Book Description

Master Math: Geometry was written for students, teachers, tutors, and parents, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and pertinent examples. It provides everything a high school or first year college student needs to know about Geometry including: explanation of deductive reasoning, how to perform proofs, definitions, theorems, and postulates.It includes explanations of deductive reasoning, examples pertaining to points, lines, plans, angles, and ratios, coverage on triangles, quadrilaterals, polygons, and much more! ... Read more

Book Description

Ross Honsberger has done it again. He has brought together another wonderful collection of elementary mathematical problems and their solutions abounding in striking surprises and brilliant ideas that reflect the beauty of mathematics. Many of these problems come from mathematical journals. Others come from various mathematical competitions such as the Tournament of the Towns, the Balkan Olympiad, the American Invitational Mathematics Exam, and the Putnam exam. And, of course, there is a problem suggested by Paul Erdös. This book is ideal for students, teachers and anyone interested in recreational mathematics. ... Read more

Book Description

"An original and courageous book, capable of conveying to a new audience the understanding that mathematical formulas can be exciting and aesthetically pleasing." —The Times Higher Education Supplement

This book acquaints (or reacquaints) you with the beauty of mathematics and the pleasures of playing with numbers. As entertaining as it is practical, it maintains a level of sophistication consistently high enough to make intelligent people think, but never aims so high that it is difficult to follow. Accompanying the formulas are over 70 amusing cartoons and diverting stories that point up how everyday events can lead to fundamental mathematical insights.

Contains 49 short, thoroughly entertaining chapters written in simple, clear language

• Proves that math is fun, functional, and accessible —not an arcane science reserved for specialists

Reviews (4)

Revelation
If, like me, you were a complete klutz at math, this book is for you. I wouldn't dream of reviling it for not being complex enough. It's attractively presented, comprehensible, and fills a need.

A book for CHILDREN, not for adults!!!
Don't be fooled by the title of this book. Yes, the book presents most of the important formulas, like Euler's eternal formula e to the power of i x pi plus one equal to zero. But that is it. There is no mathematical deduction or any related calculations . All that contained are cartoon pictures. So I would have two ratings for that book, for children, 5 stars, as this book can stimulate them to pursue mathematics further. One star for adult ( no zero ), so I give this book 3 stars on average!!!!

Beauty + Simplicity
Great book. It combines the simplicity of "where to find this formula in daily life", with comics, and a mathematical explanation. Like a gardener story to explain logarithms; or a history of 18th century to explain fractional numbers. It is an excellent gift to make that a kid love the simplicity of mathematics.
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Un gran libro. Combina la simplicidad de "donde encontrar la f-rmula en la vida diaria", con comics y explicaciones matem‡ticas. Como la historia de un jardinero para explicar logaritmos; o una historia del siglo 18 para explicar numeros fraccionales. Es un regalo excelente para hacer que un ni-o ame la simplicidad de las matem‡ticas.

Excellent and whimsical look at the history of math
This is a wonderful book detailing some of the most important, and beautiful, discoveries in the history of mathematics. Each little story explains briefly, clearly, and simply everything from complex numbers to the Pythagorean Theorem. Brought to life through a light-hearted writing style the equations are made fun and interesting. Comical characters and perfectly eccentric illustrations accompany and enliven the text and give birth to humor in mathematics. Lionel Salem's writing, his daughter Coralie's illustrations, and the wonderful premise of the book combine to make for an entertaining piece of literature for everyone from those with no background in math to a PhD mathematician.

This is an excellent book, especially for the layperson averse to or ambivalent toward mathematics. Give it to a friend, a member of the family, or maybe a struggling math student. This is a book which anyone and everyone can enjoy. ... Read more

Book Description

This book gives a systematic exposition of the modern theory ofGaussian measures. It presents with complete and detailed proofsfundamental facts about finite and infinite dimensional Gaussiandistributions. Covered topics include linear properties,convexity, linear and nonlinear transformations, andapplications to Gaussian and diffusion processes. Suitable foruse as a graduate text and/or a reference work, this volumecontains many examples, exercises, and an extensivebibliography. It brings together many results that have notappeared previously in book form. ... Read more

Book Description

"What does this have to do with real life?" is a question that plagues mathematics teachers across America, as students are confronted with abstract topics in their high school mathematics courses. The National Council of Teachers of Mathematics emphasizes the importance of making real world connections in teaching mathematics so that learning new content is meaningful to students. And in meeting NCTM national standards, this invaluable book provides many insights into the many connections between mathematics applications and the real world. Nearly 50 math concepts are presented with multiple examples of how each is applied in everyday environments, such as the workplace, nature, science, sports, and even parking. From logarithms to matrices to complex numbers, concepts are discussed for a variety of mathematics courses, including: BL algebra BL geometry BL trigonometry BL analysis BL probability BL statistics BL calculus ... Read more

