Instructor: Florent Baudier
Office: Blocker 525J
Office hours: MW 3:00-4:00 p.m. or by appointment
Lectures: MW 4:10-5:25 p.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. Optional Textbook: Tamara J. Lakins, The Tools of Mathematical Reasoning, 1st edition, American Mathematical Society, Pure and applied undergraduate texts, The Sally Series.
Exams: Homework   Term Paper Instructions   Lecture notes   Tentative Schedule

Date of Class	Material covered
Monday 01/12	general introduction, statements, predicates, logical connectives and-or-not, logical equivalence, DeMorgan's laws.
Wednesday 01/14	Quiz #1 , implication, converse, contrapositive, biconditional.
Monday 01/19	MLK Day, class does not meet.
Wednesday 01/21	Quiz #2, Quantifiers: existential and universal quantifiers, membership, rules of negation,
Monday 01/26	class cancelled due to inclement weather.
Wednesday 01/28	Quiz #3, Quantifiers: statements with multiple and mixed quantifiers Proof techniques: Modus Ponens, Modus Tollens, proof of existential statements.
Monday 02/02	Proof techniques: proof of uniqueness in existential statements, proofs of universal statements
Wednesday 02/04	Quiz #4, disproving universal statements, proof by contrapositive
Monday 02/09	proof by contradiction
Wednesday 02/11	other proof techniques (biconditional, case distinction, disjunction, backwards...) 7:15-8:45 p.m. Exam #1 (covers logic and proof techniques)
Monday 02/16	Class does not meet.
Wednesday 02/18	Quiz #5, principle of (strong) mathematical induction
Monday 02/23	sets, emptyset, subsets, equality
Wednesday 02/25	Quiz #6, unions, intersections
Monday 03/02	complements, DeMorgan Laws
Wednesday 03/04	Quiz #7, arbitrary unions, arbitrary intersections
Monday 03/09	Springbreak, no classes
Wednesday 03/11	Springbreak, no classes
Monday 03/16	power set, cartesian product
Wednesday 03/18	relations: reflexivity, symmetry, anti-symmetry, transitivity, order relations. Exam #2 (covers induction and set theory)
Monday 03/23	Class does not meet.
Wednesday 03/25	Quiz #8, equivalence relations and partitions
Monday 03/30	functions: definition, composition
Wednesday 04/01	Quiz #9, injectivity, surjectivity, bijectivity of functions
Monday 04/06	invertibility, invertibility implies bijectivity
Wednesday 04/08	Quiz #10, bijectivity implies inverstibility, functions and sets: direct images
Monday 04/13	Functions and sets: inverse images.
Wednesday 04/15	Quiz #11, Introduction to cardinal theory.
Monday 04/02	Introduction to cardinal theory.
Wednesday 04/22	Exam #3 (covers relations, functions, and cardinal theory)
Monday 04/27	Class does not meet.