Theory 2

Chapter2Nim and combinatorial games2.1Aims of the chapterThis chapter•introduces the basics of combinatorial games,and explains the central role of the game nim.A detailed summary of the chapter is given in section2.5.Furthermore,this chapter•demonstrates the use of abstract mathematics in game theory.This chapter is written more formally than the other chapters,in parts in thetraditional mathematical style of definitions,theorems and proofs.One reason fordoing this,and why we start with combinatorial games,is that this topic and styleserves as a warning shot to those who think that game theory,and this unit inparticular,is‘easy’.If we started with the well-known‘prisoner’s dilemma’(whichmakes its due appearance in Chapter3),the less formally inclined student might belulled into a false sense of familiarity and‘understanding’.We therefore startdeliberately with an unfamiliar topic.This is a mathematics unit,with great emphasis on rigour and clarity,and on usingmathematical notions precisely.As mathematical prerequisites,game theory requiresonly the very basics of linear algebra,calculus and probability theory.However,gametheory provides its own conceptual tools that are used to model and analyseinteractive situations.This unit emphasises the mathematical structure of theseconcepts,which belong to‘discrete mathematics’.Learning a number of newmathematical concepts is exemplified by combinatorial game theory,and it willcontinue in the study of classical game theory in the later chapters.2.2Learning objectivesAfter studying this chapter,you should be able to:•play nim optimally;•explain the concepts of game-sums,equivalent games,nim values and the mex rule;•apply these concepts to play other impartial games like those described in the exercises.40Game theory2.3Essential readingThis chapter of the guide.2.4Further readingVery few textbooks on game theory deal with combinatorial games.An exception ischapter1of the following book:•Mendelson,Elliot Introducing Game Theory and Its Applications.(Chapman& Hall/CRC,2004)[ISBN1584883006].The winning strategy for the game nim based on the binary system wasfirst describedin the following article,which is available electronically from the JSTOR archive:•Bouton,Charles‘Nim,a game with a complete mathematical theory.’The Annals of Mathematics,2nd Ser.,Vol.3,No.1/4(1902),pp.35–39.The definitive text on combinatorial game theory is the set of volumes‘WinningWays’by Berlekamp,Conway and Guy.The material of this chapter appears in thefirst volume:•Berlekamp,Elwyn R.,John H.Conway and Richard K.Guy Winning Ways for Your Mathematical Plays,Volume1,second edition.(A.K.Peters,2001)[ISBN1568811306].Some small pieces of that text have been copied here nearly verbatim,for example inSections2.7,2.9,and2.12below.The four volumes of‘Winning Ways’are beautiful books.However,they are notsuitable reading for a beginner,because the mathematics is hard,and the reader isconfronted with a wealth of material.The introduction to combinatorial game theorygiven here represents a very small fraction of that body of work,but may invite youto study it further.A very informative and entertaining mathematical tour of parlour games is•Bewersdorff,J¨o rg Logic,Luck and White Lies.(A.K.Peters,2005)[ISBN 1568812108].Combinatorial games are treated in part II of that book.2.5What is combinatorial game theory?This chapter is on the topic of combinatorial games.These are games with twoplayers,perfect information,and no chance moves,specified by certain rules.Familiargames of this sort are chess,go,checkers,tic-tac-toe,dots-and-boxes,and nim.Suchgames can be played perfectly in the sense that either one player can force a win orboth can force a draw.In reality,games like chess and go are too complex tofind anoptimal strategy,and they derive their attraction from the fact that(so far)it is notknown how to play them perfectly.We will,however,learn how to play nim perfectly.There is a‘classical’game theory with applications in economics which is verydifferent from combinatorial game theory.The games in classical game theory aretypically formal models of conflict and co-operation which cannot only be lost orWhat is combinatorial game theory? won,and in which there is often no perfect information about past and future moves.To the economist,combinatorial games are not very interesting.Chapters3–6of theunit are concerned with classical game theory.Why,then,study combinatorial games at all in a unit that is mostly about classicalgame theory,and which aims to provide an insight into the theory of games as usedin economics?The reason is that combinatorial games have a rich and interesting mathematical theory.We will explain the basics of that theory,in particular thecentral role of the game nim for impartial games.It is non-trivial mathematics,it isfun,and you,the student,will have learned something that you would most likelynot have learned otherwise.Thefirst‘trick’from combinatorial game theory is how to win in the game nim,using the binary system.Historically,that winning strategy was discoveredfirst(published by Charles Bouton in1902).Only later did the central importance of nim,in what is known as the Sprague–Grundy theory of impartial games,becomeapparent.It also revealed why the binary system is important(and not,say,theternary system,where numbers are written in base three),and learning that is more satisfying than just learning how to use it.In this chapter,wefirst define the game nim and more general classes of games withperfect information.These are games where every player knows exactly the state ofthe game.We then define and study the concepts listed in the learning outcomesabove,which are the concepts of game-sums,equivalent games,nim values and themex rule.It is best to learn these concepts by following the chapter in detail.Wegive a brief summary here,which will make more sense,and should be re-consulted,after afirst study of the chapter(so do not despair if you do not understand this summary).Mathematically,any game is defined by other‘games’that a player can reach in hisfirst move.These games are called the options of the game.This seemingly circulardefinition of a‘game’is sound because the options are simpler games,which needfewer moves in total until they end.The definition is therefore not circular,butrecursive,and the mathematical tool to argue about such games is that ofmathematical induction,which will be used extensively(it will also recur inchapter3as‘backward induction’for game trees).Here,it is very helpful to befamiliar with mathematical induction for proving statements about natural numbers.We focus here on impartial games,where the available moves are the same nomatter whether player I or player II is the player to make a move.Games are‘combined’by the simple rule that a player can make a move in exactly one of thegames,which defines a sum of these games.In a‘losing game’,thefirst player tomove loses(assuming,as always,that both players play as well as they can).Animpartial game added to itself is always losing,because any move can be copied inthe other game,so that the second player always has a move left.This is known asthe‘copycat’principle(lemma2.6).An important observation is that a losing gamecan be‘added’(via the game-sum operation)to any game without changing thewinning or losing properties of the original game.In section2.11,the central theorem2.10explains the winning strategy in nim.The importance of nim for impartial games is then developed in section2.12via thebeautiful mex rule.After the comparatively hard work of the earlier sections,wealmost instantly obtain that any impartial game is equivalent to a nim heap(corollary2.13).At the end of the chapter,the sizes of these equivalent nim heaps(called nim values)are computed for some examples of impartial games.Many other examples arestudied in the exercises.40Game theoryOur exposition is distinct from the classic text‘Winning Ways’in the followingrespects:First,we only consider impartial games,even though many aspects carryover to more general combinatorial games.Secondly,we use a precise definition ofequivalent games(see section2.10),because a game where you are bound to loseagainst a smart opponent is not the same as a game where you have already lost.Two such games are merely equivalent,and the notion of equivalent games is helpfulin understanding the theory.So this text is much more restricted,but to some extentmore precise than‘Winning Ways’,which should help make this topic accessible andenjoyable.2.6Nim–rulesThe game nim is played with heaps(or piles)of chips(or counters,beans,pebbles,matches).Players alternate in making a move,by removing some chips from one ofthe heaps(at least one chip,possibly the entire heap).Thefirst player who cannotmove any more loses the game.The players will be called,rather unimaginatively,player I and player II,with player Ito start the game.For example,consider three heaps of size1,1,2.What is a good move?Removingone of the chips from the heap with two chips will create the position1,1,1,thenplayer II must move to1,1,then player I to1,and then player II takes the last chipand wins.So this is not a good opening move.The winning move is to remove allchips from the heap of size2,to reach position1,1,and then player I will win.Hence we call1,1,2a winning position,and1,1a losing position.When moving in a winning position,the player to move can win by playing well,bymoving to a losing position of the other player.In a losing position,the player tomove will lose no matter what move she chooses,if her opponent plays well.Thismeans that all moves from a losing position lead to a winning position of theopponent.In contrast,one needs only one good move from a winning position thatgoes to a losing position of the next player.Another winning position consists of three nim heaps of sizes1,1,1.Here all movesresult in the same position and player I always wins.In general,a player in a winningposition must play well by picking the right move.We assume that players play well,forcing a win if they can.Suppose nim is played with only two heaps.If the two heaps have equal size,forexample in position4,4,then thefirst player to move loses(so this is a losingposition),because player II can always copy player I’s move by equalising the twoheaps.If the two heaps have different sizes,then player I can equalise them byremoving an appropriate number of chips from the larger heap,putting player II in alosing position.The rule for2-heap nim is therefore:Lemma2.1The nim position m,n is winning if and only if m=n,otherwise losing,for all m,n≥0.This lemma applies also when m=0or n=0,and thus includes the cases that oneor both heap sizes are zero(meaning only one heap or no heap at all).With three or more heaps,nim becomes more difficult.For example,it is notimmediately clear if,say,positions1,4,5or2,3,6are winning or losing positions.⇒At this point,you should try exercise2.1(a)on page28.Combinatorial games,in particular impartial games 2.7Combinatorial games,in particular impartial gamesThe games we study in this chapter have,like nim,the following properties:1.There are just two players.2.There are several,usuallyfinitely many,positions,and sometimes a particularstarting position.3.There are clearly defined rules that specify the moves that either player canmake from a given position to the possible new positions,which are called theoptions of that position.4.The two players move alternately,in the game as a whole.5.In the normal play convention a player unable to move loses.6.The rules are such that play will always come to an end because some player willbe unable to move.This is called the ending condition.So there can be nogames which are drawn by repetition of moves.7.Both players know what is going on,so there is perfect information.8.There are no chance moves such as rolling dice or shuffling cards.9.The game is impartial,that is,the possible moves of a player only depend onthe position but not on the player.As a negation of condition5,there is also the mis`e re play convention where a playerunable to move wins.In the surrealist(and unsettling)movie‘Last year atMarienbad’by Alain Resnais from1962,mis`e re nim is played,several times,withrows of matches of sizes1,3,5,7.If you have a chance,try to watch that movie andspot when the other player(not the guy who brought the matches)makes a mistake!Note that this is mis`e re nim,not nim,but you will be able tofind out how to play itonce you know how to play nim.(For games other than nim,normal play and mis`e reversions are typically not so similar.)In contrast to condition9,games where the available moves depend on the player(as in chess where one player can only move white pieces and the other only blackpieces)are called partisan games.Much of combinatorial game theory is aboutpartisan games,which we do not consider to keep matters simple.Chess,and the somewhat simpler tic-tac-toe,also fail condition6because they mayend in a tie or draw.The card game poker does not have perfect information(asrequired in7)and would lose all its interest if it had.The analysis of poker,althoughit is also a win-or-lose game,leads to the‘classical’theory of zero-sum games(withimperfect information)that we will consider later.The board game backgammon is agame with perfect information but with chance moves(violating condition8)because dice are rolled.We will be relatively informal in style,but our notions are precise.In condition3above,for example,the term option refers to a position that is reachable in onemove from the current position;do not use‘option’when you mean‘move’.Similarly,we will later use the term strategy to define a plan of moves,one for everyposition that can occur in the game.Do not use‘strategy’when you mean‘move’.However,we will take some liberty in identifying a game with its starting positionwhen the rules of the game are clear.40Game theory⇒Try now exercises2.2and2.3starting on page28.2.8Simpler games and notation for nim heapsA game,like nim,is defined by its rules,and a particular starting position.Let G besuch a particular instance of nim,say with the starting position1,1,2.Knowing therules,we can identify G with its starting position.Then the options of G are1,2,and1,1,1,and1,1.Here,position1,2is obtained by removing either thefirst or thesecond heap with one chip only,which gives the same result.Positions1,1,1and1,1are obtained by making a move in the heap of size two.It is useful to list the optionssystematically,considering one heap to move in at a time,so as not to overlook anyoption.Each of the options of G is the starting position of another instance of nim,definingone of the new games H,J,K,say.We can also say that G is defined by the movesto these games H,J,K,and we call these games also the options of G(byidentifying them with their starting positions;recall that the term‘option’has beendefined in point3of section2.7).That is,we can define a game as follows:Either the game has no move,and theplayer to move loses,or a game is given by one or several possible moves to newgames,in which the other player makes the initial move.In our example,G isdefined by the possible moves to H,J,or K.With this definition,the entire game iscompletely specified by listing the initial moves and what games they lead to,because all subsequent use of the rules is encoded in those games.This is a recursive definition because a‘game’is defined in terms of‘game’itself.We have to add the ending condition that states that every sequence of moves in agame must eventually end,to make sure that a game cannot go on indefinitely.This recursive condition is similar to defining the set of natural numbers as follows:(a)0is a natural number;(b)if n is a natural number,then so is n+1;and(c)allnatural numbers are obtained in this way,starting from0.Condition(c)can beformalised by the principle of induction that says:if a property P(n)is true for n=0,and if the property P(n)implies P(n+1),then it is true for all natural numbers.We use the following notation for nim heaps.If G is a single nim heap with nchips,n≥0,then we denote this game by∗n.This game is completely specified byits options,and they are:options of∗n:∗0,∗1,∗2,...,∗(n−1).