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Over the past few decades, there has been a considerable increase in the use of mathematical analysis, both for solving everyday problems and for theoretical developments of many disciplines. For example, economics, biology, geography and medicine have all seen a considerable increase in the use of quantitative techniques. Twenty years ago applied mathematics meant the application of mathematics to problems in mechanics and little else--now, applied mathematics, or as many people prefer to call it, applicable mathematics, could refer to the use of mathematics in many varied areas. The one unifying theme that these applications have is that of mathematical modeling, by which we mean the construction of a mathematical model to describe the situation under study. This process of changing a real life problem into a mathematical one is not at all easy, we hasten to add, although one of the overall aims of this book is to improve your ability as a mathematical modeler.
There have been many books written during the past decade on the topic of mathematical modeling; all these books have been devoted to explaining and developing mathematical models, but very little space has been given to how to construct mathematical models, that is, how to take a real problem and convert it into a mathematical one. Although we appreciate that we might not yet have the best methods for teaching how to tackle real problems, we do at least regard this mastery of model formulation as a crucial step, and much of this book is devoted to attempting to make you more proficient in this process.
Our basic concept is that applied mathematicians become better modelers through more and more experience of tackling real problems. So in order to get the most out of this book, we stress that you must make a positive effort to tackle the many problems posed before looking at the solutions we have given. To help you to gain confidence in the art of modeling we have divided the book into four distinct sections.
In the first section we describe three different examples of how mathematical analysis has been used to solve practical problems. These are all true accounts of how mathematical analysis has helped to provide solutions. We are not expecting you to do much at this stage, except to read through the case studies carefully, paying particular attention to the way in which the problems have been tackled--the process of translating the problem into a mathematical one.
The second section consists of a series of real problems, together with possible solutions and related problems. Each problem has a clear statement, and we very much encourage you to try to solve these problems in the first place without looking at the solutions we have given. The problems require for solution different levels of mathematics, and you might find you have not yet covered some of the mathematical topics required. In general we have tried to order them, so that the level of mathematics required in the solutions increase as you move through the problems. Remember that we are only giving our solutions and, particularly if you don’ t look at our solution, you might well have a completely different approach which might provide a better solution.
Here, in the third section, we try to give you some advice as to how to approach the tackling of real problem solving, and we give some general concepts involved in mathematical modeling. It must, though, again be stressed that we are all convinced that experience is the all-important ingredient needed for confidence in model formulation. If you have just read Sections I and 11 without making at least attempts at your own solutions to some of the problems set, you will not have gained any real experience in tackling real problems, and this section will not really be of much help. On the other hand, if you have taken the problem solving seriously in Section Ⅱ , you might find the general advice given here helpful.
Provided you have gained some confidence in tackling real problem solving in the earlier parts, you will be able to dabble with those problems in this section which appeal to you. Don’t feel you must work systematically through this section, but look for problems you want to solve--these are the ones that you will have most success in solving.
We hope that this book will at least point you in this direction. We are aware that this is not a finalized precise sort of text, but then using mathematics in practical problem solving is not a precise art. It is full of pitfalls arid difficulties; but don’t despair, you will find great excitement and satisfaction when you have had your first success at real problem solving!

The author of the book hopes that by reading the book, the reader can（）

A:be more proficient in mastering mathematical knowledge B:be more proficient in applying his mathematical knowledge to real problem solving C:have a better understanding of the various uses of mathematical models D:fined real excitement and satisfaction in solving problems

In recent years American society has become increasingly dependent on its universities to find solutions to its major problems. It is the universities that have been charged with the principal responsibility for developing the expertise to place men on the moon; for dealing with our urban problems, and with our deteriorating environment; for developing the means to feed the world’s rapidly increasing population. The effort involved in meeting these demands presents its own problems. In addition, this concentration on the creation of new knowledge significantly impinges on the universities’ efforts to perform their other principal functions, the transmission and interpretation of knowledge -- the imparting of the heritage of the past and the preparing of the next generation to carry it forward.
With regard to this, perhaps their most traditionally sanctioned task, colleges and universities today find themselves in a serious bind generally. On the one hand, there is the American commitment, entered into especially since World War II, to provide higher education for all young people who can profit from it. The result of the commitment has been a dramatic rise in enrollments in our universities, coupled with a radical shift from the private to the public sector of higher education. On the other hand, there are serious and continuing limitations on the resources available for higher education.
While higher education has become a great "growth industry", it is also simultaneously a tremendous drain on the resources of the nation. With the vast increase in enrollment and the shift in priorities away from education in state and federal budgets, there is in most of our public institutions a significant decrease in per capita outlay for their students. One crucial aspect of this drain on resources lies in the persistent shortage of trained faculty, which has led, in turn, to a declining standard of competence in instruction.
Intensifying these difficulties is, as indicated above, the concern with research, with its competing claims on resources and the attention of the faculty. In addition, there is a strong tendency for the institutions’ organization and functioning to conform to the demands of research rather thorn those of teaching.

According to the author, （）is the most important function of institutions of higher education.

A:creating new knowledge B:providing solutions to social problems C:making experts on sophisticated industries out of their students D:preparing their students to transmit inherited knowledge

Directions: There are five reading passages in this part. Each passage is followed by five questions. For each question there are four suggested answers marked A, B, C and D. Choose the best answer and blacken the corresponding letter on the answer sheet.
Passage One

The passage is mainly about______.

