CS/MATH 111, "Discrete Structures" Spring 2020

Schedule

• Lecture:
  • MWF 01:00PM-01:50PM.
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu.
  Office hours:
  • Monday 12:00PM-01:00PM,
  • Friday 02:00PM-03:00PM.
  Extra office hours (by appointment):
  • Wednesday 06:30PM-07:30PM,
  • Friday 12:00PM-01:00PM.

• Discussion:
  • Monday 10:00AM-10:50AM (sec 21),
  • Monday 11:00AM-11:50AM (sec 22),
  • Tuesday 06:30PM-07:20PM (sec 23).
  Teaching Assistants:
  • Huong Luu, email: hluu008@ucr.edu;
  Office hours:
  • Tuesday 05:00PM-06:00PM,
  • Wednesday 10:00AM-11:00AM,
  • Thursday 03:00PM-04:00PM.

Syllabus

Textbook: E. Lehman, T. Leighton and A. Meyer Mathematics for Computer Science.

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:

• Asymptotic notation: O(f(n)), Ω(f(n)), Θ(f(n)), asymptotic relations between basic functions: polynomial, exponential, and logarithmic functions
• Number theory: modular arithmetic, Fermat's Theorem, public-key cryptography, the RSA
• Advanced counting: inclusion-exclusion, linear recurrence equations, divide-and-conquer recurrences
• Elements of graph theory: undirected and directed graphs, connectivity, planarity, Euler cycles, Hamiltonian cycles, matchings, trees
• Other possible topics (if time suffices): elements of game theory, error-correcting codes

Remote Learning: During the campus closure, lectures, discussions and office hours will be conducted over Zoom. You can find some help and information on remote learning environments here.

Homework Assignments: Five homework assignments. To submit an assignment, you will need to upload the pdf file to Gradescope.

Homework assignments can be done individually or in groups of two (strongly recommended). Each group submits one assignment. Both students will receive the same credit (unless requested otherwise). If a student (or a group) fails to submit the assignment, he/she receives a "0".

Homework papers must be prepared with LaTeX. Handwritten assignments or assignments in Word or other word processors 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 read the homework assignment guidelines, and follow these guidelines throughout the quarter. Sloppy papers will not be graded.

Quizzes: Four 30-minute quizzes . The first "entrance" quiz will cover the prerequisite topics.

Final: Monday, June 5, 12:30PM-2:00PM . 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. In addition, extra credit assignments may be given during the lectures. Students are also strongly encouraged to take advantage of the office hours.

Grading: Quizzes 40%, Final 40%, Homeworks 20%. Course grades are expected to be determined as follows: A = 90-100%, B = 80-89%, C = 70-79%, D = 60-69%. Minor adjustments of this scale can be made at the end of the quarter.

Copyright: See UC Copyright Policies.

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 extent of plagiarism. You are required to print, read, and sign the academic integrity statement, and upload it to Gradescope no later than Monday, April 6. You can find more information here.

Lectures

Week 1	Monday, March 30 Wednesday, April 1 Friday, April 3	Review: logic, sets, functions, relations, basic summation formulas, important numbers, sequences, approximations, number theory basics, proofs, proofs by induction Reading: Chapters 1 - 5, Sections 9.1 - 9.4, 14.1, 14.2. Recommended exercises: 1.2, 1.5, 1.7, 3.2, 3.8, 3.21, 3.24, 4.1, 4.7, 5.2 - 5.7, 14.2, 14.4, 14.12, 14.15 Asymptotic notation Reading: Section 14.7 Recommended exercises: 5.2 - 5.7, 14.12, 14.26
Week 2	Monday, April 6 Wednesday, April 8, Quiz 1 (30 minutes) Friday, April 10	Number theory and cryptography Reading: Chapter 14 Recommended exercises: class problems Review: Gcd, Euclid's algorithm Computing inverses mod p Fermat's theorems Computing powers modulo an integer Reading: Chapter 9 Recommended exercises: 9.2, 9.3, 9.4, 9.10, 9.17, 9.23, 9.24
Week 3	Monday, April 13 Homework 1 is due April 14. Wednesday, April 15 Friday, April 17	Turing's code The RSA cryptosystem RSA: correctness, security, efficiency Famous open (and solved) problems in number theory Reading: Chapter 9 Recommended exercises: 9.28, 9.31, 9.36, 9.37, 9.50, 9.58, 9.70, 9.79, 9.83
Week 4	Monday, April 20 Wednesday, April 22, Quiz 2 (30 minutes) Friday, April 24	Linear recurrence equations (homogeneous) Linear recurrence equations (non-homogeneous) Reading: Chapter 22
Week 5	Monday, April 27, Homework 2 is due April 27, 11:50PM. Wednesday, April 29 Friday, May 1,	Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences Inclusion-Exclusion Integer partitions Reading: Chapter 22
Week 6	Monday, May 4 Wednesday, May 6, Quiz 3 (30 minutes) Friday, May 8, Homework 3 is due Sunday, May 10, 11:50PM.	Graphs Euler tours, Hamiltonian cycles Reading: Chapter 12.
Week 7	Monday, May 11 Wednesday, May 13 Friday, May 15	Hamiltonian cycles, Dirac's theorem, Ore's theorem Graph coloring, coloring graphs with maximum degree D Reading: Chapter 12.
Week 8	Monday, May 18, Final, Part 1 (60 minutes) Wednesday, May 20, Quiz 4 (30 minutes) Friday, May 22, Homework 4 is due May 22, 11:50PM.	Bipartite graphs: matchings, Hall's Theorem. Reading: Chapter 12.
Week 9	Monday, May 25 Memorial Day -- no class Wednesday, May 27 Friday, May 29, Homework 5 is due May 29.	Trees Planar graphs: Kuratowski's theorem. Euler's formula/inequality for planar graphs. The 4-Color Theorem. Coloring planar graphs with 6 and 5 colors. Reading: Chapter 13.
Week 10	Monday, June 1 Wednesday, June 3 Friday, June 5, Final exam	Adjacency matrices and matrix multiplication Trees. Binary trees. Applications (lower bound for comparison sorting). Reading: Section 10.3 Review

Homework Assignments

• Homework 1 due date: April 14, 11:50PM(11:50PM)
  Source files: s20_hw1.tex (latex source), macros.tex (latex macros, save in same directory).

• Homework 2, due date: Monday, April 27 (11:50PM).
  Source files: s20_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 3, due date: Sunday, May 10 (11:50PM).
  Source files: spr20_hw3.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 4, due date: Friday, May 22 (11:50PM).
  Source files: spr20_hw4.tex (latex source), macros.tex (latex macros, save in same directory).

• Homework 5, due date: Friday, June 29 (?) (11:50PM).
  Source files: spr20_hw5.tex (latex source), macros.tex (latex macros, save in same directory)
  Figures in pdf: graph_edge_color_hw5, graph3_hw5, graph4_hw5, graphHa_hw5, graphGa_hw5.

LaTeX and Homework help.

• Guidelines for homework papers.
• Overleaf
• Sample homework assignment in pdf: HwSample.pdf

Quizzes

• Quiz 1.
  • Quiz syllabus
  • Sample 1
  • Sample 2
  • Sample 3 ( Solutions )
  • Sample 4 ( Solutions )
• Quiz 2.
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2 ( Solutions )
  • Sample 3 ( Solutions )
• Quiz 3.
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2
  • Sample 3 ( Solutions )
• Quiz 4.
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2

Final

• Final Study Guide
  June 5, 12:30pm.