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Caltech Course Catalog / 2026-2027 Catalog / Courses 2026-27 / Department / ACM

Courses 2026-27: Applied & Computational Math

ACM 11

Introduction to Computational Science and Engineering

6 units (2-2-2)   |  third term
Prerequisites: Ma 1 ab, Co-requisite Ma 1 c. CS 1 or prior programming experience recommended.
This course is intended to serve as a practical introduction to the methods of computational science and engineering for students in all majors. The goal is to provide students exposure to and hands-on experience with commonly-used computational methods in science and engineering, with theoretical considerations confined to a level appropriate for first-year undergraduate students. Topics covered include computational simulation by discretization in space and time, numerical solution of linear and nonlinear equations, optimization, uncertainty quantification, and function approximation via interpolation and regression. Emphasis is on understanding trade-offs between computational effort and accuracy, and on developing working knowledge of how these tools can be used to solve a wide range of problems arising in applied math, science, and engineering. Assignments and in-class activities use MATLAB. No prior experience with MATLAB expected.
Instructor: Park
ACM 80 abc

Undergraduate Thesis

9 units   |  first, second, third terms
Prerequisites: instructor's permission, which should be obtained sufficiently early to allow time for planning the research.

Individual research project, carried out under the supervision of a member of the ACM faculty (or other faculty as approved by the ACM undergraduate option representative). Projects must include significant design effort. Written report required. Open only to upper class students. Not offered on a pass/fail basis.

Instructor: Staff
ACM 81 abc

Undergraduate Projects in Applied and Computational Mathematics

Units are assigned in accordance with work accomplished   |  first, second, third terms
Prerequisites: Consent of supervisor is required before registering.

Supervised research or development in ACM by undergraduates. The topic must be approved by the project supervisor, and a formal final report must be presented on completion of research. Graded pass/fail.

Instructor: Staff
ACM 95/100 ab

Introductory Methods of Applied Mathematics for the Physical Sciences

12 units (4-1-7)   |  second, third terms
Prerequisites: Ma 1 abc, Ma 2 or equivalents.
Complex analysis: analyticity, Laurent series, contour integration, residue calculus. Ordinary differential equations: linear initial value problems, linear boundary value problems, Sturm-Liouville theory, eigenfunction expansions, transform methods, Green's functions. Linear partial differential equations: heat equation, separation of variables, Laplace equation, transform methods, wave equation, method of characteristics, Green's functions.
Instructors: Zuev (second term), Hoffmann (third term)
ACM/IDS 101 ab

Methods of Applied Mathematics

9 units (3-3-3)   |  first, second terms
Prerequisites: Math 2/102 and ACM 95 ab or equivalent.
First term: Brief review of the elements of complex analysis and complex-variable methods. Asymptotic expansions, asymptotic evaluation of integrals (Laplace method, stationary phase, steepest descents), perturbation methods, WKB theory, boundary-layer theory, matched asymptotic expansions with first-order and high-order matching. Method of multiple scales for oscillatory systems. Second term: Applied spectral theory, special functions, generalized eigenfunction expansions, convergence theory. Gibbs and Runge phenomena and their resolution. Chebyshev expansion and Fourier Continuation methods. Review of numerical stability theory for time evolution. Fast spectrally-accurate PDE solvers for linear and nonlinear Partial Differential Equations in general domains. Integral-equations methods for linear partial differential equation in general domains (Laplace, Helmholtz, Schroedinger, Maxwell, Stokes). Homework problems in both 101 a and 101 b include theoretical questions as well as programming implementations of the mathematical and numerical methods studied in class.
Instructor: Bruno
ACM/IDS 104

Applied Linear Algebra

9 units (3-1-5)   |  first term
Prerequisites: Ma 1 abc, some familiarity with MATLAB, e.g. ACM 11 is desired.
This is an intermediate linear algebra course aimed at a diverse group of students, including sophomores in applied and computational mathematics, computer science, and information and data sciences, as well as graduate students in science and engineering. The main goal of the course is to provide an introduction to the fundamental ideas, concepts, and methods of applied linear algebra and illustrate them with important applications. Topics covered include linear systems, vector spaces and bases, fundamental matrix subspaces, inner products, norms, k-means algorithm, positive-definite and Gram matrices, application to text classification, least squares solutions and applications to data fitting, orthogonality, the QR factorization, eigenvalues and eigenvectors, the Gerschgorin theorem, the Perron-Frobenius theorem, the PageRank algorithm, the spectral theorem, optimization principles for eigenvalues, principal component analysis, spectral method for graph partitioning, and singular value decomposition with its applications.
Instructor: Zuev
ACM/EE 106 ab

Introductory Methods of Computational Mathematics

12 units (3-0-9)   |  first, second terms
Prerequisites: For ACM/EE 106 a, Ma 1 abc, Ma 2, Ma 3, ACM 11; for ACM/EE 106 b, ACM 95/100 ab or equivalent.

