# Quantitative Electives

##### To have a course considered for quantitative elective credit, submit this online form.
Course Name
APM 501
Differential Equations

Linear and nonlinear ordinary differential equations. Existence and uniqueness of solutions, limit sets, stability, Lyapunov functions, linear systems with constant coefficients. Geometry of behavior in two and three dimensions, including Poincare-Bendixson theorem, Lorenz equations, linearization, sensitive dependence on initial conditions, bifurcations.
APM 505
Applied Linear Algebra

Fundamentals of linear algebra and numerical linear algebra, including decompositions (LU, QR, SVD), Eigen values, spectral theory, least squares problems. Programming with MATLAB.
APM 520

Extends topics of APM 505. Introduces essential iterative methods, Gauss-Seidel, conjugate gradients. Methods for SVD, total least squares and root-finding applications in image analysis. Students should have basic knowledge of numerical linear algebra and a programming language.
APM 530
Mathematical Cell Physiology

Historically, mathematics has played an important role in the study of the mechanisms underlying cellular physiology. This course will provide an introduction to the development and analysis of mathematical models for various aspects of cellular physiology including diffusion, membrane transport, ion channel kinetics, excitable membranes, and calcium dynamics. We will also use computational methods to perform numerical simulations for all of the models discussed in class. The course will be organized around short lectures and accompanying homework assignments and computer laboratories, discussions motivated by relevant published articles, and student projects.
APM 531
Mathematical Neuroscience

Mathematical modeling of electrochemical processes in nerve cells. Dendritic modeling, dendritic spines and synaptic plasticity, bifurcation analysis of excitable membrane models, deterministic and stochastic methods for threshold dynamics and bursting, relaxation oscillations. Students should have had a previous graduate-level PDE course.
APM 535
Math Models in Medicine

Mathematical models for the etiology, epidemiology, pathogenesis, morphology and treatment of disease. Covers dynamical models of cancer and viral infections.
APM 553
Mathematical Population Biology

Selectively covers population biology models in the forms of systems of difference equations or ordinary differential equations. Focuses on mathematical analysis of population models as well as model formulation and simulation. Students should have a previous graduate-level course in ODE.
APM 598
Fourier Analysis and Wavelets

Fourier series and Wavelets are important mathematical building blocks for signal analysis and many other areas in science and engineering. Fourier series is the study of how a function (or signal) can be decomposed into a sum of sine and cosine waves of various frequencies. Wavelets are similar to sines and cosines in that they look like waves of various frequencies. However, they are different in that wavelets have localized support (unlike sine and cosine waves which keep repeating forever). This localization feature of wavelets allows the user to filter or modify certain parts of the signal without affecting other parts.
APM 598
Mathematical Methods for Complex Adaptive Systems
APM 598
Neuroinformatics

Modern techniques for observing and understanding the nervous system at multiple scales produce a tremendous amount of remarkably diverse data. This has led to the need for a new field of neuroinformatics, which encompasses the techniques and computational tools for data acquisition, storage, sharing, publishing, analysis, visualization, modeling and simulation. This interdisciplinary course will integrate content from neuroscience, applied mathematics, biomedical engineering and computer science to cover some of the overarching themes of neuroinformatics research.
APM 598
Dynamics, Computation and Statistics in Biosciences
This course is based on using techniques, tools, and theories from applied nonlinear dynamical systems, computational mathematics and statistical sciences (data analytics) to gain qualitative and quantitative insight into dynamical systems arising from the mathematical modeling of real-life phenomena in the natural, engineering and social sciences. Emphasis will be on the application in biological sciences (particularly disease ecology, epidemiology, and immunology).
BCH 494/594
Modern Approaches to Biochemical Data Analysis
Analysis of data in the biochemical and biological sciences has entered a new era in
recent years. The holy grail, that many believed would never be achieved 30 years ago, of predicting protein structure from primary sequence has been demonstrated and is now widely used. Quantitative and predictive relationships between structure and function of biomolecules and molecular interactions are now possible even for very complex systems. The scale of the available data and the scale upon which data can be accumulated is huge. With the advances in computational power and machine learning it is now possible to relate abstract concepts, such as chemical structure, species, location in the cell, disease state and symptoms to quantitative measures, such as binding, reaction rates, growth rates or spectral values. Many different kinds of tools are now available for approaching these problems and these tools, as well as the computational power required to use them, are readily available to ASU students. A student that takes this course will develop the ability to understand these tools and what they can do for a variety of biochemical and chemical problems. We will start with statistical and linear/nonlinear fitting and quickly move into clustering, classification and then spend much of the course focusing on machine learning approaches to analyzing the relationship between biochemical structure and function.
BME 565
Magnetic Resonance Imaging

