Book Description

An appropriate supplement for any undergraduate and graduate course in physics, Mathematica® for Physics uses the power of Mathematica®to visualize and display physics concepts and generate numerical and graphical solutions to physics problems. Throughout the book, the complexity of both physics and Mathematica® is systematically extended to broaden the range of problems that can be solved. ... Read more

Book Description

The concept of nonparametric smoothing is a central idea in statistics that aims to simultaneously estimate and modes the underlying structure. The book considers high dimensional objects, as density functions and regression. The semiparametric modeling technique compromises the two aims, flexibility and simplicity of statistical procedures, by introducing partial parametric components. These components allow to match structural conditions like e.g. linearity in some variables and may be used to model the influence of discrete variables.

The aim of this monograph is to present the statistical and mathematical principles of smoothing with a focus on applicable techniques. The necessary mathematical treatment is easily understandable and a wide variety of interactive smoothing examples are given.

The book does naturally split into two parts: Nonparametric models (histogram, kernel density estimation, nonparametric regression) and semiparametric models (generalized regression, single index models, generalized partial linear models, additive and generalized additive models). The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers.

The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity. ... Read more

Book Description

Academic life in Cambridge especially in Trinity College is viewed through the eyes of one of its greatest figures. Most of Professor Littlewood's earlier work is presented along with a wealth of new material. ... Read more

Reviews (2)

Gaiety of genius MIGHT be an understatement
Littlewood is the kind of historical scientific figure people look up to, not only because of his legacy in mathematical research but also for his towering intellectual reputation. I (shamelessly) admit here that I've read and reread this book so many times, each time picking up some nuances and details that Littlewood subtly convey between his lines. It is a glimpse into the mind of a genius. His style of writing is not out-of-fashion even many years after he put it on paper, probably in between replying to math letters from Hardy, and proving a theorem in analysis. Miscellany is nothing short than the last century's most incredible mathematical essay.

A celebration of the excitement and joy of doing mathematics
There has been a flood of recent books detailing the agony and even the mental illness of mathematicians. This book is a rare and refreshing exception. A collection of the popular writings of J. E. Littlewood, a leading mathematician of the twentieth century, it demonstrates and celebrates the intellectual excitement and even the joy of doing creative mathematics. ... Read more

Book Description

Mathematicians, scientists, engineers, and students can turn to this dictionary for definitive coverage of all branches of mathematics, both pure and applied. Featuring 3,600 terms, the book defines terms and expressions in algebra, number theory, operator theory, logic, complex numbers, finite mathematics, topology, and other areas--each with definition identified by the field in which it is primarily used. Included are numerous cross references and an appendix with tables of integrals and derivatives. ... Read more

Book Description

From algebra to number theory, statistics to mechanics, this versatile and completelyupdated reference takes in all branches of pure and applied mathematics. Featuresinclude:
• More than 3,200 cross-referenced entries, supported by dozens ofexplanatory diagrams
• Expanded, up-to-date sections on such topics as chaos, fractals,and graph theory
• Biographies of more than 200 key figures in mathematics
• Comprehensive coverage of subjects taught in both high schooland college ... Read more

Reviews (2)

Handy reference
This book is useful for anyone doing maths at college. It summarizes just about everything and is good as a quick reference to refresh your memory on something. (It is also fun just to page through, and look at all the wierd things that mathematicians have come up with). Another advantage is that if you are studying a section in maths that you are finding a little confusing or hard to grasp, the entry in this dictionary will give the important points. But don't expect too much detail, which I think is the main drawback of the book.

Really, really helpful!
Anybody who regularly does math on a more-or-less advanced level will delight in this book; it is exhaustive but managable (the size of a common pocket novel, really) and quite concise. Buyers should realize, of course, that books like these are not meant to learn you calculus or whatever; instead, it is more of a helpful hand when you need it. Now, what was that formula for partial integration, again...? ... Read more

Book Description

The Oxford User's Guide to Mathematics in Science and Engineering represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. This is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics.The book offers a broad modern picture of mathematics starting from basic material up to more advanced topics. It emphasizes the relations between the different branches of mathematics and the applications of mathematics in engineering and the natural sciences. The book addresses students in engineering, mathematics, computer science, natural sciences, high-school teachers, as well as a broad spectrum of practitioners in industry and professional researchers. A comprehensive table at the end of the handbook embeds the history of mathematics into the history of human culture. The bibliography represents a comprehensive collection of the contemporary standard literature in the main fields of mathematics. ... Read more

Book Description

Praise for Five Golden Rules

"Casti is one of the great science writers of the 1990s. . . . If you'd like to have fun while giving your brain a first-class workout, then check this book out."—Keay Davidson in the San Francisco Examiner.

"Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." —Christian Science Monitor.

"Merely knowing about the existence of some of these golden rules may spark new, interesting—maybe revolutionary—ideas in your mind." —Robert Matthews in New Scientist (United Kingdom).

"This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." —Ben Bova in the Hartford Courant

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." —Rudy Rucker, author of The Fourth Dimension.

"With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." —John Allen Paulos, author of A Mathematician Reads the Newspaper. ... Read more

Reviews (9)

Good Reading
This is a good book for those that have a degree of mathematical curiousity. Not necessarily expertise, just a decent interest in it.

The reading is easy. The presentation is great, as I have come to expect from the publisher (Wiley).

The content is very good. Note that these are from applied mathematics rather than pure mathematics. The author also makes this clear in the preface. This is an approach that I (sometimes) prefer, but just be forewarned that it is not the best of both worlds. Each topic is well explained and has many modern-day examples (e.g., Cuban Missile Crisis) worked into the text, making it all the more interesting.

Good reading and recommended.

Examples of the value of mathematics
Mathematics is a discipline that has an essential niche in modern society. From the early days of civilization where the plotting of fields for taxation required geometry to the modern international interconnection of computers, mathematics has been essential. People also constantly bet their lives on the accuracy of mathematical models. When we climb into an airplane, we are entrusting our lives to the accuracy of the mathematical models used to design that plane. And yet hardly a day goes by in the life of this reviewer without someone commenting in some way on the limited worth of mathematics. A combination of fear, insecurity and uncertainly lead to common misconceptions concerning the value of mathematics. All mathematicians have a professional duty to counter these problems any way they can. In doing this, we are not just engaging in activities to boost our job security, but in every real sense helping to insure the survival of civilization as we know it.
In this book, Casti chooses five of the most significant modern developments in mathematics and gives detailed explanations as to why they make a difference in our lives. The topics are:

1. The Maximum Theorem of Game Theory.
2. The Brouwer Fixed-Point Theorem of Topology.
3. Morse's Theorem of Singularity Theory.
4. The Halting Problem of Computer Science.
5. The Simplex Method of Optimization Theory.

Targeted at the general reader, formulas and theorems are kept to a minimum. Applications, some literally life and death, are used to emphasize the value of these concepts. As someone who experienced the apparent irrationality of the Cuban Missile Crisis of 1962, it is comforting to see it reduced to a simple "game" matrix.
With this volume, Casti has done more than his share of the professional duty of mathematicians. It is one more brick to be used in the construction of a mathematics that is cherished by all people.

Published in Journal of Recreational Mathematics, reprinted with permission.

defective
My problem with this book lies not with the writing, but with the printing: missing fifty pages, the book repeats the first quarto. Happily, the publisher graciously sent me a new copy, but prospective readers should be forwarned.

wonderful coverage of important temporary mathematics
Casti writes about 20th Century mathematics for general audiences. As he states, he uses five mathematical theorems that were proven in the 20th Century and shows how they relate to general theory and application. He gives a reasonable set of criteria to show the reader how these five theorems emerge out of the millions of theorems that mathematicians have proven in the mathematical literature of the 20th Century.

He also explains why all the theorems were developed in the first half of the century. Basically, it takes time for the impact and value of a theorem to take effect. While there may be many theorems developed in the later half of the century that will eventually prove to be more valuable than some of the five golden rules, we may not know this clearly for some time.

There seems to be a preference for theorems related to operations research. For example the Brouwer fixed point theorem from topology has applications to game theory. Von Neumann's minimax theorem was developed for game theory and its application to military strategy and economic problems. This one also falls into the realm of operations research. Finally Dantzig's simplex method provides an algorithm to solve linear programming problems and some extensions. This is also clearly in the realm of optimization problems in operations research.

Turing's halting theorem is also presented. This deals with important questions about the limitation of computing machines as it relates to mimicking human intelligence.

Many of the ideas are difficult to present in lay terms and there is a lot of development to try to make the theory understandable to the reader. But it is difficult to do these subjects justice. Casti's emphasis is clearly in applied mathematics and he excels at showing the impact of the results on our society.

Understandable but not dumbed down
Casti's text focuses on five key mathematical theories from the 20th century; this is actually somewhat misleading, since 4 of them are actually proved theorems. It's an interesting survey of applied mathematics; a number of sub-disciplines are covered here.

