Temperance (detail)
Pieter Bruegel the Elder, 1560.
MAT 511 Fundamental Concepts of Mathematics
Fall 2006
Index Course Description Syllabus and Schedule |
Temperance (detail) Pieter Bruegel the Elder, 1560. |
MAT 511 Fundamental Concepts of Mathematics
|
Index Course Description Syllabus and Schedule |
|
|
|
|
|
| 9/6 | 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. |
| 9/13 | Logic and Proofs. | Read all of chapter 1 in the text. Read Ch. 2 as preparation for next week. | Homework 1, in
html
Solutions, in html |
| 9/20 | More on Proofs. Set Theory. The Peano Axioms. | Ch 2. | Homework 2, in
html;
Solutions, in html |
| 9/27 | Review of proof methods, Mathematical Induction. | Section 2.4. | Homework 3, in
html;
Solutions, in html |
| 10/4 | More on Induction, Counting. | Section 2.5, 2.6 | Homework 4, in
html;
Solutions, in html |
| 10/11 | Relations and partitions | Sections 3.1,3.2, and 3.3 | Homework 5, in
html;
Solutions, in html |
| 10/18 | More on Relations | 3.4, 3.5 | Homework 6, in
html;
Solutions, in html |
| 10/25 | Functions | chapter 4 | Homework 7, in
html;
Solutions, in html |
| 11/1 | more Functions. | the rest of chapter 4 | Homework 8, in
html;
Solutions, in html |
| 11/8 | Cardinality | Sections 5.1, 5.2, 5.3 | Homework 9, in
html;
Solutions, in html |
| 11/15 | Construction of the Integers, Rationals, and Reals. Proof that the reals are an uncountable set. Cantor-Bernstein-Schroeder Theorem | Section 5.4 | Homework 10 in
html;
Solutions, in html |
| 11/22 | | ||
| 11/29 | Algebraic structures; Groups, subgroups, operation-preserving maps (homomorphisms) | Sections 6.1, 6.2, 6.3, 6.4 | Homework 11 in
html;
Solutions, in html: Part I, Part II |
| 12/6 | |||
| 12/13 | |||