(2.1) Note that∗0is the empty heap with no chips,which allows no moves.It is invisiblewhen playing nim,but it is useful to have a notation for it because it defines themost basic losing position.(In combinatorial game theory,the game with no moves,which is the empty nim heap∗0,is often simply denoted as0.)We could use(2.1)as the definition of∗n;for example,the game∗4is defined by itsoptions∗0,∗1,∗2,∗3.It is very important to include∗0in that list of options,because it means that∗4has a winning move.Condition(2.1)is a recursivedefinition of the game∗n,because its options are also defined by reference to suchgames∗k,for numbers k smaller than n.This game fulfils the ending conditionbecause the heap gets successively smaller in any sequence of moves.If G is a game and H is a game reachable by one or more successive moves from thestarting position of G,then the game H is called simpler than G.We will oftenprove a property of games inductively,using the assumption that the property appliesto all simpler games.An example is the–already stated and rather obvious–Sums of games property that one of the two players can force a win.(Note that this applies togames where winning or losing are the only two outcomes for a player,as implied bythe‘normal play’convention in5above.)Lemma2.2In any game G,either the starting player I can force a win,or player IIcan force a win.Proof.When the game has no moves,player I loses and player II wins.Now assumethat G does have options,which are simpler games.By inductive assumption,ineach of these games one of the two players can force a win.If,in all of them,thestarting player(which is player II in G)can force a win,then she will win in G byplaying accordingly.Otherwise,at least one of the starting moves in G leads to agame G where the second-moving player in G (which is player I in G)can force awin,and by making that move,player I will force a win in G.If in G,player I can force a win,its starting position is a winning position,and wecall G a winning game.If player II can force a win,G starts with a losing position,and we call G a losing game.2.9Sums of gamesWe continue our discussion of nim.Suppose the starting position has heap sizes1,5,5.Then the obvious good move is to option5,5,which is losing.What about nim with four heaps of sizes2,2,6,6?This is losing,because2,2and6,6independently are losing positions,and any move in a heap of size2can becopied in the other heap of size2,and similarly for the heaps of size6.There is asecond way of looking at this example,where it is not just two losing games puttogether:consider the game with heap sizes2,6.This is a winning game.However,two such winning games,put together to give the game2,6,2,6,result in a losinggame,because any move in one of the games2,6,for example to2,4,can be copiedin the other game,also to2,4,giving the new position2,4,2,4.So the secondplayer,who plays‘copycat’,always has a move left(the copying move)and hencecannot lose.Definition2.3The sum of two games G and H,written G+H,is defined asfollows:The player may move in either G or H as allowed in that game,leaving theposition in the other game unchanged.Note that G+H is a notation that applies here to games and not to numbers,evenif the games are in some way defined using numbers(for example as nim heaps).The result is a new game.More formally,assume that G and H are defined in terms of their options(via movesfrom the starting position)G1,G2,...,G k and H1,H2,...,H m,respectively.Then theoptions of G+H are given asoptions of G+H:G1+H,...,G k+H,G+H1,...,G+H m.(2.2) Thefirst list of options G1+H,G2+H,...,G k+H in(2.2)simply means that theplayer makes his move in G,the second list G+H1,G+H2,...,G+H m that hemakes his move in H.We can define the game nim as a sum of nim heaps,where any single nim heap isrecursively defined in terms of its options by(2.1).So the game nim with heaps ofsize1,4,6is written as∗1+∗4+∗6.40Game theoryThe‘addition’of games with the abstract+operation leads to an interestingconnection of combinatorial games with abstract algebra.If you are somewhatfamiliar with the concept of an abstract group,you will enjoy this connection;if not,you do not need to worry,because this connection it is not essential for ourdevelopment of the theory.A group is a set with a binary operation+that fulfils three properties:1.The operation+is associative,that is,G+(J+K)=(G+J)+K holds for allG,J,K.2.The operation+has a neutral element0,so that G+0=G and0+G=G forall G.3.Every element G has an inverse−G so that G+(−G)=0.Furthermore,4.The group is called commutative(or‘abelian’)if G+H=H+G holds for allG,H.Familiar groups in mathematics are,for example,the set of integers with addition,orthe set of positive real numbers with multiplication(where the multiplicationoperation is written as·,the neutral element is1,and the inverse of G is written asG−1).The games that we consider form a group as well.In the way the sum of two gamesG and H is defined,G+H and H+G define the same game,so+is commutative.Moreover,when one of these games is itself a sum of games,for example H=J+K,then G+H is G+(J+K)which means the player can make a move in exactly one ofthe games G,J,or K.This means obviously the same as the sum of games(G+J)+K,that is,+is associative.The sum G+(J+K),which is the same as(G+J)+K,can therefore be written unambiguously as G+J+K.An obvious neutral element is the empty nim heap∗0,because it is‘invisible’(itallows no moves),and adding it to any game G does not change the game.However,there is no direct way to get an inverse operation because for any game Gwhich has some options,if one adds any other game H to it(the intention beingthat H is the inverse−G),then G+H will have some options(namely at least theoptions of moving in G and leaving H unchanged),so that G+H is not equal to theempty nim heap.The way out of this is to identify games that are‘equivalent’in a certain sense.Wewill see shortly that if G+H is a losing game(where thefirst player to move cannotforce a win),then that losing game is‘equivalent’to∗0,so that H fulfils the role ofan inverse of G.2.10Equivalent gamesThere is a neutral element that can be added to any game G without changing it.By definition,because it allows no moves,it is the empty nim heap∗0:G+∗0=G.(2.3)However,other games can also serve as neutral elements for the addition of games.We will see that any losing game can serve that purpose,provided we considercertain games as equivalent according to the following definition.Equivalent games Definition2.4Two games G,H are called equivalent,written G≡H,if and only iffor any other game J,the sum G+J is losing if and only if H+J is losing.In definition2.4,we can also say that G≡H if for any other game J,the sum G+Jis winning if and only if H+J is winning.In other words,G is equivalent to H if,whenever G appears in a sum G+J of games,then G can be replaced by H without changing whether G+J is winning or losing.One can verify easily that≡is indeed an equivalence relation,meaning it is reflexive(G≡G),symmetric(G≡H implies H≡G),and transitive(G≡H and H≡K implyG≡K;all these conditions hold for all games G,H,K).Using J=∗0in definition2.4and(2.3),G≡H implies that G is losing if and only ifH is losing.The converse is not quite true:just because two games are winning doesnot mean they are equivalent,as we will see shortly.However,any two losing gamesare equivalent,because they are all equivalent to∗0:Lemma2.5If G is a losing game(the second player to move can force a win),thenG≡∗0.Proof.Let G be a losing game.We want to show G≡∗0By definition2.4,this istrue if and only if for any other game J,the game G+J is losing if and only if∗0+Jis losing.According to(2.3),this holds if and only if J is losing.So let J be any other game;we want to show that G+J is losing if and only if J islosing.Intuitively,adding the losing game G to J does not change which player in Jcan force a win,because any intermediate move in G by his opponent is simplycountered by the winning player,until the moves in G are exhausted.Formally,wefirst prove by induction the simpler claim that for all games J,if J islosing,then G+J is losing.(So wefirst ignore the‘only if’part.)Our inductive assumptions for this simpler claim are:for all losing games G that are simplerthan G,if J is losing,then G +J is losing;and for all games J that are simplerthan J,if J is losing,then G+J is losing.So suppose that J is losing.We want to show that G+J is losing.Any initial movein J leads to an option J which is winning,which means that there is acorresponding option J of J (by player II’s reply)where J is losing.Hence,whenplayer I makes the corresponding initial move from G+J to G+J ,player II cancounter by moving to G+J .By inductive assumption,this is losing because J islosing.Alternatively,player I may move from G+J to G +J.Because G is a losinggame,there is a move by player II from G to G where G is again a losing game,and hence G +J is also losing,by inductive assumption,because J is losing.Thiscompletes the induction and proves the claim.What is missing is to show that if G+J is losing,so is J.If J was winning,then therewould be a winning move to some option J of J where J is losing,but then,by ourclaim(the‘if’part that we just proved),G+J is losing,which would be a winningoption in G+J for player I.But this is a contradiction.This completes the proof.The preceding lemma says that any losing game Z,say,can be added to a game Gwithout changing whether G is winning or losing(in lemma2.5,Z is called G).Thatis,extending(2.3),Z losing=⇒G+Z≡G.(2.4)As an example,consider Z=∗1+∗2+∗3,which is nim with three heaps of sizes1,2,3.To see that Z is losing,we examine the options of Z and show that all ofthem are winning games.Removing an entire heap leaves two unequal heaps,whichis a winning position by lemma2.1.Any other move produces three heaps,two of40Game theorywhich have equal size.Because two equal heaps define a losing nim game Z,they can be ignored by(2.4),meaning that all these options are like single nim heaps and therefore winning positions,too.So Z=∗1+∗2+∗3is losing.The game G=∗4+∗5is clearly winning.By(2.4), the game G+Z is equivalent to G and is also winning.However,verifying directly that∗1+∗2+∗3+∗4+∗5is winning would not be easy to see without using(2.4). It is an easy exercise to show that in sums of games,games can be replaced by equivalent games,resulting in an equivalent sum.That is,for all games G,H,J,G≡H=⇒G+J≡H+J.(2.5)Note that(2.5)is not merely a re-statement of definition2.4,because equivalence of the games G+J and H+J means more than just that the games are either both winning or both losing(see the comments before lemma2.9below).Lemma2.6(The copycat principle)G+G≡∗0for any impartial game G. Proof.Given G,we assume by induction that the claim holds for all simpler games G .Any option of G+G is of the form G +G for an option G of G.This is winning by moving to the game G +G which is losing,by inductive assumption.So G+G is indeed a losing game,and therefore equivalent to∗0by lemma2.5.We now come back to the issue of inverse elements in abstract groups,mentioned at the end of section2.9.If we identify equivalent games,then the addition+of games defines indeed a group operation.The neutral element is∗0,or any equivalent game (that is,a losing game).The inverse of a game G,written as the negative−G,fulfilsG+(−G)≡∗0.(2.6) Lemma2.6shows that for an impartial game,−G is simply G itself.Side remark:For games that are not impartial,that is,partisan games,−G exists also.It is G but with the roles of the two players exchanged,so that whatever move was available to player I is now available to player II and vice versa.As an example, consider the game checkers(with the rule that whoever can no longer make a move loses),and let G be a certain configuration of pieces on the checkerboard.Then−G is the same configuration with the white and black pieces interchanged.Then in the game G+(−G),player II(who can move the black pieces,say),can also play‘copycat’.Namely,if player I makes a move in either G or−G with a white piece, then player II copies that move with a black piece on the other board(−G or G, respectively).Consequently,player II always has a move available and will win the game,so that G+(−G)is indeed a losing game for the starting player I,that is,G+(−G)≡∗0.However,we only consider impartial games,where−G=G.The following condition is very useful to prove that two games are equivalent. Lemma2.7Two impartial games G,H are equivalent if and only if G+H≡∗0.Proof.If G≡H,then by(2.5)and lemma2.6,G+H≡H+H≡∗0.Conversely,G+H≡∗0implies G≡G+H+H≡∗0+H≡H.Sometimes,we want to prove equivalence inductively,where the following observation is useful.Lemma2.8Two games G and H are equivalent if all their options are equivalent, that is,for every option of G there is an equivalent option of H and vice versa.。