The sequence covers the introductory methods in both theory and implementation of numerical linear algebra, approximation theory, ordinary differential equations, and partial differential equations. The linear algebra parts cover basic methods such as direct and iterative solution of large linear systems, including LU decomposition, splitting method (Jacobi iteration, Gauss-Seidel iteration); eigenvalue and vector computations including the power method, QR iteration and Lanczos iteration; nonlinear algebraic solvers. The approximation theory includes data fitting; interpolation using Fourier transform, orthogonal polynomials and splines; least square method, and numerical quadrature. The ODE parts include initial and boundary value problems. The PDE parts include finite difference and finite element for elliptic/parabolic/hyperbolic equations. Study of numerical PDE will include stability analysis. Programming is a significant part of the course.

Instructor: Hou
CMS/ACM/IDS 107 ab

Linear Analysis with Applications

12 units (3-0-9)   |  first term
Prerequisites: ACM/IDS 104 or equivalent, Ma 1b or equivalent.
Part a: Covers the basic algebraic, geometric, and topological properties of normed linear spaces, inner-product spaces and linear maps. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations. Topics: Completeness, Banach spaces (l_p, L_p), Hilbert spaces (weighted l_2, L_2 spaces), introduction to Fourier transform, Fourier series and Sobolev spaces, Banach spaces of linear operators, duality and weak convergence, density, separability, completion, Schauder bases, continuous and compact embedding, compact operators, orthogonality, Lax-Milgram, Spectral Theorem and SVD for compact operators, integral operators, Jordan normal form. Part b: Continuation of ACM 107a, developing new material and providing further details on some topics already covered. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.Topics: Review of Banach spaces, Hilbert spaces, Linear Operators, and Duality, Hahn-Banach Theorem, Open Mapping and Closed Graph Theorem, Uniform Boundedness Principle, The Fourier transform (L1, L2, Schwartz space theory), Sobolev spaces (W^s,p, H^s), Sobolev embedding theorem, Trace theorem Spectral Theorem, Compact operators, Ascoli Arzela theorem, Contraction Mapping Principle, with applications to the Implicit Function Theorem and ODEs, Calculus of Variations (differential calculus, existence of extrema, Gamma-convergence, gradient flows) Applications to Inverse Problems (Tikhonov regularization, imaging applications). Part b not offered 2026-27.
Instructor: Tropp
ACM 109

Mathematical Modelling

9 units (3-0-6)   |  third term

Prerequisites ACM 95/100 ab or equivalent. This course gives an overview of different mathematical models used to describe a variety of phenomena arising in the biological, engineering, physical and social sciences. Emphasis will be placed on the principles used to develop these models, and on the unity and cross-cutting nature of the mathematical and computational tools used to study them. Applications will include quantum, atomistic and continuum modeling of materials; epidemics, reacting-diffusing systems; crowd modeling and opinion formation. Mathematical tools will include ordinary, partial and stochastic differential equations, as well as Markov chains and other stochastic processes. Not offered 2026-27.

Ec/ACM/CS 112

Bayesian Statistics

9 units (3-0-6)   |  second term
Prerequisites: Ma 3, ACM/EE/IDS 116 or equivalent.

This course provides an introduction to Bayesian Statistics and its applications to data analysis in various fields. Topics include: discrete models, regression models, hierarchical models, model comparison, and MCMC methods. The course combines an introduction to basic theory with a hands-on emphasis on learning how to use these methods in practice so that students can apply them in their own work. Previous familiarity with frequentist statistics is useful but not required.

