Courses
Course  Course TItle  Units  Instructor  Description 

PSTAT 207A  Statistical Theory  4.0  Staff 
Univariate and multivariate distribution theory; generating functions; inequalities in statistics; order statistics; estimation theory: likelihood, sufficiency, efficiency, maximum likelihood; testing hypotheses: likelihood ratio and score tests, power; confidence and prediction intervals; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance. Part of a three quarter sequence with 207B and 207C. 
PSTAT 207B  Statistical Theory  4.0  Staff 
Univariate and multivariate distribution theory; generating functions; inequalities in statistics; order statistics; estimation theory: likelihood, sufficiency, efficiency, maximum likelihood; testing hypotheses: likelihood ratio and score tests, power; confidence and prediction intervals; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance. Part of a three quarter sequence with 207A and 207C. 
PSTAT 207C  Statistical Theory  4.0  Staff 
Univariate and multivariate distribution theory; generating functions; inequalities in statistics; order statistics; estimation theory; likelihood, sufficiency, efficiency, maximum likelihood; testing hypotheses: likelihood ratio and score tests, power; confidence and prediction intervals; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance. Part of a three quarter sequence with 207A and 207B. 
PSTAT 213A  Introduction To Probability Theory And Stochastic Processes  4.0  Staff 
Generating functions, discrete and continuous time Markov chains; random walks; branching processes; birthdeath processes; Poisson processes, point processes.

PSTAT 213B  Introduction to Probability Theory and Stochastic Processes  4.0  Staff 
Convergence of random variables: different types of convergence; characteristic functions, continuity theorem, laws of large numbers, central limit theorem, large deviations, infinitely divisible and stable distributions, uniform integrability. Conditional expectation.

PSTAT 213C  Introduction To Probability Theory And Stochastic Processes  4.0  Staff 
Martingales, martingale convergence, stopping times, optional sampling, optional stopping theorems and applications, maximal inequalities. Brownian motion, introduction to diffusions.

Math 214A  Ordinary Differential Equations  4.0  Staff 
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.

Math 214B  Chaotic Dynamics and Bifurcation Theory  4.0  Staff 
Hyberbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and RuelleTakens cascades to strange attractors.

ME 215A  Applied Dynamical Systems I  3.0  Moehlis 
Phaseplane methods, nonlinear oscillators, stability of fixed points and periodic orbits, invariant manifolds, structural stability, normal form theory, local bifurcations for vector fields and maps, applications from engineering, physics, chemistry, and biology.

ME 215B  Applied Dynamical Systems II  3.0  Moehlis 
Local codimension two bifurcations, global bifurcations, chaos for vector fields and maps, Smale horshoe, symbolic dynamics, strange attractors, universality, bifyrcation with symmetry, perturbation theory and averaging, Melnikov's method, canards, applications from engineering, physics, chemistry, and biology.

PHYS 219  Statistical Mechanics  4.0  Staff 
Fundamental principles of classical and quantum statistics. Noninteracting Boltzmann, Bose, and Fermi systems. Virial expansion and other approaches to interacting systems. Phase transitions.

PSY 221E  Statistical Analysis of fMRI Data  4.0  Ashby 
Experimental design and statistical analysis in fMRI research. Linear and nonlinear models of the hemodynamic response function, the general linear model in fMRI analysis, post hoc testing, group testing with the random effects model, and connectivity analysis.

PHYS 223C  Concepts and Phenomena of Condensed Matter Physics  4.0  Staff 
Lattice and electron dynamics. Elementary excitations and collective phenomena. Transport properties. Disorder and localization. Longrange order and broken symmetries. Magnetism, superconductivity and liquid crystals. Properties and structures of polymers, membranes, and selfassembling systems.

CMPSC 225 / ECE 205A  Information Theory  4.0  Van Dam, TBA 
Entropy, mutual information, and Shannon's coding theorems; lossless source coding, Huffman, ShannonFanoElias, and arithmetic codes; Channel capacity; ratedistortion theory, and lossy source coding; sourcechannel coding; algorithmic complexity and information; applications of information theory in various fields.

PSY 228  Perception  4.0  Eckstein 
Analysis of psychophysical relations in sensory processes with stress on detection, scaling, discrimination, spatial and temporal resolution, and the interaction of cue systems in perceptual behavior.

ECE 230A/ME 243A  Linear Systems I  4.0  Bamieh, Hespanha 
Internal and external descriptions. Solution of state equations. Controllability and observability realizations. Pole assignment, observers;modern compensator design. Disturbance localization and decoupling. Leastsquares control. Leastsquares estimation; kalman filters; smoothing,the separation theorem; LQG compensator design. Computational considerations. Selected additional topics. 
PSY 231  Cognitive Neuroscience  4.0  Miller 
Examination of the neurological basis of cognition with material drawn fromresearch in psychology, neurology and the neurosciences with brain injured and healthy human and nonhuman subjects. Topics include memory, language, and perception.

