Book Description

This book provides a fundamental introduction to numerical analysis.This book covers numerous topics including Interpolation and Polynomial Approximation,Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and computer science fields.

Reviews (1)

Good introduction to numercal algorithms
The book covers most of the traditional methods. It is a good choice for learning numerical methods. The book has plenty of examples and are very easy to follow. I would recommend some background on calculus and some knoledge about matlab ... Read more

Book Description

"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics."

In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life--patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.

Taking the reader on a wondrous journey through the invisible universe that surrounds us--a universe made visible by mathematics--Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers--all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture.

A brilliant exploration of an often woefully misunderstood subject The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics. ... Read more

Reviews (10)

Step into the shoes of a mathematician
I've always had a like-hate relationship with math; I didn't do well in it in college, but I've long been fascinated by physics. There are many books for the lay person about the cutting edge in physics; books like that are harder to find in the world of mathematics.

But Keith Devlin has done it. He surely captured me near the beginning when he described mathematics as the study of patterns; a wonderful description that starts to get at why mathematics seems to be the language underlying the physical universe.

This was not an easy book for a slightly math-averse person, but Devlin's explanations were always clear, and more importantly, always gave a sense of context of what he was discussing.

Bring it on, baby!
Most people either misunderstand what math is all about, or see it as a collection of rather disjointed areas collected together under a single name. Devlin does an admirable job of re-educating us all, and showing how the different areas of mathematics are linked together, often in rather surprising ways.

This book is simply brilliant. The amount of information Devlin has managed to cram between two covers is amazing. Having spent years studying this stuff, it's rather depressing to see that most of the important things I've learned can fit into a 350 page book, but then this is surely a testament to Devlin's skill.

Although this book makes no formal educational expectations of the reader, I feel that a true beginner would have trouble following a lot of parts, although they would still get the general idea. This would be better then nothing, but I think that this book would be best appreciated by those with some formal math background. I would be curious to see what a high school student would make of this, since I really wish I'd had this book back then. When you see the beautiful ways that mathematics connects the most seemingly disparate ideas, you can't help but want to learn more!

Perceiving patterns.
Devlin: "The particular topics I have chosen are all central themes within mathematics... But the fact is, I could have chosen any collection of seven or eight general areas and told the same story; That mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds. And that mathematics serves us by making the invisible visible."
At this writing it has been more than a few years since my last class in mathematics. But I liked math as a student and still do, even at the point that notation and degree of abstraction begins to hurt my head, so to speak, I still like it. There is a solidity and a beauty in mathematics that eclipses the empirical sciences. It is not only the practical applicability, logical purity, and beauty of mathematics that interest me, it is also its very immateriality. As Devlin states, "music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics."
This is a wonderful book. Before 1900, mathematics could be wholly categorized within about a dozen subjects. While advances are still being made in some of these older disciplines -- Devlin discusses how developments in number theory are being applied to encryption for such purposes as banking security -- there are now at least 60-70 somewhat distinct disciplines of mathematics. The author reveals the logical foundations, history, and current applications of number theory, mathematical logic, the calculus, relativistic geometry, topology, and probability. Applications of mathematics to such seemingly far-flung fields as linguistics, electrodynamics, and astrophysics are briefly but aptly considered. He introduces us to the patterns and progressions of perceptive minds, from the Pythagoreans, Platonists, and Peripatetics, to Pascal and Penrose, with glances at Galileo, Gauss and Godel. [Okay, enough alliteration ... just having a little fun with patterns; and patterns, as Devlin instructs, is precisely what mathematics is all about.]

Breathtaking
This book is an incredible account into the ideas of mathematics. Devlin presents simple and extremely abstract ideas into a language that just about anyone can understand. Although some previous knowledge of the fields investigated does help, this book serves as a great introduction into such things as perspective geometry, non-Euclidean geometry, network theory, topology and quantum mechanincs. It also provides some great insights into the history and uses of number theory, algebra, geometry and calculus. I've have never read a mathematical/scientific work that was written with such passion and was a complete page turner (I read it straight over the course of 3 days). I am still amazed on how such a work can be under $50 because it is worth much more than that.

Clear and engaging
Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The eight chapters cover number theory, set theory, calculus, group theory, topology, probability and the application of mathematics to the physical world. The discussion in each chapter, couched generally in English, not mathematics, is so clear that a math-phobic can understand it. By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics.

Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics. The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it. The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.

Potential purchasers should note, by the way, that this book was reworked from Devlin's "Mathematics: The Science Of Patterns". In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground." I've read both, and I have to say they're both worth getting. The two new chapters in this book are the ones on probability and the applications of mathematics in science; they're well done and interesting. However, the pictures in Science of Patterns are very high quality.

