Math 2200-001, University of Utah

Summer 2015

Summer 2015

Discrete Mathematics: Assignments

**Weeks 10+11.**

This and the next week should be devoted to preparation for the final exam. We convene on August 7th in the classroom. However, the time is different [7:30-9:30] from the class time.__Final Exam Prep.__You will have 2 hours for the final exam. The length of the exam is closer to the length of a one-hour exam, though. So please take your time before you turn in your final exam.The final exam is comprehensive. This means that I expect that you have been reading the material and working on problem sets, as assigned.

If you have not been reading the material, then the best study suggestions that I can offer you is to read everything and solve all the problems that you can get your hands on that relate to the material of the lectures. The comprehensive lecture notes are here.

If you have been reading, then the best way to study for the final is to follow the following suggestions:

- Study all of the assigned homework, patch up all the weak spots and make sure that you understand how to solve the assigned homework carefully.
- Study the previous 2 exams, patch up all the weak spots and make sure that you understand how to solve the problems of the previous exams correctly.
- Solve:
- p. 396, #32, 50, 55
- p. 405. #2, 18
- p. 413. #12, 18, 38
- p. 421. #4

**Week 9.**Due June 20th. No new problems this week.

__Exam 2 prep.__The best preparation strategy for the exam is:- At the minimum, read all of the lecture notes' material (latest update July 17th). The exam will be specifically covering Chapters 5 (Transformations) through 7 (Elements of number theory), inclusive. Some of this material is based on the discussion of your textbook as well [upto and including Chapter 4]. All of this material is represented, in some form, in the earlier assignments below [Weeks 5-8].
- Solve more problems and read more extra materials, for better results.
- You may bring to the exam a calculator, pages of notes that might help you organize your thoughts, your textbook, a [quiet] toy firetruck, etc. The work that you turn in has to be yours and yours only.
- The cautionary remarks of the Exam 1 prep [below] apply here as well.

**Week 8.**Due July 17. (The page numbers below show where the exercise set begins.)

p. 272. # 4, 6, 14, 22, 24, 26.**Week 7.**Due July 10. (The page numbers below show where the exercise set begins.)

p. 244. # 6, 12 [do this by modular arithmetic, rather than by hand], 28.

p. 255. # 2(c), 4(b), 6(a), 21.**Week 6.**Due July 1. (The page numbers below show where the exercise set begins.)

p. 176. # 12, 16, 18.

**Additional Problem.**Find a continued fraction expansion of \(\sqrt{5}\) (this is related to a Challenge Exercise on p. 50 of your lecture notes). Prove that your representation converges and estimate the speed of convergence.

**Extra Credit Problem.**Find a second, different, continued fraction expansion of \(\sqrt{5}\).

(Hint. \(x^2-4=(x-2)(2+x)\).)**Week 5.**Due June 26th. (The page numbers below show where the exercise set begins.)

p. 152. # 22, 26, 32, 72, 74.**Week 4.**Due June 19th. (The page numbers below show where the exercise set begins.)

p. 125. # 10 (parts a and b only), 26.

p. 136. # 16(e), 30.**Week 3.**Due June 12th. (The page numbers below show where the exercise set begins.)

p. 108. # 4, 6, 8, 14, 16, 20, 34.

__Exam 1 prep.__The best preparation strategy for the exam is:- At the minimum, read everything upto and including Section 1.8; and study the assignments from Weeks 1, 2, and 3 [this is the one above].
- Solve more problems (see for instance p. 111), and read more extra materials, for better results.
- You may bring to the exam a calculator, pages of notes that might help you organize your thoughts, your textbook, a [quiet] toy firetruck, etc. The work that you turn in has to be yours and yours only.
- Please do not
imagine that an open-book, open-notes exam is trivial and does not merit
preparation. This one
__does__require preparation; the open nature of the exam is meant to help you double-check your use of definitions etc. You should still know those definitions, etc. There won't be enough time to learn them during the exam.

**Week 2.**Due June 5th. (The page numbers below show where the exercise set begins.)

p. 53. # 12, 50.

p. 64. # 28.

p. 78. # 2.

p. 91. # 18, 26, 34.**Week 1.**Due May 29th. (The page numbers below show where the exercise set begins.)

p. 15. # 22, 32.

p. 22. # 20, 22, 24.

p. 34. # 10, 30.

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