Calstate LA - Caltech Student Development Program

As part of a cooperative agreement between California State University at Los Angeles and the California Institute of Technology, graduate students at Cal State LA can take certain courses at Caltech without tuition or fees. This agreement is limited to a subset of courses in the Computing and Mathematical Science (CMS) department.

Eligibility Requirements

Students participating in the Cal State LA-Caltech program must meet the following criteria:

  • Graduate student with classified standing
  • A minimum 3.50 grade point average
  • Acceptance into the Cal State LA-Caltech program
  • Limit of two Caltech courses per student per academic term

Available Courses

The courses listed below are available to Cal State L.A. students participating in the Cal State L.A-Caltech cooperative student development program. Students must have the prerequisite courses or equivalent knowledge to enroll in a particular course. Additionally, permission is required from the course instructor at Caltech.

Since the cooperative program has a limit on the number of participants each term, students who are interested in this program must complete an application form and submit it to the Associate Dean of Natural & Social Sciences. The program is only open to Cal State LA graduate students. For more information, contact Dr. Nancy McQueen in the College of Natural & Social Sciences or Dr. Robert Desharnais in the Department of Biological Sciences at Cal State L.A.

Note that the course numbering system at Caltech is different from Cal State L.A. Caltech courses numbered below 100 are undergraduate courses not available for graduate program credit. Courses in the range 100-199 are equivalent to 400-level courses at Cal State L.A. and courses numbered 200-299 are equivalent to 500-level courses at Cal State L.A.

Caltech operates on the quarter system. The number of units assigned to a course is based on the estimated number of hours of preparation per week (lectures, laboratory, and outside preparation). These are not equivalent to quarter or semester units at Cal State L.A. For example, a Caltech undergraduate needs a minimum of 486 quarter units to graduate, whereas a Cal State LA student needs 180 quarter units or a 120 semester units. To reconcile these differences, the number of units listed below are Cal State L.A. equivalent quarter/semester units based on time spent in lecture and/or laboratory only.

The following courses are available to Cal State LA graduate students:

Applied and Computational Mathematics (ACM)

​ACM 104 - Applied Linear Algebra (4/2.67 units)

  • Topics: This is an intermediate linear algebra course aimed at a diverse group of students, including junior and senior majors in applied mathematics, sciences and engineering. The focus is on applications. Matrix factorizations play a central role. Topics covered include linear systems, vector spaces and bases, inner products, norms, minimization, the Cholesky factorization, least squares approximation, data fitting, interpolation, orthogonality, the QR factorization, ill-conditioned systems, discrete Fourier series and the fast Fourier transform, eigenvalues and eigenvectors, the spectral theorem, optimization principles for eigenvalues, singular value decomposition, condition number, principal component analysis, the Schur decomposition, methods for computing eigenvalues, non-negative matrices, graphs, networks, random walks, the Perron-Frobenius theorem, PageRank algorithm. (3 hours lecture, 1 hour laboratory)
  • ​Prerequisites: ACM 100abc or equivalent; calculus of one and several variables; differential equations

ACM 106ab - Introductory Methods of Computational Mathematics I & II (3/2 units†)

  • Topics: 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 covers 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 equation. Stability analysis will be covered with numerical PDE. Programming is a significant part of the course. (3 hours lecture)
  • ​Prerequisites: ACM 100abc or equivalent; calculus of one and several variables; linear algebra; differential equations; probability and statistics.

ACM 113 - Mathematical Optimization (3/2 units†)

  • Topics: This class studies mathematical optimization from the viewpoint of convexity. Topics covered include duality and representation of convex sets; linear and semidefinite programming; connections to discrete, network, and robust optimization; relaxation methods for intractable problems; as well as applications to problems arising in graphs and networks, informa tion theory, control, signal processing, and other engineering disciplines. (3 hours lecture)
  • Prerequisites: Corequisite: ACM 104; calculus of one and several variables; linear algebra; differential equations

ACM 114ab - Parallel Algorithms for Scientific Applications I & II (3/2 units†)

  • Topics: Introduction to parallel program design for numerically intensive scientific applications. Parallel programming methods; distributed-memory model with message passing using the message passing interface; shared-memory model with threads using open MP, CUDA; object-based models using a problem-solving environment with parallel objects. Parallel numerical algorithms: numerical methods for linear algebraic systems, such as LU decomposition, QR method, CG solvers; parallel implementations of numerical methods for PDEs, including finite-difference, finite-element; particle-based simulations. Performance measurement, scaling and parallel efficiency, load balancing strategies. (3 hours lecture)
  • Prerequisites: ACM 106ab

ACM 116: Introduction to Probability Models (4/2.67 units†)

  • ​Topics: 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 intuitive feel of 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 use in future studies and research. Topics covered include sample spaces, events, probabilities of events, discrete and continuous random variables, expectation, variance, correlation, joint and marginal distributions, independence, moment generating functions, law of large numbers, central limit theorem, random vectors and matrices, random graphs, Gaussian vectors, branching, Poisson, and counting processes, general discrete- and continuous-timed processes, auto- and cross-correlation functions, stationary processes, power spectral densities. (3 hours lecture, 1 hour laboratory)
  • Prerequisites: differential equations; probability and statistics

