## Discrete Mathematics, Summer 2019

#### Time: 9am-12pm

Location: Room 1D508 in The Royal College of Music

Syllabus: click here

Piazza: click here

### Schedule:

**Tuesday, 5/21:** Propositional Logic (1.1, 1.3)

***Note*:** We will meet in the afternoon (at 1pm) this day, to not conflict with the 9am opening ceremony

**Homework:** Section 1.1, problems 2, 5ac, 6ace, 12acef, 13*, 18*, 21, 23, 25, 30; Section 1.3, problems 1ace, 3a, 5*, 8ac, 11ace, 12abc*, 22, 23*, 28, 31, 32

**Other:** Welcome dinner at 6:30pm at Urban Deli Nytorget

**Wednesday, 5/22:** Predicate Logic (1.4)

**Homework:** Section 1.4, problems 2, 3, 6, 12*, 14, 17abc, 19e*, 23abc, 28, 33

**Thursday, 5/23:** Nested Quantifiers and Rules of Inference (1.5, 1.6)

**Homework:** Section 1.5, problems 2, 3ace, 6be, 9acegi, 12acegi, 20*, 25, 28acegi*, 37, 45;

Section 1.6: problems 8, 10cde*, 13bd, 16ad*, 17, 19, 23*, 24

**Friday, 5/24:** Methods of Proof (1.7, 1.8)

**Homework:** Section 1.6, problem 11; Section 1.7, problems 1, 2, 6*, 7* (and study!)

**Other:** Walking tour of Gamla Stan (meet at Gustav Adolfs Torg at 4pm)

**Monday, 5/27:** Wrap up logic and proofs + Quiz 1 (on 1.1-1.6)

***Note*:** We will meet in the afternoon (at 1pm) this day, to not conflict with the 9am lecture

**Homework:** Section 1.7, problems 9*, 10, 13, 16*, 18, 24* (read example 9 in this section for an idea about how to proceed!)

**Other:** Lecture on Swedish Language and Culture at 9am

**Tuesday, 5/28:** Set Theory (2.1, 2.2)

**Homework:** Section 2.1, problems 1, 7, 8, 10*, 17, 25*; Section 2.2, problems 4, 14, 18, 24*, 29, 30, 31

**Other:** Dinner with Swedish Families (meet at DIS at 6pm)

**Wednesday, 5/29:** Functions (2.3)

**Homework:** Section 2.1, problems 27, 30; Section 2.2, problems 48*, 51; Section 2.3, problems 2, 14, 20*, 31, 34, 40*, 41a, 45

**Other:** Nobel Prize Museum at 1:30pm

**Thursday, 5/30:** Integers, Divisibility, and Modular Arithmetic (4.1)

***Note*:** We will meet in the afternoon (*edit* at 1pm at Hotell Zinkensdamm) this day, to not conflict with the tour

**Homework:** Section 2.3, problems 33*, 44; Section 4.1, problems 2, 3*, 5*, 8, 10abc; also, try to prove some of the statements from today’s lecture whose proofs we not given or only sketched

**Other:** Tour of the Royal Palace at 10:30am

**Friday, 5/31:** Primes and Elementary Number Theory (4.3)

**Homework:** Section 4.1, problems 24, 27, 35, 38*, 39, 41; Section 4.3, problems 2, 11, 12, 13*; also, try to develop a rule to test when a given positive integer is divisible by 3 (talk to me about this one, if you like!)

**Monday, 6/3:** Induction (5.1, 5.2) + Quiz 2

**Homework:** Section 4.3, problems 32ace, 40acegi (plus more to be added), 43, 44 (here, a “linear combination of a and b” means an expression of the form xa+yb for integers x and y, as we discussed in lecture);

Section 5.1, problems 6, 10*, 41, 51, 64*; Section 5.2, problems 12, 29

**Tuesday, 6/4:** Equivalence Relations (9.1, 9.5)

**Homework:** Section 5.2, problems 4, 25; Section 9.1, problems 4, 6*, 7 (but ignore “antisymmetric” for all of these, since we didn’t cover that concept); Section 9.5, problems 3abc, 9, 16*, 28abc, 35, 36

**Other:** Visit to Institute Mittag-Leffler

**Wednesday, 6/5:** Combinatorics (6.1-6.4)

**Homework:** Section 6.1, problems 1, 7, 8, 22, 40; Section 6.3, problems 13, 19, 33; Section 6.4, problems 3, 7, 17, 19 (Pascal’s identity was our third property of binomial coefficients), 21

(note: don’ worry about doing all of these, they are just some suggested problems for practice on Wednesday’s material before the final)

**Thursday, 6/6:** Wrap up and Review

**Homework:** Study!

**Other:** Archipelago Tour at 10:30am

**Friday, 6/7:** Final Exam

**Homework:** Don’t forget all the discrete math you’ve learned before the fall

**Other:** Concluding dinner at 6pm at Restaurant Kvarnen