PSY 232  Neuroimaging  4.0  Miller, Grafton 
Introduces students to the theoretical and practical issues involved in conducting functional magnetic resonance imaging (fMRI) experiments. Content includes basic MR physics, physiology of the BOLD signal, experimental design, image processing, statistical analysis, and brain mapping.

CMPSC 234  Randomized Algorithms  4.0  Staff  
ECE 235  Stochastic Processes in Engineering  4.0  Staff 
A firstyear graduate course in Stochas TIC processes, including: review of basic probability; gaussian, poisson, and Weiner processes; widesense stationary processes; covariance function and power spectral density; linear systems driven by random inputs; basic Wiener and Kalman filter theory. 
ECE 236  Nonlinear Control Systems  4.0  Teel 
Analysis and design of nonlinear control systems. Focus on Lyapunov stability theory, with sufficient time devoted to contrasts between linear and nonlinear systems, inputoutput stability and the describing function method.

ME 243B/ ECE 230B  Linear Systems II  4.0  Bamieh 
Internal and external descriptions. Solution of state equations. Controllability and observability realizations. Pole assignment, assignment, observers; modern compensator design. Distribance localization and decoupling. Leastsquares control. Leastsquares estimation; Kalman filters; smoothing. The seperation theorem; LQG compensator design. Computational considerations. Selected additional topics.

MCDB 251  Neurobiology I: Cellular Organization and Biophysics of the Nervous System  4.0  MA, Vandenberg 
Nervous system properties ranging from single cells to whole organisms, using examples from vertebrates/invertebrates studied in terms of morphology, physiology, behavior. (Note: PSY 269 Neuroanatomy maybe taken in place of this course)

PSY 265  Computational Neuroscience  4.0  Ashby 
Survey of methods in computational neuroscience; single cell methods including HodgkinHuxley models, occupation theory, integrateandfire models; neural network modeling including linear system theory, nonlinear dynamics, connectionism, HodgkinHuxleylike network models, models of synaptic plasticity, methods for generating predicted BOLD signals.

PSY 269  Neuroanatomy  4.0  Reese 
An examination of the organization of the vertebrate nervous system. Topicsinclude neurohistological techniques; neurology and neuropsychology; comparative neuroanatomy; neural degeneration; developmental neuroscience. (Note MCDB 251 Neuobiology may be taken in place of the course)

CMPSC 281B/ ECE 281B  Advanced Topics in Computer Vision  4.0  Turk, Wang 
Advanced topics in computer vision: image sequence analysis, spatiotemporal filtering, camera calibration and handeye coordination, robot navigation, shape representation, physicallybased modeling, regularization theory, multisensory fusion, biological models, expert vision systems, and other topics selected from recent research papers.

DYNS 592  Special Interest Group Research Seminar  1  Ashby, Giesbrecht 
Research seminar in dynamical neuroscience.

CORE Course Requirements
Course  Course TItle  Units  Instructor  Description 

PSY 265  Computational Neuroscience  4.0  Ashby 
Survey of methods in computational neuroscience; single cell methods including HodgkinHuxley models, occupation theory, integrateandfire models; neural network modeling including linear system theory, nonlinear dynamics, connectionism, HodgkinHuxleylike network models, models of synaptic plasticity, methods for generating predicted BOLD signals.

ECE 230A/ME 243A  Linear Systems I  4.0  Bamieh, Hespanha 
Internal and external descriptions. Solution of state equations. Controllability and observability realizations. Pole assignment, observers;modern compensator design. Disturbance localization and decoupling. Leastsquares control. Leastsquares estimation; kalman filters; smoothing,the separation theorem; LQG compensator design. Computational considerations. Selected additional topics. 
Math 214A  Ordinary Differential Equations  4.0  Staff 
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.

MCDB 251  Neurobiology I: Cellular Organization and Biophysics of the Nervous System  4.0  MA, Vandenberg 
Nervous system properties ranging from single cells to whole organisms, using examples from vertebrates/invertebrates studied in terms of morphology, physiology, behavior. (Note: PSY 269 Neuroanatomy maybe taken in place of this course)

PSY 269  Neuroanatomy  4.0  Reese 
An examination of the organization of the vertebrate nervous system. Topicsinclude neurohistological techniques; neurology and neuropsychology; comparative neuroanatomy; neural degeneration; developmental neuroscience. (Note MCDB 251 Neuobiology may be taken in place of the course)