小谢尔顿第二季第集中英文台词The Big Bang Theory Season 2 Episode 11Scene 1: Apartment Living RoomSheldon: The annual Christmas picture with Santa Claus is upon us.Leonard: Oh no, not this again.Penny: Yeah, why not? It could be fun.Leonard: Alright, fine. Let's get it over with.Scene 2: Outside the MallSheldon: Santa Claus! Santa Claus! We're here!Santa Claus: Ho ho ho! Merry Christmas! Have you all been good this year?Sheldon: Actually, I can prove that I have been good this year. I have a list of all my good deeds right here.Santa Claus: That's impressive. Well, hop on my lap andlet's take that picture.Scene 3: Apartment Living RoomHoward: Oh man, this picture is going to be embarrassing.Raj: Yeah, I always look weird in these kind of photos.Sheldon: Nonsense! It's all about capturing the joy of Christmas. Smile, everyone!Scene 4: Sheldon's BedroomSheldon: (looking at the Christmas picture) I lookridiculous in this picture. My glasses are crooked and my smile is weird.Amy: Oh, don't be so hard on yourself. You look adorable.Sheldon: Adorable?! That's not what I was going for.Amy: Well, the important thing is that we had fun and made some memories.Sheldon: I suppose you're right. It is a tradition after all.Scene 5: Apartment Living RoomLeonard: (holding the Christmas picture) Alright, let's put this up on the fridge. Another successful Santa picture.Penny: Yeah, I have to admit, it was kind of fun.Howard: Maybe next year we should all dress up as Santa Claus.Raj: Yeah, that would be hilarious.Sheldon: Absolutely not. My Santa picture days are over.。

