Math 2106-D, Fall 2017

Foundations of Mathematical Proof
Georgia Tech


Tentative Schedule:

Date Topics covered Read before class
August 22 Sets and operations on them Hammack 1.1-1.8
August 24 Logic, truth tables, Worksheet 1 Hammack 2.1-2.6
August 29 Statements in logic Hammack 2.7-2.12
August 31 Proofs: Introduction and first techniques Hammack 4.1-4.5
September 5 Proofs by contrapositive Hammack 5.1-5.3
September 7 Proofs by contradiction Hammack 6.1-6.4
September 12 More on proofs Hammack 7.1-7.4
September 14 Set-theoretic proofs Hammack 8.1-8.3
September 19 Review
September 21 Midterm 1
September 26 Induction Hammack 10.1-10.3
September 28 Relations, equivalence relations, partitions, integers modulo n Hammack 11.1-11.5
October 3 Functions, properties of functions, the pigeonhole principle Hammack 12.1-12.3
October 5 Compositions of functions, inverse functions, images and inverse images of functions Hammack 12.4-12.6
October 10 Fall Recess, no class
October 12 Cardinality, countable sets, uncountable sets Hammack 13.1-13.2
October 17 Comparing cardinalities, the Cantor-Bernstein-Schröder theorem Hammack 13.3-13.4
October 19 Groups Judson 3.1-3.2
October 24 Properties of groups, subgroups, and Cyclic groups Judson 3.3, 4.1
October 26 Review
October 31 Midterm 2
November 2 Symmetric groups and dihedral groups Judson 5.1-5.2
November 7 Cosets, Lagrange's theorem Judson 6.1-6.2
November 9 Fermat's Little Theorem, Euler's Totient Theorem Judson 6.3
November 14 Limits of sequences Ross 2.7-2.8
November 16 Limit theorems Ross 2.9
November 21 Monotone sequences, Cauchy sequences Ross 2.10
November 23 Thanksgiving, no classes
November 28 Subsequences Ross 2.11
November 30 Continuity Ross 3.17-3.18
December 5 Review for final exam

Syllabus: Click here for the syllabus.

Homework:

Homework 1 pdf

Homework 1 tex file

Homework 2 pdf

Homework 2 tex file

Homework 3 pdf

Homework 3 tex file

Homework 4 pdf

Homework 4 tex file

Homework 5 pdf

Homework 5 tex file

Homework 6 pdf

Homework 6 tex file

Homework 7 pdf

Homework 7 tex file

Homework 8 pdf

Homework 8 tex file

Worksheets:

Worksheet 1 pdf

Worksheet 1 tex file

Worksheet 2 pdf

Worksheet 2 tex file

Worksheet 3 pdf

Worksheet 3 tex file

Supplemental Material

Proof by Infinite Descent pdf

Proof by Infinite Descent tex file

Quiz solutions pdf

Quiz solutions tex file

Exam Material

Sample Exam I pdf

Sample Exam I tex file

Exam I solutions pdf

Exam I solutions tex file

Sample Exam 2 pdf

Sample Exam 2 tex file

Exam II solutions pdf

Exam II solutions tex file

Sample final exam pdf

Sample final exam tex file