# University-Level Mathematics Program

Courses in the University-Level Online Mathematics Program are largely self-paced. An expert instructor is available for optional office hours to meet with students online and offer assistance as they progress through the course material.

All courses carry Stanford University Continuing Studies credit, and students earn a Stanford Continuing Studies transcript. Stanford Continuing Studies credit may be transferable to other educational institutions depending on the transfer policies of the specific college or university. To request your University-Level Online Math & Physics transcript, please complete the form found here and return your request to the Stanford Continuing Studies office via email or fax (650)725-4248.

Course | Prerequisites |
---|---|

## Multivariable Differential Calculus (XM521)Differential calculus for functions of two or more variables. Topics: vectors and vector-valued functions in 2-space and 3-space, tangent and normal vectors, curvature, functions of two or more variables, partial derivatives and differentiability, directional derivatives and gradients, maxima and minima, optimization using Lagrange multipliers. |
Calculus A, B, C or equivalent |

## Multivariable Integral Calculus (XM522)Integral calculus for functions of two or more variables. Topics: double and triple integrals, change of variables and the Jacobian, vector fields, line integrals, independence of path and the fundamental theorem of line integrals, Green's theorem, divergence theorem, and Stokes' theorem. |
Multivariable Differential Calculus or equivalent |

## Linear Algebra (XM511)An introductory course in Linear Algebra. Topics: matrices, linear equations, vector spaces, bases, coordinates, linear transformations, eigenvectors, eigenvalues, and diagonalization. |
Calculus A, B, C or equivalent |

## Modern Algebra (XM609)Theory of abstract algebra, with particular emphasis on applications involving symmetry. Topics: groups, rings, fields, matrix and crystallographic groups, and constructibility. |
Linear Algebra & Multivariable Integral Calculus or equivalents |

## Real Analysis (XM615)Theory of functions of a real variable. Topics: sequences, series, limits, continuity, differentiation, integration, and basic point-set topology. |
Linear Algebra or equivalent & consent of instructor |

## Differential Equations (XM531)Basic techniques and methods for solving ordinary differential equations. Topics: linear, separable, and exact equations, existence and uniqueness theorems, difference equations, basic theory of higher order equations, variation of parameters, undetermined coefficients, series solutions, Laplace transform, systems of equations. |
Linear Algebra & Multivariable Differential Calculus or equivalents |

## Complex Analysis (XM606)Theory of differentiation and integration of complex functions. Topics: algebra of complex numbers, complex functions, multi-valued functions, exponentials, logarithms, analyticity, integrals, power series, Laurent series, residues, isolated singularities, poles and zeros. |
Linear Algebra & Real Analysis or equivalents |

## Partial Differential Equations (XM631)Theory of differential equations involving functions of more than one variable. Topics: first order equations, classification of second order equations, initial-boundary value problems for heat equation, wave and related equations, separation of variables, eigenvalue problems, Fourier series, existence and uniqueness questions. |
Multivariable Integral Calculus, Differential Equations, & Complex Analysis or equivalents |

## Elementary Theory of Numbers (XM452)Introduction to number theory and its applications. Topics: Euclid's algorithm, divisibility, prime numbers, congruence of numbers, theorems of Fermat, Euler, Wilson, Lagrange's theorem; residues of power, quadratic residues, introduction to binary quadratic forms. |
Precalculus or equivalent |

#### * These courses feature interactive, seminar-style classrooms and/or office hours. If a student is unable to attend the scheduled course times, he or she can attend the class with flexible attendance contingent on his or her continued acceptable performance. If a student’s academic performance suffers from his or her lack of attendance, this may be reflected in the final grade. If a student is able to cover course material independently outside of class, he or she will nevertheless be required to start and finish the course within the time perimeters.

## Prerequisites

The flowchart below outlines what course(s) students should begin with. In order to enroll in a course, students must satisfy the given prerequisites or the equivalent.

## Instructors

### Margarita Kanarsky, Ph.D.

Dr. Kanarsky is originally from Russia. She graduated from Moscow State University with a B.S. degree in Applied Mathematics and later earned a Ph.D. in Mathematics and a M.S. in Computer Science from Emory University (Atlanta). Dr. Kanarsky has taught mathematics and statistics at a college level for several years and has been working for EPGY since 2011. She lives in the San Francisco Bay Area with her husband and three sons. Margarita enjoys spending time with the family. She likes alpine skiing, running and swimming; she swims with a local Masters Swim Team.