Instructor: Rangel
ACM/EE/IDS 116

Introduction to Probability Models

9 units (3-1-5)   |  first term
Prerequisites: Ma 3 or EE 55, some familiarity with MATLAB, e.g. ACM 11, is desired.
This course introduces students to the fundamental concepts, methods, and models of applied probability and stochastic processes. The course is application oriented and focuses on the development of probabilistic thinking and an intuitive feel for the subject rather than on a more traditional formal approach based on measure theory. The main goal is to equip science and engineering students with necessary probabilistic tools they can apply in future studies and research. Topics covered include sample spaces, probabilities of events, random variables, expectation, variance, correlation, joint and marginal distributions, independence, moment generating functions, law of large numbers, central limit theorem, Monte Carlo method, conditional distributions, conditional expectation and variance, random vectors and matrices, random graphs, Wiener filters, Gaussian vectors, stochastic processes, Poisson process, Brownian motion, stationary processes, correlation function, and power spectral density.
Instructor: Zuev
CMS/ACM 117

Probability Theory and Computational Mathematics

12 units (3-0-9)   |  first term
Prerequisites: ACM 104 and ACM 116; or instructor's permission.
This course offers a rigorous introduction to probability theory with applications to computational mathematics. Emphasis is placed on nonasymptotic properties of probability models, rather than classical limit theorems. Topics include measure theory, integration, product measures, probability spaces, random variables and expectation, moments, Lp spaces, orthogonality, independence, concentration inequalities, distances between probability measures, the Berry-Esseen theorem, conditional expectation, and conditioning for Gaussian families.
Instructor: Park
ACM 118

Gaussian Processes and kernel methods

12 units (3-2-7)   |  second term
Prerequisites: CMS/ACM/IDS 107 or equivalent, ACM 116 or equivalent, or permission of the instructor.
This course provides a thorough and comprehensive exploration of Gaussian processes and kernel methods, bridging foundational theory with practical applications in regression, learning, and numerical analysis. It covers Gaussian vectors, processes, fields, and measures, with a particular focus on regression techniques. The course delves into kernel methods and Reproducing Kernel Hilbert Spaces (RKHS), examining key concepts such as Kernel PCA, LDA, CCA, kernel mean embedding, and operator-valued kernels. A central theme will be the interplay between kernel methods and optimal recovery techniques, with applications in statistical numerical approximation, signal processing, and machine learning.
Instructor: Owhadi
CMS/ACM/EE 122

Mathematical Optimization

12 units (4-0-8)   |  first term
Prerequisites: linear algebra.
This class develops mathematical optimization from the perspective of certificates, duality, and convexity. Topics covered include Fenchel and Lagrange duality; representation of convex sets; linear and semidefinite programming; integer programming; convex relaxations for intractable problems; and numerical methods. Throughout the course, applications of optimization to problems arising in various areas of science and engineering are presented.
Instructor: Chandrasekaran
AM/ACM 127

Calculus of Variations

9 units (3-0-6)   |  third term
Prerequisites: ACM 95/100.

First and second variations; Euler-Lagrange equation; Hamiltonian formalism; action principle; Hamilton-Jacobi theory; stability; local and global minima; direct methods and relaxation; isoperimetric inequality; asymptotic methods and gamma convergence; selected applications to mechanics, materials science, control theory and numerical methods. Not offered 2026-27.

Ma/ACM/IDS 140 abc

Probability

9 units (3-0-6)   |  first, second, third terms
Prerequisites: For 140 a, Ma 108 b is strongly recommended.

This course begins with an overview of measure theory, followed by topics that include random walks, the strong law of large numbers, the central limit theorem, martingales, Markov chains, characteristic functions, Poisson processes, and Brownian motion. Towards the end, some further topics may be covered, such as stochastic calculus, stochastic differential equations, Gaussian processes, random graphs, Markov chain mixing, random matrix theory, and interacting particle systems.

Instructors: Tamuz, El-Maazouz, L. Zhang
Ma/ACM 142 ab

Ordinary and Partial Differential Equations

9 units (3-0-6)   |  second, third terms
Prerequisites: Ma 108; Ma 109 is desirable.

The mathematical theory of ordinary and partial differential equations, including a discussion of elliptic regularity, maximal principles, solubility of equations. The method of characteristics.

Instructor: Isett
ACM/IDS 154

Inverse Problems and Data Assimilation

9 units (3-0-6)   |  Second term
Prerequisites: Basic differential equations, linear algebra, probability and statistics: ACM/IDS 104, ACM/EE 106 ab, ACM/EE/IDS 116, IDS/ACM/CS 157 or equivalent.
Models in applied mathematics often have input parameters that are uncertain; observed data can be used to learn about these parameters and thereby to improve predictive capability. The purpose of the course is to describe the mathematical and algorithmic principles of this area. The topic lies at the intersection of fields including inverse problems, differential equations, machine learning and uncertainty quantification. Applications will be drawn from the physical, biological and data sciences. Not offered 2026-27.
Instructor: Stuart
IDS/ACM/CS 157

Statistical Inference

9 units (3-2-4)   |  third term
Prerequisites: ACM/EE/IDS 116, Ma 3.

