MA 3053 - Schedule

Schedule

Schedule of topics: MA 3053, Fall 2016

Date Section       Description 
Aug 16      1.1, 1.2 Introduction, basic logic and set notation
Aug 18 1.2 Intervals, set containment and equality

Aug 23 1.2 Set operations
Aug 25 1.3 Function basics, graphs

Aug 30 1.3, 1.4 Operations on functions, composition, injections
Sep 1 1.4, 1.5 Injections, surjections, and bijections; images

Sep 6 1.5 Inverse images and inverse functions
Sep 8 1.5 Restricting functions to be injective/surjective

Sep 13 1.6, 2.1 Sequences, arbitrary unions/intersections; relations
Sep 15 2.1 Reflexive, symmetric, antisymmetric, and transitive relations

Sep 20 1.7, 2.1 Russell's Paradox, relation examples
Sep 22 Exam 1

Sep 27 2.2 Partial orderings, linear orderings
Sep 29 2.3 Equivalence relations

Oct 4 2.3 Equivalence classes, quotient spaces, and partitions
Oct 6 2.4 Defining bijections on quotient spaces

Oct 11 2.5 Modular arithmetic
Oct 13 Fall break! (No class)

Oct 18 2.5 Calculating mod n, casting out 9's technique
Oct 20 3.2 Statements, truth values, logic operators

Oct 25 3.2, 3.3 Contrapositive and converse; "if and only if", formulas
Oct 27 3.3, 3.4 Characteristic sets, quantifiers

Nov 1 3.4 Multiple quantifiers, order and negation
Nov 3 Exam 2

Nov 8 3.5 Proof strategies: universal statements
Nov 10 3.5, 4.1 Proof strategies: existential statements, well-orderings

Nov 15 4.2 Induction
Nov 17 4.2, 5.1 Strong induction, limit basics

Nov 22 5.1 More on limits
Nov 24 Thanksgiving! (No class)

Nov 29 5.1, 6.1 Limits, an introduction to countability

Dec 9 Final exam   (8:00am — 11:00am)