They're both fine books, and I can strongly recommend each of them. If you have to get one, I'd say get Science of Patterns. Even though Language of Mathematics does have some colour plates, Science of Patterns is really a gorgeous book to read with many good illustrations. I ended up buying both, and you may end up doing that too. ... Read more

Book Description

You don't have to learn math by yourself! Solving problems in groups is exciting, effective, and equitableit helps all students succeed in math. Get It Together is a collection of over 100 mathematics problems for groups of 26 students. The problems cover a wide range of math topics such as logic, functions, algebra, geometry, measurement, and number patterns at various levels of difficulty. Each problem has the same format: six clue cards provide the information needed to solve a problem. Since each member of the group has a different bit of information, everyone works together to arrive at a solution. In one problem, only some people get sick after eating a potluck meal. Was it the swamp chicken, the cheesecake, or something else? The group collaborates to discover which food was the culprit. This book is an excellent resource with teacher information on cooperative groups, assessment, problem solving and the use of manipulatives. ... Read more

Reviews (2)

Fabulous teaching tool!
Erickson's book (as well as "United We Solve") is a fabulous tool for teachers of math (as well as some social sciences). The activities are for small groups and the "rules" for solving the problems make it a good basis for evaluating both individual and group work.

I use these activities with my third and fourth graders, but the activities are also good for much older students. The topics are varied, including geometry, equations, logic, and even some social studies topics. My students love working on these, and I love watching them as they work to solve the creative problems.

I highly, highly, highly recommend this book AND "United We Solve".

We Getting It Together
I think of myself a traditional teacher. As a sixth-grade teacher of math, I believe that students need a strong foundation in the basics of mathematics. However, with Get It Together by Mr. Erikson, I found myself motivated by activities that go beyond the trendy 'math games.' There are many acitivites that have real learning value. Also, the students enjoy working together in small groups to find the answer. At least once a week, I find myself using an activity or two out of this book. It has been an excellent resource in the classroom. ... Read more

Book Description

Stefan Waner and Steven Costenoble's FINITE MATHEMATICS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice. ... Read more

Reviews (2)

Not a book to use for an On-line class
This is not a book to use for on-line classes.Does not read well and does not show step by step instructions that are easy to follow.I aced my last 2 math classes, but am having difficulty in this one.Not because of the material, but because the way the book reads.

Infinite Mistakes
What can I say...as a student I am not impressed with this book at all. It is full of mistakes. How are students supposed to correctly learn the material if their texts are full of mistakes?

I especially recommend that you steer away from buying the solutions manual. The text's solution guide does not even match the manual.

I would love to sit and list all of the mistakes, but frankly it would take me an infinite amount of time.

The book also includes free access to [a website], which inconveniently does not list the mistakes in the book. I would give the authors more credit for their book if they would put their mistakes on the website instead of forcing students to wade through murky waters. ... Read more

Reviews (3)

Excellent.
An excellent biography of Godel. Examines his personal life and mathematical work in an integrated manner. Dawson is thorough, well-researched, and shows a command of the mathematics involved. Never sensational or anecdotal, he provides the most accurate picture available of the real Godel. This is not a popular account of Godel's work, so the reader will need an understanding of fundamental mathematical logic and Godel's theorem to appreciate much of the book. But Dawson does provide a lot of history of mathematical logic, including a great chapter on developments up to 1928 that could be read by itself. The appendix provides a chronology, genealogy, and "biographical vignettes" of other important logicians.

The definitive biography of Kurt Godel
Knowing what went on in the mind of Kurt Godel will forever be unattainable. Nonetheless, John Dawson comes as close as possible to understanding what made Godel click.

Having catalogued Godel's works and personal papers, Dawson saw aspects of Godel's life that perhaps no one short of his wife had seen.

The book is a fascinating jaunt through the through the lives of one of the greatest minds of the 20th century. What is also interesting is Godel's interaction with personalities such as Einstein and Van Neumann.

While the mathematics is often abstract, as can be expected, Logical Dilemmas is a mesmerizing read.

By a Mathematician for Mathematicians
Writing a biography of anyone is difficult. How can a writer, no matter how talented, really claim to understand someone well enough to give an overview of his life? When the subject is a genius like Kurt Godel, whose name is known by few and whose work is really understood by even less, the job must be even more difficult. Fortunately, people like Mr. Dawson are will to give it a shot and he succeeds fairly well.

In putting together this biography, Mr. Dawson has the advantage of being mathematician. Additionally, he has the advantage of being the mathematician who catalogued Godel's papers after his death. This gives him a lot of insight into Godel that other writers cannot have and he weaves quotations from these papers into the biography very well. Mr. Dawson's is a well-documented and logical biography that is short on conjecture and long on footnotes. In brief, it is a biography about a mathematician clearly written by a mathematician. This is both its strength and its weakness.

Actually, I like the purely biographical sections of this book very much. The biographical information is clear and informative, though a bit dry in the academic style favored by mathematicians and scientists. Fortunately, having lived and worked among these people, I am comfortable with this style. More importantly, I feel like I have a better idea now of who Godel was and what he was like from reading this book. His focus on his work, his relationship with his family and friends (particularly his wife) and his ultimate decent into mental illness are much more in focus for me now.