1.Input versus intakeInput is everything around us we may perceive with our senses.Input is the main source of information for learning , but not all input leads to intake , which is necessary for teaching .Intake is what we pay attention to and notice.Intake may refer to information that strengthens existing knowledge, or it may fill a gap in knowledge that was noticed by the learner before.In language learning, input refers to language which a learner hears or receives and from which he or she can learn.In second or foreign language learning , a distinction is sometimes made between input and intake. Intake is input which is actually helpful for the learner. Some of the language (ie input) which a learner hears may be too rapid or difficult for the learner to understand, and therefore cannot be used in learning (i.e cannot serve as intake) 2. What is Interlanguage（1）Il refers to the language that the L2 learner produced .（2）The language produced by the learner is a system in its own right.（3）The language is a dynamic system, evolving over time.（4）IL studies moved one step beyond EA, by focusing on the learner language system, rather than only on its errors.3.Fossilization:It refers to the phenomenon in which second language learners often stop learning even though they might be far short of native-like competence. The term is also used for specific linguistic structures that remain incorrect for lengthy periods of time in spite of plentiful input.4. What is UG ?The language faculty built into the human mind consisting of principles and parameters.UG is the system of principles, conditions and rules that are elements or properties of all human languages.5. Acquisition v.s learningThe term “acquisition”is used to refer to picking up a second language through exposure, whereas the term “learning “ is used to refer to the conscious study of a second language.6. Linguistic Competence and Linguistic PerformanceLinguistic competence refers to the internalized knowledge of the language that a native speaker of that language possesses.Linguistic performance refers to the actual utterance produced by the native speaker7. Implicit versus Explicit LearningImplicit learning is acquisition of knowledge about the underlying structure by a process that takes place naturally, simply and without conscious operations.Explicit learning is a more conscious operation where a learner makes and tests hypotheses in a search for strcture.nguage learning strategiesIntentional behaviour and thoughts that learners make use of during learning in order to better help them understand, learn or remember new information .Learning strategies are classified into: 1. meta-cognitive strategies2. cognitive strategies3. socio-affective strategies9.What are the cognitive and affective factors in SLA research?Cognitive factors；（1）Intelligence（2）Language aptitude（3）Language learning strategiesAffective factors :（1）Language attitudes （2）Motivation10. Contrastive AnalysisContrastive analysis is a way of comparing languages in order to determine potential errors.The ultimate goal was to predict areas that would be either easy or difficult for learners .11. Error analysisError analysis is a type of bilingual comparison, a comparison between learners’interlanguage and a target language, while contrastive analysis between languages. (native language and target language)12. Positive evidence and negative evidencePositive evidence: input that provides information only about what is grammatical in the language.Negative evidence: input that provides direct evidence of what is ungrammatical in a language.Positive evidence comes from the speech learners hear and thus is composed of a limited set of well-formed utterance of the language being learned .Negative evidence is composed of information to a learner that his or her utterance is deviant with regard to the norms of the language being learned.1. The Monitor Model by KrashenThe Monitor Model is an overall theory of SLA, which had important implications for language teaching. Here are the five central hypotheses underlying the Monitor Model.1. The Acquisition-Learning Hypothesis2. The Monitor Hypothesis3. The Natural Order Hypothesis4. The Input Hypothesis5. The Affective Filter Hypothesis2. What it is that needs to be learnt in language acquisition （What arebranches of modern linguistic? ）Phonetics and Phonology：（1）It entails knowing what possible sounds are and what are not for its native speakers .（2）It also involves knowing what happens to words in fast speech as opposed to more carefully articulated speech.Syntax：The study of how words combine to form sentences and the rules which govern the formation of sentences. The rule is frequently known as its grammar.Morphology：The study of morphemes and their different forms , and the waythey combine in word formation .In short , morphology is the study of word formation.Semantics：（1）The study of meaning（2）There are many different approaches to the way in which meaning in language is studiedPragmatics：The study of language use in context3. The differences between the Behaviorist learning model and that of Mentalist ?Behaviorist learning model claims that children acquired the L1 by trying to imitate utterances produced by people around them and by receiving negative or positive reinforcement of their attempts to do so. Language acquisition, therefore, was considered to be environmentally determined.A mentalist model claims: 1. Language is human specific.2. Language exists as an independent faculty in the human mind.3. LAD4. Input data4. What are the differences of error analysis from contrastive analysisContrastive analysis stresses the interfering effects of a first language on second language learning and claims that most errors come from interference of the first language. (Corder ,1967). However, such a narrow view of interference ignores the intralingual effects of language learning among other factors. Error analysis is the method to deal with intralingual factors in learners’language (Corder , 1981).it is a methodology of describing Second Language Learners’language systems .Error analysis is a type of bilingual comparison, a comparison between learners’interlanguage and a target language, while contrastive analysis between languages. (native language and target language)5. Principles and parameters theory in UGDual aim : 1. Characterize the Native Speaker’s knowledge of language, or linguistic competence.2. Explain how the acquisition of such competence is possible.The universal principle is the principle of structure-dependency, which states that language is organized in such a way that it crucially depends on the structural relationships between elements in a sentence.Parameters are principles that differ in the way they work or function from language to language. That is to say there are certain linguistic features that vary across languages.6. Two groups cognitive theory concerning language learning1. Processing Approaches （1）Information processing model（2）Processability theory2. Constructionist Approaches7. Anderson’s ACTThis is another general theory of cognitive learning that has been applied to SLA Also emphasizes the automatization process.Conceptualizing three types of memory: 1. Working memory2. Declarative long term memory3. Procedural long-term memory8. McLaughlin’s Information-processing modelSLA is the acquisition of a complex cognitive skill that must progress from controlled processing to automatic processing.9. Behaviorist learning theoryBehaviorism was established by American psychologist John B. Watson in 1913 and developed by B.F. Skinner who is the founder of modern behaviorism.Behaviorism postulated that all human behaviors could be explained in terms of the way in which simple stimulus-response connections were built up.Two key notions of behaviorismHabits :habits are regular connection of stimulus and response.Errors : old habits inhabit learning new habits.Interference : This is concerned with the way in which previous learning gets in the way of learning new habits.10. Shumann’s Pidginization or Acculturation Model (语言文化适应模式）Pidginization（洋泾浜语化）In second and foreign language learning, the development of grammatically reduced form of a target language. This is usually a temporary stage in language learning. The learner’s INTERLANGAUGE may have a limited system of auxilary verbs, simplified question and negative forms, and reduced rules for TENSE, NUMBER, and other grammatical categories.11. The History of SLA Research1960s : Behavioristic View of Learning（1）Habit formation（2）Contrastive Analysis （3）Behaviorism under Attack1970s-1980s :Mentalism （1）Error Analysis and Interlangauge （2）Krashen and His Monitor Model（3）Shumann’s Pidginization or Acculturation Model Beyond 1990s: （1）The Developmental Patterns in Language Acquisition（2）Different Roles Found in Language Acquisition12.What is the difference between linguistic performance and linguistic competence?Linguistic competence refers to the internalized knowledge of the language that a native speaker of that language possesses.Linguistic performance refers to the actual utterance produced by the native speaker13. What is fossilization ? Can we avoid it in our foreign language learning? Fossilization: It refers to the phenomenon in which second language learners often stop learning even though they might be far short of native-like competence. The term is also used for specific linguistic structures that remain incorrect for lengthy periods of time in spite of plentiful input.14. Suppose you are to investigate the developmental pattern in the English learning as L2. What data would you collect and how would you collect it ?The investigation of developmental patterns in learner language aims to describe the learner language in its own right. First language acquisition researchers have found the evidence to test the behaviorist and mentalist accounts of language learning. In L2 acquisition, early learner language is characterized by the silent period, extensive use of formulas and structural and semantic simplification.Then we researched L2 acquisition in terms of the order of acquisition through the study of different features and also the sequence of stages through the study of a single feature. Considering the L2 acquisition is similar to L1 acquisition to some degree, the discussion of L2 =L1 hypothesis is introduced and briefly discussed.1. to examine whether learners’ errors change over time.2. to examine samples and data of learner language collected over a period of time in order to identify when specific linguistic features emerge.3. obligatory occasion analysis4. native-like analysis5. frequency analysis6. to infer the order of development from data of cross-sectional studies by using s number of statistical procedures .7.implicational scaling15. Why do some learners have a silent period while others do not ?Troike suggests that the reason may lie in differences in the learners’social and cognitive orientation: outer-directed and inner-directed.The former “approach language as an interpersonal task, with a predominant focus on the message they wish to convey”.The latter “approach language learning as an intrapersonal task, with a predominant focus on the language code”。

