CS/MATH 111, "Discrete Structures" Spring 2019

Schedule

• Lecture:
  • MWF 12:10PM-01:00PM, Materials Sci and Engineering 104;
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu.
  Office hours: WCH 411, Monday 02:10PM-3:00AM, or by appointment (on MWF).

• Discussion:
  • Monday 10:10AM-11:00AM, Skye Hall 171 (sec 21);
  • Monday 11:10AM-12:00PM, Skye Hall 171 (sec 22);
  • Wednesday 08:10AM-9:00AM, Materials Sci and Engineering 003 (sec 23);
  Teaching Assistant:
  • Narges Shadab, email: nshad001@ucr.edu.
  Office hours: WCH 110, Tuesday 3:10PM-4:00PM, Thursday 4:10PM-5:00PM.

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 Gradescope.

Homework assignments can be done individually or in groups of two (strongly recommended). Each group submits the assignment (in pdf) on Gradescope (one per group) and iLearn (individually). Both students will receive the same credit (unless requested otherwise). If a student fails to submit the assignment on iLearn and/or Gradescope, 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 10, 07:00PM-9:30PM, Materials Sci and Engineering 104. 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 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%, Attendance 2%. 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 by the end of Week 1. Without the signed statement, your Quiz 1 will not be considered complete.

Lectures

Week 1	Monday, April 1 Wednesday, April 3 Friday, April 5 THINGS TO DO during the first week	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 8 , Quiz 1 (30 minutes) Wednesday, April 10 Friday, April 12	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 15 Wednesday, April 17 Homework 1 is due April 17. Friday, April 19	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 22, Wednesday, April 24, Quiz 2 (30 minutes) Friday, April 26	Linear recurrence equations (homogeneous) Linear recurrence equations (non-homogeneous) Reading: Chapter 22
Week 5	Monday, April 29 Wednesday, May 1 Friday, May 3 Homework 2 is due May 4 (11:59am).	Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences Inclusion-Exclusion Integer partitions Reading: Chapter 22
Week 6	Monday, May 6 Wednesday, May 8 Friday, May 10 Quiz 3 (30 minutes)	Graphs Euler tours Reading: Chapter 12.
Week 7	Monday, May 13 Wednesday, May 15 Homework 3 is due May 15. Friday, May 17	Hamiltonian cycles, Dirac's theorem, Ore's theorem Graph coloring, coloring graphs with maximum degree D Reading: Chapter 12.
Week 8	Monday, May 20 Wednesday, May 22 Friday, May 24 Homework 4 is due May 25.	Bipartite graphs: matchings, Hall's Theorem. Trees Planar graphs Reading: Chapter 12.
Week 9	Monday, May 27 Memorial Day -- no class. Wednesday, May 29 Quiz 4 (30 minutes) Friday, May 31	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 3 Wednesday, June 5 Extra credit quiz (15 minutes). Homework 5 is due June 5 (no extension). Friday, June 7	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: Wednesday, April 17 (11:50PM).
  Source files: s19_hw1.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 2, due date: Friday, May 4 (11:59PM).
  Source files: s19_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 3, due date: Wednesday, May 15 (11:50PM).
  Source files: s19_hw3.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 4, due date: Saturday, May 25 (11:50PM).
  Source files: s19_hw4.tex (latex source), macros.tex (latex macros, save in same directory), treeforhw4.pdf (figure).
  

• Homework 5, due date: Wednesday, June 5 (11:50PM).
  Source files: s19_hw5.tex (latex source), macros.tex (latex macros, save in same directory)
  Figures in pdf: graph_edge_color_hw5, graph3_hw5 , graph4_hw5 , Graph1HW5 , graphHa_hw5 , graphGa_hw5.

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

    Final

    • Final Study Guide

      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