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Mathematical Proofs : A Transition to Advanced Mathematics by Albert D. Polimeni, Gary Chartrand and Ping Zhang (2007, Hardcover)

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This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

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Product Information

Mathematical Proofs: A Transition to Advanced Mathematics, Second Edition, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

Product Identifiers

Publisher
Addison Wesley
ISBN-10
0321390539
ISBN-13
9780321390530
eBay Product ID (ePID)
61795455

Product Key Features

Author
Ping Zhang, Gary Chartrand, Albert D. Polimeni
Publication Name
Mathematical Proofs : a Transition to Advanced Mathematics
Format
Hardcover
Language
English
Publication Year
2007
Type
Textbook
Number of Pages
384 Pages

Dimensions

Item Length
8.3in
Item Height
0.7in
Item Width
8.9in
Item Weight
24.4 Oz

Additional Product Features

Lc Classification Number
Qa9.54.C48 2008
Edition Number
2
Table of Content
0. Communicating Mathematics Learning Mathematics What Others Have Said About Writing Mathematical Writing Using Symbols Writing Mathematical Expressions Common Words and Phrases in Mathematics Some Closing Comments about Writing 1. Sets 1.1 Describing a Set 1.2 Subsets 1.3 Set Operations 1.4 Indexed Collections of Sets 1.5 Partitions of Sets 1.6 Cartesian Products of Sets Exercises for Chapter 1 2. Logic 2.1 Statements 2.2 The Negation of a Statement 2.3 The Disjunction and Conjunction of Statements 2.4 The Implication 2.5 More on Implications 2.6 The Biconditional 2.7 Tautologies and Contradictions 2.8 Logical Equivalence 2.9 Some Fundamental Properties of Logical Equivalence 2.10 Quantified Statements 2.11 Characterizations of Statements Exercises for Chapter 2 3. Direct Proof and Proof by Contrapositive 3.1 Trivial and Vacuous Proofs 3.2 Direct Proofs 3.3 Proof by Contrapositive 3.4 Proof by Cases 3.5 Proof Evaluations Exercises for Chapter 3 4. More on Direct Proof and Proof by Contrapositive 4.1 Proofs Involving Divisibility of Integers 4.2 Proofs Involving Congruence of Integers 4.3 Proofs Involving Real Numbers 4.4 Proofs Involving Sets 4.5 Fundamental Properties of Set Operations 4.6 Proofs Involving Cartesian Products of Sets Exercises for Chapter 4 5. Existence and Proof by Contradiction 5.1 Counterexamples 5.2 Proof by Contradiction 5.3 A Review of Three Proof Techniques 5.4 Existence Proofs 5.5 Disproving Existence Statements Exercises for Chapter 5 6. Mathematical Induction 6.1 The Principle of Mathematical Induction 6.2 A More General Principle of Mathematical Induction 6.3 Proof by Minimum Counterexample 6.4 The Strong Principle of Mathematical Induction Exercises for Chapter 6 7. Prove or Disprove 7.1 Conjectures in Mathematics 7.2 Revisiting Quantified Statements 7.3 Testing Statements 7.4 A Quiz of "Prove or Disprove" Problems Exercises for Chapter 7 8. Equivalence Relations 8.1 Relations 8.2 Properties of Relations 8.3 Equivalence Relations 8.4 Properties of Equivalence Classes 8.5 Congruence Modulo n 8.6 The Integers Modulo n Exercises for Chapter 8 9. Functions 9.1 The Definition of Function 9.2 The Set of All Functions from A to B 9.3 One-to-one and Onto Functions 9.4 Bijective Functions 9.5 Composition of Functions 9.6 Inverse Functions 9.7 Permutations Exercises for Chapter 9 10. Cardinalities of Sets 10.1 Numerically Equivalent Sets 10.2 Denumerable Sets 10.3 Uncountable Sets 10.4 Comparing Cardinalities of Sets 10.5 The Schröder-Bernstein Theorem Exercises for Chapter 10 11. Proofs in Number Theory 11.1 Divisibility Properties of Integers 11.2 The Division Algorithm 11.3 Greatest Common Divisors 11.4 The Euclidean Algorithm 11.5 Relatively Prime Integers 11.6 The Fundamental Theorem of Arithmetic 11.7 Concepts Involving Sums of Divisors Exercises for Chapter 11 12. Proofs in Calculus 12.1 Limits of Sequences 12.2 Infinite Series 12.3 Limits of Functions 12.4 Fundamental Properties of Limits of Functions 12.5 Continuity 12.6 Differentiability Exercises for Chapter 12 13. Proofs in Group Theory 13.1 Binary Operations 13.2 Groups 13.3 Permutation Groups 13.4 Fundamental Properties of Groups 13.5 Subgroups 13.6 Isomorphic Groups Exercises for Chapter 13 Answers and Hints to Selected Odd-Numbered Exercises References Index of Symbols Index of Mathematical Terms
Copyright Date
2008
Target Audience
College Audience
Topic
Logic
Lccn
2006-049605
Dewey Decimal
511.3/6
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics

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item 1 Mathematical Proofs A Transition by Gary Chartrand
$56.99
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item 2 MATHEMATICAL PROOFS: A TRANSITION TO ADVANCED MATHEMATICS By Gary Chartrand VG
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item 3 Mathematical Proofs : A Transition to Advanced Mathematics by Albert D....
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item 4 Mathematical Proofs A Transition by Gary Chartrand
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item 5 Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition)
$224.95
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4.6

4.6 out of 5 stars based on 7 product ratings

7 product ratings

6 users rated this 5 out of 5 stars
0 users rated this 4 out of 5 stars
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1 users rated this 2 out of 5 stars
0 users rated this 1 out of 5 stars

Would recommend

Good value

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Most relevant reviews

See all 6 reviews

2 out of 5 stars
by slurocksMar 09, 2008
For serious math majors only
I bought this book for my "Bridge to Higher Math" course that was required for my Computer Science major. I hadn't taken any other math courses prior to this, and this book definitely was not a big help. Of course, if you're buying this book, you most likely are a math major. Good luck with whatever math course you're using it for.
5 out of 5 stars
by scottcoop89Mar 03, 2013
Great book!
Great book! I bought this for a class I had to take, and it is very useful and user friendly. It's not huge, and it is very helpful in teaching how to write proofs.
5 out of 5 stars
by wjdebordJul 19, 2010
Just as good as the American Edition
Very useful in class. Examples are explained fairly well. No differences so far between international edition and American edition.
5 out of 5 stars
by heb4509Aug 12, 2010
Shipped fast
I got the book very quick. It is in the condition as seller stated. I need it for a class. I had no problems getting in contact with the seller and the response back was quick and easy.
5 out of 5 stars
by oleanderxoxoSep 18, 2011
Recommend International Edition
What I bought is the international edition: cheaper and less heavy than the US version. The materials inside are all the same. Highly recommended

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Mathematical Proofs : A Transition to Advanced Mathematics by Albert D. Polimeni, Gary Chartrand and Ping Zhang (2007, Hardcover)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

Ratings and Reviews

Most relevant reviews

For serious math majors only

Great book!

Just as good as the American Edition

Shipped fast

Recommend International Edition

Best Selling in Textbooks

Save on Textbooks

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