Class Diary

- Monday, January 13 -
- Class: Syllabus, other handouts, what the class is about, and a tiny bit of material.
- Read: Section 2.1 for Tuesday.
- Written work (due 1/24): Fill out the questionnaire posted here and return it to my office.

- Tuesday, January 14 -
- Class: Most of the material in Section 2.1.
- Read: Section 2.2 for tomorrow.
- Written work (due 1/24): 2.1.13, 2.1.17, 2.1.31, 2.1.43, 2.1.49. (This means problems 13, 17, 31, 43 and 49 from Section 2.1 of the textbook, which in my version is on pages 37-38.)
- Good practice problems: 2.1.15, 2.1.25, 2.1.52
- Extra practice problems: 2.1.7, 2.1.9, 2.1.20, 2.1.32.

- Wednesday, January 15 -
- Class: De Morgan's laws, conditional statements (including the contrapositive).
- Read: Section 2.3 for Friday.
- Written work (due 1/24): Nothing new yet.

- Friday, January 17 -
- Class: Converse and inverse, rules of inference, valid and invalid arguments, and fallacies.
- Read: Section 3.1 for Tuesday.
- Written work (due 1/24): 2.2.17, 2.2.25, 2.2.35, 2.3.9, 2.3.29, and 2.3.38.
- Good practice problems: 2.2.28, 2.2.40, 2.3.29, 2.3.39, 2.3.42
- Extra practice problems: 2.2.3, 2.2.19, 2.3.3, 2.3.7, 2.3.12, 2.3.37.

- Tuesday, January 21 -
- Class: Proofs by contradiction, don't be friends with Jim, irrationality of the square root of two and predicates and truth sets.
- Read: Section 3.2 for Wednesday.
- Written work (due 1/31): 3.1.1, 3.1.3, 3.1.8.

- Wednesday, January 22 -
- Class: Universal and existential quantifiers and negating quantified statements.
- Read: Section 3.3 for Friday.
- Written work (due 1/31): 3.1.16, 3.1.22, 3.1.26, 3.2.8.
- Good practice problems: 3.1.5, 3.1.20, 3.1.23
- Extra practice problems: 3.1.8, 3.1.11, 3.1.29.

- Friday, Jaunary 24 -
- Class: Knights and knaves with truth tables, statements with multiple quantifiers.
- Read: Section 3.4 for Monday.
- Written work (due 1/31): 3.2.21, 3.3.12, 3.3.21.
- Good practice problems: 3.2.11, 3.2.12, 3.3.14, 3.3.41, 3.3.43
- Extra practice problems: 3.2.1, 3.2.4, 3.2.15, 3.2.41, 3.3.2, 3.3.3, 3.3.12.

- Monday, January 27 -
- Class: Negating statements with multiple quantifiers, and arguments with quantified statements.
- Read: Section 4.1 for Tuesday.
- Written work (due 2/7): 3.4.15, 3.4.32.
- Good practice problems: 3.4.19, 3.4.25, 3.4.31.
- Extra practice problems: 3.4.5, 3.4.7, 3.4.17, 3.4.20.

- Tuesday, January 28 -
- Class: Section 4.1
- Read: Section 4.2 for tomorrow.
- Written work (due 2/7): 4.1.32, and this problem.

- Wednesday, January 29 -
- Class: Even and odd numbers, prime and composite numbers, and more proofs.
- Read: Section 4.3 for Friday.
- Written work (due 2/7): 4.1.40, 4.1.50, 4.1.57.
- Good practice problems: 4.1.31, 4.1.39, 4.1.56.
- Extra practice problems from 4.1: 4.1.4, 4.1.9, 4.1.12, 4.1.19, 4.1.21, 4.1.30, 4.1.36.