On the other hand, the sections that deal with Godel's mathematics are much more difficult to take. The discussion of mathematics in this book goes far beyond what most people are going to be able to handle. I fear the average reader even with a decent math background who comes across this book will drop it as soon as the mathematics starts and that is unfortunate. (I am always looking for books to promote math even among non-mathematicians. This one does not do it.) A reader who can handle the math, however, will find this book revealing. ... Read more

Book Description

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Extensive collection of problems and exercises, correlated with examples. Bibliography. 1978 edition.
... Read more

Reviews (8)

a veritable mine of information....
To paraphrase Chandrasekhar's review of Watson's Bessel functions text, this is "a veritable mine of information... indispensable to those who have occasion to use point-set topology." I don't think this book is intended to be a text (& I think the authors say so), in which case it would be terrible because it doesn't explain the concepts very much. It's mostly a catalogue of every kind of set you can come up with, every kind of topology you can put on it, and what properties it has such as what T_i axioms the space satisfies, whether it's compact, para compact, etc etc. Most of the time such things are proven, but be prepared to think hard sometimes about the proofs or fill in details. I'm the kind of student where I have trouble understanding things which are highly 'counter-intuitive' so I had trouble proving things, even when I knew definitions, when I did topology for the first time last term. Once I saw this book though I got used to all the weird things in topology (like the ordered square, R in the lower-limit topology, Sorgenfrey plane, etc etc). This book is incredibly useful as a reference.

Essential if you want to be good in point set topology
A distinct characteristic of point set topology is that it thrives on counterexamples. In fact, if you thumb through any point set topology text, almost all the theorems are in the form "If the space X is A,B,C, then the space is X,Y,Z". The point of point set topology is too determine what A,B,C are, and whether that is the minimal condition. "Can we take condition B out? Maybe hypothesis C can be weaken considerably?" How can we answer these questions? You're right, by counterexamples. Students who really wants to master point set topology should know the various counterexamples (no matter how contrived or unnatural they seem), and while textbooks usually present a counterexample to show why Theorem Three Point Five Oh will not work on weaker assumption -- most students (and teachers, too) tend to skip these parts. A collection of counterexamples presented in this book (excellent organisationm, by the way) is an essential supplement of a topology course, and it might make people 'see' through the whole thing.

a good book to combine with a regular textbook
This book has examples in it that are "missing", so to speak, from many regular topology books. It aims to shore up some of these shortcomings, with examples that the student can see and understand. There are charts and graphs, as well as a detailed explanation. Some "problems" often found in regular topology books are solved. Very few proofs, if any, are given. This is not a book meant to be studied without a regular textbook on topology, only to be used as an overall review of problems and short basic premises of topology. Use this in addition to your regular fare, but keep it close at hand when doing homework or preparing for an exam.
There are fundamentals on Cantor's Theorem, the countability or uncountability of sets, compactness, closed and bounded functions, open sets, continuity, connectedness, etc. All these are basic to topology, and this book does address them, but in a brief way. It then shows a basic overview of topology that helps greatly to understand the different fields of topology.

Great Book
As a graduate I encountered a book called "counter examples in analysis" which I found very useful. I always dreamed of such a book in topology, this book exceeds my dreams. It is great. It does not cover all the examples that I have used over the decades but it does cover some that I have never seen. The style is quite readable for a professional topologist. The book goes into a lot of interesting details (and some while not interesting to me would be another person). In short for me it is an essential book. The question is to whom else would this be interesting to. It is clearly of little use to a first year student and less to more advanced student. It's brand of topology is not the current cutting edge. So the audience for this book is limited to a small group and for these people it is top notch.

A book on Topolgy with a map
This book gave me an inspiration: it isn't the best written or the best organized, just one of the best topology books I've ever found! It gives you an idea of the areas of topology in a way that is very good and very understandable. ... Read more

Book Description

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions.A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear euqations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity.Highlights of the Handbook: ... Read more

Book Description

Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed.Ioan James is a professor at the Mathematical Institute, University of Oxford.He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford. ... Read more

Reviews (4)

Good book
This book is a collection of short biographies of notable mathematicians from Euler to von Neumann. It does a good job of explaining both a mathematicians background and the significance of their contributions to mathematics. Great to read through or as a reference to have on the shelf.

Very good historical account of lives
The only reason that this book doesn't get 5 stars is because of the fact that not enough emphasis is placed on the achievements of the mathematicians in terms of their mathematics.

However, this does not take away from the fact that is is exteremely well researched, laid out and presented. We get a meaningful insight into how these geniuses (genii?) lived and that fact that they were quite ordinary people with the same levels of hardship (and in some cases even more) as the rest of us. Perhaps an improvement could be made on further mathematicians, both past and present.

Still recommended reading.

Learn how mathematicians interacted with each other
When reading about the great ones of mathematics, I always enjoy short biographies rather than long ones. If the biographer is required to fill a large section of a book, then they tend to cover more detail than I really care for. While I do enjoy some details about the personal life of a mathematician, anything more than just a few morsels tends to detract from their accomplishments in mathematics.
James strikes the perfect balance in describing the lives of these great historical figures. Each biographical sketch is less than ten pages and he covers their life from birth to death. One valuable thing that he does is give their complete names, which is often omitted from biographies. In fact, despite all of my reading about the people of mathematics, there were some whose full names I had not known until I read this book.
The emphasis is on the lives of the people, and the general concepts of the mathematics that they created, rather than the specifics. No formulas are used in the explanations. Personal and professional interactions are a large part of the life of nearly all mathematicians, and from these biographies, we learn many of the specifics of how contemporaries reacted to each other. As is always the case, the full range of human foibles are displayed as the lives of the mathematicians unfold.
The lives of these sixty mathematicians are described in chronological order according to their birth years. Given that they all began their mathematically productive lives at different ages, this leads to some degree of overlap in both directions. Nevertheless, it is possible to easily trace the development of the major mathematical ideas as they are nurtured from early germs to towering oaks.
Mathematicians are people who find themselves in a social and political environment that they must cope with and sometimes just survive in. In this book, you will learn about sixty of them who made a major contribution, sometimes starting from a point of privilege, and other times only after great struggle. It is well worth reading for pleasure and can also be used as a resource for a course in mathematical history.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

