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Proofs and Concepts The Fundamentals of Abstract Mathematics Dave Morris

By: Contributor(s): Material type: TextTextSeries: Open textbook libraryDistributor: Minneapolis, MN Open Textbook LibraryPublisher: Lethbridge, Alberta Dave Witte Morris, Joy Morris [2013]Copyright date: ©2013Description: 1 online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
Subject(s): LOC classification:
  • QA1
  • QA37.3
Online resources:
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
Subject: 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.
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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

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.

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In English.

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