MATH 220 Section 903
Foundations of Mathematics
Fall 2016
Instructor: Florent Baudier
Office: Blocker 525C
Office hours: MTWR 2:00-3:30 p.m.
Lectures: MW 5:45-7:00pm BLOC 121
Course description: Math 220 is designed to provide a bridge between computational mathematics and theoretical mathematics (``real math''). Thus a major goal is to teach the students how to write proofs. The required core of topics include logic, set theory, number theory, induction, functions, relations, operations, and combinatorics.
Textbooks: Robert J. Bond, An Introduction to Abstract Mathematics, 1st edition, Waveland Press
Exams
Exam #1: Tuesday, September 27, 2016 7:00-8:15 p.m. (classroom: Blocker 102)
Exam #2: Thursday, November 3, 2016 7:00-8:15 p.m. (classroom: Blocker 149)
Final exam: Friday December 9, 2016 7:30-9:30am (in the regular classroom).
Schedule
Date of Class Material covered
Monday 08/29 general introduction, Section 1.1 (statements, open sentences)
Wednesday 09/31 Section 1.1 (quantifiers, negation)
Monday 09/05 Quiz #1 Section 1.1 (writing proofs)
Wednesday 09/07 Section 1.2 Compound Statements (disjunctions, conjunctions, tautologies, contradictions)
Monday 09/12 Quiz #2 , Section 1.3 (implications)
Wednesday 09/14 Section 1.3 (counterexamples)
Monday 09/19 Quiz #3 , Section 1.4 (contrapositive and converse)
Wednesday 09/21 Section 1.4 (proof by contradiction)
Monday 09/26 review chapter 1
Tuesday 09/27 Exam #1
Wednesday 09/28 Section 2.1 (sets and subsets)
Monday 10/03 Quiz #4 , Section 2.2 (combining sets)
Wednesday 10/05 Section 2.2 (combining sets)
Monday 10/10 class does not meet
Wednesday 10/12 class does not meet
Monday 10/17 Quiz #5 , Section 2.3 (collections of sets)
Wednesday 10/19 Section 3.1 Functions: Definition and Basic Properties
Monday 10/24 Quiz #6 , Section 3.2 Surjective and Injective Functions
Wednesday 10/26 Section 3.3 Composition and Invertible Functions
Monday 10/31 Quiz #7 , Section 4.1 Binary Operations
Wednesday 11/02 review chapters 2-3
Thursday 11/03 Exam #2
Monday 11/07 Section 4.1 Binary Operations
Wednesday 11/09 Section 4.2 Equivalence Relations
Monday 11/14 discussion about exam 2
Wednesday 11/16 Section 4.2 Equivalence Relations, partial orderings
Monday 11/21 Quiz #8 , Section 4.2 Equivalence Relations, Partial orderings
Wednesday 11/23 reading day, no classes
Monday 11/28 Quiz #9 , Section 5.1 The Integers: Axioms and Basic Properties, Section 5.2 Induction
Wednesday 11/30 Section 5.2 Induction, Well-Ordering Principle, Section 5.3 The Division Algorithm and Greatest Common Divisors
Monday 12/05 Fall redefined day, students attend their Friday classes
Wednesday 12/07 last day of classes, Quiz #10 , Section 5.3 The Division Algorithm and Greatest Common Divisors, Section 5.4 Primes and Unique Factorization, Section 5.5. Congruences