He does an excellent job of bringing the math down to a reasonable level without dumbing it down. Most of the book can be understood with simple logic and algebra; truly understanding a few of the theorems (not just appreciating them) does take a little calculus. Knowing some more advanced math (like topology) helps, but a reasonably mathematically-inclined person with less formal education will be able to follow it just fine. I'd like to see more popular math books at this level; this is somewhere between the level of Paulos' series of books ("Innumeracy" et al) and an undergrad maths textbook.

It's interesting to see a side of mathematics not often covered in high school maths courses. I really recommend this book to anyone with more than a passing interest in mathematics; it may even rejuvenate your interest to a more active level. ... Read more

Reviews (2)

dandy book
This a very helpful book. I know a home-skooler wacko who distrusts government but trusts this volume enough it is the main textbook in maths for her 6 year old. I claim responsibility for introducing wacko and her treble wacko hubby to his book ... desperation, the kid is not going to be engineer material [but I can hope] but I am trying to save him from a life of flipping hamburgers.
That written, much of this book covers what was called 'practical math' ... really useful stuff not 'rocket science' stuff culled from an MIT blackboard.
This book not only well written and understandable it is totally without the sick 'humor' which seems to be in style in maths books.

For those who need to brush up their math ....
Many of us forget math concepts we were introduced to at school. For a quick brush up, this is a good reference book. Fractions, decimals, percents, arithmetic concepts, elementary algebra, trigonometry and other such items are all covered. Besides, in keeping with its title of "everyday math," the book also goes into such things are interest rates, IRA and 410(k) math, stocks, mortgages, basic book-keeping and even casino gambling! The occasional anecdote or story pertaining to math (one was on the titles of alcohol measures such as jeroboams and rehoboams, another on the Father of Algebra) give welcome breaks from the technical text. ... Read more

Book Description

The goal of this book is to show students how mathematicians think and to glimpse some of the fascinating things they think about.Bond and Keane develop students' ability to do abstract mathematics by teaching the form of mathematics in the context of real and elementary mathematics.Students learn the fundamentals of mathematical logic; how to read and understand definitions, theorems, and proofs; and how to assimilate abstract ideas and communicate them in written form.Students will learn to write mathematical proofs coherently and correctly. ... Read more

Book Description

This volume is a collection of writing projects suitable in a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations.The projects vary in their level of difficulty and in the mathematics that they require, but are similar in the mode of presentation and use of applications.Students see these problems as real in a way that textbooks problems are not, even though many of the characters involved (dime–store detectives and CEOs) are obviously fictional.The stories are sometimes fanciful and sometimes grounded in standard scientific applications, but the mere existence of the story draws the students in and makes the problem relevant.

The book is the combined effort of four instructors who have used writing projects in their own courses.They provide an easy-to-use, widely applicable set of course materials that instructors can adopt andadapt to their own courses.

An extensive set of class-tested projects is included along with:

•implementation notes which highlight student difficulties,
•information about project solutions, and
•advice for grading writing projects. ... Read more

Book Description

Mathematics Handbook for Science and Engineering is a comprehensive handbook for scientists, engineers, teachers and students at universities. The book presents in a lucid and accessible form classical areas of mathematics like algebra, geometry and analysis and also areas of currents interest like discrete mathematics, probability, statistics, optimization, computer science and numerical analysis. It concentrates on definitions, results, formulas, graphs and tables and emphazises concepts and methods with applications in technology and science. ... Read more

Reviews (2)

Excellent Engineering Math Reference
This book has everything (geometry, trig, linear algebra, diff eq, calculus, ...) in a cleanly laid out format. Many figures are provided to clarify definitions. The presentation is clear and concise - usually I do not need to consult another reference for additional details. Out of my math/mechanical engineering book collection, this is probably my favorite book.

Strong Recommend Mathematical Handbook for Science and Eng.
Handbook of Mathematics" contains the fundamental knowledge for Science and Engineer students. I am using the third edition a lot when I do the algorithm performance analysis. Also the nice and big printing style is enjoyable to read. It contains anything which a computer programmer need to know. ... Read more

Book Description

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form.

This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work. ... Read more

Reviews (3)

provides insight into how mathematicians think
To most people, "philosophy of mathematics" probably sounds like the driest subject in the world. I admit that a typical person in the street would probably never want to read this book, but many people who would be put off by the title would find it fascinating.

