Many graduate students outside of mathematics include undergraduate mathematics courses in their graduate course of study. There are two main routes to accomplish this. The first is to take one or more of our graduate foundational mini-courses. These are specially designed 5-week intensive mini-courses for graduate students in foundational mathematics. The second is to enroll in the graduate version of one of our undergraduate courses. These courses share the same lectures and many assignments and projects with the undergraduate version, but have some additional requirements for enrolled graduate students. The extra requirements usually explore how the course fits into the students' graduate course of study.

## 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.

**Questions?** Please contact **Brian Fitzpatrick** at bfitzpat@math.duke.edu or **Jack Bookman **at bookman@math.duke.edu for more information.

## Graduate version of Undergraduate Courses

The Mathematics has created graduate course numbers for most of its undergraduate courses which were most popular among graduate students. These courses have numbers in the 700’s and are paired with an undergraduate course numbered less than 500. Students in the graduate classes will attend the same lectures as the undergraduate students and do the same homework, tests and projects. In addition, the graduate students will have some extra assignments designed to help explore the relevance of the course to the graduate students' course of study. A full list of the graduate course and the paired undergraduate course is given below.

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 |