关于UTAUT2模型研究的系统文献综述作者：李瑞红王根强鲍阳来源：《科技资讯》2021年第19期摘要：随着信息技术的发展，网上交易越来越便捷，完全融入了人们的日常生活。

了解消费者对信息技术的接受度成为国内外学术界研究的热点。

该研究对之前关于整合型技术接受与使用理论2（UTAUT2）的研究进行了系统性的文献综述。

基于此文献综述，研究人员可以更好地通过UTAUT2模型对消费者的行为意图进行了解，并对消费者的技术接受度进行更深入的研究。

关键词：技术接受度 UTAUT2 行为意图信息技术中图分类号：F724.6 文献标识码：A文章编号：1672-3791（2021）07（a）-0017-03Abstract： With the development of information technology， online transactions are becoming more and more convenient and fully integrated into people's daily life. Understanding consumers' acceptance of information technology has become a research hotspot in academic circles at home and abroad. This study makes a systematic literature review on the previous research on integrated technology acceptance and use theory 2 （UTAUT2）. Based on this literature review， researchers can better understand consumers' behavior intention through UTAUT2 model and conduct more in-depth research on consumers' technology acceptance.Key Words： Acceptance of Technology; UTAUT2; Behavioral intention; Information technology随着信息通信技术和智能手机的飞速发展，移动应用软件已经成为人们日常生活中不可或缺的一部分。