This course will provide a foundation in the fundamental concepts of Magnetic Resonance Spectroscopy and Imaging as well as their applications to measure physiological processes and changes with respect to disease. On completing the course, students should understand 1) basic MRI physics, 2) MR image formation, 3) sources of MR image contrast, 4) origin of artifacts 5) conventional and unconventional MR acquisition methods in a quantitative manner. They should become familiar with various MRI pulse sequences and contrast manipulation techniques. Students will also learn about specific applications such as DTI, Angiography, BOLD fMRI and use of MRI for molecular imaging and oncology. Several local MR experts will also present guest lectures on specialized topics during this course.
BME 591
Information Extraction for Biomedical Text Mining

The growing volume of biomedical literature with its highly complex structure and specialized vocabulary, presents unparalleled challenges to text miners that are only compounded by the lack of lexicons and annotated corpora for its automatic processing. In this class, we will survey natural language processing methods used for information extraction and how they are currently applied in the biomedical domain. Emphasis will be placed on lexical and syntactic methods.
BME 591
Image Analytics and Informatics

This course focuses on the principles of image analytics and informatics. The course first introduces the common imaging modalities (CT, MRI, PET, and ultrasound, etc.), then addresses advanced topics in image analysis (including nonlinear diffusion filtering, PDE-based image filtering, mixture modeling, Markov random field-based image segmentation, and parametric and geometric deformable-models), and ends by describing recent activities in imaging informatics (e.g. radiological informatics, picture archiving and communication system, computer aided diagnosis in medical imaging).
BME 598
Basic Ultrasound Imaging
The course will teach basic principles of sound wave propagation in human tissues, ultrasound instrumentation, and sonographic image generation. Labs will include hands-on experience with a commercial ultrasound system for cardiovascular imaging. The course also incorporates in-class interactive literature reviews and discussions on applications of medical ultrasound imaging and novel technologies in sonography.
BME 598
Cellular & System Modeling
This course will cover basic design principles of biological systems at both cellular level and tissue level, with an emphasis on better understanding of certain fundamental biological processes, such as cell fate decision (death and differentiation), time-keeping (cell cycle, circadian rhythm [2017 Nobel Prize] and p53 oscillation). Topics covered include mathematical model construction and validation, biochemical kinetics and equilibrium, parameter estimation and sensitivity analysis, basic bifurcation theories, multiscale modeling and optimal intervention in biological systems. Practical numerical tools and strategies for simulating and analyzing the models will be introduced, with an emphasis on how to interpret simulation results and how to make novel yet testable predictions and new experiment designs to test these predictions. Both lecture and active learning experience will be included in each class. This is course is intended for students ranging from master, to junior Ph. D students in BME, Math, Physics, and other quantitative sciences. Basic knowledge of molecular biology and cell biology is preferred but not required.
BME 598
Neuromechanics of Balance and Gait

This course covers topics of sensory and neural control of balance and gait. In addition, biomechanics and the tools utilized in the laboratory to evaluate balance and gait will be studied. Finally, topics of pathological gait will be incorporated.
BME 598
Computational Neuroscience
BME 598
Biomechanics/Human Physical Capability

Biomechanics is the application of engineering mechanics to understand the biological function and organization of the neuromuscular system. In this course, the student will develop the necessary technical skills to process and analyze biomechanical data. The student will master signal processing, 2D kinematics and kinetics, anthropometry, spring-mass models, mechanical work, energy and power.
BME 598/ BME 566
Biomedical Instrumentation Imaging/ Medical Imaging Instrumentation

Understand the theory behind major biomedical imaging methods such as MRI and ultrasound.
BME 598
Engineering Models for Physiological Engineers

This course is designed to give graduate and upper division bioengineering students the ability to understand qualitatively and quantitatively the complex structure-function physiological relationships that exist in living systems. The laboratory exercises are integral to the course and provide an opportunity to apply and investigate physiological principles that are first introduced in the lectures.
BME 598
Nonlinear Dynamics of Gene Networks

