Please see below for lecture summaries, homework and other study material. For your grades, please see Canvas.
| Date | Topics |
| Jun.01. | Basic definitions and notation about sets. Element membership vs subset containment. Equality of sets. Cartesian products. Power sets.
Notes.
HW1 (due Fri., Jun. 3): 1.1: 3, 12, 18, 31; 1.2: 9, 15; 1.3: 13, 14, 15; 1.4: 14, 15. |
| Jun.02. | Operations on sets. Venn diagrams. More proofs of set equalities. DeMorgan's Law. Notes. |
| Jun.03. | Indexed sets. Statements and truth tables. How to prove various
types of statements. Notes.
HW2 (due Tue., Jun. 7): 1.5: 2, 6, 10; 1.6: 2, 6; 1.7: 4, 10; 1.8: 2, 4, 8, 14; 2.1: 4, 10. |
| Jun.06. | Logical equivalences. Open statments and quantifiers. Notes. |
| Jun.07. | The multiplication, addition, and subtraction principles for counting. First counting problems. Notes.
HW3 (due Tue., Jun. 10): 2.5: 6, 8, 10; 2.6: 3, 12. 2.7: 4, 8; 3.3: 2, 4, 8, 10; 3.4: 3, 4, 10, 12. |
| Jun.08. | Permutation vs combinations. More counting problems. Notes. |
| Jun.09. | Combinatorial proofs. Counting worksheet. Notes. Worksheet. |
| Jun.10. | The binomial theorem. Pascal's triangle. Midterm I. Notes.
HW4 (due Tue., Jun. 14): 3.5: 4, 8, 9, 10, 18; 3.6: 2, 3, 4, 7. |
| Jun.13. | The inclusion-exclusion principle. Multisets and the bars-and-stars method. Notes. |
| Jun.14. | More bars-and-stars problems. Multiset permutations. Summary
of counting problem types.
Notes.
HW5 (due Fri., Jun. 17): 3.7: 4, 6, 8, 12; 3.8: 2, 5, 7, 8, 10, 12, 14; 3.9: 2, 3, 4. |
| Jun.15. | The pigeonhole and division principles. More combinatorial identities. Notes. |
| Jun.16. | Foundational definitions related to integer division. Direct proofs of conditional statements. Notes. |
| Jun.17. | More direct proofs.
Worksheets on counting (multisets) and direct proofs. Notes. Worksheet on more counting problems. Worksheet on proofs.
HW6 (due Tue., Jun. 21): 3.10: 6, 7, 8. Chapter 4: 4, 10, 12, 16, 20, 26. |
| Jun.20. | Proofs via contrapositives. Proofs by contradiction. Proving equivalences. Recommendations for mathematical writing. Notes. |
| Jun.21. | Proofs of existential claims. Constructive vs. non-constructive proofs. Notes. Worksheet on more proofs.
HW7 (due Fri., Jun. 24): Ch. 5: 6, 7, 22, 28; Ch. 6: 8, 9, 10, 14; Ch. 7: 6, 12, 32, 33. |
| Jun.22. | Proofs of set containments and set equalities. Disproofs and true/false problems. Notes. |
| Jun.23. | Mathematical induction and strong mathematical induction. Notes. Third worksheet on proofs. |
| Jun.24. | An inductive proof about graph theory. Midterm II. Notes.
HW8 (due Tue., Jun. 28): Ch. 8: 6, 19, 20, 30; Ch. 9: 8, 18, 22; Ch. 10: 4, 6, 8. |
| Jun.27. | More inductive proofs: fundamental theorem of arithmetic, Fibonacci numbers. Notes. Worksheet on induction. |
| Jun.28. | Relations and equivalence relations. Notes.
HW9 (due Fri., Jul. 1): Ch. 10: 16, 20, 21, 26, 42; 11.2: 14, 15; 11.3: 2, 4, 8. |
| Jun.29. | Partitions from equivalence relations. Basic notions concerning functions. Notes. |
| Jun.30. | Proof and counting problems on functions. Review for final exam. Notes. |
| Jul.01. | Final exam. |