## Foundations of Mathematical Proof

Department:
MATH
Course Number:
2106
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Fall and Spring semesters

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.

Prerequisites:

MATH 1502 or MATH 1512 or MATH 1504 or MATH 1555 or ((MATH 1552 or MATH 15X2 or MATH 1X52) and (MATH 1553 or MATH 1554 or MATH 1564 or MATH 1522 or MATH 1X53))

Course Text:

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

Topic Outline:

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.