CS/MATH 111, "Discrete Structures" Winter 2019

Schedule

• Lecture:
  • MWF 01:10PM-02:00PM, Bourns Hall A125 (sec 1);
  • MWF 12:10PM-01:00PM, CHASS Interdisc. South 1121 (sec 2);
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu.
  Office hours: WCH 411, Monday 02:10PM-3:00AM, or by appointment (on MWF).

• Discussion:
  • Monday 05:10PM-06:00PM, Sproul Hall 2360 (sec 21);
  • Tuesday 11:10AM-12:00PM, Materials Sci and Eng 003 (sec 22).
  • Thursday 09:10AM-10:00AM, Sproul Hall 2351 (sec 23);
  • Thursday 02:10PM-03:00PM, Skye Hall (Surge Hall) 170 (sec 24);
  Teaching Assistants:
  • Andres Calderon, email: aocalderon.ucr@gmail.com;
  • Shreya Reddy Seelam, email: sseel005@ucr.edu.
  Office hours: WCH 110, Monday 04:10PM-05:00PM, Tuesday 12:10PM-01:00PM, Thursday 10:10AM-11:00AM.

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, March 18, 07:00PM-9:30PM, HUMN 400 (sec. 1, sec 2). 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%. 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, January 7 Wednesday, January 9 Friday, January 11 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, January 14 Wednesday, January 16, Quiz 1 (30 minutes) Friday, January 18	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, January 21 Martin Luther King Day -- no class Homework 1 is due January 23. Wednesday, January 23 Friday, January 25	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, January 28, Quiz 2 (30 minutes) Wednesday, January 30 Friday, February 1	Linear recurrence equations (homogeneous) Linear recurrence equations (non-homogeneous) Reading: Chapter 22
Week 5	Monday, February 4 Homework 2 is due February 5. Wednesday, February 6 Friday, February 8	Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences Inclusion-Exclusion Integer partitions Reading: Chapter 22
Week 6	Monday, February 11 Quiz 3 (30 minutes) Wednesday, February 13 Friday, February 15 Homework 3 is due February 16.	Graphs Euler tours Reading: Chapter 12.
Week 7	Monday, February 18 President's Day -- no class Wednesday, February 20 Friday, February 22	Hamiltonian cycles, Dirac's theorem, Ore's theorem Graph coloring, coloring graphs with maximum degree D Reading: Chapter 12.
Week 8	Monday, February 25 Homework 4 is due February 25. Wednesday, February 27 Quiz 4 (30 minutes) Friday, March 1	Bipartite graphs: matchings, Hall's Theorem. Reading: Chapter 12.
Week 9	Monday, March 4 Wednesday, March 6 Friday, March 8	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, March 11 Wednesday, March 13 Homework 5 is due March 14. Friday, March 15	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, January 23 (11:50PM).
  Source files: w19_hw1.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 2, due date: Tuesday, February 5 (11:50PM).
  Source files: w19_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 3, due date: Saturday, February 16 (11:50PM).
  Source files: w19_hw3.tex (latex source), macros.tex (latex macros, save in same directory).
  

• Homework 4, due date: Monday, February 25 (11:50PM).
  Source files: w19_hw4.tex (latex source), macros.tex (latex macros, save in same directory).
  
  
• Homework 5, due date: Thursday, March 14 (11:50PM).
  Source files: w19_hw5.tex (latex source), macros.tex (latex macros, save in same directory)
  Figures in pdf: graph_edge_color_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
  • 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
  • Sample Final 1 ( Solutions )
  • Sample Final 2
  • Sample Final 3
  • Sample Final 4 ( 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

    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