Course goals
| Level | Standard |
|---|---|
| D | Execute an algorithm correctly in familiar situations. Identify a theorem or definition that is related. |
| C | Reproduce statements of definitions and theorems. Execute an algorithm correctly in novel situations. Use the algorithm as part of a solution to familiar types of problems. |
| B | Recognize situations where a definition or theorem does or does not apply. Appreciate subtleties and edge cases in definitions, theorems, and algorithms. Identify opportunities to use an algorithm. |
| A | Use multiple ideas in the same problem. Understand how an algorithm works. Transform problems into forms suitable for application of an algorithm or theorem. Appreciate relevance of concepts beyond specific course content. |
| Level | The implication relation |
|---|---|
| D | Recall the truth table of the implication relation. |
| C | Use and interpret the implication relation in mathematical statements. |
| B | Assess the validity of mathematical statements involving implication. Use relationships between implication and other mathematical concepts. |
| A | Write mathematical proofs involving implication. Recognize and discover relationships between implication and other mathemaitcal concepts. |
Weekly topics
| Week | Topics | Exams |
|---|---|---|
| August 17-21 | Propositional logic | |
| August 24-28 | Variables and Quantifiers | |
| August 31-September 4 | Proof strategies | |
| September 7-11 Labor Day week |
Sets | |
| September 14-18 | Functions | Exam 1 |
| September 21-25 | Injectivity and surjectivity | |
| September 28-October 2 | Induction | |
| October 5-9 | Strong induction | |
| October 12-16 | Relations, equivalence relations, and partitions | |
| October 19-23 | Finite, countable, and uncountable sets | Exam 2 |
| October 26-30 | Division, divisibility, and the Euclidean algorithm | |
| November 2-6 | Prime numbers and modular arithmetic | |
| November 9-13 | Counting principles and inclusion-exclusion | |
| November 16-20 | Additional topics | |
| November 23-27 | Fall break: no classes | |
| November 30-December 4 | Additional topics |