Aportaciones Mat.Invest.Aportaciones Matem´a ticas: Investigaci´o n.[Mathematical Contributions:Research]Soc.Mat.Mexicana,M´e xico.(Formerly Aportaciones Mat.Notas Investigaci´o n)†Aportaciones Mat.Notas Investigaci´o n Aportaciones Matem´a ticas:Notas de Investigaci´o n.[MathematicalContributions:Research Notes]Soc.Mat.Mexicana,M´e xico.(Continued as Aportaciones Mat.Invest.)†Aportaciones Mat.Textos Aportaciones Matem´a ticas: Textos.[Mathematical Contributions:Texts]Soc.Mat.Mexicana,M´e xico.§E Appl.Algebra put.Applicable Algebra in Engineering,Communication and Computing.Springer,Heidelberg.ISSN0938-1279.§E Appl.Anal.Applicable Analysis.An International Journal.Gordon and Breach,Yverdon.ISSN0003-6811.§E Appl.Categ.Structures Applied Categorical Structures.A Journal Devoted to Applications of Categorical Methods inAlgebra,Analysis,Order,Topology and Computer Science.Kluwer Acad.Publ.,Dordrecht.ISSN0927-2852.†put.Control Signals Circuits Applied and Computational Control,Signals,and Circuits.Birkh¨a userBoston,Boston,MA.ISSN1522-8363.§E put.Harmon.Anal.Applied and Computational Harmonic Analysis.Time-Frequency and Time-Scale Analysis,Wavelets,Numerical Algorithms,andApplications.Academic Press,Orlando,FL.ISSN1063-5203.†Appl.Log.Ser.Applied Logic Series.Kluwer Acad.Publ., Dordrecht.†Appl.Math.Applications of Mathematics.Springer,New York.ISSN0172-4568.§Appl.Math.Applications of Mathematics.Acad.Sci.Czech Repub.,Prague.ISSN0862-7940.∗†Appl.Math.Applied Mathematics.Chapman&Hall/CRC, Boca Raton,FL.(Formerly put.)§E put.Applied Mathematics andComputation.North-Holland,New York.ISSN0096-3003.†Appl.Math.Engrg.Sci.Texts Applied Mathematics and Engineering Science Texts.CRC,Boca Raton,FL.∗rm.Applied Mathematics and Informatics.Tbilisi Univ.Press,Tbilisi.ISSN1512-0074.∗§Appl.Math.J.Chinese Univ.Ser.A Applied Mathematics.A Journal of Chinese Universities.Series A.Appl.Math.J.Chinese Univ.,m.,Hangzhou.(FormerlyGaoxiao Yingyong Shuxue Xuebao Ser.A)(See also Appl.Math.J.Chinese Univ.Ser.B)ISSN1000-4424.§Appl.Math.J.Chinese Univ.Ser.B Applied Mathematics.A Journal of Chinese Universities.Ser.B.Appl.Math.J.Chinese Univ.,m.,Hangzhou.(See also Appl.Math.J.Chinese Univ.Ser.A and Gaoxiao Yingyong Shuxue。

The Department of Mathematics at [University Name] stands as a beacon of academic excellence and innovation in the field of mathematics. With a rich history of nurturing talent and fostering research, the department has earned a reputation for its rigorous curriculum, distinguished faculty, and vibrant academic community. This article aims to provide an overview of the department's achievements, its curriculum, faculty, research initiatives, and the impact it has on both students and the broader academic community.I. History and BackgroundEstablished in [Year], the Department of Mathematics has grown from a small group of dedicated faculty and students to a vibrant and diverse academic community. Over the years, the department has played a pivotal role in shaping the mathematical landscape of [University Name]. It has produced numerous notable alumni who have gone on to achieve great success in various fields, including academia, industry, and public service.The department's commitment to excellence is evident in its long-standing partnership with leading research institutions and industry partners. This collaboration has not only enriched the department's research portfolio but has also provided students with invaluable opportunities for internships, co-op programs, and real-world problem-solving experiences.II. Curriculum and Academic ProgramsThe Department of Mathematics offers a comprehensive curriculum that spans undergraduate and graduate programs, catering to a diverse range of interests and career aspirations. The curriculum is designed to provide students with a strong foundation in mathematical theory and practical skills, enabling them to excel in their chosen fields.A. Undergraduate ProgramsThe undergraduate program in mathematics provides students with a solid understanding of the fundamental concepts and techniques of mathematics. The curriculum includes a variety of courses, such as calculus, linearalgebra, real analysis, and abstract algebra. Students can also choose from a range of elective courses to specialize in areas such as applied mathematics, statistics, and computational mathematics.The department also offers a dual-degree program in mathematics and another field, such as engineering or computer science, to provide students with a broader skill set and enhance their employability.B. Graduate ProgramsThe graduate program in mathematics is designed to prepare students for careers in research, academia, and industry. The program offers both a Master's and a Ph.D. degree, with concentrations in pure mathematics, applied mathematics, and interdisciplinary fields.The curriculum includes advanced courses in algebra, analysis, geometry, and topology, as well as research seminars and workshops. Graduate students are encouraged to engage in original research under the guidance of experienced faculty members.III. Faculty and Research InitiativesThe Department of Mathematics boasts a distinguished faculty of scholars and educators who are committed to excellence in teaching and research. The faculty members are actively involved in various research initiatives, contributing to the advancement of mathematical knowledge and its applications in various fields.A. Research AreasThe department's research initiatives span a wide range of topics, including:1. Algebra and Number Theory2. Analysis and Differential Equations3. Geometry and Topology4. Probability and Statistics5. Computational Mathematics6. Mathematical PhysicsB. Collaborations and PartnershipsThe faculty members collaborate with researchers from other departments and institutions, both within and outside the country. These partnerships have led to numerous joint publications, research grants, and international conferences.IV. Impact on Students and the Academic CommunityThe Department of Mathematics has a profound impact on its students, preparing them for successful careers and fostering their intellectual growth. The department's commitment to excellence is reflected in the following aspects:A. Student SuccessThe department has a strong track record of student success, with a high percentage of graduates finding employment in their chosen fields. Many alumni have gone on to pursue advanced degrees and achieve notable accomplishments in their respective careers.B. Academic Community EngagementThe department actively engages with the academic community through various events, such as seminars, workshops, and conferences. These events provide a platform for faculty, students, and researchers to share their knowledge, exchange ideas, and foster collaboration.C. Public EngagementThe department is committed to promoting mathematics and itsapplications to the general public. The department organizes outreach programs, workshops, and lectures aimed at inspiring and educating the public about the beauty and importance of mathematics.V. ConclusionThe Department of Mathematics at [University Name] is a premier institution that continues to excel in teaching, research, and publicengagement. With a dedicated faculty, rigorous curriculum, and vibrant academic community, the department has established itself as a leading center for mathematical education and research. As the field of mathematics continues to evolve, the department is poised to play an even more significant role in shaping the future of mathematics and its applications.。