- Friday, January 31 -
- Class: Rational numbers and divisibility.
- Read: Section 4.4 for Monday.
- Written work (due 2/7): 4.2.30, 4.2.39, 4.3.26.
- Good practice problems: 4.2.19, 4.2.23, 4.2.29, 4.2.37, 4.3.24, 4.3.30, 4.3.31.
- Extra practice problems: 4.2.3, 4.2.15, 4.2.20, 4.2.33, 4.3.24, 4.3.32, 4.3.35.

- Monday, February 3 -
- Class: Proper proof of Theorem 4.3.4, discussion of unique factorization, and then a worksheet on sections 4.1-4.3. (Worksheet solutions are posted on Canvas.)
- Read: Nothing new. We'll start 4.4 tomorrow.
- Written work (due 2/12, next Wednesday): 4.3.37, 4.3.40, 4.3.41
- Good practice problems: 4.3.38, 4.3.45, 4.3.47.
- Extra practice problems: 4.3.39, 4.3.42.

- Tuesday, February 4 -
- Class: Proofs by contrapositive and contradiction. Also, the quotient-remainder theorem and using that.
- Read: Section 4.6 - we're doing this sort of in tandem with the material in 4.4.
- Written work (due 2/12): 4.4.21, 4.4.43, 4.6.14.
- Good practice problems: 4.4.14, 4.4.17, 4.4.24 (this is a trick question), 4.6.9, 4.6.16 (this is hard)
- Extra practice problems: 4.4.23, 4.4.43, 4.6.19, 4.6.29.

- Wednesday, February 5 -
- Class: More examples of the quotient-remainder theorem, and some stuff about rationality.
- Read: Section 4.7 for Friday.
- Written work (due 2/12): 4.4.33, 4.6.15
- Good practice problems: 4.4.32, 4.4.40, 4.6.31.
- Extra practice problems: 4.4.50-4.4.52, 4.6.35.

- Friday, February 7 -
- Class: Review of proof that 2^(1/2) is irrational, some more properties of rational and irrational numbers, discussion of prime numbers (and their infinitude) and the start of a discussion of algorithms.
- Read: Section 4.8 for Monday.
- Written work (due 2/12): 4.7.19, 4.7.31.
- Good practice problems: 4.7.15, 4.7.23, 4.7.32.
- Extra practice problems: 4.7.3, 4.7.21. 4.7.22.

- Monday, February 10 -
- Class: Completion of proofs about and discussion of the Euclidean algorithm. Then a review worksheet on Chapters 2-4.
- Read: Section 5.1 for Tuesday.
- Written work (due 2/21): 4.8.16, and 4.8.20.
- Good practice problems: 4.8.15, and 4.8.19.

- Tuesday, February 11 -
- Class: Sequences, sums (including telescoping ones). Number of zeros at the end of n!.
- Read: Section 5.2 for next Monday.
- BRING QUESTIONS TO CLASS TOMORROW! (Sorry for the all caps.)
- Written work (due 2/21): 5.1.28, 5.1.47.
- Good practice problems: 5.1.77, 5.1.38, 5.1.41.

- Wednesday, February 12 -
- Class: Passed out practice exam, and took questions from students about material and format of the exam.
- Read: Nothing new.
- Written work: Nothing more this week.

- Friday, February 14 -
- Class: First midterm exam.
- Read: Nothing new.

- Monday, February 17 -
- Class: Went over exam and discussed sequences and the "foreshadowing of induction".
- Read: Nothing new.
- Written work: Nothing new.

- Tuesday, February 18 -
- Class: Formal structure of induction and examples with divisibility and proving summation formulas.
- Read: Section 5.3 for Wednesday.
- Written work (due 2/28): 5.2.7, 5.2.11, 5.2.15, 5.2.23, 5.3.12.
- Good practice problems: 5.2.2, 5.2.5, 5.2.18, 5.2.33, 5.2.35, 5.3.9, 5.3.18.
- Extra practice problems: 5.2.13, 5.3.8, 5.3.10, 5.3.13.

