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

Week 1	Monday, April 2 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, April 4 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, April 6 Review, cont. Reading: Recommended exercises:
Week 2	Monday, April 9 Asymptotic notation Reading: Section 14.7 Recommended exercises: 14.30, 14.32	Wednesday, April 11 Asymptotic notation (cont.) Reading: Recommended exercises:	Friday, April 13 Quiz 1 (25 minutes) Asymptotic notation, cont. Reading: Recommended exercises:
Week 3	Monday, April 16 Number theory and cryptography Gcd, Euclid's algorithm 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, April 18 Breaking Turing's code (page 202-210) Turing's code, version 2 (page 202-213) Congruences, remainders, inverses modulo n Reading: Chapter 8 Recommended exercises: 8.23, 8.25	Friday, April 20 Homework 1 due Fermat's Little Theorem and its applications Computing powers modulo n Reading: Chapter 8 Recommended exercises: 8.23, 8.25
Week 4	Monday, April 23 RSA: correctness, security, efficiency Reading: Chapter 8 Recommended exercises: 8.37	Wednesday, April 25 RSA: correctness, security, efficiency (cont.) Reading: Recommended exercises:	Friday, April 27 Quiz 2 (25 minutes) Famous open (and solved) problems in number theory Reading: Recommended exercises:
Week 5	Monday, April 30 Linear recurrence equations Reading: Section 8.1 (page 189), Section 21.1, 21.3, 21.4 Recommended exercises:	Wednesday, May 2 Linear recurrence equations Reading: Section 21.1-21.4 Recommended exercises:	Friday, May 4 Homework 2 due Linear recurrence equations (non-homogeneous) Reading: Section 21.1-21.4 Recommended exercises:
Week 6	Monday, May 7 Divide-and-conquer recurrences Reading: Section 21.2. 21.4 Recommended exercises:	Wednesday, May 9 Divide-and-conquer recurrences Reading: Recommended exercises:	Friday, May 11 Quiz 3 (25 minutes) Inclusion-Exclusion Reading: Recommended exercises:
Week 7	Monday, May 14 Inclusion-Exclusion Reading: Recommended exercises:	Wednesday, May 16 Inclusion-Exclusion: integer partitions. Reading: Recommended exercises:	Friday, May 18 Homework 3 due Graphs, basic definitions and properties Reading: Recommended exercises:
Week 8	Monday, May 21 Graphs: Euler tours Reading: Chapter 11. Recommended exercises: 11.3, 11.4, 11.7, 11.30	Wednesday, May 23 Hamiltonian cycles, Dirac's theorem Reading: Recommended exercises:	Friday, May 25 Quiz 4 (25 minutes) Bipartite graphs: matchings, Hall's Theorem. Reading: Recommended exercises:
Week 9	Monday, May 28 Memorial Day. No Class.	Wednesday, May 30 Bipartite graphs: matchings, Hall's Theorem. Trees Reading: Chapter 11. Recommended exercises:	Friday, June 1 Homework 4 due Trees Planar graphs: Kuratowski's theorem. Reading: Chapter 12. Recommended exercises: 12.2, 12.3, 12.6, 12.8
Week 10	Monday, June 4 Euler's formula/inequality for planar graphs. Reading: Chapter 12. Recommended exercises:	Wednesday, June 6 The 4-Color Theorem. Coloring planar graphs with 6 and 5 colors. Trees. Binary trees. Applications (lower bound for comparison sorting). Reading: Section 9.3 Recommended exercises:	Friday, June 8 Homework 5 due Games, NIM Reading: Recommended exercises:

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.

• Guidelines for homework papers
• Homework assignment template>:
  • Sample homework assignment in pdf: HwSample.pdf
  • Source LaTeX document: HwSample.tex
  • An auxiliary file with LaTeX macros: macros.tex
  • Blank homework template
• LaTeX guides/manuals:
  • Wikibooks LaTeX guide (recommended for absolute beginners)
  • "The not so short introduction ..."
  • "An introduction to LaTeX ..."
  • Some LaTeX examples (lots of other examples can be found with Google)
  • Installing LaTeX

Quizzes

• Quiz 1, Friday, April 13
  • Quiz syllabus
  • Sample 1
  • Sample 2
  • Sample 3 ( Solutions )
  • Sample 4 ( Solutions )
  • Sample 5 ( Solutions )
  • Sample 6 ( Solutions )
• Quiz 2, Friday, April 27
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2 ( Solutions )
  • Sample 3 ( Solutions )
  • Sample 4 ( Solutions )
  • Sample 5 ( Solutions )
• Quiz 3, Friday, May 11
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2
  • Sample 3
  • Sample 4 ( Solutions )
  • Sample 5 ( Solutions )
  • Sample 6 ( Solutions )
• Quiz 4, Friday, May 25
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2
  • Sample 3
  • Sample 4 ( Solutions )
  • Sample 5 ( Solutions )
  • Sample 6 ( Solutions )

Final

• Final Study Guide
• Sample Final 1
• Sample Final 2
• Sample Final 3
• Sample Final 4 ( Solutions )
• Sample Final 5 ( Solutions )
• Sample Final 6 ( Solutions )
• Sample Final 7 ( Solutions )

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

• Leonhard Euler
• Pierre de Fermat
• Kazimierz Kuratowski
• Marshall Hall
• Paul Dirac
• William Rowan Hamilton
• Ron Rivest
• Adi Shamir
• Leonard Adleman

A Few Other Resources

• Lecture notes from Univ. of Chicago
• Discrete Mathematics course at Brown University
• Lots of resources on discrete mathematics
• The A. Turing home page

Good Causes (not related to class)

• Medecins Sans Frontieres. There are doctors, and then there are real doctors ...
• Riverside Humane Society (pet adoption)
• Food not Bombs
• Greenpeace