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 minicourses. These are specially designed 5week intensive minicourses 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 MiniCourse for Graduate Students
These 5week courses are aimed exclusively at graduate students and have numbers 79092 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 selfstudy. Students should check the schedule for a given term to see the offerings.

MATH 79092: Introduction to Differential Calculus  This module will build the tools and concepts necessary for students to understand optimization.
 MATH 79092: Introduction to Discrete Probability  This module will cover counting problems, probability distributions, joint distributions, conditional probability and the Central Limit Theorem.
 MATH 79092: Introduction to Linear Algebra  This module will cover basic matrix operations, solving systems of linear equations using elimination, leastsquares approximation problems, and an introduction to eigenvalues and eigenvectors.
 MATH 79092: Matrix Decompositions and Data  An introduction to the application of matrix decompositions and their applications to datadriven problems. Topics include eigenvalues, eigenvectors, diagonalization, Jordan canonical form, QRdecompositions, singular value decomposition, and principal component analysis.
 MATH 79092: Introduction to Integral Calculus  This module will cover the basics of integration and change of variables for probability distributions.
 MATH 79092: Multivariable Calculus  An introduction to realvalued 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 