mat511 - indexSummer2010

Temperance (detail)
Pieter Bruegel the Elder, 1560.


Date	Topics	Reading	Homework
6/1	Introduction and Administrivia. Inductive vs. Deductive reasoning. Brief historical overview of the rise and importance of mathematical proof and logic. Review of propositional logic and introduction to quantifiers.	Chapter 1 of the text.	None assigned.
6/3	Logic and Proofs.	Read all of chapter 1 in the text. Read Ch. 2 as preparation for next week.	Homework,
6/8	More on Proofs. Set Theory. The Peano Axioms.	Ch 2.	Homework,
6/10	Review of proof methods, Mathematical Induction.	Section 2.4.	Homework,
6/15	More on Induction, Counting.	Section 2.5, 2.6	Homework,
6/17	Relations and partitions	Sections 3.1,3.2, and 3.3	Homework,
6/22	More on Relations	3.4, 3.5	Homework,
6/24	Functions	chapter 4	Homework,
6/29	more Functions.	the rest of chapter 4	Homework,
7/1	Cardinality	Sections 5.1, 5.2, 5.3	Homework,
7/3	Construction of the Integers, Rationals, and Reals. Proof that the reals are an uncountable set. Cantor-Bernstein-Schroeder Theorem	Section 5.4	Homework,
7/8	Algebraic structures; Groups, subgroups, operation-preserving maps (homomorphisms)	Sections 6.1, 6.2, 6.3, 6.4	Homework,
7/13	Final Grade Discussion
7/15	Note Change! No Final Examination,possibly Note Change!

Syllabus and Schedule