大学英语综合教程2第三版答案【篇一：全新版大学英语(第二版)综合教程3答案unit1-unit8】ass=txt>unit 1p3：after listeningcomplete the following statements according to what you have heard.1.taking a break2.escaping relief out in the country fast move3.the pollution of the citysmog4.changes in the way we livep10: content questionspair workone of you asks the first six questions and the other answers. starting from question7, change roles. when you have finished, the teacher may want to put some of the questions to you to check your progress.1. write and live on a farm.2. because they grow nearly all of their fruits and vegetables. they have enough eggs, honey and wood. they are very close to nature and can enjoy the beautiful scenery. besides, they can go skiing and skating in winter.3. no. sometimes the good life can get pretty tough.4. they were buried under five feet of snow from december through march.5. when the first spring came, it brought two floods. the second flood refers to the good harvest in the growing season.6. he decided to quit his job and start to freelance.7. he has to crawl into black-bear dens for “sports illustrated”, hitch up dogsled racing te ams for “smithsonian” magazine, check out the lake champlain “monster” for “science digest”, and canoe through the boundary waters wilderness area of minnesota for “destinations”.8. as for insurance, they have only bought a poor man’smajor-medical policy and the policy on their two cars.9. they cut back their expenses without appreciably lowering their standard of living. for example：they patronize local restaurants instead of more expensive places in the city. they still attend the opera and ballet but only a few times a year. they eat less meat, drink cheaper wine and see fewer movies.10. a tolerance for solitude and lots of energy.11. they will leave with a feeling of sorrow but also with a sense of pride at what they’ve been able to accomplish.12. they chose to live in the country because they want to improve the quality of their lives. yes, they have finally realized their dream.p11: text orqanizationworking on your owndo the exercises and then compare your answers with a partner.1. parts paragraphs main ideaspart oneparas. 1-3 the writer views his life inthe country as a self-reliantand satisfying one.part twoparas. 4-7 life in the country is goodyet sometimes very hard.part three paras. 8-11 after quitting his job, thewriter’s income wasreduced, but he and hisfamily were able tomanage to get by.part fourparas. 12-15a tolerance for solitudeand a lot of energy havemade it possible for thefamily to enjoy their life inthe country.2. happy moments and events hardships1) growing nearly all their fruits and 1)working hard both vegetablesin winter and in summer2) canoeing, picnicking, long bicycle 2)harsh environment rides, etc. and weather condition3) keeping warm inside the house 3)anxious moments after the in winter writer quit his job4) writing freelance articles4)cutting back on daily expenses5) earning enough money while 5) solitudemaintaining a happy family life.p12 language sense enhancement1. (1)special qualities(2)a tight budget (3)entertain(4)anyway (5)involved (6)requirement (7)on a small scale(8)temptation (9)instead (10)machineryp15: vocabularyi1. 1)on balance 2)resist 3)haul 4)wicked 5)illustrated6)budget7)lowering8)boundary 9)involved10) economic 11)blasting 12)just about2. 1)cut back/down 2)pick up 3)get by 4)get through5)face up to 6)turn in 7)making up for 8)think up3. 1)pursued his mathematical studies and taught himself astronomy.2)often generate misleading thoughts.3)attach great importance to combining theory with practice in our work.4)be suspected of doing everything for money.5)before he gets through life.4. 1)their indoora profitto invest in2)devicethe improvementon a global scale3)stackedtemptationnever dined outp18 ii . confusable words1.1)house 2)home 3)home family 4)household2.1)doubt2)suspected 3)doubted 4)suspected 5)suspect p19 iii. word formation1)rise 2)final 3)regular 4)cash 5)hows whys 6)upped7)yellowed 8)bottled 9)lower 10)searchp 20: comprehensive exercisei . cloze1.(1)gets by (2)temptation (3)get through (4)improvements(5)aside from (6)suspect (7) supplement (8)profit(9)stacking2. (1)replaced (2)consider (3)quit (4)world (5)tough(6)fuels (7)provide (8)luxuries (9)balance (10)ideal p21 ii. translation【篇二：全新版大学英语综合教程3 第二版课后练习答案】unit 1 vocabulary 1) on balance 5) illustrated 9) involved 2) resist6) budget 10) economic 3) haul7) lowering 11) blasting 4) wicked8) boundary 12) just about2．1)cut back/ down 2) pick up 3) get by4) get through 5)face up to6) turn in7) making up for 8) think up 3. 1) pursued his mathematical studies and taught himself astronomy 2) often generate misleading thoughts 3) attach great importance to combining theory with practice in our work 4) be suspected of doing everything for money 5) before he gets through life 4. 1) their indoor, a profit, to invest in 2) device, the improvement, on a global scale 3) stacked, temptation, never dined out ii confusable words 1. 1) house 2) home3) home, family 4) household 2. 1) doubt 2) suspect 3) doubted 4) suspected 5) suspect iii. word formation 1) rise 2) final 3) regular 4) cash 5) hows, whys 6) upped 7) yellowed 8) bottled 9) lower 10) search comprehensiveexercises i. cloze 1. text-related 1) get by 2)temptation 3) get through 4) improvements 5) aside from 6) suspect 7) supplement 8) profit 9) stacking 2. (theme-related) 1) replaced 2) consider 3) quit 4) world 5) tough 6) fuels 7)provide 8) luxuries 9) balance 10) ideal ii. translation1. we have a problem with the computer system, but i think it’s fairly minor.unit 2 vocabulary 1) decades5) slender 9) on the side 2) historic 6) web 10) authorized 3) imposed7) bade 11) terminal 4) religious 8) site 12) make the best of 2. 1) went through 2) stood up for 3) laid down 4) take on 5) let (us) down 6) drawon7) fall into 8) pass for3. 1) the europeans are fully confident that the americans will not be able to justify their measures to protect the struggling american steel industry. 2)clintonis, in the eyes of joe klein, staff writer of the new yorker and authorof the natural, the most talented politician of his generationand the most compelling. 3) theres not much you can do if people are really intent on destroying themselves with drugs. 4) a different experience of the world could forge a completely different approach to life.5) it is our conviction that cloning of human beings is bound to cause many ethical and social problems in the long run. 4.1) as for, do not compel, capture of, have forged 2) at huge risk, the mission, shelter 3) who abolished, in the eyes of, racial ii. words with multiple meanings 1. ill tell you in a minute how i have attained the genuine sense of belonging inamerica, but first let me hear about your french trip. 2. most mcdonalds look almost the same on the outside, but actually there are about 16 different basic designs. 3. loaning money from the banks is but one of the methods we can use to get through a financial crisis.4. this second-hand car has been nothing but trouble; its always breaking down.5. in your resume youve mentioned everything but one vital point.6. our technicians have discovered a simple but effective solution to the problem.7. iam sorry, but i think you shouldnt have lingered on over coffee and missed the last bus.. 8. the bankruptcy of the companywas not caused by evil, but by simple ignorance iii. usage 1) lonely2)friendly3) weekly, monthly 4)lovely 5) cowardly6)kindly/ saintly 7) lively8)motherly comprehensiveexercises i. cloze 1. text-related 1)forged 2) stand up 3) compelled4)convictions 5)mission 6)abolish 7) intent on 8) risk9)in the eyes of 10)threats 2. (theme-related) 1) assistance 2) involved 3) estimated 4)coincidence 5)emerged 6) referred 7) numerous 8) stationed 9)concern 10)captureii. translation1. though greatly affected by the consequences of the global financial crisis, we are still confident that we can face up to the challenge and overcome the crisis.2. under threat of constant sand storms, we were compelled to leave our cherished village and move to the new settlement.3. according to a recentonline survey, a lot of consumers say they may be motivatedto consider buying products shown in tv commercials. 4. having spotted a truck driver dumping contaminated waste alongside the river, the old man reported to the police at once.5. some scientists hold to the firm conviction that people will come to like genetically modified crops someday since they can increase yields and help combat hunger and disease in the developing world. shortly after he achieved freedom henson became intent on assisting fugitive slaves. he secretlyreturned to theunited statesfromcanadaseveral times to help others to travel the underground railroad to freedom. once some slave catchers closed in on the escaping slaves and henson when they were on the run. he disguised them and successfully avoided capture. later he built a small settlement indresdenincanadafor escaped slaves, setting up a chapel and a school. he held to the conviction that slavery would be abolished, and the day was bound to come when racial discrimination no longer existed.unit 3 vocabulary 1.1) threatens 2) by a small margin3)civilize 4)closed up5)wandered 6) paste 7) without so much as 8) sideways 9) hook up to 10) universal 11) chart 12) bathed in 2.1)narrowed down2)looked back on 3)cut off 4)fit into5)wear(the other) down 6)lies in7)put up 8)stand for 3. 1)...which is likely to make people vulnerable to asthma has been found by researchers at the department of clinical medicine in oxford. 2)...with mirrored doors had to be built in so as to make their small bedroom look larger. 3)...feature the space shuttle challenger blowing up in january 1986---killing all seven crew. 4)...threatened to keep the pupils in after school, they were quieted at once. 5)... are a major barrier to the countrys economic growth due to the fact that/because imported oil has absorbed 40% of its foreign exchange.4. 1) looked back on/ atmosphere/urban life 2)era/ hooked up to the / the electronic 3) the suburb / a sophisticated / system / analyze / make errors ii. 1) away2)inside/in3)forward/through4)back 5)off 6)home7) back down 8)in...out iii. 1) internet is not such an unusual word as it used to be 2) most men do not look unattractive in them 3) wealthy as she is, she is not unconcerned by her sudden unemployment 4) the claim is not uealistic in view of a sharp decrease in the citys violent crimes. 5)his poor health is not uelated to his unhealthy way of life. comprehensive exercises 1. cloze 1. 1) statistics2)rural3)era4)stood for 5)on the latch6)vulnerable7)barrier 8)electronic 9)reflection 10)civilized 2. 