Instructor: Florent Baudier
Office: Blocker 525C
Office hours: MW 11:30 AM-12:30 PM 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
Course description:
Math 300 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:
Section 901: Friday, September 27, 9:10-10:00 a.m. (classroom: Blocker 148).
Section 903: Friday, September 27, 10:20-11:10 a.m. (classroom: Blocker 148).
Exam #2:
Section 901: Wednesday, October 30, 8:00-10:00 p.m. (classroom: Blocker 149).
Section 901: Wednesday, October 30, 8:00-10:00 p.m. (classroom: Blocker 149).
| Date of Class |
Material covered |
| Monday 08/26 |
organizational laius, statements, predicates |
| Wednesday 08/28 |
basic logical connectives: conjunction, disjunction, negation, implication, contrapositive, converse, biconditional |
| Friday 08/30 |
problem session |
| Monday 09/02 |
quantifiers: existential, universal |
| Wednesday 09/04 |
membership |
| Friday 09/06 |
Quiz #1, problem session |
| Monday 09/09 |
proof techniques: existential proofs, uniqueness proofs |
| Wednesday 09/11 |
proof techniques: universal proofs |
| Friday 09/13 |
Quiz #2, problem session |
| Monday 09/16 |
proof techniques: proof by contrapositive |
| Wednesday 09/18 |
proof techniques: proof by contradiction |
| Friday 09/20 |
Quiz #3, problem session |
| Monday 09/23 |
proof techniques: proving disjunction statements, proof by cases, working backwards |
| Wednesday 09/25 |
review for exam #1 |
| Friday 09/27 |
Exam #1 |
| Monday 10/30 |
principle of mathematical induction |
| Wednesday 11/02 |
principle of strong mathematical induction |
| Friday 10/05 |
Quiz #4, problem session |
| Monday 10/07 |
sets, subsets |
| Wednesday 10/09 |
complement |
| Friday 10/11 |
Quiz #5, problem session |
| Monday 10/14 |
union and intersection of two sets |
| Wednesday 10/16 |
arbitrary union and intersection |
| Friday 10/18 |
Quiz #6, problem session |
| Monday 10/21 |
Power set |
| Wednesday 10/23 |
Cartesian products |
| Friday 10/25 |
Quiz #7 , problem session |
| Monday 10/28 |
problem session, review for exam #2 |
| Wednesday 10/30 |
problem session, review for exam #2 Exam #2 (8-10pm)
Practice 1
Practice 2 |
| Friday 11/01 |
binary relations: definition, classical properties, examples |
| Monday 11/04 |
equivalence relations and partitions |
| Wednesday 11/06 |
functions: definition, terminology, examples |
| Friday 11/08 |
Quiz #8, problem session |
| Monday 11/11 |
equality between functions and composition of functions |
| Wednesday 11/13 |
injectivity, surjectivity |
| Friday 11/15 |
Quiz #9 , problem session |
| Monday 11/18 |
bijectivity and invertibility |
| Wednesday 11/20 |
direct image of a set, inverse image of a set |
| Friday 11/22 |
Quiz #10 , problem session |
| Monday 11/25 |
class canceled |
| Wednesday 11/27 |
reading day, no classes |
| Friday 11/29 |
Thanksgiving Holiday |
| Monday 12/02 |
Fall redefined day, Friday classes, problem session, review for the final |
| Wednesday 12/04 |
Last day of classes, problem session, review for the final |
| Friday 12/07 |
Final examinations start, no classes |
| Monday 12/09 |
Final exam-Section 901 , 8-10am |
| Tuesday 12/10 |
Final exam-Section 903 , 8-10am |