MATH 19: Calculus
Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions (including exponentials and logarithms). You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Kimport, S. (PI)
;
Ohrt, C. (PI)
;
Wang, Y. (PI)
;
Chaturvedi, S. (TA)
;
Chen, S. (TA)
;
Datta, I. (TA)
;
Mackey, W. (TA)
MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications
This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, datadriven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and dataintensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underl
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This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, datadriven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and dataintensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (a crucial part of how GPS works). The course emphasizes computations alongside an intuitive understanding of key ideas, making students wellprepared for further study of mathematics and its applications to other fields. The widespread use of computers makes it more important, not less, for users of math to understand concepts: in all scientific fields, novel users of quantitative tools in the future will be those who understand ideas and how they fit with applications and examples. This is the only course at Stanford whose syllabus includes nearly all the math background for
CS 229, which is why
CS 229 and
CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between
Math 51 and
CME 100, see the FAQ on the placement page on the math department website. Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
...
more instructors for MATH 51 »
Instructors:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
He, J. (PI)
;
Kuperberg, V. (PI)
;
Love, J. (PI)
;
Lucianovic, M. (PI)
;
Mazzeo, R. (PI)
;
McConnell, S. (PI)
;
Ohrt, C. (PI)
;
Sloman, L. (PI)
;
Taylor, C. (PI)
;
Wei, F. (PI)
;
Wieczorek, W. (PI)
;
Zhu, B. (PI)
;
Cant, D. (TA)
;
Fayyazuddin Ljungberg, B. (TA)
;
Love, J. (TA)
;
Wei, F. (TA)
;
Zou, J. (TA)
MATH 53: Ordinary Differential Equations with Linear Algebra
Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of secondorder equations to oscillations, matrix exponentials, Laplace transforms, stability of nonlinear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 104: Applied Matrix Theory
Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, leastsquares, the condition number of a matrix, algorithms for solving linear systems.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
EE 103/
CME 103 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
EE 103 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106.
Terms: Aut, Win, Spr, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Kazeev, V. (PI)
;
Taylor, C. (PI)
;
Ying, L. (PI)
;
Guijarro Ordonez, J. (TA)
;
Liu, Y. (TA)
;
Luo, S. (TA)
MATH 106: Functions of a Complex Variable
Complex numbers, analytic functions, CauchyRiemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (
Math 116 offers a more theoretical treatment.) Prerequisite: 52.
Terms: Spr, Sum

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Zaman, A. (PI)
MATH 113: Linear Algebra and Matrix Theory
Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. (
Math 104 offers a more applicationoriented treatment.)
Terms: Aut, Win, Spr, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 114: Introduction to Scientific Computing (CME 108)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Marsden, A. (PI)
;
Aboumrad, G. (TA)
MATH 115: Functions of a Real Variable
The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Honors math majors and students who intend to do graduate work in mathematics should take 171. Prerequisite: 21.
Terms: Aut, Spr, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Thorner, J. (PI)
;
Nuti, P. (TA)
MATH 197: Senior Honors Thesis
Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum

Units: 16

Repeatable for credit

Grading: Letter (ABCD/NP)
Instructors:
Fox, J. (PI)
;
Kojima, F. (PI)
;
Luk, J. (PI)
;
Montanari, A. (PI)
;
Ryzhik, L. (PI)
;
Soundararajan, K. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
Vondrak, J. (PI)
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