Statistical Inference is a branch of mathematical engineering that studies ways of extracting reliable information from limited data for learning, prediction, and decision making in the presence of uncertainty. This is an introductory course on statistical inference. The main goals are: develop statistical thinking and intuitive feel for the subject; introduce the most fundamental ideas, concepts, and methods of statistical inference; and explain how and why they work, and when they don't. Topics covered include summarizing data, fundamentals of survey sampling, statistical functionals, jackknife, bootstrap, methods of moments and maximum likelihood, hypothesis testing, p-values, the Wald, Student's t-, permutation, and likelihood ratio tests, multiple testing, scatterplots, simple linear regression, ordinary least squares, interval estimation, prediction, graphical residual analysis.

Instructor: Zuev
IDS/ACM/CS 158

Fundamentals of Statistical Learning

9 units (3-3-3)   |  second term
Prerequisites: ACM/IDS 104, ACM/EE/IDS 116, IDS/ACM/CS 157.

The main goal of the course is to provide an introduction to the central concepts and core methods of statistical learning, an interdisciplinary field at the intersection of applied mathematics, statistical inference, and machine learning. The course focuses on the mathematics and statistics of methods developed for learning from data. Students will learn what methods for statistical learning exist, how and why they work (not just what tasks they solve and in what built-in functions they are implemented), and when they are expected to perform poorly. The course is oriented for upper level undergraduate students in IDS, ACM, and CS and graduate students from other disciplines who have sufficient background in linear algebra, probability, and statistics. The course is a natural continuation of IDS/ACM/CS 157 and it can be viewed as a statistical analog of CMS/CS/CNS/EE/IDS 155. Topics covered include elements of statistical decision theory, regression and classification problems, nearest-neighbor methods, curse of dimensionality, linear regression, model selection, cross-validation, subset selection, shrinkage methods, ridge regression, LASSO, logistic regression, linear and quadratic discriminant analysis, support-vector machines, tree-based methods, bagging, and random forests. Not offered 2026-27.

Instructor: Zuev
ACM/EE/IDS 170

Mathematics of Signal Processing

12 units (3-0-9)   |  third term
Prerequisites: ACM/IDS 104, CMS/ACM/EE 122, and ACM/EE/IDS 116; or instructor's permission.

This course covers classical and modern approaches to problems in signal processing. Problems may include denoising, deconvolution, spectral estimation, direction-of-arrival estimation, array processing, independent component analysis, system identification, filter design, and transform coding. Methods rely heavily on linear algebra, convex optimization, and stochastic modeling. In particular, the class will cover techniques based on least-squares and on sparse modeling. Throughout the course, a computational viewpoint will be emphasized. Not offered 2026-27.

Instructor: Hassibi
ACM/IDS 180 ab

Multiscale Modeling

12 units (3-0-9)   |  first, third terms
Prerequisites: CMS 107, CMS 117 or explicit email permission from instructor.

Part a: Multiscale methodology for partial differential equations (PDEs) and for stochastic differential equations (SDEs). Basic theory of underlying PDEs; basic theory of Gaussian processes; basic theory of SDEs; multiscale expansions. Part b: Transition from quantum to continuum modeling of materials. Schrodinger equation and semi-classical limit; molecular dynamics and kinetic theory; kinetic theory, Boltzmann equation and continuum mechanics. Not offered 2026-27.

Instructor: Staff
ACM 190

Reading and Independent Study

Units by arrangement

Graded pass/fail only.

Instructor: Staff
ACM 201

Partial Differential Equations

12 units (4-0-8)   |  first term
Prerequisites: ACM 95/100 ab, ACM/IDS 101 ab, ACM 11 or equivalent.