This course will cover introduction of molecular biology in the context of engineering gene networks, mathematical modeling and nonlinear dynamics analysis of gene networks, review of modern high throughput experimental approaches used in validating mathematical predictions, and stochastic simulation of gene networks. This is course is intended for students ranging from senior undergraduate, master, to junior Ph.D students in BME, Math, Physics, and other quantitative sciences. Calculus, Linear Algebra, and Probability is required. Basic knowledge of molecular biology and genetics is preferred but not required.
BME 598
Modeling and Simulation of Physiological Systems
BME 598
Modeling for Molecular & Cellular Engineering
BME 598
Biomedical Image Processing

Image processing is a powerful engineering tool that enables many of todays advanced biomedical applications. The objectives of this course are to equip students with practical image processing skills and to familiarize them with state- of-the-art methods. Techniques including segmentation, registration, motion estimation, interpolation, and 3D/4D reconstruction will be explored for various types of image data. These techniques will be presented in the context of cutting-edge applications from research and industry that are driven by image data from MRI, CT, PIV, microscopy, and other relevant modalities. This course is designed to be highly experiential; students will be challenged to develop effective solutions for important current problems based on real-world data.
BME 598
Cyber Biomedical Systems

This class will train Biomedical Engineering students in the engineering principles involved in the development of computational systems for biomedical and healthcare applications.  The focus is on core conceptual principles rather than on the nuts-and-bolts of designing and synthesizing such systems. As embedded computing becomes more common in healthcare in the form of devices involved in prostheses, diagnosis, monitoring and therapy in clinical, home, hand-held or on-body settings it is increasingly critical to understand how to design and develop robust and reliable embedded systems while preserving optimality in power, performance and form factors. This class will cover engineering principles involved in the modeling, design and analysis of hybrid systems that involve embedded computers controlling and interacting with biomedical systems. The Intel Galileo and the Arduino microcontrollers will be used as an exemplary platforms for the development of such cyber-biomedical systems. The project component of this class will involve a final 6-week student design project on a bioengineering problem of the students choice.
BME 598
Biostatistics with Computational Applications

This course will cover the use of computation as a tool for biostatistical data analysis and methods development, especially for research in the field of biomedical informatics.  Major topics will include parametric and non-parametric regression, Monte Carlo techniques, resampling methods, and power analysis.  Students will use the R statistical programming language to display and analyze data, and to evaluate statistical procedures and algorithms.
BME 598
Electrochemical Biosensor Design

The goal of this course is to understand applications of mathematical modeling of transport and surface chemistry interactions (or molecular recognition element) through literature and via experimentation. The student(s) will be expected to learn the literature, the basics of electrode fabrication and characterization, electrochemical techniques, data analysis, and development of a model based upon theory and experimental data. These models will range from the thermodynamics of the system, to circuit modeling of data. Students will develop a conceptual knowledge of the electrode surface and determine maximum adsorption and immobilization of the molecular recognition elements, i.e. proteins. Furthermore students will learn through literature as well as hands on experience to demonstrate the reaction rates, kinetics, and nyquist models developed through the course work.
BME 598
Polymeric Drug Delivery

This course covers the science behind polymer chemistry with an emphasis on their utilization for drug delivery. As such, the course utilizes mathcad and matlab to develop and analyze drug release kinetics from polymer systems and model their distribution through the body. The final project was focused on generating models to fit experimental data from an original research article.
BME 598
Modeling Neuromechanical Systems

This course aims to provide students with the ability to develop and use mathematical models of neural and musculoskeletal systems. The models and simulation exercises will emphasize the dynamic interactions between the neural, muscular and skeletal systems and the roles of nonlinear processes in that enable our ability to control posture and locomotion in complex environments. The course will require extensive use of the Matlab©/Simulink© tools for homework assignments and projects, but prior experience with these tools is not required.
BME 598/BME 494
Systems Biology of Disease

In this course, students will learn how to apply mathematical, statistical, and machine learning methods to real-world patient datasets to make biologically or clinically meaningful decisions. Specifically, students will learn to cluster single-cell data to define cell types, develop a classifier of disease status, learn how to assess the statistical significance of overlaps between genes or other biological entities, use multi-omic data to construct meaningful networks, and, finally, how to project dynamics onto scRNA-seq networks using RNA velocity. Primary literature will be used to discuss exemplary applications of these systems biology methodologies for medical applications. Students registered in 598 will have a final project that requires them to learn to apply at least one of the tools and/or concepts discussed in class on a real-world dataset of their choosing.
BME494/598
Finite Element Modeling for Biomedical Applications

