TY  - GEN
AU  - Bloch, Ethan D. 
TI  - Proofs and fundamentals: a first course in abstract mathematics
SN  - 9781461428107
U1  - 511.3 
PY  - 2013///
CY  - New York
PB  - Springer
KW  - Proof theory
KW  - Combinatorial analysis
KW  - Symbolic and mathematical
N1  - Table of Contents

Part I. Proofs. 
1. Informal logic --
2. Strategies for proofs --

Part II. Fundamentals. 
3. Sets --
4. Functions --
5. Relations --
6. Finite sets and infinite sets --

Part III. Extras. 
7. Selected topics --
8. Explorations
N2  - This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis.

This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations.

A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. 


http://www.springer.com/in/book/9781441971265

ER  -