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Introduction to Mathematical Structures and Proofs (Undergraduate Texts in Mathematics)

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Introduction to Mathematical Structures and Proofs (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

Reviews of the first edition: "...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. --Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." --S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors. The new material in this second edition includes four more topics in number theory, a brief introduction to complex numbers, and a section on graph theory and combinatorial topics related to graphs. Introducing these additional topics gives the reader an even broader view of the mathematical experience.

Synopsis:

This updated and revised second edition is designed to help students advance from basic calculus to higher-level linear and abstract algebra and number theory. It introduces an array of fundamental structures and shows how to balance intuition and rigor.

Synopsis:

As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study.

Synopsis:

"...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. - Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." - S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.

About the Author

Gerstein's primary areas of research have been in quadratic forms and number theory and he has published extensively in these areas. The author's first edition of "Introduction to Mathematical Structures and Proofs" has sold to date (8/2/2010) over 6000 copies and has gone through 5 printings. Gerstein himself has a transition course at UC, Santa Barbara (Math 8-A transition to higher mathematics) from his book since its first publication date. The first edition also received 2 glowing reviews by Steve Krantz for the American Mathematical Monthly, and S. Gottwald for Zentralblatt.

Table of Contents

-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index

Product Details

ISBN:
9781461442646
Author:
Gerstein, Larry J.
Publisher:
Springer
Subject:
Mathematics-Logic and Philosophy
Subject:
Logic
Subject:
Cantor s theory cardinality
Subject:
Russell s paradox
Subject:
Schroeder-Bernstein theorem
Subject:
fundamental theorem of arithmetic
Subject:
Inclusion-exclusion principle
Subject:
Mathematical Induction
Subject:
textbook transition course mathematics
Subject:
transition course textbook mathematics
Subject:
Mathematical Logic and Foundations
Subject:
Analysis
Subject:
Number Theory
Subject:
Combinatorics
Subject:
Cantor s theorems
Subject:
counting principles
Subject:
number-theoretic functions
Subject:
Proof techniques
Subject:
relations and partitions
Subject:
set constructions
Subject:
transition course
Copyright:
Edition Description:
2nd ed. 2012
Series:
Undergraduate Texts in Mathematics
Publication Date:
20120606
Binding:
HARDCOVER
Language:
English
Pages:
414

Related Subjects

Humanities » Philosophy » Logic
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Number Theory

Introduction to Mathematical Structures and Proofs (Undergraduate Texts in Mathematics) New Hardcover
0 stars - 0 reviews
$67.25 In Stock
Product details 414 pages Springer - English 9781461442646 Reviews:
"Synopsis" by , This updated and revised second edition is designed to help students advance from basic calculus to higher-level linear and abstract algebra and number theory. It introduces an array of fundamental structures and shows how to balance intuition and rigor.
"Synopsis" by , As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study.
"Synopsis" by , "...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. - Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." - S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.
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