This course will deal with the implementation of finite element methods focusing on examples from Biomedical Engineering. It will be particularly relevant to students who are interested in solving biomedically-relevant problems in non-idealized and heterogeneous tissue domains. The course will also cover methods of incorporating freeform biological shapes into computational models, 3-D image segmentation and multiple image-modality registration. The course will cover the basics of Finite Element methods, such as shape functions and sparse matrix methods, giving students enough background to allow them to intelligently operate complex commercial software or to construct their own models. A substantial portion of the course will involve students developing and solving their own models.
BMI 515
Applied Biostatistics in Medicine and Informatics

Comprehensive treatment of the statistical methods used most often to analyze quantitative data collected in medical and biomedical informatics studies, including clinical trials, epidemiologic studies, studies of the accuracy and performance of screening and diagnostic tests, and studies to develop predictive models. Students learn to use SAS statistical software to analyze biomedical data.
BMI 591
Image Analytics and Informatics

Image processing and analysis using mathematical derivations and algorithms.Fair amount of Math involved including Calculus, linear algebra, statistics, and probability theory and so can be considered as a quantitative course.
BMI 598
Biostatistics with Computational Applications

This course will cover the use of computation as a tool for biostatistical data analysis and methods development, especially for research in the field of biomedical informatics. Major topics will include parametric and non-parametric regression, Monte Carlo techniques, resampling methods, and power analysis. Students will use the R statistical programming language to display and analyze data, and to evaluate statistical procedures and algorithms.
CEE 598
Environmental Data and Analysis

This course introduces and explains the statistical methods used to describe, analyze, test, and model environmental data. Specifically, the class focuses on exploratory data analysis, the main probability distributions used to describe environmental data, hypothesis testing, time series analysis, and multivariate data analysis.
CSE 569
Fundamentals of Statistical Learning and Pattern Recognition

Concepts of statistical pattern recognition, Bayesian decision theory, parameter estimation, discriminant analysis, basics of artificial neural networks, basics of data clustering. Knowledge of college-level calculus, linear algebra, basic probability theory and proficiency in computer programming is necessary to be successful in this course.
CHE 598
Polymer Principles and Processing

The course syllabus does not describe the included math component of the course in my opinion. We have had homework and exams that include molecular weight calculations, radius of gyration, extrapolation of data, modeling of polymer chain movement, calculating end to end chain distance, etc.
CHE 598/CHE 494
Six Sigma Methodology/Engineering Experimentation

Principles of the Six Sigma Methodology; Measurement System Evaluation; Factorial Design and Other Applied Statistical Concepts.

ECN 525
Applied Regression Models
Simple linear regression, multiple regression, indicator variables, and logistic regression. Emphasizes business and economic applications.

ECN 527
Categorical Data Analysis
Discrete data analysis in business research. Multidimensional contingency tables and other discrete models.

EEE 407
Digital Signal Processing

Application of time and frequency domain analysis techniques to signal processing problems; achievement of the following outcomes with corresponding performance indicators: Minimum sampling frequency to represent a CT signal given its spectrum; frequency domain effects of undersampling; ZT and its region of convergence from DT sequence; Filter design methods given filter specifications, use of software tools to assist in filter design, application of DT filtering to real data; Relation of DFT/FFT coefficients to frequency information, use of FFT programs with real data and system analysis applications.
EEE 505
Time-Frequency Signal Processing

Joint time-frequency analysis of time-varying signals and systems; linear and quadratic time-frequency representations; applications in current areas of signal processing.
EEE 507
Multidimensional signal processing

Processing and representation of multidimensional signals. Design of systems for processing multidimensional data. Introduces image and array processing issues.
EEE 508
Digital Image & Video Processing & Compression

Fundamentals of digital image perception, representation, processing, and compression. Emphasizes image coding techniques. Signals include still pictures and motion video.
EEE 511
Artificial Neural Computation

Networks for computation, learning function representations from data, learning algorithms and analysis, function approximation and information representation by networks, applications in control systems and signal analysis.
EEE 541
Electromagnetic Fields and Guided Waves
Polarization and magnetization; dielectric, conducting, anisotropic, and semiconducting media; duality, uniqueness, and image theory; plane wave functions, waveguides, resonators, and surface guided waves.
EEE 581
Filtering of Stochastic Processes