Captivating!
Don't miss these captivating tales of the life and the times of mathematicians starting from the period of Tsar Peter the Great of Russia, and right up to recent times, at least up to and including the Cold War. Even if you aren't in math, I think you are likely to be caught up in the drama of the various lives, times, and events. The writing is fast paced and engaging, much like that of Constance Reid's books: "Hilbert", or "Courant"... Over the tumultous historical periods, it has been said that mathematicians have been more likely than others to have been uprooted in the upheavals of history, perhaps because they are concerned with theories and ideas that are more universal. But their lives are still much affected by the times and the events of history: The French Revolution(Galois, Poisson, Fourier...), the Napolionic Wars(Cauchy, Abel...), the period of Bismarck and Nationalism in Europe(Weierstrass, Cantor, Lie...), the Russian Revolution(Alexander, Kolmogorov...), the two World Wars, and the crisis period between WWI and WWII(Banach, Hadamard, Courant, Hilbert...), and the Cold War(von Neumann, Wiener...). The pictures on the cover give you a sample of the profiles in the book: G. Polya, K. Weierstrass, A. N. Kolmogorov, N. Wiener, S. Kovalevskaya, and S.-D. Poisson. Even if you won't get to meet them in person (I was a guest at George Polya's ninetieth birthday!), this book is the next best thing. ... Read more

Book Description

Math Review for Standardized Tests is designed specifically to review, refresh, reintroduce, diagnose, and give you a fighting chance by focusing squarely on a test-oriented math review.

This is the most unique math guide available today! It combines insights and strategies for problem types while reviewing the most needed basic skills: arithmetic, algebra, geometry, and word problems.

Each review section includes:

• A diagnostic test
• Rules and concepts with examples
• Practice problems
• Complete (understandable) explanations
• A review test
• A glossary

If you're planning on taking the *SAT, ACT, GRE, GMAT, *PSAT, CBEST, NTE, or any other standardized test, this book is designed for you!

*SAT and PSAT are registered trademarks of the College Board, which was not involved in the production of, and does not endorse this product. ... Read more

Reviews (12)

This book is a Math Bible!
This has to be one of the best books I have ever purchased! I love this book because it breaks down difficult concepts step by step so even "math dummies" can understand. This book is also a great review of concepts such as calculating percentages, and breaking down really hard word problems. It covers EVERYTHING! I have recommended this book to everyone I know. It gave me the knowledge and confidence to pass the math sections on the CBEST and MSAT. Parents, it is also a good resource to have for your children. As a teacher, I know that sometimes students don't understand a concept taught in school. This book can help.

Math Review Rocks!
This book is written so well it makes learning Math easy! I've been away from Math classes for 20+ years and suddenly my employer requires a degree. This book is an EXCELLENT supplement to my text books. My college math books are written by people who are trying to impress you by how smart THEY are. They make simple concepts very complicated. I would have had a rough start if it wasn't for Cliff's Math Review.

Easy Review and Learning
I had to study for the College Level Assesment test in FL, and I hadn't had a math class since my sophomore year in high school! This book was fantastic to sit down with and review things that nobody remembers (like fractions...eek!) and some of the things that I had never learned (like some of the algebra).

There is an assessment test at the beginning to show you what you most need to work on, and tells you on what page to find that information. There are also several practise tests, as well as pages that explain the problems, in detail, so that you can figure out what the heck you did wrong! :-)

This is a fantastic review session, and I would recommend it for the GMAT (studying for now) or any other standardised tests over ANY of the other books I had purchased!

Excellent Math Review
After being out of math for 6 years, reading this book made me wonder why I needed a year to complete an algebra class compared to the week that I spent reviewing this book.

Seriously though this is an excellent and straight to the point book. Excellent process of:

1. Test First
2. Review any problems you missed (points you right to the page you need)
3. Re-test
4. Re-review, etc..

This is not a book of just tests, it also contains a ton of well thought out teaching. Each section also contains practice problems and answers.

Quit reading my review and just go buy it!

Good Basic's
Yes this is a very clear and easy to understand math book. This book help me to move on to higher math problems. ... Read more

Book Description

"Mathematical Olympiad Challenges" is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals.

The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems.