1) together 2)liable3)shift4)electric 5)cautious6)sophisticated7)thieves 8)break9)chances 10)signs ii. translation 1.1) the internet is changing the way people live, (no matter) whether they are in urban or rural areas.2)medium-sized and small companies are more vulnerable to the threat of the global economic crisis than large ones. 3)with regard to our term paper, the professor asked us to analyze the unemployment chart first, and then provide criticalreflections on the nations economic development. 4)it never occurred to him that their team would win the basketball match by a large margin. 5) looking back on my twenty years teaching in high school, i attribute my success to patience, talent, and the constant pursuit of knowledge. 2. it is almost impossible to keep a determined burglar out. all you can do is discourage him for a few minutes. thus exposing him to police patrols. common sense tells us that lighting is a barrier to criminal activity. a light should be fixed in the doorway and switched on at night. make sure/assure yourself that you dont leave the door on the latch if you happen to be the last to come in. if you decide to buy a sophisticated electronic alarm system, be sure to ask for its signs and put them up on both windows and doors. in addition you may have it hooked up to a police station.【篇三：全新版大学英语综合教程3(第二版)课后练习答案】abularyi.1.1) on balance5) illustrated9) involved2) resist 6) budget 10) economic3) haul7) lowering 11) blasting4) wicked 8) boundary12) just about2.1)cut back/ down 2) pick up 3) get by4) get through5)face up to6) turn in7) making up for 8) think up3.1) pursued his mathematical studies and taught himself astronomy2) often generate misleading thoughts3) attach great importance to combining theory with practice in our work4) be suspected of doing everything for money5) before he gets through life4.1) their indoor, a profit, to invest in2) device, the improvement, on a global scale3) stacked, temptation, never dined outii confusable words1. 1) house 2) home3) home, family 4) household2. 1) doubt 2) suspect 3) doubted 4) suspected 5) suspectiii. word formation1) rise 2) final 3) regular 4) cash 5) hows, whys6) upped 7) yellowed 8) bottled 9) lower 10) searchcomprehensive exercisesi. cloze1. text-related1) get by 2) temptation 3) get through 4) improvements5) aside from 6) suspect 7) supplement 8) profit9) stacking2. (theme-related)1) replaced 2) consider 3) quit 4) world 5) tough6) fuels 7) provide 8) luxuries 9) balance 10) idealii. translation1. we have a problem with the computer system, but i think it’s fairly minor.2. my father died when i was too young to live on my own. the people of my hometown took over (responsibility for) my upbringing at that point.3. the toys have to meet strict/ tough safety requirements before they can be sold to children.4. radio and television have supplemented rather than replaced the newspaper as carriersof news and opinion.5. when it comes to this magazine, it is/ carries a digest of articles from many newspapers and magazines around the world.a decade ago, nancy did what so many americans dream about. she quit an executive position and opened/ set up a household device store in her neighborhood. people like nancy made the decision primarily for the improvement in the quality of their lives.but, to run a small business on a small scale is by no means an easy job. without her steady income, nancy had to cut back on her daily expense. sometimes she did not even have the money to pay the premium for the various kinds of insurance she needed.fortunately, through her own hard work, she has now got through the most difficult time. she is determined to continue pursuing her vision of a better life.unit 2vocabularyi.1.1) decades5) slender9) on the side2) historic 6) web10) authorized3) imposed7) bade 11) terminal4) religious8) site12) make the best of2.1) went through2) stood up for3) laid down4) take on5) let (us) down6) draw on7) fall into8) pass for3.1) the europeans are fully confident that the americans will not be able to justify their measures to protect the struggling american steel industry.2) clinton is, in the eyes of joe klein, staff writer of the new yorker and author of the natural, the most talented politician of his generation and the most compelling.3) theres not much you can do if people are really intent on destroying themselves with drugs.4) a different experience of the world could forge a completely different approach to life.5) it is our conviction that cloning of human beings is bound to cause many ethical and social problems in the long run.4.1) as for, do not compel, capture of, have forged2) at huge risk, the mission, shelter3) who abolished, in the eyes of, racialii. words with multiple meanings1. ill tell you in a minute how i have attained the genuine sense of belonging in america, but first let me hear about your french trip.2. most mcdonalds look almost the same on the outside, but actually there are about 16 different basic designs.3. loaning money from the banks is but one of the methods we can use to get through a financial crisis.4. this second-hand car has been nothing but trouble; its always breaking down.5. in your resume youve mentioned everything but one vital point.6. our technicians have discovered a simple but effective solution to the problem.7. i am sorry, but i think you shouldnt have lingered on over coffee and missed the last bus..8. the bankruptcy of the company was not caused by evil, but by simple ignorance iii. usage1) lonely2)friendly 3) weekly, monthly 4)lovely5) cowardly6)kindly/ saintly 7) lively8)motherlycomprehensive exercisesi. cloze1. text-related1)forged 2) stand up3) compelled 4)convictions5)mission6)abolish 7) intent on8) risk 9)in the eyes of10)threats2. (theme-related)1) assistance2) involved3) estimated4)coincidence 5)emerged 6) referred 7) numerous 8) stationed9)concern 10)captureii. translation1. though greatly affected by the consequences of the global financial crisis, we are still confident that we can face up to the challenge and overcome the crisis.2. under threat of constant sand storms, we were compelled to leave our cherished village and move to the new settlement.3. according to a recent online survey, a lot of consumers say they may be motivated to consider buying products shown in tv commercials.4. having spotted a truck driver dumping contaminated waste alongside the river, the old man reported to the police at once.5. some scientists hold to the firm conviction that people will come to like genetically modified crops someday since they can increase yields and help combat hunger and disease in the developing world.shortly after he achieved freedom henson became intent on assisting fugitive slaves. he secretly returned to the united states from canada several times to help others to travel the underground railroad to freedom. once some slave catchers closed in on the escaping slaves and henson when they were on the run. he disguised them and successfully avoided capture. later he built a small settlement in dresden in canada for escaped slaves, setting up a chapel and a school. he held to the conviction that slavery would be abolished, and the day was bound to come when racial discrimination no longer existed.unit 3vocabularyi.1.1) threatens 2) by a small margin3)civilize 4)closedup5)wandered6) paste 7) without so much as 8) sideways9) hook up to 10) universal 11) chart 12) bathed in2. 1)narrowed down2)looked back on 3)cut off 4)fit into5)wear(the other) down 6)lies in7)put up 8)stand for3. 1)...which is likely to make people vulnerable to asthma has been found by researchers at the department of clinical medicine in oxford.2)...with mirrored doors had to be built in so as to make their small bedroom look larger.3)...feature the space shuttle challenger blowing up in january 1986---killing all seven crew.4)...threatened to keep the pupils in after school, they were quieted at once.5)... are a major barrier to the countrys economic growth due to the fact that/because imported oil has absorbed 40% of its foreign exchange.4. 1) looked back on/ atmosphere/urban life2)era/ hooked up to the / the electronic3) the suburb / a sophisticated / system / analyze / make errors ii. 1) away2)inside/in 3)forward/through4)back5)off 6)home7) back down 8)in...outiii. 1) internet is not such an unusual word as it used to be2) most men do not look unattractive in them3) wealthy as she is, she is not unconcerned by her sudden unemployment4) the claim is not uealistic in view of a sharp decrease in the citys violent crimes.5)his poor health is not uelated to his unhealthy way of life.comprehensive exercises1. cloze1. 1) statistics2)rural3)era4)stood for 5)on the latch6)vulnerable7)barrier 8)electronic 9)reflection 10)civilized2. 1) together 2)liable3)shift4)electric 5)cautious6)sophisticated7)thieves 8)break9)chances 10)signsii. translation1.1) the internet is changing the way people live, (no matter) whether they are in urban or rural areas.2)medium-sized and small companies are more vulnerable to the threat of the global economic crisis than large ones.3) with regard to our term paper, the professor asked us to analyze the unemployment chart first, and then provide critical reflections on the nations economic development.4)it never occurred to him that their team would win the basketball match by a large margin.5) looking back on my twenty years teaching in high school, i attribute my success to patience, talent, and the constant pursuit of knowledge.2. it is almost impossible to keep a determined burglar out. all you can do is discourage him for a few minutes. thus exposing him to police patrols. common sense tells us that lighting is a barrier to criminal activity. a light should be fixed in the doorway and switched on at night. make sure/assure yourself that you dont leave the door on the latch if you happen to be the last to come in. if you decide to buy a sophisticated electronic alarm system, be sure to ask for its signs and put them up on both windows and doors. in addition you may have it hooked up to a police station.unit 4vocabularyi.1.1) accordingly 2) loose 3) concentration 4)stimulating 5) fabric 6)if anything7) reality 8) intuition9) trifle10) at the turn of the century11) mess12) undermine2. 1) approve of2) slow down 3) taken in4) sucked into5) set apart 6) dozed off 7)call forth 8)stretch into9) keep up with 10)believe in3. 1)...provided inspiration for many artists and musicians over the decades.2)...is credited to his powers of imagination3)...on the foundations of an agricultural revolution4)...not to make any complaints in the presence of the nurse.5)...the outbreak of the second world war.4. 1) flaw/came to the conclusion/would get nowhere2) in a row/dozed off/a mess of3) outbreak of/ has undermined / has strainedii. 1)with christmas only a week away2) with his physical condition improving day by day3) with our gdp growing steadily4) with all the shops closed5) with her eyes closed6) with the fog lifting during the night。