ACM 216: Markov Chains, Discrete Stochastic Processes and Applications (3/2 units†)

  • Topics: Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations. (3 hours lecture)
  • Prerequisites: ACM 116

Control and Dynamical Systems (CDS)

CDS 101 - Design and Analysis of Feedback Systems (4/2.67 units†)

  • Topics: An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear vs. nonlinear models, and local vs. global behavior. This course is taught concurrently with CDS 110, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems. (2 hours lecture)
  • Prerequisites: Calculus of one and several variables; linear algebra; differential equations

CDS 110 - Introduction to Feedback Control Systems (6/4 units†)

  • Topics: An introduction to analysis and design of feedback control systems, including classical control theory in the time and frequency domain. Input/output modeling of dynamical systems using differential equations and transfer functions. Stability and performance of interconnected systems, including use of block diagrams, Bode plots, the Nyquist criterion, and Lyapunov functions. Design of feedback controllers in state space and frequency domain based on stability, performance and robustness specifications. (3 hours lecture)
  • Prerequisites: Calculus of one and several variables; linear algebra; differential equations

CDS 112 - Control System Design (5/3.33 units†)

  • Topics: Optimization-based design of control systems, including optimal control and receding horizon control. Robustness and uncertainty management in feedback systems through stochastic and deterministic methods. Introductory random processes, Kalman filtering, and norms of signals and systems. (3 hours lecture)
  • Prerequisites: Calculus of one and several variables; linear algebra; differential equations

​CDS 140 - Introduction to Dynamics (3/2 units†)

  • Topics: Basics topics in dynamics for continuous state systems in continuous and discrete time, using linear and nonlinear differential equations and maps. Topics include equilibria/invariant sets, stability, Lyapunov functions/invariants, attractors and periodic solutions. Introduction to structural stability, bifurcations and eigenvalue crossing conditions. (3 hours lecture)
  • ​Prerequisites: ACM 104; calculus of one and several variables; linear algebra; differential equations

CDS 212 - Introduction to Modern Control (5/3.33 units†)

  • Topics: Introduction to modern control systems with emphasis on the role of control in overall system analysis and design. Examples drawn from throughout engineering and science. Open versus closed loop control. State-space methods, time and frequency domain, stability and stabilization, realization theory. Time-varying and nonlinear models. Uncertainty and robustness. (3 hours lecture)
  • Prerequisites: ACM 104; CDS 110; calculus of one and several variables; linear algebra; differential equations

CDS 213 - Robust Control (3/2 units†)

  • Topics: Linear systems, realization theory, time and frequency response, norms and performance, stochastic noise models, robust stability and performance, linear fractional transformations, structured uncertainty, optimal control, model reduction, m analysis and synthesis, real parametric uncertainty, Kharitonov's theorem, uncertainty modeling. (3 hours lecture)
  • Prerequisites: CDS 212

CDS 240 - Nonlinear Dynamical Systems (3/2 units†)

  • Topics: Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. (3 hours lecture)
  • Prerequisites: CDS 140

​† Quarter system units/Semester system units at Cal State LA

The following courses are availbale for Fall 2017:

ACM 104    Applied Linear Algebra, TR 2:30-4:30
ACM 106a  Intro Methods of Computational Mathematics, TR 1:00-2:25
ACM 116    Intro to Probability Models, TR 9:00-10:25

Complete course descriptions can be found at:

http://cms.caltech.edu/academics/course_desc

Visit the following web page for course schedules:

http://cms.caltech.edu/academics/course_schedule

Note that these courses are not offered every term and amy not be offered in some years.

 

Application Procedure

To participate in the Cal State LA-Caltech program, complete the following steps:

  1. Decide on which Caltech course(s) interest you. (They must be courses from the list above.)
  2. Take note of the prerequisites for the desired Caltech courses (see above).
  3. Take note of when the Caltech courses are being offered.
  4. Download and complete the application.
  5. Obtain documentation that you meet the prerequisites. You can use unofficial transcripts, but they must include grades.
  6. Submit the completed and signed application and supporting documentation for prerequisites to Dr. Nancy McQueen at the College of Natural & Social Sciences (ASC Wing B 223; nmcquee@calstatela.edu) by September 11, 2017 for courses to be taken in Fall 2017. You may scan and email the completed application form.

Applicants will be notified by email regarding their acceptance into the program in about one week following the application deadline.

pdf icon Cal State LA-Caltech Program Application Form

 

More Information

For more information, contact Dr. Nancy McQueen in the College of Natural & Social Sciences or Dr. Robert Desharnais in the Department of Biological Sciences at Cal State L.A. This program is administered through Cal State LA. Do not contact Caltech regarding this program.

pdf icon Cal State LA-Caltech Program flier