This course offers an introduction to the theory of Partial Differential Equations (PDEs) commonly encountered across mathematics, engineering and science. The goal of the course is to study properties of different classes of linear and nonlinear PDEs (elliptic, parabolic and hyperbolic) and the behavior of their solutions using tools from functional analysis with an emphasis on applications. We will discuss representative models from different areas such as: heat equation, wave equation, advection-reaction-diffusion equation, conservation laws, shocks, predator prey models, Burger's equation, kinetic equations, gradient flows, transport equations, integral equations, Helmholtz and Schrödinger equations and Stoke's flow. In this course you will use analytical tools such as Gauss's theorem, Green's functions, weak solutions, existence and uniqueness theory, Sobolev spaces, well-posedness theory, asymptotic analysis, Fredholm theory, Fourier transforms and spectral theory. More advanced topics include: Perron's method, applications to irrotational flow, elasticity, electrostatics, special solutions, vibrations, Huygens' principle, Eikonal equations, spherical means, retarded potentials, water waves, various approximations, dispersion relations, Maxwell equations, gas dynamics, Riemann problems, single- and double-layer potentials, Navier-Stokes equations, Reynolds number, potential flow, boundary layer theory, subsonic, supersonic and transonic flow. Not offered 2026-27.

Instructor: Staff
ACM/IDS 204

Topics in Linear Algebra and Convexity

9 units (3-0-6)   |  third term
Prerequisites: CMS 107a and CMS/ACM 122; or instructor's permission.

The content of this course varies from year to year among advanced subjects in linear algebra, convex analysis, and related fields. Specific topics for the class include matrix analysis, operator theory, convex geometry, or convex algebraic geometry. Lectures and homework will require the ability to understand and produce mathematical proofs. Not offered 2026-27.

Instructor: Staff
ACM 206

Topics in Computational Mathematics

9 units (3-0-6)   |  third term
Prerequisites: ACM 106 ab; linear algebra at the level of ACM 104 or ACM 107; probability theory at the level of ACM 116 or ACM 117; some programming experience.

This course provides an introduction to Monte Carlo methods with applications in Bayesian computing and rare event sampling. Topics include Markov chain Monte Carlo (MCMC), Gibbs samplers, Langevin samplers, MCMC for infinite-dimensional problems, convergence of MCMC, parallel tempering, umbrella sampling, forward flux sampling, and sequential Monte Carlo. Emphasis is placed both on rigorous mathematical development and on practical coding experience. Not offered 2026-27.

Instructor: Staff
ACM 210

Numerical Methods for PDEs

9 units (3-0-6)   |  third terms
Prerequisites: ACM 11, 106 or instructor's permission.

Finite difference and finite volume methods for hyperbolic problems. Stability and error analysis of nonoscillatory numerical schemes: i) linear convection: Lax equivalence theorem, consistency, stability, convergence, truncation error, CFL condition, Fourier stability analysis, von Neumann condition, maximum principle, amplitude and phase errors, group velocity, modified equation analysis, Fourier and eigenvalue stability of systems, spectra and pseudospectra of nonnormal matrices, Kreiss matrix theorem, boundary condition analysis, group velocity and GKS normal mode analysis; ii) conservation laws: weak solutions, entropy conditions, Riemann problems, shocks, contacts, rarefactions, discrete conservation, Lax-Wendroff theorem, Godunov's method, Roe's linearization, TVD schemes, high-resolution schemes, flux and slope limiters, systems and multiple dimensions, characteristic boundary conditions; iii) adjoint equations: sensitivity analysis, boundary conditions, optimal shape design, error analysis. Interface problems, level set methods for multiphase flows, boundary integral methods, fast summation algorithms, stability issues. Spectral methods: Fourier spectral methods on infinite and periodic domains. Chebyshev spectral methods on finite domains. Spectral element methods and h-p refinement. Multiscale finite element methods for elliptic problems with multiscale coefficients. Not offered 2026-27.

Instructor: Staff
ACM/IDS 213

Topics in Optimization

9 units (3-0-6)   |  third term
Prerequisites: ACM/IDS 104, CMS/ACM/EE 122.

Material varies year-to-year. Example topics include discrete optimization, convex and computational algebraic geometry, numerical methods for large-scale optimization, and convex geometry. Not offered 2026-27.

