Training in mathematics and statistics is a necessary component of the Simon PhD program coursework. In order to prepare you for success we offer three mini courses each summer before the official start of classes. Our Summer Math program is included in your full-tuition scholarship.

While not mandatory, these classes are strongly recommended and highly encouraged. Courses meet during the months of July and August.

PhD Architecture
Topic 1: Linear Algebra

The goal of this course is to give an introduction to linear algebra.

Topics include:

  • Gaussian elimination, matrix operations, matrix inverses.
  • Vector spaces and subspaces, linear independence, and the basis of a space.
  • Row space and column space of a matrix, fundamental theorem of linear algebra, linear transformations.
  • Orthogonal vectors and subspaces, orthogonal bases, and Gram-Schmidt method.
  • Orthogonal projections, linear regression.
  • Determinants: how to calculate them, properties, and applications.
  • Calculating eigenvectors and eigenvalues, basic properties.
  • Matrix diagonalization, application to difference equations and differential equations.
  • Positive definite matrices, tests for positive definiteness, singular value decomposition.
  • Classification of states, transience and recurrence, classes of states. Absorption, expected reward.
  • Stationary and limiting distributions.

PhD Idea

Topic 2: Optimization

This course covers:

  • Optimization in Rn
  • Weierstrass Theorem
  • Unconstrained optimization
  • Lagrange Theorem and equality constraints
  • Kuhn-Tucker Theorem and Inequality constraints
  • Convexity
  • Parametric Monotonicity and Supermodularity

PhD Graphic Design

Topic 3: Probability Theory

This course teaches:

  • Random Variable
  • Distribution
  • Independence
  • Transformations and Expectations
  • Common Families of Distributions
  • Multiple Random Variables
  • Markov Chains