An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.

At the level of:

Book of Proof (3rd edition), by Richard Hammack

Abstract Algebra: Theory and Applications (2019 edition), by Thomas Judson

Elementary Analysis: The Theory of Calculus, by Kenneth Ross

The following chapters and sections from all three books:

From Book of Proof (3rd edition), by Richard Hammack

• Sets (Chapter 1)

• Logic (Chapter 2)

• Direct Proof (Chapter 4)

• Contrapositive Proof (Chapter 5)

• Proof by Contradiction (Chapter 6)

• Proving Non-Conditional Statements (Chapter 7)

• Proof Involving Sets (Chapter 8)

• Disproof (Chapter 9)

• Mathematical Induction (Chapter 10)

• Relations (Chapter 11)

• Functions (Chapter 12)

• Cardinality of Sets (Chapter 14)

From Abstract Algebra: Theory and Applications, by Thomas Judson

• Groups (Chapter 3)

• Cosets and Lagrange theorem (Sections 6.1 and 6.2)

From Elementary Analysis: The Theory of Calculus, by Kenneth Ross

• The Completeness Axiom (Section 4 from Chapter 1)

• Sequences (Sections 7, 9, 10, 11 from Chapter 2)

• Continuity (Section 17 from Chapter 3)

Texts and topics may vary slightly according to time availability and instructor’s interest.