A:how individuals can help make a difference B:running a neighborhood meeting to solve its problems C:citizens’ reactions to the problems they face D:solving problems through group action

Most Americans don’t like to get advice from members of their family. When they need advice, they don’t usually 61 people they know. 62 , many Americans write letters to newspapers and magazines which give advice 63 many different subjects, including family problem, sex, the use 64 the language, health, cooking, childcare, clothes, and how to buy a house or a car. 65 newspapers regularly print letters 66 readers with problems. Along 67 the letters there are answers written 68 people who are supposed to know how to 69 such problems. Some of these writers are doctors; 70 are lawyers or educators. But two of the most famous writers of advice 71 women without special training 72 this kind of work. One of them answers letters 73 to “Dear Abby”. The other is addressed 74 “Dear Ann Landers”. Experience is their preparation for 75 advice. There is one writer who has not lived long 76 to have much experience. She is a girl named Angel Cavaliere, who started writing 77 for newspaper readers 78 the age of ten. Her advice to young readers now 79 regularly in the Philadelphia Bulletin in a column 80 DEAR ANGEL.

77（）

A:advise B:answers C:advice D:problems

阅读下面的短文，文中有15处空白，每处空白给出了4个选项，请根据短文的内容从4个选项中选择1个最佳答案。

A:questions B:problems C:possibilities D:issues

Please let me know if any problems (arise).

A:become B:occur C:come D:find

When something goes wrong, it can be very satisfying to say," Well, it’s so-and-so’s fault. "or "I know I’m late, but it’s not my fault ; the car broke down. "It is probably not your fault, but once you form the habit of blaming somebody or something else for a bad situation, you are a loser. You have no power and could do nothing that helps change the situation. However, you can have great power over what happens to you if you stop focusing on whom to blame and start focusing on how to remedy the situation. This is the winner’s key to success.
Winners are great at overcoming problems. For example, if you were late because your car broke down, maybe you need to have your car examined more regularly. Or, you might start to carry along with you the useful phone numbers, so you could call for help when in need. For another ex-ample, if your colleague causes you problems on the job for lack of responsibility or ability, find ways of dealing with his irresponsibility or inability rather than simply blame the person. Ask to work with a different person, or don’t rely on the person. You should accept that the person. Ask to work with a different person, or don’t rely on this person. You should accept that the person is not reliable and find creative ways to work successfully regardless of how your colleague fails to do his job well.
This is what being a winner is all about—creatively using your skills and talents so that you are successful no matter what happens. Winners don’t have fewer problems in their lives ; they have just as many difficult situations to face as anybody else. They are just better at seeing those problems as challenges and opportunities to develop their own talents. So, stop focusing on "whose fault it is". Once you are confident about your power over bad situations, problems are just stepping stones for success.

According to the passage, winners（）

A:deal with problems rather than blame others B:meet with fewer difficulties in their lives C:have responsible and able colleagues D:blame themselves rather than others

When something goes wrong, it can be very satisfying to say," Well, it’s so-and-so’s fault. "or "I know I’m late, but it’s not my fault ; the car broke down. "It is probably not your fault, but once you form the habit of blaming somebody or something else for a bad situation, you are a loser. You have no power and could do nothing that helps change the situation. However, you can have great power over what happens to you if you stop focusing on whom to blame and start focusing on how to remedy the situation. This is the winner’s key to success.
Winners are great at overcoming problems. For example, if you were late because your car broke down, maybe you need to have your car examined more regularly. Or, you might start to carry along with you the useful phone numbers, so you could call for help when in need. For another ex-ample, if your colleague causes you problems on the job for lack of responsibility or ability, find ways of dealing with his irresponsibility or inability rather than simply blame the person. Ask to work with a different person, or don’t rely on the person. You should accept that the person. Ask to work with a different person, or don’t rely on this person. You should accept that the person is not reliable and find creative ways to work successfully regardless of how your colleague fails to do his job well.
This is what being a winner is all about—creatively using your skills and talents so that you are successful no matter what happens. Winners don’t have fewer problems in their lives ; they have just as many difficult situations to face as anybody else. They are just better at seeing those problems as challenges and opportunities to develop their own talents. So, stop focusing on "whose fault it is". Once you are confident about your power over bad situations, problems are just stepping stones for success.

According to the passage, winners （　） .

A:deal with problems rather than blame others B:meet with fewer difficulties in their lives C:have responsible and able colleagues D:blame themselves rather than others

When something goes wrong, it can be very satisfying to say," Well, it’s so-and-so’s fault. "or "I know I’m late, but it’s not my fault ; the car broke down. "It is probably not your fault, but once you form the habit of blaming somebody or something else for a bad situation, you are a loser. You have no power and could do nothing that helps change the situation. However, you can have great power over what happens to you if you stop focusing on whom to blame and start focusing on how to remedy the situation. This is the winner’s key to success.
Winners are great at overcoming problems. For example, if you were late because your car broke down, maybe you need to have your car examined more regularly. Or, you might start to carry along with you the useful phone numbers, so you could call for help when in need. For another ex-ample, if your colleague causes you problems on the job for lack of responsibility or ability, find ways of dealing with his irresponsibility or inability rather than simply blame the person. Ask to work with a different person, or don’t rely on the person. You should accept that the person. Ask to work with a different person, or don’t rely on this person. You should accept that the person is not reliable and find creative ways to work successfully regardless of how your colleague fails to do his job well.
This is what being a winner is all about—creatively using your skills and talents so that you are successful no matter what happens. Winners don’t have fewer problems in their lives ; they have just as many difficult situations to face as anybody else. They are just better at seeing those problems as challenges and opportunities to develop their own talents. So, stop focusing on "whose fault it is". Once you are confident about your power over bad situations, problems are just stepping stones for success.

According to the passage, winners（）

A:deal with problems rather than blame others B:meet with fewer difficulties in their lives C:have responsible and able colleagues D:blame themselves rather than others