Book Description

This examination of the fiscal health of local governments offers a "how-to" approach to identifying and solving financial problems. It will serve as a primer for readers interested in understanding financial processes and alternatives, and as a practical guide for those who need access to fiscal measurement tools. Its principal selling point lies in its assumptions:instead of using the vocabulary and research agendas of economists (such as Musgrave, Fisher), finance scholars (Ladd/Yinger) and political scientists (Peterson/Strachota), it will appeal to readers who lack sophisticated knowledge in these areas and nevertheless need practical advice.

The book stems from the "Fiscal Health Education Program," an applied economics program at the University of Minnesota.It uses three measures of fiscal health-financial condition, trend analysis, and financial trend monitoring system-as the basis for advocating particular fiscal strategies. The book examines the tools that can be used to assess the condition of a local government's fiscal health and some of the policy causes or remedies for certain situations, as well as some of the strategies governments can pursue to maintain and improve health.

*How-to approach will appeal to readers who lack sophisticated knowledge
* Contains discussion questions and anonymous case studies of actual cities and municipalities
* Presents practical methods for identifying and solving common fiscal problems ... Read more

Book Description

The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually by the MAA American Mathematics Competitions since 1976.

The IMO is the world mathematics championship for high school students. It takes place annually in a different country. The IMO competitions help to discover, encourage and challenge mathematically gifted young people all over the world.

The USAMO and the Team Selection Test (TST) are the last two stages of the selection process leading to representing the United States of America in the IMO. The preceding examinations are the AMC 10 or AMC 12 and the American Invitational Mathematics Examination (AIME). Participation in the AIME, USAMO, and the TST is by invitation only, based on performance in the preceding exams of the sequence.

Through the AMC contests and the IMO, young gifted mathematicians are identified and recognized while they are still in secondary school. Participation in these competitions provides them with the chance to measure themselves against other exceptional students from all over the world.

Editors, Andreescu and Feng provide remarkable solutions developed by the examinationcommittees, contestants, and experts, during or after the contests.They also provide a detailed report of the 1995-2000 USAMO/IMO results,and a comprehensive guide to other materials emphasizing advancedproblem-solving. This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to developtheir interest in mathematics outside the school curriculum and todeepen their knowledge ofmathematics. ... Read more

Reviews (1)

Some of the best problems ever created
Problems that are used in the mathematical Olympiads are a very select set. They must of course be challenging, but not too challenging. Since they are to be taken by high school students, most areas of mathematics are off-limits, severely restricting the range of solution techniques. Subtleties can be used in the problem, but only to a well-established point. I enjoy reading them, because these restrictions make the writing of such problems an art form.
This collection contains the six problems used in the 2001 United States of America Mathematical Olympiad (USAMO), the nine problems used in the 2001 International Mathematical Olympiad (IMO) American team selection test and the six problems used in the 2001 IMO. It is designed as study material for those preparing for possible competition in future Olympiads.
The problems themselves take up only the first seven pages of the book. Hints to the solutions take up the next four pages and formal solutions the remaining eighty-eight pages. Problem credits, a glossary of key theorems and previous Olympiad results complete the book. Reading these problems is an exercise that all mathematicians should engage in. They are some of the best ever written, sometimes knowing that the solutions require only "simple" mathematics makes them all the more difficult to find. I often think of potential solution strategies, only to reject them as using techniques officially out of bounds. I encourage everyone to take a look at these problems.

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

Reviews (20)

A math book that's actually understandable
Finally! A math book which is acutally well written, has enough examples to illustrate key concepts, and has enough problems to keep the math student busy. Discrete mathematics is a fairly involved subject and books on the topic range from relatively basic to extremely difficult treatises which only a PhD or a math professor could understand. Discrete and Combinatorial Mathematics : An Applied Introduction by Ralph Grimaldi is a book which will appeal to both sides of the spectrum. The book is written so that most undergraduate students will have little difficulty understanding, but graduate students will also find it indispensable as a reference. The illustrated examples are actually relevant to the homework problems, which is often missing in mathematical texts. Finally, the book does not try to overwhelm the reader with lofty proofs or stilted language. Each chapter builds on the previous subjects learned. That's all I can ask for in a math text. I like the coverage of combinatorics in the first chapter, which does a better job than many probability textbooks. And be sure to understand Euclid's theroem and the examples given in the book. Quite a few high-tech companies will ask you about the problem Grimaldi gives as an example of Euclid's theorem in their job interviews.

