Math 2200-001, University of Utah
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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