Key features of this work include:

Problems clustered in three self-contained sectionsComplete solutions provided separatelyBackground material, representative examples, and beautiful diagrams to supplement each problem setMaterial successfully tested in classrooms as well as in national and international competitionsHistorical insights and asides presented to stimulate further inquiry

Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem-solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops. ... Read more

Reviews (5)

This book is amazing!
I remember the first time I touched this book, i fell so in love with it that it was very hard for me to remember how many other things I had to do during my day. It really illustrated how every problem you solve (or at least try really hard) can be an entire lesson you can use later on.
It is very well organized, even the problems in each section are set in a way that each one helps with the previous one in case a more creative solution doesn't show up...
I love this book, and I really recommend it for any student studying for any math contest around the world. It really helped me, and I'm sure it will do the exact same thing to anyone with the desire to spend countless hours solving beautiful math problems. Good luck, God bless you all :)
Pura vida.

Fantastic Book!
This is a marvelous book for lovers of mathematical problems. Scattered about are wonderful problems in Geometry, Trig, Algebra and Analysis, Invariants, and Number Theory. A truly delightful read that will have you working on some problems for hours. Each section introduces the reader to the concept or technique needed to solve the problems in each section. The problem sets start off with a few "warm-up" problems that quickly build up to some that require keen (some brilliant!) insight. A true gem among most problem books since this book is not merely a book of problems, but also contains clear presentations and introductions to various concepts in mathematics. The solutions are a true delight, the ingenuity and beauty of mathematical problem solving is captured exquisitely in this fabulous book. Highly Recommended. A++

Review for Mathematical Olympiad Challenges.
The book, Mathematical Olympiad Challenges", is a delightful book on problem solving written by two of the leaders of the craft. Mathematical problem solving is a skill that can be honed like any other and this book is an ideal tool for the job. Problem solving usually involves elementary mathematics; this does not mean "easy mathematics". An elementary mathematical problem is one that is easily stated and can be understood by anyone who has had basic training in the subject (up to calculus). The solution, though, may be quite hard and may require a great deal of ingenuity and thought.

It should be noted that being an exceptional problem solver does not necessarily make one a good mathematician, but it helps. This is certainly true of the second author who is also a renowned mathematician in the field of knot theory and three dimensional topology.

As mentioned the two authors have a sterling record in the arena of problem solving and in coaching would be problem solvers. I am more familiar with Razvan Gelca who led the University of Michigan team to a top five finish in the highly competitive and extremely challenging Putnam exam. This exam is administered yearly and is open to all college students in North America; usually around 430 universities and colleges send teams to compete in the Putnam. The exam has been offered since the thirties and finishing at the top carries a great deal of prestige. Razvan's superior abilities led to the spectacular success of the Michigan team which was no mean feat.

My own experience with the book has been one of revelation with each passing page. I used the book to teach the problem solving course at the University of Michigan, Ann Arbor, and it helped me immensely. The book possesses a variety of topics in elementary mathematics, ranging from algebra to geometry to trigonometry to number theory. Each chapter is divided into sections and each section has a theme. In keeping with the theme, the authors mention some useful formulae and/or facts that may be used in that section. This is followed by a demonstration of some dazzling problem solving techniques applied to a couple of problems. This is then followed by a list of challenging problems of varying levels of difficulty, all related to the theme of the section. There are roughly 18 such sections and many, many problems to think about. The rest of the book, which is the bulk of it, is dedicated to providing elegant solutions to every problem posed in the first part. Occasionally a problem merits more than one solution and sometimes the way is pointed to some interesting mathematics. The authors also acknowledge the source of many of the problems in the book which is a good indicator of the pedigree of the problem. Almost every solution is a gem and each problem demands its own style of solution. As noted earlier, problem solving is a skill and the authors try and succeed in conveying that idea in the problems and solutions they present.

Here is a sample problem from the book; if you can't do it and want to know how, check out the book:

"Show that any cube can be divided into 'n' cubes for any integer 'n' bigger than 54."

In summary if you are interested in figuring out puzzles, if you are a problem solver of elementary mathematical problems, or if you are just plain curious how a large fraction of mathematicians got hooked on mathematics, I would highly recommend you give this book a try. You may learn something and may even enjoy yourself in the process.

Pure delight!
I have spent many entertaining hours going through the book only to realize how rusty I became in these last 25 years that passed since I was faighting a hopeless battle in the Romanian solvers' contest against the first author.

The book is centered around a number of tools, tricks, techniques, as you want to name them, which are then used to solve a number of problems depending on them.

The problems are carefully arranged in increasing order of difficulty (maybe that's the reason I was able to solve some of the first entries!), so that the reader is not immediately discouraged by problems too hard to solve.

The actual selection of the problems clearly reflects the taste of the authors. Not a bad taste, I would say, if one notices that Titu Andreescu was the man behind the brilliant success of the USA olimpic team in 1994 (all whose members got then the maximum possible number of points).

I was one of the coaches of an olimpic team myself and I know how fast one goes through a list, I would say through *any* list of problems with these gifted guys. From this point of view, the book is an essential instrument for all who contemplate being involved in problem solving training.

But the book is a good teaching tool for high school teachers who wish to challenge their best students with more interesting problems. As another potential pool of customers, I would say that those old sea wolfs as myself, who get bored from time to time of the technicalities of professional maths will find this book a nice companion.

Yes, I like this book and I warmly recommend it to all lovers of problem solving.