A classic introduction to discrete and combinatorial math
Grimaldi surveys the world of discrete math and combinatorics in his book, which is suitable for a full-year college course in the subject. The book is chock full of examples and proofs, although explanations would sometimes be more effective if less terse and more conversational. Grimaldi's book focuses on the practical, focusing on elements of discrete and combinatorial math that are used in engineering, science, and computer science. For example, the book teaches about finite state machines and graph theory; I've made good use of both subjects in my work in the software industry. Disclaimer: I, too, am a former student of Grimaldi's.

I can't stand discrete!
...that shouldn't reflect badly on this book though. While I think discrete sucks, I think this book does a good job for the discrete courses I did. I think the examples are good & helpful with doing the problems, and the problems range from easy verifications of theorems or mechanical computations to trickier problems or proofs of theorems. This book was pretty good, IMO. (for a discrete text anyway)

#1 discrete math book
The book is very well-written, clear and precise. I have read a couple of other books for discrete math courses, but found nothing exciting there; mostly frustrating errors, bad examples and confusion. Grimaldi's book covers pretty much everything you need to understand and apply in Discrete Mathematics. The exercises are well designed, in increasing difficulty. For most of the exercises, one can find similar examples in the text. Parts 1 and 2 of the book are by far the best read in Fundamentals and Enumeration I have ever encountered. Section 11 of Part 3 is a very nice introduction to Graph Theory. My only suggestion for improvement is some revision of sections 12 and 13 on graph algorithms - these can be simplified in terms of notation and description. Part 4 is for more advanced readers; it is usually used in a second course in Discrete mathematics. However, without being as exhaustive as the first three parts, the fourth part is presented with the same clarity and detail as the other three. I would strongly recommend this book not only to anyone who teaches Discrete mathematics, but also to any student who studies Discrete mathematics from a different book. If you are frustrated about the material; Grimaldi's book would give you the understanding and clarity you need. Definitely a five star product!

The best one about the subject
In my oponion this book is excellent. It is clear and full of useful examples and worthy problems. The style of the auther is very nice. He solves the examples by explaining wrong ways which many of students may think of as correct ways. This characteristic is one of the best points about this book. ... Read more

Book Description

The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics, its proofs often having great elegance and beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics.

The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day. ... Read more

Book Description

Topics include set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean algebra in communication systems. ... Read more

Book Description

KEYBENEFIT:This new book is written in a conversational, accessible style,offering a great deal of examples. It gradually ascends in difficulty to helpthe student avoid sudden changes in difficulty.Discussesanalysis from the start of the book, to avoid unnecessary discussion on realnumbers beyond what is immediately needed. Includes simplified and meaningfulproofs. Features Exercises and Problems at the end of each chapter aswell as Questions at the end of each section with answers at the end ofeach chapter. Presents analysis in a unified way as the mathematics based oninequalities, estimations, and approximations. ... Read more

Reviews (4)

Newest of the Best!
I have always been hoping that there are more modern textbooks on the undergraduate math that are written by great mathematicians. This one is one of the first to appear on the market. Thanks for Professor Mattuck! I love you, and love your book more!!! Hehe....Oh, by the way, one day if you see a movie called A Wonderful Mind, then you'll find a guy featured in it whose name is Abel Maple. The future greatest mathematician of the 22 century. Just kidding!

Great introduction to analysis
The book is slow to begin but it does a great job in explaining all the concepts. The author explains the proofs and theorems and it introduces some intermediate ideas to understand the theorems and definitions. The book contains a lot of exercise of different nature and difficulty. It covers a great range of subjects but not enough on the Rn. The book is basic in it contain, it is not difficult to read and follow. It can serve as an introduction to analysis. I would recommend it if you want an introduction to analysis.

A great introduction to analysis
This is an unusual and beautifully written introduction to real analysis. The presentation is carefully crafted and extremely lucid, with wonderfully creative examples and proofs, and a generous sprinkle of subtle humor. The layout of the pages is exceptionally attractive. The author has clearly put a great deal of thought and effort into producing an analysis text of the highest quality.

Most of the book concentrates on real-valued functions of a single (real) variable. There is a gradual and careful development of the ideas, with helpful explanations of elementary matters that are often skipped in other books. For instance, prior to the chapter on limits of sequences, the book has a chapter on estimation and approximation, discussing algebraic laws governing inequalities, giving examples of how to use these laws, and developing techniques for bounding sequences and for approximating numbers. Proofs involving "epsilons" and "arbitrarily large n" make their first appearance here.

