Math 113

Discrete Structures, Fall 2020 (Sections F01, F02)

Instructor: Kyle Ormsby
Text: Discrete Structures, by Ormsby and Perkinson. (Last update: Nov 22, 2020.)
Additional (optional) resource: Discrete Mathematics: Elementary and Beyond, by Lovász, Pelikán, and Vesztergombi
For details on attending the following, see our Moodle page:
  • Office hours: M 3-4pm, W 11:05am-12:05pm, and by appointment.
  • Problem sessions: TuTh 7-8pm.
  • Drop-in tutoring: SuMTuWTh 7-9pm.
Exams
  • Exam 1: Distributed Wednesday, September 23 and due Friday, September 25.
  • Exam 2: Distributed Wednesday, October 21 and due Friday, October 23.
  • Final Exam: TBA (sometime in December 10–15).
Course Information & Syllabus
Current week
Week 1: August 31 - September 4
Monday: Welcome and warm up.
Here is an article about Ron Graham, a renowned pioneer in discrete mathematics: Ron Graham. The video Graham's number, linked to in that article, is recommended.
Group problems: Solutions.
Wednesday: Beginning counting.
Lecture/quiz (remember to hit the SUBMIT QUIZ button at the end). [Note: Lecture/quiz links turn into review video links after class 🤓]
Group problems: Solutions.
Friday: The language of sets.
Lecture/quiz.
Group problems: Board F01.1, F01.2, F01.3, F02.1. F02.2. F02.3. Solutions.

Video of the week The eight queen problem.

Week 2: September 7 - September 11
Monday: No class. Labor Day.
Wednesday: Additive and multiplicative counting.
Lecture/quiz. Turn in: HW2W.
Group problems: Solutions.

Friday: Functions.
Lecture/quiz. Turn in: HW2F.
Group problems: Board F01.1, F01.2, F01.3, F02.1, F02.2, F02.3. Solutions.

Video of the week Counting to 1000 on two hands.

Week 3: September 14 - September 18
Monday: Permutations and combinations.
Lecture/quiz. Turn in: HW3M
Group problems: Board F01, Board F02. Solutions.

Wednesday: Equivalence relations.
Lecture/quiz. Turn in: HW3W
Group problems: Board F01, Board F02. Solutions.

Friday: Pascal's triangle and the binomial theorem.
Lecture/quiz. Turn in: HW3F
Group problems: Board F01, Board F02. Solutions.

Video of the week 43,252,003,274,489,856,000 Rubik's Cube Combinations

Week 4: September 21 - September 25
Monday: Induction.
Lecture/quiz. Turn in: HW4M.
Group problems: Board F01, Board F02. Solutions.
Wednesday: Exam review. (Exam distributed today.) Turn in: HW4W.
Group problems. Solutions.
Friday: Something awesome. Turn in exam.
Group problems: Board F01, Board F02. Solutions.

Video of the week   5 Unusual Proofs (created by Kelsey Houston-Edwards, Reed class of 2013)

Week 5: September 28 - October 2
Monday: Inclusion/exclusion.
Lecture/quiz. Turn in: HW5M.
Group problems. Solutions.

Wednesday: Pigeonhole principle.
Lecture/quiz. No homework due today.
Group problems. Solutions.

Friday: Vertices, edges, and degree.
Lecture/quiz. Turn in: HW5F.
Group problems: Board F01, Board F02. Solutions.

Video of the week   The Mandelbrot Set - Numberphile

Week 6: October 5 - October 9
Monday: Paths and cycles.
Lecture/quiz. Turn in: HW6M.
Group problems. Solutions.

Wednesday: Trees and vertebrates.
Lecture/quiz. Turn in: HW6W.
Group problems. Solutions.

Friday: Dyck paths and parentheses.
Lecture/quiz. Turn in: HW6F.
Group problems: Board F01, Board F02. Solutions.

Video of the week   River crossings, vertex covers, and Alcuin numbers

Week 7: October 12 - October 16
Monday: Full binary trees.
Lecture/quiz. Turn in: HW7M.
Group problems. Solutions.

Wednesday: Noncrossing partitions.
Lecture/quiz. Turn in: HW7W.
Group problems. Solutions.

Friday: Parking functions.
Lecture/quiz. Turn in: HW7F.
Group problems: Board F01, Board F02. Solutions.

Video of the week   The associahedron

Week 8: October 19 - October 23
Monday: Catalan structures and trees.
Lecture/quiz. Turn in: HW8M.
Group problems. Solutions.

Wednesday: Exam review.
Turn in: HW8W.
Group problems. Solutions.

Friday: Something awesome.
Turn in exam.
Group problems. Intro video. Board F01, Board F02. Solutions. Solution video.

Video of the week   Hand sanitizer, toilet paper, and \(1/e\).

Week 9: October 26 - October 30
Monday: Probability spaces.
Lecture/quiz. Turn in: HW9M.
Group problems. Solutions.
Wednesday: Independence.
Lecture/quiz. No HW due.
Group problems. Solutions.

Friday: Conditional probability.
Lecture/quiz. Turn in: HW9F.
Group problems. Board F01, Board F02. Solutions.

Blog of the week Simpson's paradox as a semi-algebraic set.

Week 10: November 2 - November 6
Monday: Expected value.
Lecture/quiz. Turn in: HW10M.
Group problems. Solutions.
Wednesday: Special random variables
Lecture/quiz. Turn in: HW10W.
Group problems. Solutions.
Friday: Divisibility and primes.
Lecture/quiz. Turn in: HW10F.
Group problems. Board F01, Board F02. Solutions.

Video of the week   Why it's impossible to tune a piano.

Week 11: November 9 - November 13
Monday: Distribution of primes.
Lecture/quiz. Turn in: HW11M.
Group problems. Solutions.

Wednesday: Fermat's little theorem.
Lecture/quiz. Turn in: HW11W.
Group problems. Solutions.
Friday: Euclidean algorithm.
Lecture/quiz. Turn in: HW11F.
Back-solving the Euclidean algorithm for Bézout's identity (video).
Group problems. Board F01, Board F02. Solutions.

Video of the week   Gaps between primes.

Week 12: November 16 - November 20
Monday: Modular arithmetic.
Lecture/quiz. Turn in: HW12M.
Group problems. Solutions.
Wednesday: Modular units and Euler's totient function.
Lecture/quiz. Turn in: HW12W.
Group problems. Solutions.
Friday: Sunzi's theorem.
Lecture/quiz. Turn in: HW12F.
Group problems. Board F01, Board F02. Solutions.

Video of the week   Card trick.

Week 13: November 23 - November 27
Thankgiving vacation. No class this week.

Week 14: November 30 - December 4
Monday: Recurrence relations and the difference operator.
Lecture/quiz. Turn in: HW14M.
Group problems. Board F01, Board F02. Solutions.
Wednesday: Generating functions.
Lecture/quiz. Turn in: HW14W.
Group problems. Board F01, Board F02. Solutions.
Friday: Review.
Turn in: HW14F.
Group problems. Board F01, Board F02. Solutions.

Video of the week   Catalan numbers via generating functions.

Week 15: December 7 - December 11
Monday: Review Pictionary!
Turn in: HW15M.
Final review sheet. Board F01, Board F02.
Wednesday: Reading period.
Friday: Reading period.

Week 16: December 14 - December 18
Three-hour exam distributed by email on Monday at 9am, due via Gradescope by Tuesday at 11pm. See the review sheet for more details.
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