The basic question is how we should think about mathematics. When we do mathematics, are we describing an independent reality, following arbitrary rules, building a social construct? One can ultimately say only so much about this particular question, but it leads off in many wonderful directions. To me, the highlight of this book is the article by Thurston, which provides a beautiful description of how mathematicians actually think about and do mathematics. It really rings true to me (I'm a mathematician too), and is much better than any other account I've ever seen.

In general, whenever people seriously discuss the philosophy of mathematics, they are likely to make revealing comments about their approach to the field. People who are curious about this (e.g., students considering studying mathematics, or anyone who has heard about the results of mathematics and wonders about the mindset behind them) should read the book. As a bonus, once they start reading the essays they'll rapidly start caring about the philosophical issues as well, even if they've never thought about them before.

Philosophy of mathematics reconsidered
After almost a century in which the attempt was made to reduce philosophy of mathematics to set theory, philosophers have begun to reconsider the traditional approaches. The Tymoczko volume provides a solid intro to these new approaches, that is both readable and insightful. A background in formal logic, or traditional philosophy of mathematics, is not presupposed, as there are basic essays that should get the reader up to speed on the terminology. Nor does one have to be a mathematician to appreciate the thoughts presented. At the same time, I don't believe any mathematician would be offended or alarmed by the presentations of this book.

Ultimately, there is no final consensus offered. Rather, the topic is reinvigorated with a collection of fresh approaches that do not falsify the experience of mathematics by trying to reduce it to something else.

I suggest a closely related book
Hi, I'm one of the contributors to Tymoczko's anthology, and I would like to suggest a related book on the quasi-empirical view of mathematics. That's my book "The Limits of Mathematics" just published by Springer Verlag. Together these two books make a nice set. Greg Chaitin, IBM Research ... Read more

Book Description

This is a calculations book aimed at working electricians and those attempting to pass the Electrician’s Exam. Like nothing currently on the market, this manual details and annotates key calculations electricians use in the field. Electricians can either learn the underpinnings of the calculation or simply “plub and chug” their way through the problem. A final chapter provides the basics of the algebra and trigonometry used throughout the book, and a wealth of self-tests are also included. ... Read more

Book Description

This step-by-step teaching program offers students the opportunity to master math facts without fingers. It has been used successfully with students learning math facts for the first time as well as those students who need remedial work or have special needs. ... Read more

Reviews (2)

It is OK. But find another book if you can.
I bought this book based on the first review. I found the book not so great. It showed some tricks. But I know more tricks than what the book has shown--I am just an average science major with no teaching or math degree on my belt.

The 3x5 card approach does not seem very smart, either. I don't see how it is better than "practice,practice, practice". There must be a better way for teaching kids math. Does anybody have any suggetions of a better math-teaching book?

Excellent resource for teachers and parents
This is a very helpful book to teach math facts, especially for those students who find it difficult to memorize basic facts. There are lots of neat tricks to share with students to make math fun and successful. I recommend this book for parents and teachers of third and second graders. ... Read more

Book Description

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere--in science, art, history, and our everyday lives.

Here is some of what you'll find in this volume:

Mathematics and Science
Mathematical biology: Mathematics was key to cracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code.

Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology's most fundamental questions: What is the size and shape of the universe?

Mathematics and Everyday Life
Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them!

Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks.

Elegance in Mathematics
Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments in the elegant world of elliptic curves and modular functions.

The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems.

These are just some of the topics of current interest that are covered in this latest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers. ... Read more

Book Description

Students throughout the world fear and dread solving word problems. As students reading skills have declined, so have their abilities to solve word problems. This book offers solutions to the most standard and non-standard word problems available. It follows the suggestions of the National Council of Teachers of Mathematics (NCTM) and incorporates the types of problems usually found on standardized math tests (PSAT, SAT, and others). ... Read more

Book Description

Shift register sequences are used in a broad range of applications,particularly in random number generation, multiple access and pollingtechniques, secure and privacy communication systems, error detecting andcorrecting codes, and synchronization pattern generation, as well as in moderncryptographic systems. The first edition of Shift Register Sequences, publishedin 1967, has been for many years the definitive work on this subject. In therevised edition, Dr. Golomb has added valuable supplemental material. Therevised Edition contains a comprehensive bibliography of some 400 entries whichcover the literature concerning the theory and applications of shift registersequences. Written in a clear and lucid style, Dr. Golomb's approach iscompletely mathematical with rigorous proofs of all assertions. The proofs,however, may be omitted without loss of continuity by the reader who isinterested only in results. Dr. Golomb is considered one of the foremost expertsin the world with respect to combinatorial and geometrical aspects of codedcommunications. ... Read more