The overall presentation of the book is carefully thought out. Each chapter is broken up into small sections, and each section emphasizes one principle idea or theorem. The proofs of the main theorems are lovely, and give both intuitive explanations and rigorous details. Genuinely interesting examples and problems illuminate the key ideas. Each chapter contains a mix of problems: "questions" that help students test their grasp of the main points of each section, "exercises" that are intermediate in scope, and more difficult "problems". (A solutions manual is available for instructors from the publisher.)

The careful explanations, even of "elementary" matters, and two appendices on sets, numbers, logic, and methods of argumentation, make the book suitable for a first analysis course in which students have had no prior exposure to proofs. There is ample material for a one-semester, or in some cases a one-year, course.

In summary, I believe that this is the best introductory real analysis book on the market. Students and instructors alike will find it a joy to read.

Pretty good
I used this book, with Mattuck teaching, for a one semester course in real analysis. I found the book clear in most places. It is less terse than the Rudin book, which is also used in analysis courses. ... Read more

Reviews (1)

Necessary reading if you are responsible for calculus
For decades, there is been a strong wind of change in the teaching of calculus. While much of it has been a result of the advance of technology, there are other factors driving the change. This short book is a summary of some of the consequences of the changes. It should come as no surprise that the results are all over the place. Nevertheless, if you are part of the changes, are about to become a part or just want to know what's going on, then you should read these summaries. Some of them will no doubt surprise you. ... Read more

Book Description

A visual journey to the intersection of math and imagination, guided by an award-winning author
Mathematics is right brain work, art left brain, right? Not so. This intriguing book shows how intertwined the disciplines are. Portraying the work of many contemporary artists in media from metals to glass to snow, Fragments of Infinity draws us into the mysteries of one-sided surfaces, four-dimensional spaces, self-similar structures, and other bizarre or seemingly impossible features of modern mathematics as they are given visible expression. Featuring more than 250 beautiful illustrations and photographs of artworks ranging from sculptures both massive and minute to elaborate geometric tapestries and mosaics of startling complexity, this is an enthralling exploration of abstract shapes, space, and time made tangible.
Ivars Peterson (Washington, DC) is the mathematics writer and online editor of Science News and the author of The Jungles of Randomness (Wiley: 0-471-16449-6), as well as four previous trade books. ... Read more

Reviews (3)

Excellent Combination of Math and Art
Fragments of Infinity is one of my favorite books. One reason is because the author Mr. Peterson gives an indept explanation as to how mathematics and art work together. I really loved the pictures and illustrations. I actually used them as a guideline for my own artistic creations. I've even made several model spaceships with the information given. This book also has an excellent source of information for students of mathematics to use on everyday homework assignments. I would suggest this book for an artistic person, whether it be a child or adult, who has a problem with math because "Fragments of Infinity" is an excellent resource to enhance one's understanding of math along with the creativity of art.

Lovely choice of art but needlessly limited - and shaky math
"Fragments of Infinity: A Kaleidescope of Math and Art" is a compilation of beautiful examples of mathematical art. It will give the lay reader more than an inkling of the connection between advanced math and beauty -- a connection that is ordinarily very difficulat to convey. And it will give the mathematics professional something to savor as well.

Unfortunately, the book has two major flaws:

1) It entirely omits art from computer graphics, which is perhaps the largest source of extraordinarily beautiful mathematically-based art these days -- and it is art which translates to the printed page just as well as traditional sculpture or painting does, and

2) This book displays a shaky grasp of mathematical concepts by the author and most likely an absence of fact-checking by the publisher. For example, although the book's main mathematical topic is geometry/topology, the author shows on page 141 that he does not even comprehend what a Moebius band is, where he claims that the triangular but assymetric recycling symbol is a Moebius band (correct), but that the symbol having full 3-way symmetry is not a Moebius band (incorrect). Unfortunately, gaffes like this are widespread in the author's previous books as well.

A great combination of art and mathematics
Mathematics and art have many things in common, something that practitioners of both often go to great lengths to refute. In this book, Ivars Peterson, one of the truly great practitioners of the art of popular mathematical writing, shows us how intertwined they really are. The sculptures that he describes and explains are truly astonishing. I looked at some of the photos for several minutes, seeing many different things, even though I was limited to the two dimensional projection. Without a doubt, the piece itself must be truly breathtaking.
Many popular mathematics books have delved into the synergy of math and art, but never to this extent or with this effectiveness. This is by far the best book I have ever seen in this area and I recommend it to my artist friends as well as those who practice math. ... Read more