Offered Summer 2019: Math 503/503G Applied Discrete MathematicsJanuary 29, 2019
MATH 503/503G: APPLIED DISCRETE MATHEMATICS (3 credit hours)
This course is entirely online and will run from 6/3/19 through 7/26/19.
Prerequisites: MT200 (introduction to writing mathematical proofs) or equivalent and MT357 (proof-based introduction
to linear algebra) or equivalent. Previous coursework in discrete mathematics would be helpful but is not required.
Note: When taken as MT503, this course will count as a list B elective in the mathematics major.
An introduction to topics that frequently arise in applications of discrete mathematics in bioinformatics, computer science, and
digital communications technology. The course will be divided into four modules described below: Enumeration, Recurrence
Relations, Graph Theory, and Coding Theory. Each module will start with a short video introduction, a description of the
learning objectives, reading assignments, and link to a blog where online discussions will take place. The reading assignments
will come from lecture notes that I post and from the text. Online discussion will center around questions posed in the lecture
notes. Each module will conclude with a set of problems that you work on individually and submit to me for grading. Your
participation in the group discussion will count for 50% of your grade and the individual homework assignments will count
for 50% of your grade.
Text: Combinatorics: Topics, Techniques, Algorithms, Peter J. Cameron, Cambridge Univ. Press. Additional course notes
will be made available via Blackboard.
• Permutations, combinations, inclusion/exclusion, Pigeonhole Principle, binomial identities, multinomial coefficients,
and generalized binomial coefficients.
• Derangements, partitions, Catalan and Bell numbers, Stirling numbers of the first and second kind.
• Counting selections, ordered or unordered, with or without replacement, from multi-sets.
• Linear and nonlinear recurrence relations.
• Solution of homogeneous, linear recurrence relations with constant coefficients using eigenvalues and eigenvectors of
• Solution of recurrence relations using ordinary and exponential generating functions.
• Directed and undirected graphs, basic definitions/results.
• Eulerian and Hamiltonian cycles, trees, graph coloring.
• The mathematics of Google’s page ranking algorithm.
• Linear and nonlinear block codes, basic definitions/results.
• Bounds on the size of a code.
• Erasure codes. (Used in internet and cell-phone communications.)
For more information, see Prof. Michael Adams, VH2148, email@example.com.