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| 9/3 | Introduction and Administrivia. Inductive vs. Deductive reasoning. Brief historical overview of the rise of importance of mathematical proof and logic. Review of propositional logic and introduction to quantifiers. | Chapter 1 of the text. | None assigned. Think about stuff. |
| 9/10 | Logic and Proofs. | Read all of chapter 1 in the text. Read Ch. 2 as preparation for next week. | Homework 1, in pdf or
html
Solutions, in pdf or html |
| 9/17 | More on Proofs. Set Theory. The Peano Axioms. | Ch 2. | Homework 2, in pdf or
html;
(fixed typo in problem 3 on 9/21/03). Solutions, in pdf or html |
| 9/24 | Review of proof methods, Mathematical Induction. | Section 2.4. | Homework 3, in pdf or
html;
Solutions, in pdf or html |
| 10/1 | More on Induction, Counting. | Section 2.5, 2.6 | Homework 4, in pdf or
html;
Solutions, in pdf or html |
| 10/8 | No class held. Even though your calendar and mine says that this day is a wednesday, the university calendar says this is a monday. (This is to make up for the mondays lost to other holidays). | ||
| 10/15 | Relations and partitions | Sections 3.1,3.2, and 3.3 | Homework 5, in pdf or
html;
Solutions, in pdf or html |
| 10/22 | More on Relations | 3.4, 3.5 | Homework 6, in pdf or
html;
Solutions, in pdf or html |
| 10/29 | Functions | chapter 4 | Homework 7, in pdf or
html;
Solutions, in pdf or html |
| 11/5 | more Functions. | the rest of chapter 4 | Homework 8, in pdf or
html;
Solutions, in pdf or html |
| 11/12 | Cardinality | sections 5.1, 5.2, 5.3 | Homework 9, in pdf or
html;
Solutions, in pdf or html |
| 11/19 | Construction of the Integers, Rationals, and Reals. Proof that the reals are an uncountable set. | Handout from Eves. See also discussions of construction of the integers and rationals and of the reals via Dedekind Cuts. Optionally, the notion of Surreal Numbers extends the notion further than you might expect possible. | Homework 10, in pdf or
html;
Solutions, in pdf or html |
| 11/26 | Thanksgiving. Class not held. (According to the University, classes are in session this evening. Feel free to come to class, but I won't be there. If you do come, let me know what you did.) | ||
| 12/3 | finish cardinality. | Chapter 5, Welcome to the Hotel Infinity!. | |
| 12/10 | Let's see what happens | ||
| 12/17 | | ||