Proofs and Concepts: the fundamentals of abstract mathematics
|Publisher:||University of Lethbridge|
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.
Table of Contents:
Part I. Introduction to Logic and Proofs
- What is Logic?
- Propositional Logic
- Two-Column Proofs
Part II. Sets and First-Order Logic
- Sets, Subsets, and Predicates
- Operations on Sets
- First-Order Logic
- Quantifier Proofs
- Divisibility and Congruence
Part III. Other Fundamental Concepts
- Proof by Induction
- Equivalence Relations
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