Proofs and Concepts The Fundamentals of Abstract Mathematics
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 stu...
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| Main Authors: | , |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Lethbridge, Alberta
Dave Witte Morris, Joy Morris
[2013]
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| Series: | Open textbook library.
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| Subjects: | |
| Online Access: | Access online version |
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Table of 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