M1,M2) on
the two midterms and the score (F) on the final as the
maximum of four quantities:
.25 M1 + .25 M2 + .5 F,
.33 M1 + .67 F,
.33 M2 + .67 F,
F.
|
| Material actually covered | Suggested exercises | ||
|---|---|---|---|
| Jan 21 | Section 1.1:
Propositions. Implications. Precedence of logical operators. Section 1.2: Introduction. Logical Equivalences (Tables 1,2,3; De Morgan's laws.) | Section 1.1:
1--2, 12--13, 23--31; optionally 7--11, 14--15, 21--22. Section 1.2: 7--10, 12--13. | |
| Jan 26 | Section 1.2: Tables 5,6. | Section 1.2: 14--29. | |
| Jan 28 | No class | ||
| Feb 2 | Section 1.3: Quantifiers. Table 2. Translating
from English into logical expressions. Section 1.4: Translating statements involving nested quantifiers. Translating sentences into logical expressions. Negating nested quantifiers. The order of quantifiers. | Section 1.3: 9--10, 11-20, 33--34; optionally,
41--47. Section 1.4: 8--13; 26--28. | Homework 1 posted |
| Feb 4 | Section 1.5: Modus ponens. Hypothetical syllogism. | --- | |
| Feb 9 | Section 1.5: Table 1. Example 6. Example 7. | Section 1.5: 1--6. | Homework 1 accepted for grading |
| Feb 11 | Section 1.5: Fallacies. Direct proofs. Definition 1. Example 14. Indirect proofs. Example 15. Proofs by contradicition. Example 20. | Section 1.5: 11--13. | |
| Feb 16 | Thales of Miletus; Pythagoras of Samos; Plato; Euclid of Alexandria. Section 1.5: Example 21. Barber of Seville (Section 1.1, Exercise 40) and part 4 of Homework 1. | --- | |
| Feb 18 | Section 1.5: Proof by cases. Example 23. Existence proofs. Examples 26 and 27. | --- | |
| Feb 23 | Section 1.6: Introduction. The power set. Cartesian product. Section 1.7: Introduction. Set identities. | Section 1.6: 1--26. Section 1.7: 1--23. | |
| Feb 25 | Section 1.6: Using set notation with quantifiers. Section 1.8: Introduction. One-to-one and onto functions. Inverse functions. Some important functions. | Section 1.6: 27--28. Section 1.8: 1--19. | Homework 2 posted |
| Mar 1 | Section 10.1: Introduction. Boolean expressions and Boolean functions. Identities of Boolean algebra. | Section 10.1: 1--11. | |
| Mar 3 | Section 10.2: Sum-of-products expansion. | Section 10.2: 1--6. | Homework 2 accepted for grading |
| Mar 8 | MIDTERM 1 (material covered from Jan 21 to Feb 25) | ||
| Mar 10 | Section 10.4: Introduction. The Quine-McCluskey method. | Section 10.4: 22--25. | |
| Mar 15 | Spring Recess | ||
| Mar 17 | Spring Recess | ||
| Mar 22 | Section 2.4: Introduction. Division. Primes. The division algorithm. Greatest common divisors and least common multiples. Modular arithmetic. | Section 2.4: 1--7, 21--22, 28--32, 36--39, 42--47; optionally, 8--13 | |
| Mar 24 | Section 3.1: Proof strategies. Examples 1,2,3,4. Conjecture and counterexamples. Example 13. | Section 3.1: optionally, 1--10, 22--30. | |
| Mar 29 | Section 3.3: Introduction. Mathematical induction. Why mathematical induction is valid. Examples 1--3, 5. | Homework 3 posted | |
| Mar 31 | Section 3.3: Example 11. | ||
| Apr 5 | Section 3.3: Examples 6--10. Strong Induction. Examples 13--15. The well-ordering property. | Section 3.3: Exercises 1--24, 31--35, 50--54. | Homework 3 accepted for grading |
| Apr 7 | Proving correctness of programs: Example 1 from the lecture notes. | ||
| Apr 12 | Section 3.6. Example 2 from the lecture notes. | Section 3.6: Exercises 1--4, 7, 9--10, 12. Examples 3 and 4 from the lecture notes. | |
| Apr 14 | Section 11.2. | Section 11.2: Exercises 1--15. | |
| Apr 19 | Definition 1 from Section 11.1 (p.741). Section 11.3: Definitions 1--4, Example 5. Section 11.4: Definition 1, Example 1, Theorem 1. | ||
| Apr 21 | Section 11.4: Example 5. The if part of the proof of Kleene's theorem. | Homework 4 posted | |
| Apr 26 | Homework 4 accepted for grading | ||
| Apr 28 | MIDTERM 2 (material covered from Mar 10 to Apr 19) | ||
| May 3 | Review | ||
| May 11 (Tuesday) | FINAL 12:00 -- 3:00 | in Hardenbergh Hall B2, College Avenue Campus |