MATH 220
Foundations of Mathematics
Fall 2018
Instructor: Florent Baudier
Office: Blocker 525C
Office hours: MW 2:30-5:00 p.m. or by appointment
Lectures:
Section 901: MWF 9:10 a.m.-10:00 a.m. BLOC 148
Section 903: MWF 10:20 a.m.-11:10 a.m. BLOC 148
Section 907: MWF 11:30 a.m.-12:20 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: Monday, September 24, 7-9 p.m. (classroom: Blocker 169)
Exam #2: Monday, October 29, 7-9 p.m. (classroom: Blocker 169)
Final exam:
Section 901: Monday, December 10, 8:00-10:00 a.m. (in the regular classroom).
Section 903: Tuesday, December 11, 8:00-10:00 a.m. (in the regular classroom).
Section 907: Wednesday, December 12, 10:30 a.m-12:30 a.m. (in the regular classroom).
Homework   Term Paper Instructions   Lecture notes  
Schedule
Date of Class Material covered
Monday 08/27 organizational meeting
Wednesday 08/29 statements, predicates, basic logical connectives
Friday 08/31 implication
Monday 09/03 contrapositive, converse, biconditional
Wednesday 09/05 quantifiers
Friday 09/07 Quiz #1, quantifiers
Monday 09/10 Quiz #2, proof techniques: existential proofs
Wednesday 09/12 proof techniques: uniqueness proofs
Friday 09/14 Quiz #3, proof techniques: universal proofs
Monday 09/17 Quiz #4, proof techniques: universal proofs
Wednesday 09/19 proof techniques: proof by contrapositive
Friday 09/21 Quiz #5, proof techniques: proof by contradiction
Monday 09/24 review for exam #1 Exam #1 (7-9pm)
Wednesday 09/26 proof techniques: proving biconditional statements, proving disjunction statements
Friday 09/28 Quiz #6, proof techniques: proof by cases, working backwards
Monday 10/01 Quiz #7 principle of mathematical induction
Wednesday 10/03 Quiz #8, principle of strong mathematical induction
Friday 10/05 class cancelled
Monday 10/08 Quiz #9, going over the solution of exam #1
Wednesday 10/10 sets, subsets
Friday 10/12 class cancelled
Monday 10/15 Quiz #10, union and intersection of two sets
Wednesday 10/17 complement
Friday 10/19 Quiz #11, arbitrary unions
Monday 10/22 Quiz #12, arbitrary intersections
Wednesday 10/24 problems on set operations
Friday 10/26 Quiz #13 , problems on induction
Monday 10/29 review for exam #2, Exam #2 (7-9pm)
Wednesday 10/31 Cartesian products
Friday 11/02 Quiz #14, power set
Monday 11/05 Quiz #15, functions (definition and terminology)
Wednesday 11/07 composition of functions
Friday 11/09 Quiz #16, problems on properties of functions
Monday 11/12 Quiz #17, surjectivity, injectivity
Wednesday 11/14 bijectivity, invertibility
Friday 11/16 Quiz #18 , problems on surjectivity, injectivity, bijectivity, invertibility
Monday 11/19 class does not meet
Wednesday 11/21 Reading Day, no classes
Friday 11/23 Thanksgiving Holiday
Monday 11/26 Quiz #19 , direct image of a set
Wednesday 11/28 inverse image of a set
Friday 11/30 Quiz #20 , problems on functions and sets
Monday 12/03 Fall redefined day, Friday classes, review for the final
Wednesday 12/05 Last day of classes, review for the final
Friday 12/07 no classes
Monday 12/10 Final exam-Section 901 , 8-10am
Tuesday 12/11 Final exam-Section 903 , 8-10am
Wednesday 12/12 Final exam-Section 907, 10:30am-12:30pm