* Core Competency Courses for PhD Neural Engineering Track.

* Biol 469 (BB H) Neurobiology (3) Comprehensive examination of neuroanatomy and physiology designed to integrate the principles of neurochemistry, neuroendocrinology, and molecular biology.

* Biol 470 (BB H) Functional and Integrative Neurosciences (3) Neurobiological function in motivated behaviors, motor and sensory functions, learning and memory development, sexual differentiation, and pathology.

* E SC 400H ELECTROMAGNETIC FIELDS/ E SC 596 INDEPENDENT STUDY IN ELECTROMAGNETIC FIELDS ( 3) Irrotational and solenoidal fields, potentials, vector and scalar field and wave equations, harmonic and wave functions in various coordinates, radiation. Prerequisite: E E 210 , MATH 250.

E SC 417 (MATSE) ELECTRICAL AND MAGNETIC PROPERTIES ( 3) Electrical conductivity, dielectric properties, piezoelectric and ferroelectric phenomena; magnetic properties of ceramics. Prerequisite: MATSE 400 , MATSE 402 , PHYS 214

E MCH 461 (M E 461) Applied Finite Element Analysis (3) Computer modeling and fundamental analysis of solid, fluid and heat flow problems using existing computer codes. Prerequisites: CMPSCI 201; E MCH 013 or 110H or 210.

E SC 481 ELEMENTS OF NANO/MICRO-ELECTROMECHANICAL SYSTEMS PROCESSING AND DESIGN ( 3) Interdisciplinary fundamentals of nano/microelectromechanical systems (NEMS/ MEMS), including design, fabrication and machining of miniature systems. Draws from mechanics, science and materials. Prerequisite: E MCH 013 , or E MCH 215 , or E SC 312

E SC 484 BIOLOGICALLY INSPIRED NANOMATERIALS ( 3) Advances in biomolecular-based Science and technology at the physical/life sciences interface. Prerequisite: PHYS 214 , MATH 230

E SC 497 B INTRODUCTION TO BRAIN MACHINE INTERFACES. Lectures and laboratory course introducing the fundamentals of scalp based EEG brain machine interfaces and the relevant signal processing involved.

* E MCH 524A Mathematical Methods In Engineering (3) Application of special functions, orthogonal series, and boundary-value problems in mechanics and other engineering fields. Prerequisite: MATH 250.

E MCH 524B Mathematical Methods In Engineering (3) Solution techniques for boundary-value problems in curvilinear coordinates, integral transforms; Green's functions, potentials, application to diffusion, vibration, wave propagation. Prerequisite E MCH 524A or E SC 504H.

E MCH 533 Scanned Image Microscopy (3) Imaging principles, quantitative data acquisition techniques, and applications for scanned image microscopy are discussed. Prerequisite: E MCH 440

E SC 541 LASER-MATERIALS INTERACTIONS (3) Laser beam interactions with metallic, ceramic, polymeric and biological materials; effects of wavelength, power, spatial and temporal distributions of intensity.

E SC 577 ENGINEERED THIN FILMS (3) Broad overview of the preparation-characterization-property relations for thin films used in a wide range of industrial applications. Prerequisite: MATH 251 , PHYS 237

* E SC 597F INTRODUCTION TO NEURAL ENGINEERING: FUNDAMENTALS OF INTERFACING WTIH BRAIN ( 3) Biophysical basis of neural function, measureable signals, and neural stimulation; fundamentals of hardware-brain interfaces; survey of modern applications.

E SC 529 (PHYS 529) NEURAL CONTROL ENGINEERING (3) Principles of nonlinear Kalman filtering for state estimation and control of neural systems including single neurons, networks, cortex, Parkinson's disease.

E SC 597B (STS 597A) PERSPECTIVES IN NEUROETHICS AND NEUROLAW (1) This course explores the ethical and legal implications of recent developments in neuroscientific research, and of their current and potential applications.

