# Foundational Courses for Graduate Students

## Foundational Mini-Course for Graduate Students

These 5-week courses are aimed exclusively at graduate students and have numbers 790-92 with different section numbers depending on the topic. They are designed to help students acquire basic mathematical skills so that they might take additional courses in the mathematical sciences as well as be more successful in self-study. Students should check the schedule for a given term to see the offerings.

• MATH 790-92: Introduction to Differential Calculus - This module will build the tools and concepts necessary for students to understand optimization.
• MATH 790-92: Introduction to Discrete Probability - This module will cover counting problems, probability distributions, joint distributions, conditional probability and the Central Limit Theorem.
• MATH 790-92: Introduction to Linear Algebra - This module will cover basic matrix operations, solving systems of linear equations using elimination, least-squares approximation problems, and an introduction to eigenvalues and eigenvectors.
• MATH 790-92: Matrix Decompositions and Data - An introduction to the application of matrix decompositions and their applications to data-driven problems. Topics include eigenvalues, eigenvectors, diagonalization, Jordan canonical form, QR-decompositions, singular value decomposition, and principal component analysis.
• MATH 790-92: Introduction to Integral Calculus - This module will cover the basics of integration and change of variables for probability distributions.
• MATH 790-92: Multivariable Calculus - An introduction to real-valued functions of several variables and their applications. Topics include vectors, partial derivatives, optimization, integration, and continuous distributions.

Undergraduate Course Number Graduate  Course Number Course Name
212 712 Multivariable Calculus
216 716 Linear Algebra and Differential Equations
218 718 Matrices and Vector Spaces
221 721 Linear Algebra and Applications
230 730 Elementary Probability
333 733 Complex Analysis
340 740 Advanced Introduction to Probability
353 753 Ordinary and Partial Differential Equations
356 756 Elementary Differential Equations
375 757 Introduction to Linear Programming and Game Theory
401 701 Introduction to Abstract Algebra
403 703 Advanced Linear Algebra
411 711 Topology
412 713

Topological Data Analysis

431 731 Advanced Calculus
451S 751S Nonlinear Ordinary Differential Equations
453 754 Introduction to Partial Differential Equations
465 765 Introduction to High Dimensional Data Analysis