Instructor: Staff
ACM/IDS 216

Markov Chains, Discrete Stochastic Processes and Applications

9 units (3-1-5)   |  second term
Prerequisites: ACM/EE/IDS 116 or equivalent.
Introduction to Markov chains and processes covering discrete and continuous state-spaces in both discrete and continuous time settings. Topics include irreducibility, aperiodicity, stationary and equilibrium distributions, convergence behavior, transience and recurrence, and the Ergodic Theorem. Emphasis on Markov Chain Monte Carlo (MCMC) algorithms, particularly Metropolis-Hastings and Simulated Annealing, with practical applications in scientific computing. Additional topics include coupling from the past, convergence rates, and an introduction to Markov Decision Processes.
Instructor: Owhadi
ACM 217

Advanced Topics in Probability

9 units (3-0-6)   |  second term
Prerequisites: CMS 107a and CMS/ACM 117; or instructor's permission.
Topic varies by year. 2026-27: High-dimensional probability. This class treats probabilistic and geometric phenomena that occur in high-dimensional linear spaces. These insights have applications in machine learning, statistics, algorithms, numerical analysis, and related fields. Specific topics may include concentration inequalities, suprema of random processes, random matrix theory, phase transition phenomena, and universality laws. This course requires the ability to understand and produce mathematical proofs.
Instructor: Tropp
ACM 221 ab

Quantum algorithms for scientific computation

9 units (3-0-6)   |  second term
Quantum computers have the potential to revolutionize how we think about computing. This two-quarter graduate course introduces recent advances in quantum algorithmic techniques for scientific computation. The two quarters are designed to form a sequence, but each may also be taken independently. The first quarter focuses on algorithms based on unitary evolution of pure states, including block encoding, linear combination of unitaries, qubitization, quantum signal processing, quantum singular value transformation, Hamiltonian simulation, quantum algorithms for solving linear systems, differential equations, and query lower bounds. The second quarter extends the discussion to general quantum channels and more statistical aspects of quantum computation, with topics including quantum Markov chains, Lindblad dynamics, mixing time, phase and eigenvalue estimation, and statistical lower bounds. The emphasis throughout is on general algorithmic principles rather than hardware-specific implementation. By the end of the sequence, students will have a solid foundation in modern quantum algorithms for scientific computation and be prepared to read current research and develop new algorithms in their own work. Part b not offered 2026-27.
Instructor: Lin
Ae/ACM/ME 232 ab

Computational Fluid Dynamics

9 units (3-0-6)   |  second, third terms
Prerequisites: Ae/APh/CE/ME 101 abc or equivalent; ACM 100 ab or equivalent; ACM 104.

Development and analysis of algorithms used in the solution of fluid mechanics problems. Numerical analysis of discretization schemes for partial differential equations including interpolation, integration, spatial discretization, systems of ordinary differential equations; stability, accuracy, aliasing, Gibbs and Runge phenomena, numerical dissipation and dispersion; boundary conditions. Survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible Euler and Navier-Stokes equations, including shock-capturing methods.

Instructors: Colonius, Meiron
ACM 256

Special Topics in Applied Mathematics: Optimal Transport

9 units (3-0-6)   |  second term
Prerequisites: Familiarity with analysis and probability, e.g. ACM 105 and ACM 116 is desired.
How can the mass of a reference distribution be rearranged to match a target distribution, subject to a minimal transportation cost? This problem was first formulated in the realm of logistics and measure transport is nowadays an indispensable tool in modern applications such as image retrieval, inverse problems, cancer detection, shape and image registration, and machine learning. This class will introduce the foundations of measure transport at the intersection of analysis, probability and optimization, its applications and connections to various fields and explore modern computational methods.
Instructor: Hellmuth
ACM 257

Special Topics in Financial Mathematics

9 units (3-0-6)   |  third term
Prerequisites: ACM 95/100 or instructor's permission.

A basic knowledge of probability and statistics as well as transform methods for solving PDEs is assumed. This course develops some of the techniques of stochastic calculus and applies them to the theory of financial asset modeling. The mathematical concepts/tools developed will include introductions to random walks, Brownian motion, quadratic variation, and Ito-calculus. Connections to PDEs will be made by Feynman-Kac theorems. Concepts of risk-neutral pricing and martingale representation are introduced in the pricing of options. Topics covered will be selected from standard options, exotic options, American derivative securities, term-structure models, and jump processes. Not offered 2026-27.

Instructor: Staff
ACM 270

Advanced Topics in Applied and Computational Mathematics

Hours and units by arrangement   |  first, second, third terms

Advanced topics in applied and computational mathematics that will vary according to student and instructor interest. May be repeated for credit. Not offered 2026-27.

Instructor: Staff
ACM 300

Research in Applied and Computational Mathematics

Units by arrangement
Instructor: Staff
Published Date: Aug. 7, 2026