MATH 300
Foundations of Mathematics
Spring 2025
Instructor: Florent Baudier
Office: Blocker 525J
Office hours: TR 2:30-3:45 p.m. or by appointment
Lectures: TR 3:55-5:10 p.m. BLOC 121
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.
Optional 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, February 11, 3:55-5:10 p.m. (in the regular classroom).
Exam #2:
Tuesday, March 18, 3:55-5:10 p.m. (in the regular classroom).
Exam #3:
Thursday, April 24, 3:55-5:10 p.m. (in the regular classroom).
Homework   Term Paper Instructions   Lecture notes  
Tentative Schedule
Date of Class Material covered
Tuesday 01/14 general introduction, statements, predicates, logical connectives and-or-not
Thursday 01/16 Quiz #1 , DeMorgan's laws, logical equivalence, implication
Tuesday 01/21 class canceled due to inclement weather.
Thursday 01/23 Quiz #2, logical connectives: converse, contrapositive, biconditional.
Quantifiers: existential and universal quantifiers, membership.
Tuesday 01/28 Quantifiers: rules of negation, statements with multiple and mixed quantifiers
Proof techniques: Modus Ponens, Modus Tollens.
Thursday 01/30 Quiz #3, Proof techniques: proof of existential statements, proof of uniqueness in existential statements, proofs of universal statements
Tuesday 02/04 disproving universal statements, proof by contrapositive
Thursday 02/06 Quiz #4, proof by contradiction
Tuesday 02/11 Exam #1 (covers logic and proof techniques)
Thursday 02/13 other proof techniques
Tuesday 02/18 principle of mathematical induction
Thursday 02/20 Quiz #5, principle of strong mathematical induction
Tuesday 02/25 sets, emptyset, subsets, equality
Thursday 02/27 Quiz #6, unions, intersections
Tuesday 03/04 complements, DeMorgan Laws
Thursday 03/06 Quiz #7, arbitrary unions, arbitrary intersections
Tuesday 03/11 Springbreak, no classes
Thursday 03/12 Springbreak, no classes
Tuesday 03/18 Exam #2 (covers induction and set theory)
Thursday 03/20 power set, cartesian product
Tuesday 03/25 relations: reflexivity, symmetry, anti-symmetry, transitivity, equivalence relations
Thursday 03/27 Quiz #8, equivalence relations and partitions
Tuesday 04/01 functions: definition, composition
Thursday 04/03 Quiz #9, injectivity, surjectivity, bijectivity of functions
Tuesday 04/08 invertibility, invertibility implies bijectivity
Thursday 04/10 Quiz #10, bijectivity implies inverstibility, functions and sets: direct images
Tuesday 04/15 Functions and sets: inverse images
Thursday 04/17 Quiz #11, introduction to cardinal theory
Tuesday 04/22 review for exam #3
Thursday 04/24 Exam #3 (covers functions)
Tuesday 04/29 Fall redefined day, class does not meet