CS/MATH 111, "Discrete Structures" Fall 2017

Schedule

• Lecture: TR 8:10AM-9:30PM, WCH 138.
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu.
  Office hours: WCH 110, Tuesday 10:00-11:00AM, or by appointment.

• Discussion: F 8:10AM-9:00AM (sec 21), R 2:10PM-3:00AM (sec 22), W 9:10AM-10:00AM (sec 23).
  Teaching Assistant: Chengkuan Hong, email: chong009@ucr.edu.
  Office hours: WCH 110, Monday 1:10-2:00PM, Wednesday 10:10-11:00AM, Thursday 3:10-4:00PM.

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

Homework Assignments: Five homework assignments. To submit an assignment you will need to upload the pdf file into ilearn and turn-in a paper copy in class.

Homework assignments can be done individually or in groups of two (strongly recommended). Each homework will have three problems. An individual assignment consists of the first two problems. A group assignment consists of all three. Each group submits one paper with two names on it and both students will receive the same credit (unless requested otherwise).

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: Saturday, December 9, 2017, 7:00PM-10:00PM.

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 take advantage of the office hours. In case of a conflict with regular walk-in office hours, special appointments can be arranged. 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 = 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.

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 turn it in no later than Thursday, October 5 (before the quiz). Without the signed statement, your Quiz 1 will not be considered complete.

Lectures

Week 0	Tuesday, September 26 No Class	Thursday, September 28 THINGS TO DO during the first week Review: logic, sets, functions, relations, basic summation formulas, important numbers, sequences 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
Week 1	Tuesday, October 3 Review (cont.): approximations, number theory basics, proofs, proofs by induction Reading: Chapters 1 - 5, Sections 9.1 - 9.4, 14.1, 14.2. Recommended exercises: 4.1, 4.7, 5.2 - 5.7, 14.2, 14.4, 14.12, 14.15	Thursday, October 5 Quiz 1 (30 minutes) Asymptotic notation Reading: Section 14.7 Recommended exercises: 5.2 - 5.7, 14.12, 14.26
Week 2	Tuesday, October 10 Number theory and cryptography Reading: Chapter 14 Recommended exercises: class problems Review: Gcd, Euclid's algorithm Gcd, Euclid's algorithm,	Thursday, October 12 Homework 1 is due at 8AM. Number theory and cryptography 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	Tuesday, October 17 Turing's code The RSA cryptosystem Reading: Chapter 9 Recommended exercises: 9.28, 9.31, 9.36, 9.37, 9.50, 9.58, 9.70, 9.79, 9.83	Thursday, October 19 Quiz 2 (30 minutes) RSA: correctness, security, efficiency Famous open (and solved) problems in number theory Reading: Chapter 9 Recommended exercises:
Week 4	Tuesday, October 24 Linear recurrence equations (homogeneous) Reading: Chapter 22 Recommended exercises:	Thursday, October 26 Homework 2 is due at 8AM. Linear recurrence equations (cont.) Reading: Chapter 22 Recommended exercises:
Week 5	Tuesday, October 31 Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences Reading: Chapter 22 Recommended exercises:	Thursday, November 2 Divide-and-conquer recurrences (cont.) Inclusion-Exclusion Integer partitions Reading: Chapter 22 Recommended exercises:
Week 6	Tuesday, November 7 Homework 3 is due at 8AM. Inclusion-Exclusion Integer partitions Reading: Chapter 15.	Thursday, November 9 Quiz 3 (30 minutes). The quiz starts at the beginning of class! Graphs Euler tours Reading: Chapter 12.
Week 7	Tuesday, November 14 Hamiltonian cycles, Dirac's theorem, Ore's theorem Reading: Chapter 12.	Thursday, November 16 Homework 4 is due at 8AM. Graph coloring, coloring graphs with maximum degree D Reading: Chapter 12.
Week 8	Tuesday, November 21 Quiz 4 (30 minutes) Bipartite graphs: matchings, Hall's Theorem. Reading: Chapter 12.	Thursday, November 23 Thanksgiving Break
Week 9	Tuesday, November 28 Trees Planar graphs: Kuratowski's theorem. Reading: Chapter 13.	Thursday, November 30 Euler's formula/inequality for planar graphs. The 4-Color Theorem. Coloring planar graphs with 6 and 5 colors. Reading: Chapter 13. Recommended exercises:
Week 10	Tuesday, December 5 Homework 5 is due at 8AM. Adjacency matrices and matrix multiplication Trees. Binary trees. Applications (lower bound for comparison sorting). Reading: Section 10.3 Recommended exercises:	Thursday, December 7 Review

Homework Assignments

• Homework 1, due date: Thursday, October 12 (8AM)
  Source files: f17_hw1.tex (latex source), macros.tex (latex macros, save in same directory).
  Solutions
• Homework 2 due date: Thursday, October 26 (8AM)
  Source files: f17_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
  Solutions
• Homework 3 due date: Tuesday, November 7 (8AM)
  Source files: f17_hw3.tex (latex source), macros.tex (latex macros), tiling_hw3_f17.pdf (figure)
  Solutions
• Homework 4, due date: Thursday, November 16 (8AM)
  Source files: hw4.tex (latex source), macros.tex (latex macros), pseudocode.tex, treeforhw4.pdf (figure)
  (latex macros, save in same directory).
  Solutions
• Homework 5, due date: Tuesday, December 5 (8AM)
  Source files: hw5.tex (latex source), macros.tex (latex macros, save in same directory)
  Figures in pdf: bipartite_graphG_hw5 , bipartite_graphH_hw5 , color_graph_hw5, graph_edge_color_hw5.
  Solutions

LaTeX and Homework help.

• Guidelines for homework papers.
• Overleaf
• Sample homework assignment in pdf: HwSample.pdf
• 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 on windows
  • Installing LaTeX on macintosh

Quizzes

• Quiz 1.
  • Quiz syllabus
  • Sample 1
  • Sample 2
  • Sample 3 ( Solutions )
  • Sample 4 ( Solutions )
• Quiz 2, Thursday, October 19.
  • Quiz syllabus
  • Sample 1
  • Sample 2 ( Solutions )
  • Sample 3 ( Solutions )
• Quiz 3, Thursday, November 9.
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 4 ( Solutions )
• Quiz 4, Tuesday, November 21.
  • Quiz syllabus
  • Sample 1 ( Solutions )
  • Sample 2
  • Sample 4

  Final

  • Final Study Guide
  • Sample Final 1 ( Solutions )
  • Sample Final 2
  • Sample Final 3

  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

  Useful Links

  • Lecture notes from Univ. of Chicago
  • Discrete Mathematics course at Brown University
  • Lots of resources on discrete mathematics
  • Devlin's Angle, essays by K.Devlin.
  • The A. Turing home page