CS/MATH 111, "Discrete Structures" Fall 2019

Schedule

• Lecture:
  • TR 3:30PM-4:50PM, Olmsted 1208 (sec 1).
  • TR 08:00AM-09:20AM, Pentland Hills B-107 (sec 2);
  Instructor: Elena Strzheletska, email: elenas@cs.ucr.edu.
  Office hours: WCH 411, Tuesday 9:30AM-10:30AM, Thursday 2:30PM-3:20PM or by appointment.

• Discussion:
  • Friday 12:00PM-12:50PM, WCH 141 (sec 21);
  • Friday 10:00AM-10:50AM, Sproul Hall 2339 (sec 22);
  • Wednesday 04:00PM-04:50PM, Skye Hall 171 (sec 23);
  • Monday 10:00AM-10:50AM, Watkins Hall 2240 (sec 24).
  Teaching Assistants:
  
  • Yifei Ding, email: yding007@ucr.edu (sec 21, 22);
  • Sara Abdali, email: sabda005@ucr.edu (sec 23, 24).
  Office hours: WCH 110,
  • Monday 11:00AM-11:50AM,
  • Wednesday 5:00PM-6:30PM,
  • Friday 11:00AM-11:50AM.

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 (both students) submit the assignment (in pdf) on iLearn and Gradescope, and 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: Saturday, December 7, 11:00AM-2:30PM . 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 no later than Thursday, October 4 (before the quiz). Without the signed statement, your Quiz 1 will not be considered complete.

Lectures

Week 0	Tuesday, September 24 No Class	Thursday, September 26 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 1 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 3 Quiz 1 (30 minutes) Asymptotic notation Reading: Section 14.7 Recommended exercises: 5.2 - 5.7, 14.12, 14.26
Week 2	Tuesday, October 8 Number theory and cryptography Reading: Chapter 14 Recommended exercises: class problems Review: Gcd, Euclid's algorithm Gcd, Euclid's algorithm,	Thursday, October 10 Homework 1 is due Friday, October 11, at 11:50PM. 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 15 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 17 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 22 Linear recurrence equations (homogeneous) Reading: Chapter 22 Recommended exercises:	Thursday, October 24 Homework 2 is due Friday, October 25, 11:50PM. Linear recurrence equations (cont.) Reading: Chapter 22 Recommended exercises:
Week 5	Tuesday, October 29 Linear recurrence equations (non-homogeneous) Divide-and-conquer recurrences Reading: Chapter 22 Recommended exercises:	Thursday, October 31 Quiz 3 (30 minutes) Divide-and-conquer recurrences (cont.) Inclusion-Exclusion Integer partitions Reading: Chapter 22 Recommended exercises:
Week 6	Tuesday, November 5 Graphs Euler tours Reading: Chapter 12.	Thursday, November 7 Homework 3 is due Saturday, November 9, 11:50PM. Graphs Euler tours, Hamiltonian cycles Reading: Chapter 12.
Week 7	Tuesday, November 12 Hamiltonian cycles, Dirac's theorem, Ore's theorem Reading: Chapter 12.	Thursday, November 14 Graph coloring, coloring graphs with maximum degree D Reading: Chapter 12.
Week 8	Tuesday, November 19 Quiz 4 (30 minutes) Bipartite graphs: matchings, Hall's Theorem. Reading: Chapter 12.	Thursday, November 21 Homework 4 is due Thursday, November 21, 11:50PM. Trees Planar graphs: Kuratowski's theorem. Reading: Chapter 13.
Week 9	Tuesday, November 26 Euler's formula/inequality for planar graphs. The 4-Color Theorem. Coloring planar graphs with 6 and 5 colors. Reading: Chapter 13. Recommended exercises:	Thursday, November 28 Thanksgiving Break Homework 5 is due Sunday, December 1, 11:50PM.
Week 10	Tuesday, December 3 Adjacency matrices and matrix multiplication Trees. Binary trees. Applications (lower bound for comparison sorting). Reading: Section 10.3 Recommended exercises:	Thursday, December 5 Review

Homework Assignments

• Homework 1, due date: Friday, October 11 (11:50PM).
  Source files: f19_hw1.tex (latex source), macros.tex (latex macros, save in same directory).
  
  
• Homework 2 due date: Friday, October 25 (11:50PM)
  Source files: f19_hw2.tex (latex source), macros.tex (latex macros, save in same directory).
  
  
• Homework 3 due date: Saturday, November 9 ( 11:50PM).
  Source files: f19_hw3.tex (latex source), macros.tex (latex macros, save in same directory).
  
  
• Homework 4, due date: Thursday, November 21 (11:50PM).
  Source files: hw4.tex (latex source), pseudocode.tex, macros.tex (latex macros) (latex macros, save in same directory).
  
  
• Homework 5, due date: Sunday, December 1 (11:50PM).
  Source files: hw5.tex (latex source), macros.tex (latex macros, save in same directory)
  Figures in pdf: graph_edge_color_hw5, graph3_hw5.pdf , graph4_hw5.pdf , graphGa_hw5.pdf, graphHa_hw5.pdf.

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

  Final

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

  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