EVERYDAY FREE SHIPPING on $25 & up - Excludes marketplace items & rentals.
EVERYDAY FREE SHIPPING on $25 & up - Excludes marketplace items & rentals.
EVERYDAY FREE SHIPPING on $25 & up - Excludes marketplace items & rentals
Search
Proofs and Fundamentals : A First Course in Abstract Mathematics

Proofs and Fundamentals : A First Course in Abstract Mathematics - 00 edition

ISBN13: 978-0817641115

Cover of Proofs and Fundamentals : A First Course in Abstract Mathematics 00 (ISBN 978-0817641115)
ISBN13: 978-0817641115
ISBN10: 0817641114
Cover type:
Edition/Copyright: 00
Publisher: Birkhauser Boston, Inc.
Published: 2000
International: No

USED
Sold Out
FREE Shipping on $25+
  • Ships Today
  • 30-Day Returns
  • Condition: Very Good
Sold Out

Other Editions for Proofs and Fundamentals : A First Course in Abstract Mathematics

More Shipping Options

Proofs and Fundamentals : A First Course in Abstract Mathematics - 00 edition

ISBN13: 978-0817641115

Ethan Bloch

ISBN13: 978-0817641115
ISBN10: 0817641114
Cover type:
Edition/Copyright: 00
Publisher: Birkhauser Boston, Inc.

Published: 2000
International: No
Summary

Proofs and Fundamentals: A First Course in Abstract Mathematics is designed as a 'transition' course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra, and real analysis.

This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material including sets, functions, and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics, and the Peano Postulates. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and writing are never compromised. The material is presented in the way that mathematicians actually use it; good mathematical taste is preferred to overly clever pedagogy. There is a key section devoted to the proper writing of proofs. The text has over 400 exercises, ranging from straightforward examples to very challenging proofs.

The excellent exposition, organization and choice of topics will make this text valuable for classroom use as well as for the general reader who wants to gain a deeper understanding of how modern mathematics is currently practiced by mathematicians.

Author Bio

Bloch, Ethan : Bard College, Annandale-on-Hudson, NY

Table of Contents

Introduction
To the Student
To the Instructor

Part I: PROOFS
1. Informal Logic

1.1 Introduction
1.2 Statements
1.3 Relations Between Statements
1.4 Valid Arguments
1.5 Quantifiers

2. Strategies for Proofs
2.1 Mathematical Proofs-What They are and Why We Need Them
2.2 Direct Proofs
2.3 Proofs by Contrapositive and Contradiction
2.4 Cases, and If and Only If
2.5 Quantifiers in Theorems
2.6 Writing Mathematics

Part II: FUNDAMENTALS
3. Sets
3.1 Introduction
3.2 Sets-Basic Definitions
3.3 Set Operations
3.4 Indexed Families of Sets

4. Functions
4.1 Functions
4.2 Image and Inverse Image
4.3 Composition and Inverse Functions
4.4 Injectivity, Surjectivity and Bijectivity
4.5 Set of Functions

5. Relations
5.1 Relations
5.2 Congruence
5.3 Equivalence Relations

6. Infinite and Finite Sets
6.1 Cardinality of Sets
6.2 Cardinality of the Number Systems
6.3 Mathematical Induction
6.4 Recursion

Part III: EXTRAS
7. Selected Topics
7.1 Binary Operations
7.2 Groups
7.3 Homomorphisms and Isomorphisms
7.4 Partially Ordered Sets
7.5 Lattices
7.6 Counting: Products and Sums
7.7 Counting: Permutations and Combinations

8. Number Systems
8.1 Back to the Beginning
8.2 The Natural Numbers
8.3 Further Properties of the Natural Numbers
8.4 The Integers
8.5 The Rational Numbers
8.6 The Real Numbers and the Complex Numbers
8.7 Appendix: Proof of Theorem 8.2.1

Appendix: Properties of Numbers
Hints for Selected Exercises
References
Index

List price: $0.00
  • Marketplace
  • From

Other Editions for Proofs and Fundamentals : A First Course in Abstract Mathematics

Cover of Proofs and Fundamentals 2nd edition

Proofs and Fundamentals - 2nd edition

ISBN13: 978-1441971265
More Shipping Options