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Proofs and Concepts: the fundamentals of abstract mathematics

Proofs and Concepts: the fundamentals of abstract mathematics

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Proofs and Concepts: the fundamentals of abstract mathematics

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Book Details:

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Year:2013
Publisher:University of Lethbridge
Pages:201 pages
Language:english
Since:29/09/2015
Size:1.03 MB
License:Pending review

Content:

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

  • Functions
  • Cardinality
  • Proof by Induction
  • Equivalence Relations

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