Modeling, estimation, and filtering of stochastic processes, with emphasis on the Kalman filter and its applications in signal processing and control.
EEE 591
Machine Learning Basics with Application to FPGAs

The goal of this course is to provide students with a firm
mathematical and practical background for analyzing data, choosing and implementing
Machine Learning solutions for problems. Students will learn to use Python or Matlab
libraries and for shallow learning and PyTorch for a deep learning project. Confronted
with potential machine learning projects in the future they will be able to make good
solution choices and understand the results. Methods will be described to deploy these models in digital logic. This may be done using FPGAs or ASICs. This deployment will be described generally using Hardware Description Language (HDL) specifically System Verilog. Applications to physical
problems will be discussed.
EEE 591
Python for Rapid Engineering Solutions

Engineers in industry frequently need to solve quickly problems that may be new to them. This goal of this course is for students to learn how to achieve rapid engineering solutions using Python libraries and functions readily available on the internet. The Python libraries include NumPy, SciPy, matplotlib, pandas, and scikit-learn for example. The focus is on rapid solutions on wall-clock time, not necessarily CPU time. At the end of this course, the student will have been exposed to wide variety of computational problems from engineering and physics and have become acquainted with a typical approach to their solution using Python. When confronted with similar problems in the future, the student will know how to attack the problem and where to look for more detailed knowledge.
EEE 598
Low power Bioelectronics

The course will begin with fundamental theory and techniques for low power analog circuit design especially subthreshold CMOS and BJT circuits (e.g. translinear circuits) them move to biomedical applications and bio-inspired systems focused upon neuromorphic circuits. Then it will touch on concepts such as wireless challenges for implants, energy harvesting and electrochemistry.
EEE 598
Computational Image Understanding and Pattern Analysis
This graduate course introduces students to the field of computer vision, whose broad goal is to create algorithms and systems for processing of visual signals (images, videos etc.) for low-level, mid-level, and high-level perceptual tasks. This course presents the broad principles and techniques for devising computer vision algorithms starting from understanding the imaging process for a pin-hole camera, understanding lenses, image-statistics such as gradients and edges, 3D structure estimation, motion estimation, illumination modeling to perceptual tasks such as shape recognition, texture modeling, face recognition, activity recognition, and scene recognition. The class will be a mixture of in-class lectures and discussions, and individual and group projects.
EEE 598
Statistical Machine Learning
Machine learning explores the design, analysis, and construction of algorithms that can learn from data and make inferences or predictions about future outcomes. The focus is on a methodical approach that will highlight the role of statistical and computational methods in analysis of data. This course includes a near equal dose of theory and practice with the goal of providing a thorough grounding in the fundamental methodologies and algorithms in machine learning. The focus will be a methodical way of learning that begins from the theoretical underpinnings of machine learning focused broadly on two distinct types of learning methods, namely supervised and unsupervised learning. Within each type, various well-studied and formulated approaches will be studied.
EGR 598
Topic: Applied Linear Algebra for Engineers

Linear algebra with applications to robotic systems, data analysis and machine learning.
EGR 598
Finite Element Modeling and Analysis

Discusses principles of Finite elements in engineering system analysis. Requires students to be familiar with both mathematical and simulation based finite element analysis. Software Skills: Solidworks and NX/NASTRAN
IEE 412
Intro to Financial Engineering

This course is an intensive exploration course on advanced financial and engineering topics such as the application of stochastic models to stock and derivatives pricing and financial risk management. This course focuses on the statistics, calculus, and methods used by engineers to mitigate financial risks.
IEE 511
Analysis of Decision Processes

Students will understand rational and behavioral processes for defining problems and making decisions in single and multi-attribute decision environments. Economic concepts such as utility theory and the value of information will be covered. Modeling and tradeoff analysis for multicriteria problems and recent research results in human decision processes will also be covered.
IEE 520
Statistical Learning for Data Mining

Surveys data analysis methods for massive data sets and provides experience in analysis with computer software.
IEE 570

Process monitoring with control charts (Shewhart, cusum, EWMA), feedback adjustment and engineering process control, process capability, autocorrelation, selected topics from current literature.
IEE 571
Quality Management

Tool quality concepts, quality strategies, quality and competitive position, quality costs, vendor relations, the quality manual, and quality in the services. Pre-requisite: Engineering Graduate Student.
IEE 572
Design/Engineering Experiments

