CS/MATH 111, "Discrete Structures" Spring 2021

Schedule

• Lecture:
  • MWF 11:00AM - 11:50AM (sec 2)
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu
  Office hours:
  • Monday 12:00PM - 12:50PM,
  • Wednesday 12:00PM - 12:50PM.
  
  
  • MWF 3:00PM - 3:50PM (sec 1)
  Instructor: Marek Chrobak, email: marek@cs.ucr.edu
  Office hours:
  • Thursday 1:00PM - 1:50PM,
  • Thursday 06:00PM - 06:50PM.

• Discussion:
  • Monday 10:00AM - 10:50AM, (Huong Luu, sec. 21),
  • Tuesday 11:00AM - 11:50AM (Huong Luu, sec. 22),
  • Tuesday 06:30PM - 7:20PM (Huong Luu, sec 23),
  • Thursday 11:00AM - 11:50AM (Phillip Park, sec 24).
  
  Teaching Assistants:
  • Huong Luu, email: hluu008@ucr.edu
  • Phillip Park, email: ppark006@ucr.edu
  
  Office hours:
  • Monday 01:00PM - 01:50PM,
  • Tuesday 10:00AM - 10:50AM,
  • Thursday 03:00PM - 03:50AM,
  • Friday 10:00AM - 10:50AM.

Syllabus

Recommended textbooks:

• K. Rosen, Discrete Mathematics and its Applications
• O. Levin, Discrete Mathematics.
• 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 tours, Hamiltonian cycles, matchings, trees
• Other possible topics (if time suffices): elements of game theory, error-correcting codes

Remote Learning: During the campus closure, lectures, discussions and office hours will be conducted over Zoom. The lectures and discussions will be recorded. You can find some help and information on remote learning environments here.

Homework Assignments: Five homework assignments. To submit an assignment, you will need to upload the pdf file to Gradescope.

Homework assignments can be done individually or in groups of two (strongly recommended). Each group submits one assignment. Both students will receive the same credit (unless requested otherwise). If a student (or a group) fails to submit the assignment, 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 quizzes. The first "entrance" quiz will cover the prerequisite topics and will not be counted toward your grade.

Final: Monday, June 7, 8am.

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. In addition, extra credit assignments may be given during the lectures. Students are also strongly encouraged to take advantage of the office hours.

Grading: Quizzes 45%, Final 30%, Homeworks 25%. Course grades are expected to be determined as follows: A (A-, A, A+) = 90-100%, B (B-, B, B+) = 80-89%, C (C-, C, C+) = 70-79%, D (D-, D, D+) = 60-69%. Minor adjustments of this scale can be made at the end of the quarter. However, in order to get a D-, one has to receive at least 60%.

Copyright: See UC Copyright Policies.

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 upload it to Gradescope no later than Monday, April 5. You can find more information here.

Lectures

Week 1	Monday, March 29 Wednesday, March 31 Friday, April 2 Quiz 1 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.
Week 2	Monday, April 5 Wednesday, April 7, Friday, April 9	Asymptotic notation Number theory and cryptography Review: Gcd, Euclid's algorithm Fermat's theorems Computing powers modulo an integer Review: Computing inverses mod p
Week 3	Monday, April 12 Wednesday, April 14 Friday, April 16 Homework 1 is due April 16	The RSA cryptosystem RSA: correctness, security, efficiency Famous open (and solved) problems in number theory
Week 4	Monday, April 19 Wednesday, April 21 Friday, April 23 Quiz 2	Linear recurrence equations (homogeneous) Linear recurrence equations (non-homogeneous)
Week 5	Monday, April 26 Wednesday, April 28, Friday, April 30 Homework 2 is due April 30	Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences
Week 6	Monday, May 3 Wednesday, May 5 Friday, May 7 Homework 3 is due May 7	Inclusion-Exclusion Integer partitions Graphs
Week 7	Monday, May 10 Quiz 3 Wednesday, May 12, Friday, May 14	Euler tours Hamiltonian cycles, Dirac's theorem, Ore's theorem Bipartite graphs
Week 8	Monday, May 17, Wednesday, May 19, Homework 4 is due May 19 Friday, May 21 Quiz 4	Bipartite graphs: matchings, Hall's theorem Trees Planar graphs Euler's formula/inequality for planar graphs
Week 9	Monday, May 24 Wednesday, May 26 Friday, May 28 Homework 5 is due May 28	Planar graphs: Kuratowski's theorem Graph coloring, coloring graphs with maximum degree D Coloring planar graphs with 6 and 5 colors, the 4-Color theorem
Week 10	Monday, May 31 Memorial Day -- no class Wednesday, June 2, Friday, June 4	Adjacency matrices and matrix multiplication Binary trees, applications (lower bound for comparison sorting) Review

Homework Assignments

LaTeX and Homework help.

• Guidelines for homework papers.
• Overleaf
• Sample homework assignment in pdf: HwSample.pdf

Quizzes

• Quiz 1.
  • Quiz syllabus
• Quiz 2.
  • Quiz syllabus
• Quiz 3.
  • Quiz syllabus
• Quiz 4.
  • Quiz syllabus

Final

• Final Study Guide
  

Other Books

• V. Shoup, A Computational Introduction to Number Theory and Algebra
• 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
• D. J. Velleman, How to Prove It
• 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

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