PHYS 597A: Graphs and networks in systems biology Lecturer: Reka Albert Many complex systems are dificult to describe and understand because they are composed of large numbers of elements interacting in a non-ordered way. A good example is cellular biology: diverse cellular components (genes, proteins, enzymes) participate in various reactions and regulatory interactions, forming a robust system. A very useful representation of complex systems is given by graphs (or networks), where we denote the components with nodes and their interactions by edges. The properties of these interaction graphs can then be analyzed by graph theoretical and statistical mechanics methods and this information

PHYS 597B: Introduction to Computational Neuroscience (Jin). (3) The course will focus on computational properties of neurons and networks, and principles underlying neural computation.

497E Magnetic Resonance Systems (3) Fundamentals of hardware and applications of nuclear magnetic resonance, magnetic resonance imaging, and nuclear quadrupolar resonance. Prerequisites: EE 330, EE 350, BIOE 301 or PHYS 400.

502 Introduction to Bioelectric Phenomena (3) Electric phenomena in nerve and muscle membrane potentials, Hodgkin-Huxley equations, volume conductor problem, applications to electrocardiography, electroencephalography, plethysmography. Professors David Geselowitz.

504 Physiological Systems Analysis (3) Application of systems theory, control theory, and analytic modeling strategies to the study of physiological systems. Prerequisites: BIOL 472, MATH 250. Professor Roger Gaumond.

506 Medical Imaging (3) Medical diagnostic imaging techniques, including generation and detection of ultrasound, X-ray, and nuclear radiation; instrumentation and biological effects. Prerequisite: PHYS 202. Professor Nadine Smith.

507 Biomedical Signal Processing (3) Data acquisition and digital signal processing focusing on bimedical signal processing issues, including linear phase filters, spectral analysis and wavelets.Prerequisites: BIOE 401, 402, Bioll 041 or 472, Math 250. Professor Nadine Smith. (* EE 453 is an alternative)

508 (MATSE 508) Biomedical Materials (3) Properties and methods of producing metallic, ceramic, and polymeric materials used for biomedical applications. Professor Paul Brown.

510 Biomedical Applications of Microelectromechanical Sytems (BIOMEMS) and Bio Nanotechnology (3) Effective Date: SP2005 Introduction to BioMEMS and Bionanotechnology. Topics include: electromechanical and chemical biosensors, microfluidics microscale separations, and surface patterning for cellular engineering. Prerequisite: E E 418, BIOE 201. Professor Jeffrey Zahn.

517 (MATSE 517) Biomedical Materials Surface Science (3) Special properties of surfaces as an important causative and mediating agent in the biological response to materials. Professor Erwin Vogler.

CSE 455 (MATH 455). INTRODUCTION TO NUMERICAL ANALYSIS I (3:3:0) Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from CSE/MATH 451 and CSE/MATH 455. Prerequisites: MATH 220; MATH 230 or 231; 3 credits in Computer Science and Engineering.

CSE 456 (MATH 456). INTRODUCTION TO NUMERICAL ANALYSIS II (3:3:0) Polynomial and piecewise polynomial approximation, matrix-least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations. Prerequisite: CSE 455.

CSE 485 (E E 485). DIGITAL IMAGE PROCESSING (3:3:0) Overview of digital image processing techniques and their applications, image sampling, enhancement, restoration, and analysis; computer projects. Prerequisites: E E 317 or 350, CMPSC 201C or CSE 103.

CSE 550 (MATH 550). NUMERICAL LINEAR ALGEBRA (3:3:0) Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors. Prerequisite: CSE 456 or MATH 441.

CSE 551 (MATH 551). NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3:3:0) Methods for initial value and boundary value problems. Convergence and stability analysis, automatic error control, stiff systems, boundary value problems. Prerequisite: CSE (MATH) 451 or 456.

CSE 583. PATTERN RECOGNITION–PRINCIPLES AND APPLICATIONS (3:3:0) Decision-theoretic classification, discriminant functions, pattern processing and feature selection, syntactic pattern recognition, shape analysis and recognition. Prerequisite: Graduate Standing.

