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.)

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