Can I write in Portuguese ?
Este é o melhor livro que já vi sobre olimpíadas de matématica, comparando-se com o Winning Solutions e Problems Solving Strategies que também são vendidos pela Amazon.com, que é sem dúvida a maior e melhor livraria do mundo. Este livro cita vários problemas conhecidos de importantes olimpíadas como IMO e ASIAN PACIFIC além de outras, além de abordar interessantes técnicas de como resolver problemas como substituição de variáveis trigonométricas. Pode ser considerado realmente um incomparável e imperdível livro que todos os alunos e professores de olimpíada de matemática deveriam ter... É realmente um tesouro matemático ! ... Read more

Book Description

This book focuses on the technology of D-branes in Superstring and M-theory, presenting the main ideas and recent discoveries in a pedagogical manner. It will serve as an introduction to welcome and guide newcomers to this exciting field, and an indispensible reference for seasoned practitioners. The book starts by introducing the key features of string theory and the theoretical tools needed to get to grips with D-branes. It then builds up the subject in a logical way, discussing further aspects of string theory and advanced applications as the text progresses. ... Read more

Reviews (5)

Great book... once all the errors are corrected.
While it provides a (in some sense) self-contained introduction to string theory, it is no secret that this was not the intended focus of this text (as indicated even by its title), so prior knowledge of string theory would be highly beneficial. It does however provide a novel viewpoint from which it introduces string theory, and it is so far the best/only text on D-Branes, which is a subject that has become vitally entangled with string theory, so it is worth reading for anyone in the field.

Unfortunately, the deal-breaker is that there are many non-trivial errors throughout the text, which makes it difficult to be sure you understand what you think you are learning. A positive outlook comes from the fact that the author has an errata webpage where errors are being collected, so maybe there will be a future printing with most errors corrected that would deserve 4 or 5 stars.

A very good introduction
I haven't read this book in any great detail, but I have read certain sections of it, and leafed through the entire content. I think this is a very good introduction to certain aspects of string theory with an emphasis on D-branes. There is no way that any single textbook can cover the entire theory, starting from the oscillator formalism, and all the way to the most recent developments. The subject is simply too enormous for that.

This book is a highly commendable effort by the author. We need more such books.

Really Useful!
This is the book I was waiting for. I know some string theory before, and this got me back into it fast, and then on to D-branes and supergravity and things like that. String duality and D-brane black holes is what I wanted to know more about and it is introduce and explained just great! And there is lots of discussion and other explanation of many other topics. The book is good at connecting many topics together in a useful way.

An great introduction to the subject
...If you want an intoduction to string theory, sure you should start with G,S & W or Polchinski. However, D-branes are hardly covered in these texts and I found this book a great entry point for this subject. How are you going to learn about AdS/CFT, black holes, F-theory etc by sticking to those other books?

Superficial
Stick to Polchinski, and Green, Schwarz, Witten. Books written by authors that actually have a grasp of the subject. ... Read more

Book Description

An up-to-date analysis of the SAR wavefront reconstruction signal theory and its digital implementation With the advent of fast computing and digital information processing techniques, synthetic aperture radar (SAR) technology has become both more powerful and more accurate. Synthetic Aperture Radar Signal Processing with MATLAB Algorithms addresses these recent developments, providing a complete, up-to-date analysis of SAR and its associated digital signal processing algorithms. This book introduces the wavefront reconstruction signal theory that underlies the best SAR imaging methods and provides clear guidelines to system design, implementation, and applications in diverse areas-from airborne reconnaissance to topographic imaging of ocean floors to surveillance and air traffic control to medical imaging techniques, and numerous others. Enabling professionals in radar signal and image processing to use synthetic aperture technology to its fullest potential, this work:
* Includes M-files to supplement this book that can be retrieved from The MathWorks anonymous FTP server at ftp://ftp.mathworks.com/pub/books/soumekh
* Provides practical examples and results from real SAR, ISAR, and CSAR databases
* Outlines unique properties of the SAR signal that cannot be found in other information processing systems
* Examines spotlight SAR, stripmap SAR, circular SAR, and monopulse SAR modalities
* Discusses classical SAR processing issues such as motion compensation and radar calibration ... Read more

Book Description

With the same user-friendly, quirky, and perceptive approach that made Innumeracy a bestseller, John Allen Paulos travels though the pages of the daily newspaper showing how math and numbers are a key element in many of the articles we read every day.From the Senate, SATs, and sex, to crime, celebrities, and cults, he takes stories that may not seem to involve mathematics at all and demonstrates how a lack of mathematical knowledge can hinder our understanding of them. ... Read more

Reviews (22)

All the Quantification That's Fit to Print
I found Professor Paulos's book, Innumeracy, to be a delightful expression of the key elements of mathematical ignorance that can be harmful, along with many new ways to see and think about the world around. You can imagine how much more pleased I was to find that A Mathematician Reads the Newspaper is an improvement over that valuable book. Every editor and newspaper writer should be required to read and apply this book before beginning their careers. Almost all those who love the news will find some new appreciation for how it could be better reported. Those who will benefit most are those with the least amount of background in math, logic and psychology. Although the subjects are often related to math, if you can multiple two numbers together using a calculator you will probably understand almost all of the sections. If you already know math well, this book will probably only provide amusement in isolated examples and you may not find it has enough new to really educate you. Most of the points are regularly treated in the mathematics literature.