- Wednesday, February 19 -
- Class: Strong induction examples with second-order recurrences (divisibility and inequalities). Discussion of the last example from the notes, but we didn't actually do it.
- Read: Section 5.4 for Friday.
- Written work (due 2/28): 5.3.21, 5.4.7.
- Good practice problems: 5.3.28, 5.3.31, 5.3.36.
- Extra practice problems: 5.3.18, 5.3.26, 5.3.29, 5.3.36.

- Friday, February 21 -
- Class: Three more examples of proving things via strong induction, including the last example from Wednesday.
- Read: Section 6.1 for Monday.
- Written work (due 2/28): 5.4.10, 5.4.14, and this problem.
- Good practice problems: 5.4.5, 5.4.8, 5.4.16, 5.4.29.
- Extra practice problems: 5.4.1, 5.4.7, 5.4.19, 5.4.25.

- Monday, February 24 -
- Class: Sets and subsets.
- Read: Section 6.2 for Tuesday. (We might start the material in 6.2 tomorrow.)
- Written work (due 3/6): 6.1.6, 6.1.10.
- Good practice problems: 6.1.1, 6.1.3, 6.1.5, 6.1.8, 6.1.30.
- Extra practice problems: 6.1.11, 6.1.18.

- Tuesday, February 25 -
- Class: Power sets and cartesian products.
- Read: Nothing new.
- Written work (due 3/6): 6.1.23, 6.1.31.
- Good practice problems: 6.1.22, 6.1.25, 6.1.33.
- Extra practice problems: 6.1.25, 6.1.26, 6.1.35.

- Wednesday, February 26 -
- Class: Proving set equalities and parallels with logic.
- Read: Nothing new.
- Written work (due 3/6): 6.2.14, 6.2.22, 6.2.35.
- Good practice problems: 6.2.6, 6.2.8, 6.2.19.
- Extra practice problems: 6.2.1, 6.2.13, 6.2.22.

- Friday, February 28 -
- Class: More discussion of proofs and more examples with Cartesian products and power sets.
- Read: The parts of Section 6.4 about Russell's paradox and the halting problem. Also read Section 7.1.
- Written work (due 3/6): 6.2.38, 6.2.41, and this problem.
- Good practice problems: 6.2.39, 6.2.40.

- Monday, March 2 -
- Class: Russell's paradox, the halting problem, and the start of functions.
- Read: Section 7.2 for tomorrow.
- Written work (due 3/20): 6.4.23, 7.1.2 (only parts a-e).
- Good practice problems: 6.4.19, 6.4.26, 7.1.11.
- Extra practice problems: 6.4.22, 7.1.3, 7.1.4.

- Tuesday, March 3 -
- Class: Image and inverse images, well-definedness. Then we started 7.2 and talked about one-to-one (injective) functions.
- Read: Section 7.3 for tomorrow.
- Written work (due 3/27): 7.1.14, 7.1.42, 7.1.43.
- Good practice problems: 7.1.38, 7.1.45, 7.1.47.
- Extra practice problems: 7.1.15, 7.1.34, 7.1.48.

- Wednesday, March 4 -
- Class: Onto functions, bijections, and inverses.
- Read: We'll start 7.3 tomorrow, and we might talk briefly about 7.4.
- Written work (due 3/27): 7.2.17, 7.2.37, and this problem.
- Good practice problems: 7.2.8, 7.2.27, 7.2.41.
- Extra practice problems: 7.2.4, 7.2.11, 7.2.36, 7.2.40.

- Friday, March 6 -
- Class: Composition of functions.
- Read: Section 8.1 for Monday March 16.
- Written work (due 3/27): 7.3.15, 7.3.22.
- Good practice problems: 7.3.4, 7.3.8.
- Extra practice problems: 7.3.19, 7.3.26.

- Note: For the rest of the semester all class materials will be posted on Canvas. (I'm trying to make it so you get everything in one place.)

vBack to course homepage.

Last modified: Monday, 23-Mar-2020 11:56:03 EDT