Simon Fraser University
Engaging the World

Course Outlines

Spring 2024 - MACM 201 D400

Discrete Mathematics II (3)

Class Number: 3948

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 8 – Apr 12, 2024: Mon, Wed, Fri, 8:30–9:20 a.m.
    Surrey

  • Exam Times + Location:

    Apr 17, 2024
    Wed, 3:30–6:30 p.m.
    Surrey

  • Prerequisites:

    MACM 101 or (ENSC 251 and one of MATH 232 or MATH 240).

Description

CALENDAR DESCRIPTION:

A continuation of MACM 101. Topics covered include graph theory, trees, inclusion-exclusion, generating functions, recurrence relations, and optimization and matching. Quantitative.

COURSE DETAILS:

Topics
 
 Review of Basic Counting Techniques

  • Permutations
  • Combinations
  • Inclusion-exclusion
  • Counting in Graphs

Probability
  • Review of Finite Probability
  • Conditional Probability
  • Random Variables and Expectation

Advanced Enumeration
  • Introduction to Generating Functions
  • Calculational Techniques 
  • Partitions of Integers (optional)

Recurrence Relations
  • First-Order Linear Recurrence Relations
  • Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
  • Nonhomogeneous Recurrence Relations
  • The Method of Generating Functions 
  • Divide-and-Conquer Algorithms (optional)

Graph Theory
  • Definitions
  • Subgraphs, Complements, and Graph Isomorphism
  • Vertex Degree: Euler Trails and Circuits 
  • Planar Graphs
  • Hamilton Paths and Cycles
  • Graph Coloring and Chromatic Number (optional) 

Trees
  •  Characterizations of Trees and Prufer Codes
  •  Rooted Trees and Depth-First-Search Spanning Trees
  •  Articulation Points and Biconnected Components (optional)
  •  Minimum Spanning Trees: Kruskal's and Prim's Algorithms

Assignments

Assignments will be posted on the course web page on each Friday. Solutions are due the following Friday 11:30 pm.

There will be no make-up midterm tests. The weight for a missed test (for medical reasons or under other reasonable circumstances approved by the instructor) will be added to the weight of the final examination. Missed assignments will earn zero credit. There will be a total of 10 assignments of which the best 7 will be considered towards your final grade. There may be opportunities for additional bonus points through in-class quizzes.

Grading

  • Assignments 10%
  • Midterm 1 (February 2) 20%
  • Midterm 2 (March 8) 20%
  • Final Exam (Date to be announced) 50%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient). 

Materials

RECOMMENDED READING:

Discrete Combinatorial Mathematics: An Applied Introduction,
5 / E
Ralph P. Grimaldi,
Pearson Education
ISBN: 9780321385024

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html