theory词根
theory词根是指英语单词中的“theory”一词的词根。

词根是
指单词中不变的部分，可以用来推导出一些有关联的单词，并有助于理解这些单词的含义。

“theory”一词的词根为“theor-”，源自希腊语中的“theoria”，意为“观察、思考、研究”。

因此，“theor-”在许多单词中都表示“思考、推测、研究”的意思。

例如，单词“theoretical”就是由“theor-”和“-ical”组成，表示“理论的、推测的”。

单词“theorist”则是由“theor-”和“-ist”组成，表示“理论家、学者”。

此外，许多单词中也包含“theor-”的变体，例如“theolog-”（神学）、“theosoph-”（神秘主义）等等。

这些单词的词根都与“theor-”有着密切的关联。

因此，了解“theory”一词的词根可以帮助我们更好地理解相关单词的含义，同时也有助于扩展我们的词汇量和语言能力。

- 1 -。

课程教学大纲课程名称（中文）：信息技术基础（全英文）课程名称（英文）： Fundamentals of Information Technology 课程性质：（通识必修、通识选修、学科基础、专业必修、专业选修、教师教育）学分：2+2学时：72，其中理论学时：36，实践（实验）学时：36授课对象：中法工商管理创新实验班授课语言：英文开课院系：计算中心课程网址：大夏学堂https:///webapps/blackboard/execute/m odulepage/view?course_id=_360_1&cmp_tab_id=_706_1&editMode =true&mode=cpview撰写人：江红一、课程简介（英文）DescriptionThis Course is designed to enable students to use Information Technology (IT) systems and applications independently to support a range of information processing activities. It is designed to develop a broad knowledge of the theoretical concepts, principles, boundaries and scope of IT applications. These activities will be centred on using software applications packages (Windows, Word, Excel, PowerPoint, HTML, Access) tomeet complex information requirements while paying attention to security and the needs of other users.二、课程目标ObjectivesOn completion of the Course the students should be able to:1. Operate a range of IT equipment independently, giving attention to security and to other users.2. Use a range of software application packages to meet complex information requirements.三、教学内容、学时分配和作业要求Weekly Teaching GuideTeaching Schedule:四、教材、参考书目或其他学习材料⚫计算机专业英语教程（第2版），江红主编，清华大学出版社，2017.8. ISBN：9787302473190⚫计算机专业英语教程，江红主编，清华大学出版社，2012.1.ISBN: 9787302255321⚫信息技术基础（IT Fundamentals）双语教程. 江红主编，清华大学出版社，2008.11. ISBN: 9787302184232⚫（美）Timothy J. O'Leary, Linda I. O'Leary 著，计算机专业英语(Computing Essentials)，北京：高等教育出版社，2012. ISBN：9787040115451五、考核办法与评价结构比例六、教学和实践环境要求：Lecturing and Practicing Requirements:⚫Computer + Data projector⚫Speaker + microphone, etc., multimedia devices⚫Local Area Network⚫Windows 7 (English Version)⚫Office 2013 (Word, Excel, PowerPoint, Access) (English Version)⚫WINRAR⚫Authoring Tools: Dreamweaver, FrontPage, etc.。

乐理基础知识一、引言乐理（Music theory）是指对音乐的理论研究和系统化总结的学科。

作为音乐的基础知识，学习乐理可以帮助我们更好地理解音乐的结构和内涵，提高我们的音乐素养和表演能力。

本文将介绍乐理的基本概念和知识，帮助读者建立起对乐理的初步了解。

二、音的基本属性音乐是由一系列音组成的，因此了解音的基本属性是学习乐理的基础。

音有三个基本属性：音高、音长和音色。

1. 音高音高（Pitch）是指音的高低。

不同音高的音可以通过频率来表示，频率越高，音高越高。

一般用来表示音高的记号有乐谱上的五线谱、简谱和赫兹（Hz）等。

2. 音长音长（Duration）是指音的持续时间。

音可以分为长音、短音和延音等，不同的音长可以通过乐谱上的音符来表示，如全音符、二分音符、四分音符等。

3. 音色音色（Timbre）是指不同乐器演奏同一音高时所产生的声音特点。

每个乐器都有自己独特的音色，如钢琴的音色清亮、小提琴的音色圆润。

音色的不同使得音乐更加丰富多彩。

三、音程和和弦1. 音程音程（Interval）是指两个音高之间的距离。

音程有两个基本属性：大小和品质。

音程的大小用音程的级数来表示，品质则表示了音程的纯、大、小或增减等属性。

学习音程可以帮助我们更好地理解和演奏音乐中的音高关系。

2. 和弦和弦（Chord）是由三个或更多音同时演奏而产生的音响效果。

最基本的和弦是三音和弦，由根音、三度音和五度音构成。

和弦的基本类型有大三和弦、小三和弦和属七和弦等。

和弦的变化和运用是音乐中十分重要的一部分。

四、调性和调式1. 调性调性（Tonality）是指音乐作品中对音调关系的组织和安排。

调性分为 major（大调）和 minor（小调）两种。

在大调中以C 大调为例，音阶的音程关系为全全半全全全半，而在小调中以 A 小调为例，音程关系为全半全全半全全。

2. 调式调式（Mode）是指以某个音为音阶的主音，再以该音为基准的调性。

常见的调式有七音调式和五音调式等。

《泛函分析》读书笔记课程题目：泛函分析任课教师：高云兰博士学生姓名：***学生学号：********2008年12月10日《泛函分析》读书笔记Reading Notes about Functional Analysis崔继峰所谓的泛函呢，就是一般函数，泛函分析当然就是一般函数的分析研究。

在学习泛函之前，需要有扎实的《实变函数》知识。

大学期间，曾用半年时间学过由南开大学刘炳初教授编著，科学出版社出版的《泛函分析》，讲课的是哈尔滨工业大学的包革军教授，他讲泛函的最大特点是把泛函与几何图形有机结合，把艰深的纯理论讲的惟妙惟肖。

在进入研究生学习阶段，《泛函分析》作为计算数学研究生的基础理论课程，是必选的。

我们选用的教材是由武汉大学刘培德教授主编，武汉大学出版社出版的《泛函分析（第二版）》，该教材是面向本科生的，系里之所以考虑选择此教材，是由于考虑到有些学生在本科阶段没有或者很粗浅的认识了《泛函分析》这门课程，主讲该课程的是高云兰博士，她的方向就是算子方面的研究，所以讲解该课程那是轻车熟路了。

课时大约是48学时（粗略估计）。

由于以下两方面的原因：1）对于《泛函分析》认识很粗浅；2）第一次写读书笔记（尤其是专业课类），不知道如何从略。

所以读书笔记可能从在诸多问题，希望老师见谅！下面我从几个方面写本学期学习《泛函分析》的感受和认识。

我本着这样态度写该笔记：1）了解泛函是什么，泛函的发展（很多教材把这个从略）2）把空间的理论知识系统学习，对于其他理论的学习作抛砖引玉之用。

3）学习泛函的实际作用（也就是附录里的滤波器理论的应用）。

泛函分析是研究拓扑线性空间到拓扑线性空间之间满足各种拓扑和代数条件的映射的分支学科。

它是20世纪30年代形成的。

从变分法、微分方程、积分方程、函数论以及量子物理等的研究中发展起来的，它运用几何学、代数学的观点和方法研究分析学的课题，可看作无限维的分析学。

一、泛函分析的产生十九世纪以来，数学的发展进入了一个新的阶段。