In the introduction, Professor Paulos reveals a long and abiding love for newspapers. And he reads a lot of them. He subscribes to the Philadelphia Inquirer and the New York Times, skims the Wall Street Journal and the Philadelphia Daily News, and occasionally looks at USA Today (he likes weather maps in color on occasion), the Washington Post, the suburban Ambler Gazette, the Bar Harbor Times, the local paper of any city he is in, and the tabloids.

This knowledge is reflected in the book's structure. There are four sections, reflecting the typical four section format of many weekday papers. The four sections are:

(1) Politics, Economics and the Nation

(2) Local, Business and Social Issues

(3) Lifestyle, Spin and Soft News

(4) Science, Medicine and the Environment

Then, within each section, he uses a headline and subtitle for each subsection to capture the essence of a story type that we have all read lots of. For example, "Lani 'Quota Queen' Guinier: Voting, Power, and Mathematics" is the subsection that looks at how different ways of compiling votes would affect the power of individual interest groups and minorities. "SAT Top Quartile Score Declines: Correlation, Prediction and Improvement" examines all of those many stories we read about the SAT and what they really mean. Each subsection tends to run from 2-5 pages. As a result, this book can be read in 10 minute intervals very comfortably. In that sense, it's an ideal book for commuters who've finished reading their daily paper and still have more time on their hands.

This book covers many of the same topics as Innumeracy. I suggest that if you feel you really understand that subject that you skip the relevant subsection here unless you find the treatment amusing in its opening lines. Professor Paulos tends to repeat examples from Innumeracy and while that makes the book easier to understand, the repetition can dull your interest.

I found the book to be most appealing when it pointed out the fundamental absurdity of some approach that is commonly used now. One of the most powerful examples involved pointing out that putting one pint of toxic material into the ocean would create a frequency of molecules in the entire ocean that would sound scary to anyone, even though the material would be extremely dilute. Naturally, as an author, I was in complete agreement with his point about the too infrequent reviewing of new books (except on Amazon.com, of course!). My mind was also expanded by the problem of whether Moslems should pray towards Mecca straight through the Earth or as though they were traveling over the top of the Earth.

You probably won't agree with all of his solutions . . . or even think that all of the problems he cites are important ones. But you'll find yourself amused and informed more often than not. That's better than you can expect from all but a tiny fraction of nonfiction books. Take a peek at "Recession Forecast If Steps Not Taken" as a test of your potential interest in the book. This subsection explores chaos theory and why it's not possible to forecast accurately all of the things that people regularly claim to forecast (such as the weather, the economy and many social trends).

After you finish the book, I suggest that you pick out a newspaper article that falls into some of these errors . . . and write a letter to the editor suggesting how it could have been improved. If we all did that even once a year, newspaper reporting would soon improve and we would all be better informed.

Intriguing and entertaining - a perfect "commuting" book.
Althought it took a few chapters to get in to the groove of the book, "A Mathematician Reads the Newspaper" quickly drew my interest. Although some topics are repetitive, and at times you wonder what the point is, in essence the author does a good job at teaching us how to understand what we read. Broken down in short (2-3 page) chapters, this book is ideal for people who need something to read for 5-10 minutes - although it is just as rewarding in a longer-term reading session. The use of complex math is limited, and he explains things well - although some may have to re-read his mathematical and logical points to fully understand them. Overall, for people intrigued with logic, mathematics, or understanding how people perceive the world, it's a worthy read.

Disappointed
The book is dedicated "To storytelling number-crunchers and number-crunching storytellers," and I consider myself in this group. However, the book is written for those who are not really familiar with statistics and number crunching. Some interesting topics and stories, but no Aha's.

An excellent book
Well worth the read. It's not preachy like Innumeracy, it entertainingly goes through the ways that news sources screw up their numbers.

A mixed bag
This book had a few good examples of how numbers are used and abused in the media. The book was genenrally good when it kept its discussion to narrowly defined cases (the contamination of a pollutant in the water, e.g.). However, the discussion of the broader issues, especially any topic to do with ethics, came across as astoundingly naive and uncritical its hidden assumptions. Much as the author would like to believe, not every problem is quantifiable, at least not in the simplistic way done here. Read this book if you want to see a reason why mathematicians do not hold all the answers. ... Read more

Book Description

The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences.The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory.The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will beavailable on an accompanying website in both Fortran and C++. ... Read more

Reviews (4)

misprint and misleading!!
There are lots of misleading in Ch. 3. - Specific error formulas. See the original Bevington's 1st ed., and compare the formulas. I think this misleading should be corrected. Standard deviation is ALWAYS positive!!..

Great Book
I make measurements frequently and this book is great for providing the background to analyze your data.

I took undergraduate level statistics and it never really gave the practical applied background in how to analyze data. It merely presented concepts and presumed you knew how and why to apply them. This book is very good at helping you to understand the how and why.

I have read a number of other statistics book in search of the practical applied information provided in this book and did not find it in the other books.

The writing is clear and consice. There is enough background provided for even those unexposed to statistics.

I have not tried the software. Most of the formulas are easy to apply and can be implemented in simple programs or spreadsheets in very little time.

