CS/MATH 111, "Discrete Structures" Spring 2018

 Schedule

• Lecture: MWF 12:10-1:00PM, WCH 138.
Instructor: Marek Chrobak, WCH 354, phone: (951) 827-2244, email: marek@cs.ucr.edu.
Office hours: Thursday 10:30AM-12PM, in WCH 354, or by appointment.

• Discussion: T 10:10AM-11AM (sec 21), T 11:10AM-12PM (sec 22), W 8:10AM-9AM (sec 23).
Teaching Assistant: Huong Luu.
Office hours: Thursday 1-3PM, in WCH 110.

 Syllabus

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:

• 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
• 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

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 gradescope. (Click here for the instructions.)

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, with each problem starting on a separate page and clearly marked. 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. We recommend that you install LaTeX on your own machine, but you can also use LaTeX through overleaf.com.

Homework papers must be well written, in grammatical English, self-contained, and aesthetically formatted. Each problem should start on a new page. 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 April 13. The first quiz will cover the prerequisite topics.

Final: Thursday, June 14, 11:30AM - 2:00PM, WCH 138. 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 Friday, April 20, via ilearn. 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.

 Lectures

 Homework Assignments

• Homework 1, due date: Friday, April 20 (12PM)
Source files: 18s_hw1.tex (latex source), macros.tex (latex macros, save in same directory).
• Homework 2, due date: Friday, May 4 (12PM)
Source files: 18w_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
• Homework 3, due date: Friday, May 18 (12PM)
• Homework 4, due date: Friday, June 1 (12PM)
• Homework 5, due date: Friday, June 8 (12PM)

LaTeX and Homework help.

 Quizzes

 Final

 Other Books

• V. Shoup, A Computational Introduction to Number Theory and Algebra (free)
• K. Rosen, Discrete Mathematics and its Applications
• S. Lipschutz, M. Lipson, Schaum's Outline of Discrete Mathematics
• K. Bogart, C. Stein, R. Drysdale, Discrete Mathematics for Computer Science
• B. Kolman, R. Busby, S. Ross, Discrete Mathematical Structures
• R.C. Penner, Proof techniques and Mathematical Structures
• F. Preparata, R. Tzu-Yau Yeh, Introduction to Discrete Structures for Computer Science and Engineering
• S. Ross, Topics in Finite and Discrete Mathematics
• K. Joshi, Foundations of Discrete Mathematics
• R. Mc Eliece, R. Ash, C. Ash, Introduction to Discrete Mathematics
• N.L. Biggs, Discrete Mathematics
• I. Anderson, A First Course in Combinatorial Mathematics
• S. Barrett, Discrete Mathematics, Numbers and Beyond
• R.J. Wilson, Introduction to Graph Theory
• S. Foldes, Fundamental Structures of Algebra and Discrete Mathematics
 Some Wikipedia Entries

 A Few Other Resources

 Good Causes (not related to class)