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Introduction to Mathematical Thinking: Algebra and Number Systems, by Will J. Gilbert, Scott A. Vanstone
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Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.
- Sales Rank: #778486 in Books
- Published on: 2004-08-01
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .80" w x 7.00" l, 1.04 pounds
- Binding: Paperback
- 312 pages
Most helpful customer reviews
4 of 4 people found the following review helpful.
Very good book, but I wish they saved some trees.
By karpov
I used a previous edition of this book in my first year university college, and it was really good. However, what I really hate is how this newer edition (which my wife later got for her math course) contains some errors which existed in the previous edition. Seriously, guys, stop bankrupting poor students and killing trees - new edition requires more than just reordering end-of-chapter problems and numbering chapters from 1 instead of zero.
1 of 1 people found the following review helpful.
Close, but no cigar.
By R136a1
This book provides a very brief introduction to mathematical reasoning. You will get a glimpse of this in the first chapter on logic and proofs where you will learn about propositional logic, conditional statements, sets and quantifiers. You will learn how to formulate conjectures and write some pretty descent proofs. This book contains several sections that are motivated from topics in number theory (diophantine equations, congruences and the Euclidean algorithm) before digressing into a separate chapter on basic mathematical notions from the principle of mathematical induction, recursion, and the binomial theorem to a quick look at real and rational numbers as building blocks for later sections...
The subsequent chapters, however, are a jumbled up assortment of topics from various courses. There is a chapter on functions and bijections where you will learn about cardinality and permutations (linear algebra); a brief foray into cryptography with a section on public- and private-key cryptography and the RSA scheme (number theory); an overview of the complex plane and the properties of complex numbers with a look at De Moivre's Theorem (complex variables); and finally, the fundamental theorem of algebra, which concludes with a look at equations over a finite field (abstract algebra). The inclusion of these topics does not necessarily make this book a comprehensive one, as you are barely scratching the surface with any of these topics. So let's be clear about one thing: this book has breadth, not depth. There is a lot material to gain insight from, which does gives the reader an idea of what is to come in later years. So I suppose you can make of this book what you will and take from it what you want. However, I think it could have been great had it not tried to cover so many broad topics.
1 of 1 people found the following review helpful.
Not worth the money.
By zack
If you need this book for a class then get it, otherwise don't waste your money. It is poorly written and there is much better information online by simply searching what you are trying to learn.
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