assignments
Practice problems for Section 1.1: 1, 6, 8a,d, 14, 16, 19, 25, 29, 31, 45
Practice problems for Section 1.2: 1, 3, 7, 16, 19, 20a,d,f, 32, 35 (notice the definition of "unless" directly before the exercise), 43, 45, 47
Practice problems for Section 1.3: 1, 3, 6, 13a, 22, 24, 25, 26, 27, 37, 38a
Assignment 1 due Monday, September 16. For each of the following problems, be sure to include explanations of your answers: 1.1.54, 1.2.28, 1.2.34, 1.2.49 c-f, 1.3.40 (as politically incorrect as it might seem...)
Practice problems for Section 2.1: 2, 3, 13, 14, 16ace, 18abe, 19, 21ac, 22a, 23a, 26bd
Practice problems for Section 2.2: 1, 3ac, 4ac, 6, 11, 13, 18, 20-24 even (these are all good -- just do enough so that you're comfortable with definitions), 29-35 odd (same here), 38, 40
Assignment 2 due Monday, September 23. 2.1.29, 2.1.31cd, 2.2.25, 2.2.26b, 2.2.45
Practice problems for Section 2.3: 2ab, 3ab, 10ac, 14, 16, 18, 32, 33, 36, 40abe, 43a
Section 3.1 practice problems: 9, 19, 22, 24, 31, 31, 34-36, 41, 50
Section 3.2 practice problems: 4, 8, 9, 12, 13, 14, 17, 18, 27, 30
Assignment 3 due Thursday, October 3. 2.3.43c, 2.3.44, 3.1.27, 3.1.52, 3.2.19, 3.2.29, 3.2.31
Section 3.3 practice problems: 22-24, 35ab, 41, 44
Section 3.4 practice problems: 3, 5, 7b, 13, 17, 20, 29, 36, 44
Section 3.6 practice problems: 1, 3, 5, 10, 14, 16, 17, 19, 24, 27
Section 3.7 practice problems: 3, 5, 7, 16, 20, 26, 34
Assignment 4 due Thursday, October 10. 3.3.45(see problems 41-44), 3.4.37, choose one of 3.4.45 or 3.4.46 or 3.4.47, also do 3.6.26, 3.7.31ab, 3.7.35
Midterm Thursday, October 17 covering sections 2.1-2.3, 3.1-3.4, 3.6, 3.7
Exam corrections due Monday, October 28. On a /separate/ sheet of paper, correct all mistakes that you made on the exam. Turn in your corrections together with your exam at the beginning of class. This assignment will count as a quiz grade.
Reading for Monday, October 28. Work through examples 4.3.2 and 4.3.3 in the book. Be ready to discuss these and similar problems in class. Also, find the mistake in the following "proof" that all horses are the same color.
Claim: All horses are the same color.
Proof by induction: (Base case.) Take a set of only one horse. Every horse in the set is the same color, so the claim is true for n=1.
(Inductive step.) Suppose the claim is true for n=k. That is, given a set of k horses, all of them are the same color. Take a set of k+1 horses. Then the first k of them are all the same color, and the last k of them are all the same color. Therefore, they all have the same color, and the claim is true for n=k+1. By the principle of mathematical induction, all horses are the same color.
Section 4.1 practice problems: 3, 10, 12, 38, 40, 46, 48, 52, 54
Section 4.2 practice problems: 3, 5, 6, 10, 32
Section 4.3 practice problems: 3,6(typo in part c -- it should be P(k+1)), 8, 16, 24, 30, 31
Section 4.4 practice problems: 1, 4, 15
Assignment 5 due Thursday, October 31. 4.2.14, 4.3.32, 4.4.17, bonus: 4.4.16
Section 6.1 practice problems: 3, 9, 12, 18, 31
Section 6.2 practice problems: 1, 6, 9, 17, 19, 28ab, 31
Assignment 6 due Thursday, November 7. 6.1.33, 6.2.30, 6.2.27
Section 6.3 practice problems: 3, 6, 9, 14, 24
Section 6.4 practice problems: 6, 8, 11acf, 15, 24
Section 6.5 practice problems: 1, 3, 5, 10
Section 6.6 practice problems: 5, 6, 9, 14
Section 6.7 practice problems: 1, 5, 7, 11, 15, 19, 24, 26, 28
Assignment 7 due Monday, November 18 6.3.25, 6.4.11bg, 6.5.15, 6.6.20, 6.7.17, 6.7.23
One page, typed summary of project due Thursday, November 21. Include in your summary
- the topic you will study,
- problems (or exercises) you hope to solve,
- theorems whose proofs are given that you would like to understand,
- book(s) you will use,
- how your topic relates to, utilizes, and/or builds on what we have learned in class
Assignment 8 due Monday, November 25 7.3.33
Section 10.4 practice problems: 3, 14, 19, 31
Assignment 9 due Monday, December 9 10.4.45, public key encryption problem sent over email.
Final projects due Saturday, December 14
*Project proposal 10%: (completed)
*Written portion 60%: Write up the solutions to 3-4 difficult problems related to your topic. Include in your write-up the statement of at least one important theorem of the subject, together with a sketch of the proof (that is, a general outline of how the theorem is proved, even if you don't write up all of the details). Also include the statements of any lesser-known theorems and definitions that you use when solving your problems. For full credit, your work must be legible and detailed.
*Presentation 30%: Give a 15 minute presentation on your topic to the class. As a rule of thumb, the first five minutes should be directed toward somebody who hasn't seen anything beyond what we have learned in class, the second five minutes should be directed toward someone who has some idea of your topic, and the last five minutes should be directed toward an "expert" on the topic. Your goal is to give the class a sense of your topic and to teach them something new. Make sure to include at least one proof in your presentation, even if it is an elementary proof. I will be strict about timing, so be sure you have a full 15 minutes of material and not much more. Also, be prepared to answer questions afterward.
