CS/MATH 111, "Discrete Structures"
Winter 2018



Textbook: E. Lehman, T. Leighton and A. Meyer Mathematics for Computer Science. You only need to print the sections that will be covered in class.

Prerequisites: CS10, CS/MATH11, MATH 9C (or equivalents). The prerequisites are strictly enforced.

Prerequisites by Topic: basic programming, logic (propositional, predicate), sets, operations on sets, sequences, relations (equivalence, partial orderings), functions, combinations, basic counting methods, elementary linear algebra (matrices, determinants), proof methods (induction, contradiction), elementary number theory.

Topics Covered:

Homework Assignments: Five homework assignments, due every second Friday (except last), starting January 26. To submit an assignment you will need to upload the pdf file into ilearn and turn-in a paper copy in class.

Homework assignments are designed for groups of two, although students also have an option to work on them solo. Each homework will have three problems. Students working in groups must solve all three problems. Each group submits one paper with two names on it and both students in the group will receive the same credit (unless requested otherwise). Students that submit individual assignments only need to solve the first two problems for full credit.

Homework papers must be formatted in LaTeX. Handwritten assignments or assignments in Word or other word processors \emph{will not be accepted}. LaTeX templates for homework assignments and other help with LaTeX will be available.

Homework papers must be well written, in grammatical English, self-contained, and aesthetically formatted. During the first week of the quarter you are required to review the homework assignment guidelines, and follow these guidelines throughout the quarter. Sloppy papers will not be graded.

Quizzes: Four quizzes, in lecture, every second Friday, starting on January 19. The first quiz, on Friday, January 19, will cover the prerequisite topics.

Final: Wednesday, March 21, 8:00AM - 10:30AM, Bourns A125. The final is comprehensive.

Attendance: Regular attendance at lectures and discussions is strongly advised. Some of the presented material may not be covered in the book or in posted lecture notes. Students are also strongly encouraged to attend office hours. In case of a conflict with regular walk-in office hours, email the instructor or TA to set up an appointment. Students that are at risk of failing the class may be required to attend office hours.

Grading: Quizzes 40%, Final 40%, Homeworks 20%. Course grades are expected to be determined as follows: A = 85-100%, B = 75-84%, C = 65-74%, D = 60-64%. Minor adjustments of this scale can be made at the end of the quarter.

Academic Integrity: Zero-tolerance policy on plagiarism is enforced. Cheating on homework assignments or tests will result in an F grade for the course and a disciplinary action, independently of the severity of plagiarism. You are required to print, read, and sign the academic integrity statement, and turn it in no later than Wednesday, January 24. (You can turn it in with Homework 1.) Without the signed statement, your Homework 1 will not be considered complete.

Piazza Discussion Group: Please sign-up for the piazza discussion group, following instructions that will be distributed on ilearn. Participation in piazza discussions is strongly encouraged.


Week 1 Monday, January 8
THINGS TO DO in week 1
Review: logic, sets, functions, relations, basic summation formulas, important numbers, sequences
Reading: Chapters 1-5, Sections 8.1-8.3, 14.1, 14.2.
Recommended exercises: 1.2, 1.5, 1.7, 3.2, 3.8, 3.21, 3.24, 4.1, 4.7
Wednesday, January 10
Review (cont.): approximations, number theory basics, proofs, proofs by induction
Reading: Sections 14.1, 14.2, 15.1-15.10
Recommended exercises: 15.2, 15.4, 15.12, 15.15
Friday, January 12
Review (cont.)
Asymptotic notation
Reading: Section 14.7
Recommended exercises: 14.12, 14.20, 14.30, 14.32
Week 2 Monday, January 15
Martin Luther King Holiday.
No class.
Wednesday, January 17
Asymptotic notation (cont.)
Reading: Section 14.7
Recommended exercises: 14.12, 14.20, 14.30, 14.32
Friday, January 19
Quiz 1 (25 minutes)
Asymptotic notation (cont.)
Week 3 Monday, January 22
Number theory and cryptography
Breaking Turing's code (page 202-210)
Reading: Sections 8.1, 8.2, 8.3, 8.4, 8.5, 8.6
Recommended exercises: 8.2, 8.3, 8.4, 8.17, 8.20, 8.22
Wednesday, January 24
Number theory and cryptography
Gcd, Euclid's algorithm, computing inverses mod p
Reading: Sections 8.1, 8.2, 8.3, 8.4, 8.5, 8.6
Recommended exercises: 8.2, 8.3, 8.4, 8.17, 8.20, 8.22
Friday, January 26
Fermat's Little Theorem
Reading: Chapter 8
Recommended exercises: 8.23, 8.25

Homework 1 due
Week 4 Monday, January 29
Fermat's Little Theorem
Turing's code, version 2 (page 202-213)
Computing powers modulo an integer
Reading: Chapter 8
Recommended exercises: 8.23, 8.25
Wednesday, January 31
RSA: correctness, security, efficiency
Reading: Chapter 8
Recommended exercises: 8.37
Friday, February 2
Quiz 2 (25 minutes)
RSA: correctness, security, efficiency (cont.)
Week 5 Monday, February 5
Famous open (and solved) problems in number theory
Linear recurrence equations
Reading: Section 8.1 (page 189), Section 21.1, 21.3
Wednesday, February 7
Linear recurrence equations
Reading: Section 21.1, 21.3
Friday, February 9
Linear recurrence equations
Reading: Section 21.3, 21.4

Homework 2 due
Week 6 Monday, February 12
Linear recurrence equations (non-homogeneous)
Reading: Section 21.2. 21.4
Wednesday, February 14
Linear recurrence equations (cont.)
Divide-and-conquer recurrences
Reading: Section 21.2. 21.4
Friday, February 16
Quiz 3 (25 minutes)
Divide-and-conquer recurrences
Reading: Section 21.2. 21.4
Week 7 Monday, February 19
Presidents Day.
No class.
Wednesday, February 21
Divide-and-conquer recurrences (cont.)
Integer partitions
Reading: Section 15.12
Friday, February 23
Integer partitions (cont.)

Homework 3 due
Week 8 Monday, February 26
Reading: Chapter 11.
Recommended exercises: 11.3, 11.4, 11.7, 11.30
Wednesday, February 28
Euler tours
Hamiltonian cycles, Dirac's theorem
Recommended exercises:
Friday, March 2
Quiz 4 (25 minutes)
Dirac's theorem (cont.)
Week 9 Monday, March 5
Bipartite graphs: matchings, Hall's Theorem.
Reading: Chapter 11.
Recommended exercises: 11.21, 11.22, 11.23, 11.25, 11.8, 11.10, 11.11, 11.12
Wednesday, March 7
Planar graphs: Kuratowski's theorem.
Reading: Chapter 12.
Recommended exercises: 12.2, 12.3, 12.6, 12.8
Friday, March 9
Euler's formula/inequality for planar graphs. Reading: Chapter 12.

Homework 4 due
Week 10 Monday, March 12
Euler's formula/inequality for planar graphs.
The 4-Color Theorem. Coloring planar graphs with 6 and 5 colors.
Reading: Chapter 12.
Wednesday, March 14
Adjacency matrices and matrix multiplication
Trees. Binary trees. Applications (lower bound for comparison sorting).
Reading: Section 9.3
Friday, March 16
Games, NIM

Homework 5 due

  Homework Assignments

LaTeX and Homework help.



  Other Books

  Some Wikipedia Entries

  A Few Other Resources

  Good Causes (not related to class)