In short, I recommend this book to anyone making measurements of any kind.

"Updated" classic, but still vintage '92
Robinson's second edition continues the late Bevington's tradition of clear and concise writing, making this book a priceless reference for scientists. Robinson has added discussions of modern problems such as resolving closely-spaced peaks in a spectrum. The new version also adds chapters on Monte Carlo techniques and maximum-likelihood analysis, both powerful tools for data analysis made possible by better computers.

The chapter structure has been modified considerably, so those who have grown comfortable with the first edition over the past decades may not be able to find things as easily. Other than that, most of the weaknesses are computer-related. Much has changed even since 1992.

Robinson added an appendix on graphical presentation. This sounds promising but is a pretty trivial discussion of when to use linear or logarithmic axes and the advantages of a historgram. Might be useful for a very young student, but these days playing with such things is easy in any graphing program.

Many of the computer code snippets have been removed. Most of them were only a few lines of code with lots of comment lines anyway. The codes that remain have been moved from the main text to a densely-packed appendix, which makes them more difficult to study while reading the text.

The codes themselves have been updated from old FORTRAN to a structured language, but I would have preferred C or FORTRAN 90 over the chosen PASCAL. The latter may be useful for undergraduate students, but I've never seen a PASCAL compiler in a working physics lab.

The included disk is a now-obsolete 5.25" floppy. I had to hunt for a machine that could read it and copy over to a 3.5" disc. The text claims repeatedly that the disc has both FORTRAN 77 and PASCAL routines on it, but my copy only has the PASCAL.

In the end, it's the textual content that is important, and this book is a fantastic basic discussion of data analysis and statistics for students and a great reference for the practicing scientist.

A classic returned!
Bevington's first edition of this book dates to the late 60's when Fortran ruled the world. I was crushed when I lost my copy in the mid 70's and am delighted to find he's written a modern updated edition! ... Read more

Book Description

With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica. ... Read more

Book Description

Hardbound. This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include:

Historical outline

Curve and surface methods

Scientific Visualization

Implicit methods

Reverse engineering.

This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject. ... Read more

Book Description

The field of digital computer architecture has grown explosively in the past two decades. Through a steady stream of experimental research, tool-building efforts, and theoretical studies, the design of an instruction-set architecture has been transformed into one of the most quantitative branches of computer technology. However, this explosive growth has led to unprecedented harware complexity and almost intolerable development costs. The challenge faxing current and future computer designers is to institute simplicity where we now have complexity; to use fundamental theories being developed in this area to gain performance and ease-of-use benefits from simpler circuits; to understand the interplay between technological capabilities/limitations and sound architectural decisions. Computer arithmetic plays a key role in the computer designers' quest for user-friendliness, compactness, simplicity, high performance, low cost, and low power. Parhami's Computer Architecture emphasizes both the underlying theory and actual hardware designs. and links computer arithmetic to other subfields of computing. It is the first computer arithmetic book to cover all topics important for a balanced and complete view of the field ... Read more

Reviews (5)

Very superficial look at computer arithmetic
Although the author does a good job at explaining arithmetic in the areas of RNS and SD arithmetic, the other topics are done very superficially. The book is a good reference, but you can find better books on understanding computer arithmetic.

The WORST book there is!
I think 2 stars rating for this book are more than it deserves.
I've bought many technical books and learned them on my own but
I've never seen a book that is so bad. Having this as class text
book and coupling with a not so good instructor, you really gets
it coming. PLEASE, STAY AWAY FROM THIS BOOK!
there many good books on this subject out there, don't torture
yourself and waste money on this terrible book. The bottom line is, the
author tries to make subjects more complicated than they
really are.

An excellent book for the ASIC architect.
I found this book to be extremely helpful in my every-day work. No where else have I found such a concise and accurate description of hardware-friendly number systems and arithmetic algorithms. It's the first place I go when I have a an arithmetic-intensive algorithm to architect. Simply put, my designs got better after I got this book.

Overly complex and not many examples of material
Not a very good book in my opinion, I will admit I am just getting started into it but even in the number representation chapters he takes very simple material and makes it very complicated. Radix number representation is not complex but if I was trying to learn from this book I would be very intimidated. (and for the review complimenting the circles explaining 1 and 2's compliment, those aren't some original idea those circles are in pretty much every explanation of the topic) Needless to say I am somewhat scared of whats ahead, if the author has made simple material like number representation complex, I can't imagine how more complex material will be covered. -And my big point is that very few examples are given in the book. And then ( the cardinal sin of engineering/science books) complex questions are asked in the book with no real reference in the material. This book was most likely put together from lecture notes and if I had a professor on hand to answer questions that would be okay, but as far as I know they run for over 50K a year and I can't afford that. Avoid

-forgive my bad spelling I was in a hurry

One good book
Excellent book if you want to get into DETAILS of computer arithmetic and its hardware implementation.

The lecture style is great as it becomes easy to take breaks in between. It also makes the text very modular, allowing you to choose and read.

It has plenty of diagrams making the text very readable. I like the circle diagrams that the author has used to show the number representation system. ... Read more

Book Description

This book provides an overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. A unified model-building strategy for both linear and nonlinear models is presented and applied to the