Analysis of variance and experimental design. Topics include strategy of experimentation, factorials, blocking and confounding, fractional factorials, response surfaces, nested and split-plot designs. Check with IEE department for pre-requisite.
IEE 578
Regression Analysis

Regression model building oriented toward engineers and physical scientists. Topics include linear regression, diagnostics, biased and robust fitting, nonlinear regression.
IEE 581
Six Sigma Methodology

The six sigma process improvement strategy of define, measure, analyze, improve, and control (DMAIC). Integrates and deploys statistical methods and other six sigma problem solving via the DMAIC framework. Requires background in design of experiments, statistical quality control, and regression analysis.
IEE 582
Response Surfaces/Process Optimization

Classical response surface analysis and designs including steepest ascent, canonical analysis, and multiple responses. Other topics include process robustness studies, robust design, and mixture experiments. Pre-requisites: Engineering MS, MSE or PHD; IEE 572 with C or better.
IEE 598
Network Flows

Many real-life problems are formulated with a “network” structure, and efficient algorithms have been developed to solve the result problems exploiting the “network” structure. The objective of this course is to provide knowledge and skills to students so that they are very comfortable and competent in addressing such problems, whether they arise in their professional career or in their research. Since the current instructor has expertise in transportation, logistics and control, many of the network models in the course will arise from applications in related to these topics – routes, traffic flows, location of facilities, scheduling, etc.
KIN 512
Biomechanics of the Skeletal System

This course introduces students to the principles of the bio-mechanics of the skeletal system and how different biological materials can affect this. Another main topic is to discuss the bio-mechanics of injury, and possible rehabilitation routes for the injuries. For graduate students, there is a project that be either a teaching/research presentation, literature review, or method demonstration and collection.
KIN 540
Sport Biomechanics

Qualitative and quantitative analyses of selected sports performance and human movements to help reduce injury risk and maximize performance. The course is the study and analysis of human movement patterns in sport. The analysis of these patterns may help people perform their chosen sporting activity better and reduce the risk of injury. We want to think enthusiastically about analyzing movement patterns, understanding the fundamentals of joint movements, and be able to describe from video observation, pictorially, and methodologically how to measure and quantify the relevant patterns that can lead to successful in outcome. We also consider motor control along with kinematic, kinetic, and energetics that result due to various movements and how they relate to efficiency in movement for the sport performer.
MAE 471
Computational Fluid Dynamics

Numerical solutions for selected problems in fluid mechanics.
MAE 501
Linear Algebra in Engineering

Development and solution of systems of linear algebraic equations. Applications from mechanical, structural, and electrical fields of engineering.
MAE 502
Partial Differential Equations in Engineering

Development and solution of partial differential equations in engineering. Applications in solid mechanics, vibrations, and heat transfer.
MAE 527
Finite Elements for Engineers

Direct stiffness, method of weighted residuals, weal formulation, and variational techniques in the solution of engineering problems. Cross-listed as CEE 526.
MAE 547
Mechanical Design and Control of Robots

This course deals with robotic designs, involving quite a lot of mathematical equations. Homogeneous Transformations, 3D Kinematics, Geometry of motion, forward and inverse kinematics, workspace and motion trajectories, dynamics, control, and static forces.
MAE 471/561
Computational Fluid Dynamics

Students should be able to classify PDSs, derive finite difference formulas, determine truncation errors, code solvers for and solve elliptic, parabolic, and hyperbolic equations and systems of linear equations using time advancement explicit and implicit schemes and iterative methods, determine the accuracy, consistency, and stability of differencing schemes, code solvers for and solve the incompressible Navier-Stokes equations.
MAE 557
Mechanics Composite Materials

Analysis, design, and applications of laminated and chopped fiber reinforced composites. Micro- and macromechanical analysis of elastic constants, failure, and environmental degradation. Design project.
MAE 561
Computational Fluid Dynamics

Finite-difference and finite-volume techniques for solving the subsonic, transonic, and supersonic flow equations. Method of characteristics. Numerical grid-generation techniques.
MAE 571
Fluid Mechanics

This course covers basic kinematic, dynamic, and thermodynamic equations of the fluid continuum and their application to basic fluid models.
MAE 598

This class covers theoretical, programming, and application knowledge of non-linear finite element methods.  After this course, students should understand the associated continuum mechanics and constitutive models for non-linear material response.  The course also presents a survey of new methods in computation mechanics research for facture, damage, and multi-scale analysis.
MAE 598
Digital Control: Design and Implementation

