Proofs and concepts : the fundamentals of abstract mathematics

Format:

Book

Author/Creator:

Morris, Dave Witte, author.

Morris, Joy, author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Place of Publication:

Lethbridge, Alberta Dave Witte Morris, Joy Morris [2013]

Language Note:

In English.

Summary:

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.

Contents:

Part I. Introduction to Logic and Proofs

1. What is Logic?

2. Propositional Logic

3. Two-Column Proofs

Part II. Sets and First-Order Logic

4. Sets, Subsets, and Predicates

5. Operations on Sets

6. First-Order Logic

7. Quantifier Proofs

8. Divisibility and Congruence

Part III. Other Fundamental Concepts

9. Functions

10. Cardinality

11. Proof by Induction

12. Equivalence Relations

Notes:

Description based on print resource