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CS55 - Spring 2012
MW 2:45-4:00 in Millikan 134 Edmunds 114
Prof. Chen

5/20/2014: I've archived all of the notes and problem sets (ie, most of the links below don't work) and am only leaving up the syllabus for reference. If you're looking for the material, you may be able to find a link to a more recent offering of the class here or here.

### News

Please check here regularly for assorted announcements. You are responsible for being aware of any information posted here.
• 4/26/2012: problem set 12: in option two (let's make a deal), the simulation for the second version should show that the probability of winning when you always switch and when you never switch are the same. That probability shouldn't be 50%, but rather something else. You should turn in output showing the probabilities of winning both when you always switch and when you never switch.
• 4/18/2012: problem set 12: for full credit on the graph coloring problem, the heuristic you implement needs to be non-trivial. (In other words, you can't just color every vertex a different color, not even for general graphs.)
• 4/13/2012: In problem set 10, problem 1b, the text given does not agree with the book problem number given. The book problem number is correct (problem 19 on page 474); the version of the problem set online has been updated to have the correct text.
• 3/27/2012: Sample midterm available here
• 3/25/2012: Problem 2 on ps8: in the preamble to problem 2, the second factorial in the second option should be in the denominator. This has been fixed in the version posted on the web. (can download here: <pdf>)
• 2/22/2012: Problem 1b on ps5: the lowercase a should be an uppercase A
• 2/13/2012: Problem 3b on ps4 was missing two key minus signs. That has been fixed in the version posted on the web. (can download here: <pdf>)
• 2/9/2012: From now on TA hours will be Monday 8:30-10pm (Evan F.) and Tuesday 8-10pm (Joel), still in the CS lab.
• 2/8/2012: Sample midterm available here
• 2/8/2012: My office hours next Wednesday (2/15) are cancelled.
• 2/1/2012: On ps3 you may want to read problem 2 in part 2 (gives the statement of the division theorem) before doing some of the questions in problem 1.
• 1/19/2012: The class will be moving to Edmunds 114 (whiteboards!) for the rest of the semester.
• ### Information

CS55 is an introduction to discrete mathematics for computer scientists. In particular, we will study finite mathematical structures and ways to build them, count them, and analyze them. The topics and examples will be chosen to relate to concepts of interest in the design and analysis of computer algorithms. The stated prerequisite is cs51, though what I really care about is that you have some experience with computing concepts and programming (ie, cs30 is fine).

The textbook for this class is Ensley and Crawley's "Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games" (Amazon link). Copies will be available at Huntley Bookstore.

We'll meet Mondays and Wednesdays from 2:45-4:00 in Millikan 134 Edmunds 114.

• ### Lectures

Any topic that's listed for a date in the future should be taken as tentative. Any topic that's listed for a date at least 2 days in the past is what was actually covered in that lecture.

Week Date In class reading Assignment due
definitions, notation, sequences, game basics
slides <pdf>
1.1-1.2
Appendix A
2 (Mon) 1/23 intro propositional logic, implications,
knights & knaves
slides <pdf>
1.3-1.4
(Wed) 1/25 logical arguments,
predicate logic, working with quantifiers
slides <pdf>
1.5, 2.1 ps1 <pdf>
3 (Mon) 1/30 proofs, if-and-only-if, numbers vs. numerals
slides <pdf>
2.1-2.2, 2.6
(Wed) 2/1 proofs, induction/recursion
slides <pdf>
2.2-2.4 ps2 <pdf>
4 (Mon) 2/6 more on induction: sums, sequences, weak vs. strong, variations
slides <pdf>
2.3-2.4
more on recurrences (guess-and-check, closed form, recursion tree)
slides <pdf>
2.4-2.5 ps3 <pdf>
5 (Mon) 2/13 review
slides <pdf>
(Wed) 2/15
*** midterm #1 ***
6 (Mon) 2/20 sets
slides <pdf>
3.1-3.3
(Wed) 2/22 sets, boolean algebra, circuits
slides <pdf>
3.3-3.5 ps4 <pdf>
7 (Mon) 2/27 functions, inverses,
infinity, diagonalization
slides <pdf>
4.1-4.3
(Wed) 2/29 more functions, asymptotics - big-O
slides <pdf>
4.1-4.3, 4.8 ps5 <pdf>
8 (Mon) 3/5 relations, counting
slides <pdf>
4.4-4.5, 5.1-5.3
(Wed) 3/7 counting
slides <pdf>
5.2-5.4, 2.5 ps6 <pdf>
(Mon) 3/12
*** no class: Spring Break ***
(Wed) 3/14
9 (Mon) 3/19 counting, intro to discrete probability
slides <pdf>
6.1
(Wed) 3/21 more discrete probability, equally likely outcomes, disjoint vs. independent events
slides <pdf>
6.1-6.2 ps7 <pdf>
10 (Mon) 3/26 conditional probability, bernoulli trials
slides <pdf>
6.3-6.4
(Wed) 3/28 random variables, expected values, compression
Evan's notes <pdf>
6.3-6.4 ps8 <pdf> <tex>
11 (Mon) 4/2 review
slides <pdf>
(Wed) 4/4
*** midterm #2 ***
12 (Mon) 4/9 probability, intro to graphs: terminology, eulerian circuits
slides <pdf>
6.1-4, 7.1
(Wed) 4/11 graph representations, proofs on graphs
slides <pdf>
7.2, 7.4 ps9 <pdf> <tex>
13 (Mon) 4/16 more proofs on graphs, eulerian circuits, hamiltonian cycles, TSP
slides <pdf>
7.2, 7.7
(Wed) 4/18 graphs: coloring, isomorphism, planarity
slides <pdf>
7.3 ps10 <pdf> <tex>
14 (Mon) 4/23 proofs on graphs, graphs for puzzles
slides <pdf>
7.6
(Wed) 4/25 game trees, binary trees
slides <pdf>
ps11 <pdf> <tex>
15 (Mon) 4/30 wrap-up, numbers vs. numerals, stable marriage problem
slides <pdf>
(Wed) 5/2 review ps12 <pdf> <tex>

The final exam will be on Monday, May 7 at 2pm.

### Problem Sets

• ps1, due 2:45pm on 1/25. <pdf>
• ps2, due 2:45pm on 2/1. <pdf>
• ps3, due 2:45pm on 2/8. <pdf>
• ps4, due 2:45pm on 2/22. <pdf>
• ps5, due 2:45pm on 2/29. <pdf>
• ps6, due 2:45pm on 3/7. <pdf>
• ps7, due 2:45pm on 3/21. <pdf>
• ps8, due 2:45pm on 3/28. <pdf> <tex>
• ps9, due 2:45pm on 4/11. <pdf> <tex>
• ps10, due 2:45pm on 4/18. <pdf> <tex>
• ps11, due 2:45pm on 4/25. <pdf> <tex>
• ps12, due 2:45pm on 5/2. <pdf> <tex>