This course focuses on the analysis and design of control systems in which the digital computer plays a major role. The course reviews necessary topics on continuous control and introduces key effects of sampling. It covers elements on discrete system analysis; z-transform; sampled-data systems; sampling theorem and combined discrete and continuous system and the phenomenon of aliasing. Moreover, the course focuses on deterministic design methods for digital control systems (root-locus, frequency response, pole placement and estimators). Multivariable, optimal control and Kalman filtering are then discussed. Nonlinear control and system identification are finally introduced. Emphasis will be given on digital control implementation topics and a case study on robot control will be presented.
MAE 598
Finite Elements in Engineering

Introduces ideas and methodology of finite element analysis. Applications to solid mechanics, heat transfer, fluid mechanics, and vibrations.
MAE 598
Machine Learning for Engineers

The goal of this course is to equip engineering students a working understanding of machine learning and to better prepare for the future job market. It reviews linear algebra and probability theory and provides a discussion of information theory and its application in machine learning. It goes on to discuss several machine learning models, while providing the mathematical basis of each of these models. Assignments and projects test student understanding of the machine learning models and make use of python and Matlab programming tools.
MAT 420
Scientific Computing

Surveys and applies programming languages, libraries, and scientific visualization tools. Programming assignments emphasize software development skills. Pre-requisites: CSE 205 with C or better; MAT 274 (or 275) with C or better; MAT 342 (or 343) with C or better.
MAT 423
Numerical Analysis I

Analysis and algorithms for numerical solutions linear/nonlinear equations, direct solvers, iterative procedures, optimization. Determination of eigenvalues. Elementary computer arithmetic.
MAT 442

Fundamentals of linear algebra, dual spaces, invariant subspaces, canonical forms, bilinear and quadratic forms, and multi-linear algebra.
MAT 451
Mathematical Modeling

Detailed study of 1 or more mathematical models that occur in the physical or biological sciences.
MAT 452
Introduction to Chaos and Nonlinear Dynamics

Properties of nonlinear dynamical systems; dependence on initial conditions; strange attractors; period doubling; bifurcations; symbolic dynamics; Smale-Birkhoff theorem; and applications.
MAT 455
Introduction to Fractals and Applications

Fractals; self-similar structures, fractals with iterated function systems of maps, computing fractals, fractal dimensions, chaotic dynamics on fractals, applications.
MAT 460
Vector Calculus

Vectors, curvilinear coordinates, Jacobians, implicit function theorem, line and surface integrals, Green's, Stokes', and divergence theorems. Not open to students with credit in MAT 372.
MAT 462
Applied Partial Differential Equations

Second-order partial differential equations, emphasizing Laplace, wave, and diffusion equations.  Solutions by the methods of characteristics, separation of variables, and integral transforms.
MAT 475
Differential Equations

Linear and nonlinear ordinary differential equations, asymptotic behavior of solutions, stability, existence and uniqueness, limit sets, Poincar-Bendixson theorem.
MAT 503
Mathematical Cell Physiology

Mathematical modeling of dynamical aspects of cell physiology. Diffusion, membrane transport, intracellular calcium channel kinetics, calcium oscillations and waves. Lecture, computing lab.
MAT 543
Abstract Algebra I
Groups, modules, rings and fields, Galois theory, homological algebra, and the representation theory.
MSE 501
Linear Algebra in Engineering

Development and solution of systems of linear algebraic equations. Applications from mechanical, structural, and electrical fields of engineering.
MSE 511
Mathematical and Computer Methods in Materials

Mathematical, computational and statistical methods and computer programming used to model materials science phenomena and materials engineering applications.
MSE 526
Material Physics

A review of the fundamental concepts of the physics of materials. Bonding and structure in crystals; diffraction from periodic structures; elasticity; point defects; dislocations; lattice vibrations; thermal properties. The periodic potential and the resulting band structure. Elementary quantum and statistical mechanics concepts are utilized.
MSE 598
Intro to FEA for Matl Design and Characterization
Finite element method (FEM) is one of the most potent engineering design utilities in the modern world, which provides solutions to problems with abrupt changes in materials properties, complicated geometries, and diverse boundary conditions. With the aid of finite element analysis (FEA), it is feasible to select materials and designs that satisfy desired requirements (e.g., reduced weight and cost). As a result, the application of FEA can considerably shorten the time span of making products from intellectual concepts to the production line.
OMT 548
Statistical Methods for Research

