University-level Mathematics Courses

These courses, offered year-round, correspond to regular Stanford University courses. Students who successfully complete any of these courses and matriculate as undergraduates at Stanford may use these credits towards their bachelor's degrees. All courses are billed per course. Each course is scheduled to take approximately 15 weeks to complete, although students may progress more quickly if they wish. Each course must be completed within 6 months of the student's official start-date for that course. (Adult students interested in these courses should contact Marc Sanders.)

EPGY has guidelines regarding what course(s) to begin with. In order to enroll in a course, students must satisfy the given prerequisites or the equivalent.

Courses M51A, M52A, and M52B are graded on a pass/no-credit basis. (The other courses are graded using the standard letter grades.)

M51A Linear Algebra
An introductory course in Linear Algebra. Topics: linear spaces, transformations, matrices, eigenvalues, eigenvectors, and linear operators. Prerequisite: M52A. (4 units).
Please note the prerequisite! Course graded on a pass/no-credit basis.

M52A Multivariable Differential Calculus
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. Prerequisite: M042. (4 units). Course graded on a pass/no-credit basis.

M52B Multivariable Integral Calculus
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. Prerequisite: M52A. (3 units). Course graded on a pass/no-credit basis.

M53A Differential Equations
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. Prerequisites: M51A and M52A. (4 units).

M106 Complex Analysis
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. Prerequisites: M51A and M115. (3 units).

M109 Modern Algebra
Theory of abstract algebra, with particular emphasis on applications involving symmetry. Topics: groups, rings, fields, matrix and crystallographic groups, and constructibility. Prerequisites: M51A and M52B. (3 units).

M115 Real Analysis
Theory of functions of a real variable. Topics: sequences, series, limits, continuity, differentiation, integration, and basic point-set topology. Prerequisites: M52B. (3 units).

M131 Partial Differential Equations
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. Prerequisites: M52B, M53A, M106. (3 units).

M146 Point-Set Topology
Theory of topological spaces and introduction to algebraic topology. Topics: open sets, closed sets, functions and continuity, bases, products, metric spaces, connectedness, compactness, homotopy, fundamental group, and covering spaces. Prerequisites: M106 or M115. (3 units). In development.

M152 Elementary Theory of Numbers
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. Prerequisite: M013. (3 units).

M157 Introduction to Logic
A standard introduction to sentential and first-order logic. Topics: semantics and syntax of sentential logic, truth tables, inference rules, proofs, and counterexamples, quantification, symbolizing English sentences, consistency proofs and independence. Prerequisite: M013. (4 units).