Be careful to justify your solution when a problem calls for it. Good reasoning is the main point in this course.
| Date | Topic | Reading | Problems |
|---|---|---|---|
| 1/14/04 | Introduction to Introduction to Mathematical Reasoning | preface and pp4-10 | 1.14 (the sets should be intervals), 1.17, 1.25, 1.33, 1.36, 1.41ef, 1.42, 1.45 (identify the `non'functions and give counterexamples), 1.47, 1.50. solutions (except for 1.50) |
| 1/16/04 | Sets, functions, and numbers | pp10-20 | |
| 1/19/04 | Proofs | pp25-43 | |
| 1/21/04 | Proofs (cont) | 2.2, 2.4abd, 2.8, 2.16a, 2.21, 2.22, 2.30, 2.32, 2.40, 2.47 (in both parts,give a counterexample if the statement is false and a proof if the statement is true), 2.51a, Extra credit: 2.54 (if you get this one, turn it in directly to me on a separate sheet of paper); solutions. | |
| 1/23/04 | Induction | pp50-62 | |
| 1/26/04 | Induction (cont) | pp63-71 | |
| 1/28/04 | Induction (cont) | 3.11, 3.15, 3.16, 3.26, 3.33, 3.38, 3.50; solutions | |
| 1/30/04 | Induction/Decimal Expansions | pp76-87 | |
| 2/2/04 | Decimal Expansions | ||
| 2/4/04 | Injections, surjections, bijections | for practice (i.e. do not turn in): 4.1, 4.8, 4.9, 4.22, 4.24 to turn in: 4.2, 4.6, 4.12, 4.21 (assume n is odd), 4.25, 4.31, 4.34ab, 4.36a ; solutions for extra credit (work alone, turn in directly to me): 4.21 (n even), 4.36 (prove your formula is correct). |
|
| 2/6/04 | Composition/Cardinality | pp87-92 | |
| 2/9/04 | Cardinality | ||
| 2/11/04 | Cardinality | Homework assignment 5 ;
solutions |
|
| 2/13/04 | Prime factorization | pp123-126 | |
| 2/16/04 | Euclidean algorithm | pp126-129 | |
| 2/18/04 | Review for exam | Homework assignment 6 | |
| 2/20/04 | Exam 1; solutions | ||
| 2/23/04 | Euclidean algorithm and consequences | ||
| 2/25/04 | Equivalence relations | pp139-141 | Homework assignment 6, extended ; solutions |
| 2/27/04 | Equivalence relations (cont) | ||
| 3/1/04 | Congruences | ||
| 3/3/04 | Applications of congruences | pp142-145 | Homework assignment 7; solutions |
| 3/5/04 | Chinese remainder theorem | ||
| 3/15/04 | Invertibility mod n | pp149-150 | |
| 3/17/04 | Fermat's little theorem | pp147-149 | Homework assignment 8, solutions |
| 3/19/04 | RSA encryption | handout | |
| 3/22/04 | Rational numbers | pp376-377 (really!) | |
| 3/24/04 | Rational numbers--arithmetic and order | pp157-162 | Homework assignment 9, solutions |
| 3/26/04 | Rational numbers (cont) | ||
| 3/29/04 | Real numbers | pp256-258 (really!) | |
| 3/31/04 | Review for exam 2 | No new homework | |
| 4/2/04 | Exam 2; solutions | ||
| 4/5/04 | Limits | pp259-263 | |
| 4/7/04 | Limits (cont) | Homework assignment 10 , solutions | |
| 4/14/04 | Limits (cont) | pp271--275 | |
| 4/16/04 | Bounded sequences | pp276-279 | |
| 4/19/04 | Cauchy sequences | Homework assignment 11 (due Tuesday 4/27 by 5 PM in my mailbox); solutions | |
| 4/21/04 | Decimal Expansions | pp263-267 | |
| 4/23/04 | Cardinality of the real numbers | ||
| 4/26/04 | Decimal expansions of rational numbers | ||
| 4/28/04 | Review for the final | Review sheet for final | |