Graduate

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Course Information

Overview


Please note that only a subset of the following graduate courses will be offered each year, depending on instructor availability and student interest. Please consult the Course Schedule for the graduate courses offered in the current semester.

Category  Courses 
Core Courses

Advanced courses in mathematics, covering core topics tested in the PhD Qualifying Examinations. Course details are listed below.
MAS710 - Continuous Methods
MAS711 - Discrete Methods
MAS712 - Algebraic Methods
MAS713 - Mathematical Statistics
MAS714 - Algorithms and Theory of Computing
Elective (Topic) Courses

Specialized courses offered based on student and lecturer interest. The precise course contents are subject to variation.
MAS720 - Topics in Discrete Mathematics I
MAS721 - Topics in Scientific Computation I
MAS722 - Topics in Pure Mathematics I
MAS723 - Topics in Probability and Statistics I
MAS725 - Topics in Discrete Mathematics II
MAS726 - Topics in Scientific Computation II
MAS727 - Topics in Pure Mathematics II
MAS728 - Topics in Probability and Statistics II
MAS740 - Topics in Discrete Mathematics III
MAS741 - Topics in Scientific Computation III
MAS742 - Topics in Pure Mathematics III
MAS743 - Topics in Probability and Statistics III
Seminar Courses

Seminars on new research developments in the Mathematical Sciences
MAS790 - Graduate Seminar – Discrete Mathematics I
MAS791 - Graduate Seminar – Discrete Mathematics II
MAS792 - Graduate Seminar – Scientific Computation I
MAS793 - Graduate Seminar – Scientific Computation II
MAS794 - Graduate Seminar – Pure Mathematics I
MAS795 - Graduate Seminar – Pure Mathematics II
MAS796 - Graduate Seminar – Statistics I
MAS797 - Graduate Seminar – Statistics II


Detailed Course Descriptions

Course Type Description
AUs
MAS 710 - Continuous Methods
  • Abstract integration (basic topology, general Lebesgue-like integrals and measures)
  • Positive Borel measures (Riesz representation theorem for positive linear functionals)
  • Lp-spaces
  • Integration on product spaces
  • Abstract differentiation
  • Holomorphic functions
4 AU
MAS 711 - Discrete Methods
  • Enumeration
  • Graph and network algorithms
  • Finite fields and applications
  • Boolean algebras
  • Polyhedra and linear programming
  • Algorithmic complexity
4 AU
MAS712 - Algebraic Methods
  • Groups, rings, and fields
  • Basic techniques of Group Theory
  • Galois Theory
4 AU
MAS713 - Mathematical Statistics
  • Review of probability, random variables and their distributions, moments and inequalities
  • Point estimation in parametric setting
  • Point estimation in nonparametric setting
  • Interval estimation and hypothesis test
4 AU
MAS714 - Algorithms and Theory of Computing
  • Turing machines
  • Time complexity and space complexity
  • Algorithm design and analysis (greedy, divide and conquer, dynamic programming)
  • Graph algorithms
  • Network flow.
4 AU