CSE 598B. Group Theory and Applications in Robotics, Computer Vision/Graphics and Biomedical Image Analysis. Group theory, the ultimate theory for symmetry, is a powerful tool that has a direct impact on research in robotics, computer vision, computer graphics and medical image analysis. This course starts by introducing the basics of group theory but abandons the classical definition-theorem-proof model. Instead, it relies heavily on intuitions in (1) 3D Euclidean space, images and patterns; (2) a geometric computational model; and (3) concrete, real world applications in robotics, computer vision, computer graphics and medical image analysis drawing from the instructor’s many years of research experience and from an emerging, vibrant, interdisciplinary international research community. Instructor: Professor Yanxi LIU yanxi@cse.psu.edu Prerequisites: Basic algebra, transformations, computer vision/image analysis, robotics or approval of the instructor.

E E 428 LINEAR CONTROL SYSTEMS (3) State variables; time-domain and frequency-domain design and analysis; design of feedback control systems; Root Locus. Prerequisite: E E 310 , E E 350

E E 429 INTRODUCTION TO DIGITAL CONTROL SYSTEMS ( 3) Sampling and hold operations; A/D and D/A conversions; modeling of digital systems; response evaluation; stability; basis of digital control; examples. Prerequisite: E E 351 , E E 428

EE 453 - FUNDAMENTALS OF DIGITAL SIGNAL PROCESSING (3) Design of FIR and IIR filters; DFT and its computation via FFT; applications of DFT; filter implementation, finite arithmetic effects. Course contains a significant laboratory component. (Alternative to BIOE 507)

E E 456 (E SC;EGEE) INTRODUCTION TO NEURAL NETWORKS ( 3) Artificial Neural Networks as a solving tool for difficult problems for which conventional methods are not applicable. Prerequisite: CMPSC 201C or CMPSC 201F ; MATH 220

EE 485 (CSE) - AN INTRODUCTION TO DIGITAL IMAGE PROCESSING (3) Overview of digital image processing techniques and their applications, image sampling, enhancement, restoration, and analysis; computer projects. Course contains a significant programming component.

* EE 553 - TOPICS IN DIGITAL SIGNAL PROCESSING (3) Parametric modeling, spectrum estimation, efficient transforms and convolution algorithms, multirate processing, and selected applications involving non-linear and time-variant filters. Prerequisite: EE 453.

EE 557 - MULTIDIMENSIONAL SIGNAL PROCESSING (3) Multidimensional sampling, weak causality, recursibility , multidimensional transforms, stability, global and local state-space models, multidimensional filters, and multidimensional spectrum estimation. Prerequisite: EE 453.

STAT 500 APPLIED STATISTICS ( 3) Descriptive statistics, hypothesis testing, power, estimation, confidence intervals, regression, one- and 2-way ANOVA, Chi-square tests, diagnostics. Prerequisite: one undergraduate course in statistics

STAT 510 APPLIED TIME SERIES ANALYSIS ( 3) Identification of models for empirical data collected over time. Use of models in forecasting. Prerequisite: STAT 462 or STAT 501 or STAT 511

STAT 512 DESIGN AND ANALYSIS OF EXPERIMENTS ( 3) AOV, unbalanced, nested factors; CRD, RCBD, Latin squares, split-plot, and repeatd measures; incomplete block, fractional factorial, response surface designs; confounding. Prerequisite: STAT 511

STAT 515 STOCHASTIC PROCESSES I ( 3) Conditional probability and expectation, Markov chains, the exponential distribution and Poisson processes. Prerequisite: MATH 414 , STAT 414 , or STAT 513

STAT 517 (MATH) PROBABILITY THEORY ( 3) Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics. Prerequisite: MATH 403

MATH 516 STOCHASTIC PROCESSES (3) Markov chains; generating functions; limit theorems; continuous time and renewal processes; martingales, submartingales, and supermartingales; diffusion processes; applications. Prerequisite: MATH 416

MATH 523 NUMERICAL ANALYSIS I (3) Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization. Prerequisite: MATH 456

MATH 550 (CSE) NUMERICAL LINEAR ALGEBRA (3) Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors. Prerequisite: MATH 441 or MATH 456

Neural Engineering PhD Track in ESM