CS70: DISCRETE MATHEMATICS FOR COMPUTER SCIENCE, FALL 2007

ORIENTATION

The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in Computer Science. The course aims to present these ideas "in action"; each one will be geared towards a specific significant application. Thus, students will see the purpose of the techniques at the same time as learning about them.

Math55 and CS70 cover similar material; Math55, however, typically covers a wider range of topics in less depth and with fewer applications, and is less closely tailored to Computer Science. L&S Computer Science majors must take CS70; EECS students are strongly encouraged to take CS70 rather than Math55, especially if they are intending to major in Computer Science and/or if they found the more conceptual parts of CS61A enjoyable and relatively straightforward.


PERSONNEL

INSTRUCTOR: Alistair Sinclair (sinclair at cs, 677 Soda, 643-8144)
LECTURES: Tuesday, Thursday 11:00-12:30
PLACE: 106 Stanley
OFFICE HOURS: Monday 1:30-2:30, Tuesday 12:45-1:45 in 677 Soda

TEACHING ASSISTANTS:
Assane Gueye (agueye at eecs, 307 Cory, 643-4176)
Luqman Hodgkinson (luqman at berkeley dot edu, 592 Soda, 642-5422)
Vahab Pournaghshband (vahab at eecs, 594 Soda)

DISCUSSION SECTIONS:
Note: Sections begin in Week 2
101: W 1-2, 179 Stanley; Assane
102: W 2-3, 179 Stanley; Assane
104: W 3-4, 61 Evans; Luqman
103: W 4-5, 179 Stanley; Vahab
105: W 5-6, 61 Evans; Luqman

TA OFFICE HOURS:
Assane: W 10-11 & Th 1-2 in 212 Cory
Luqman: Tu 4:30-5:30 & W 4-5 in 592 Soda
Vahab: Tu 3:30-4:30 & W 5-6 in 751 Soda

RECENT ANNOUNCEMENTS


LECTURES

The following is a list of topics covered, together with the corresponding lecture notes and suggested reading from the Rosen book or other sources where appropriate. The Rosen readings are optional, but may be useful in providing you with extra information and/or a treatment of a topic from a different perspective.

Topic Readings
8/28 Overview/Propositional Logic Notes [ps] [pdf]
Rosen Sections 1.1-1.4
8/30 Proofs Notes [ps] [pdf]
Rosen Sections 1.5-1.7
9/4 Proofs (continued) As above
9/6 Induction Notes [ps] [pdf]
Rosen Chapter 4
9/11 Induction (continued) As above
9/13 Induction (completed); Stable Marriage Notes [ps] [pdf]
[Not covered in Rosen]
9/18 Stable Marriage (continued) As above
9/20 Modular arithmetic and gcd Notes [ps] [pdf]
Rosen Sections 3.4-3.6
9/25 Inverses and extended gcd As above
9/27 Polynomials Notes [ps] [pdf]
[Not covered in Rosen]
10/2 Review Session Sample midterm 1 [ps] [pdf]
10/4 Secret sharing As for 9/27
10/9 Error-correcting codes Notes [ps] [pdf]
[Not covered in Rosen]
10/11 Graphs: Eulerian Tours Notes [ps] [pdf]
Rosen Sections 9.1, 9.2, 9.5
10/16 Graphs: de Bruijn sequences, hypercubes As above
10/18 Hamiltonian cycles. Counting Notes [ps] [pdf]
Rosen Sections 5.1, 5.3, 5.4
10/23 Counting (continued). Introduction to Probability Notes [ps] [pdf]
Rosen Section 6.1
10/25 Introduction to Probability (continued) As above
10/30 Conditional Probability Notes [ps] [pdf]
Rosen Section 6.2
11/1 Conditional Probability (continued). Two Killer Apps. Notes [ps] [pdf]
[Not covered in Rosen]
11/6 Two Killer Apps (continued). Random Variables & Expectation Notes [ps] [pdf]
Rosen Sections 6.2 & 6.4
11/8 Random Variables & Expectation (continued). Some Important Distributions Notes [ps] [pdf]
[Mostly not covered in Rosen]
11/13 Review Session Sample midterm 2 [ps] [pdf]
11/15 No lecture (midterm this evening) ---
11/20 Some Important Distributions (continued). Variance Notes [ps] [pdf]
Rosen Section 6.4
11/27 Chebyshev's Inequality. IID Random Variables Notes [ps] [pdf]
Rosen Section 6.4
11/29 The Central Limit Theorem. How to Lie with Statistics Notes [ps] [pdf]
Not covered in Rosen
12/4 Infinity & Countability Notes [ps] [pdf]
Rosen Section 2.4 (end of)
12/6 Self-Reference & Computability Notes [ps] [pdf]
Rosen, pages 176-177

HOMEWORKS

Unless otherwise indicated, homeworks will be due by 5:00pm on Thursdays. Turn in your homeworks in the box labeled "CS70" on the 2nd floor of Soda Hall. Please begin your answer to each problem on a new sheet of paper, and make sure that each sheet is labeled with your name, SID number, section number, and "CS70--Fall 2007". You should clip, not staple the separate problems together (but if you use multiple sheets for one problem those should be stapled). Reason: Different problems may be graded in parallel by different readers. Warning: You risk receiving no credit for any homework that does not conform to the above regulations! Please take the time to write clear and concise solutions; we will not grade messy or unreadable submissions. The lowest two homework scores will be dropped. No late homeworks will be accepted.

EXAMS

There will be two midterms and one final. The midterm dates are as follows:

First Midterm: Wednesday 10/3, 6-8pm, in 10 Evans
Second Midterm: Thursday 11/15, 7-9pm, in 10 Evans

Anybody who has a legitimate conflict with one of these dates should contact the instructor as soon as possible.

ASSESSMENT

Your grade in the class will be determined as follows: Homeworks 20%; Midterms 20% each; Final 40%.

DISCUSSION SECTIONS

Handouts from discussion sections are posted below. Note that these have not been subjected to the same degree of scrutiny as other materials in the course.