MATH 220 Section 905
Foundations of Mathematics
Fall 2017
Instructor: Florent Baudier
Office: Blocker 525C
Office hours: Tuesdays 8:30-10:30 a.m. and Thursdays 3:45-5:00pm or by appointment
Lectures: TR 11:10 a.m.-12:25 p.m. BLOC 148
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.
Textbook: Tamara J. Lakins, The Tools of Mathematical Reasoning, 1st edition, American Mathematical Society, Pure and applied undergraduate texts, The Sally Series.
Exams
Exam #1: Tuesday, September 26, 2017 11:10 a.m.-12:25 p.m. (classroom: Blocker 148)
Exam #2: Thursday, October 31, 2017 11:10 a.m.-12:25 p.m. (classroom: Blocker 148)
Final exam: Friday, December 8, 2017, 3:00-5:00 p.m. (in the regular classroom).
Homework   Term Paper Instructions   Lecture notes  
Schedule
Date of Class Material covered
Tuesday 08/28 class cancelled due to inclement weather
Thursday 09/31 general introduction, Section 1.1 (language, logic and proof: language and logic)
Tuesday 09/05 Quiz #1 , Section 1.2 (language, logic and proof: language and logic)
Thursday 09/07 Section 2.1 (techniques of proofs: direct proofs)
Tuesday 09/12 Quiz #2 , Section 2.1 (techniques of proofs: direct proofs)
Thursday 09/14 Section 2.2 (techniques of proofs: proofs by contradiction and contrapositive)
Tuesday 09/19 Quiz #3 , Section 2.3 (techniques of proofs: two important theorems)
Thursday 09/21 Section 2.3 (techniques of proofs: two important theorems), Section 2.4 (techniques of proofs: proofs of statements involving mixed quantifiers)
Tuesday 09/26 Exam #1 (covers sections 1.1-2.3)
Thursday 09/28 Section 3.1 (induction: principle of mathematical induction)
Tuesday 10/03 Quiz #4 , Section 3.2 (induction: principle of strong mathematical induction)
Thursday 10/05 Section 4.1 (the language of sets, emptyset, subsets, equality)
Tuesday 10/10 Quiz #5 , Section 4.2 (operations on sets, intersection, union)
Thursday 10/12 Section 4.2 (operations on sets, complement, DeMorgan's laws)
Tuesday 10/17 Quiz #6 , Section 4.3 (arbitrary unions and intersections)
Thursday 10/19 Section 4.3 (arbitrary unions and intersections)
Tuesday 10/24 Quiz #7 , Section 4.3 (power set, partitions)
Thursday 10/26 review for exam 2
Tuesday 10/31 Exam #2 (covers sections 2.4-5.5)
Thursday 11/02 Section 5.1 (functions)
Tuesday 11/07 Quiz #8 , Section 5.2 (function composition).
Thursday 11/09 Section 5.3 (injective and surjective functions)
Tuesday 11/14 Quiz #9 , Section 5.4 (invertible functions).
Thursday 11/16 Section 5.5 (functions and sets).
Tuesday 11/21
Thursday 11/23 Thanksgiving, reading day, no classes
Tuesday 11/28 Quiz #10 , Section 7.1-7.2 (relations, equivalence relations).
Thursday 11/30 Quiz #11 , Section 7.3 (partitions)
Tuesday 12/05 Fall redefined day, students attend their Thursday classes, Quiz #12 , review for the final
Thursday 12/07 reading day, no classes