Multivariate statistical techniques to analyze research data. Uses statistical software and applications.
PHY 541
Statistical Physics
This course studies postulates of statistical mechanics, equilibrium ensembles, Bose and Fermi statistics, density matrix, modern theory of phase transitions, fluctuations, and linear response theory.
PHY 542
Biophysics

Overview of modern biology, length scales: emphasizes molecular and cellular biology. Non-equilibrium systems: compare and contrast stochastic processes in biological and physical systems.
PHY 571
Quantum Physics

Review modern physics, chemistry, math. Differential equation, operator, matrix formulations. Free particle, bound state problems. Examples from physics, chemistry and nanoscience.
PSY 531
Multiple Regression in Psychological Research

Multiple regression and correlation, hierarchical regression, interactions, curvilinear relationships, categorical predictors, ANOVA in regression, regression diagnostics, regression graphics.
PSY 532
Analysis of Multivariate Data

Matrix algebra for multivariate procedures, component and factor analysis, canonical and discriminant analysis, classification, MANOVA, logistic regression, hierarchical linear model.
STP 420
Introduction Applied Statistics

Introductory probability, descriptive statistics, sampling distributions, parameter estimation, tests of hypotheses, chi-square tests, regression analysis, analysis of variance, and nonparametric tests.
STP 421
Probability

This course will provide an introduction to probability theory and some of its applications in the natural sciences (Taken from course website).
STP 427
Mathematical Statistics

Limiting distributions, interval estimation, point estimation, sufficient statistics, Linear Regressions, and tests of hypotheses.
STP 429
Experimental Statistics

Statistical inference for controlled experimentation. Multiple regression, correlation, analysis of variance, multiple comparisons, and nonparametric procedures.
STP 494
Machine Learning / Statistical Learning
Modern computing power has enabled the development of powerful tools for uncovering complex high dimensional relationships. These tools form a basic component of the interrelated areas known as statistics, Machine Learning, big data, artificial intelligence, and data science.
STP 530
Applied Regression Analysis

Method of least squares, simple and multiple linear regression, polynomial regression, analysis of residuals, dummy variables and model building. Prerequisite: Graduate Student (degree or non degree seeking).
STP 531
Applied Analysis of Variance

Factorial designs, balanced and unbalanced data, fixed and random effects, randomized blocks, Latin squares, analysis of covariance, and multiple comparisons. .
STP 532
Applied Nonparametric Statistics

One-sample test, tests of 2 or more related or independent samples, measures of correlation, and tests of tend and dependence. Prerequisite: STP 420 (or its equivalent).
STP 533
Applied Multivariate Analysis

Discriminant analysis, principal components, factor analysis, cluster analysis, and canonical correlation.
STP 535
Applied Sampling Methodology

Simple random, stratified, cluster sampling; variance estimation in complex surveys; nonparametric superpopulation approaches; nonresponse models; computational methods.
STP 540
Computational Statistics

Presents computational tools for statistical inference and data analysis. Uses R software (the lingua franca of statistics) in a wide variety of examples. Emphasizes simulation of random variables, Monte Carlo experiments, evaluation of statistical models via cross-validation, construction of confidence intervals via bootstrap and hypothesis testing via permutations. Focuses on the numerical solution of least squares problems, on stepwise methods for model building and on estimation of regression models for high-dimensional data. Presents computational tools for maximum likelihood estimation with an emphasis on estimation of logistic regression models. Assumes a mathematical and statistical maturity that is required for admission as a graduate student in statistics, including mathematical proofs, linear algebra, multiple semesters of calculus, coding and statistical concepts.
STP 598
Machine Learning/Statistical Learning
Modern computing power has enabled the development of powerful tools for uncovering complex high dimensional relationships. These tools form a basic component of the interrelated areas known as statistics, Machine Learning, big data, artificial intelligence, and data science.
STP 598
Time Series
• ARIMA and related models.
• Linear state space models.
• Regression with dependent errors.
• Spectral methods.
• Hidden Markov models with associated inference.
• Multivariate models.
• Miscellaneous topics.
TEM 505
Data Driven Decision Making

This course addresses the challenge of making choices under uncertainty. Data driven decision making impacts a wide variety of fields, from sports to finance to driverless cars. This course covers the methodologies related to data driven thinking including applied statistics, behavioral statistics and economics, scenario planning, optimization, algorithms, risk and game theory.