Professional Master of Computational Analytics
The Professional Master of Computational Analytics is an interdisciplinary program designed to provide knowledge and essential skills to deal with realworld applications in a wide range of industries. This program focusses on the following areas: numerical computing, discrete and fast algorithms, modeling and simulation, data science, inverse problems, statistical models, multiphysics, large data analysis, and related applications. With such knowledge and skills, graduates will be capable of working and thinking more dynamically when it comes to solving challenging problems.
Degree Plan
Course #   Title  LT  LB  CR  Fall Semester       ICS  502  Machine Learning  3  0  3  MATH  557  Applied Linear Algebra  3  0  3  MATH  576  Applied Numerical Methods I  3  0  3  PETE  547  Computational Multiphysics Modeling  3  0  3     12  0  12  Spring Semester       COE  588  Modeling and Simulations  3  0  3  ICS  574  Big Data Analytics  3  0  3  MATH  578  Applied Numerical Methods II  3  0  3  MATH  619  Project  0  0  IP     9  0  9  Summer Term       MATH  585  Computational Inverse Problem  3  0  3  MATH  619  Project  0  0  6     3  0  9    Total Credit Hours    30 

Course Descriptions
COE 588 Modeling and Simulations (303)
Approaches to the simulation problem (event scheduling, processbased, etc.). Modeling and simulation of queuing systems. Probability, stochastic processes, and statistics in simulation. Random number generation. Monte Carlo methods. Building valid and credible simulation models. Output data analysis. Simulation formalisms. Software techniques for building simulators. Using contemporary tools like Matlab and SimEvents. Case studies in science and engineering.
Prerequisite: Graduate Standing
ICS 502 Machine Learning (303)
Introduction to machine learning; supervised learning (linear regression, logistic regression, classification, support vector machines, kernel methods, decision tree, Bayesian methods, ensemble learning, neural networks); unsupervised learning (clustering, EM, mixture models, kernel methods, dimensionality reduction); learning theory (bias/variance tradeoffs); and reinforcement learning and adaptive control.
Note: Not to be taken for credit with ICS 485
Prerequisite: Graduate Standing or Consent of Instructor
ICS 574 Big Data Analytics (303)
Introduction and foundation of big data and bigdata analytics. Sources of big data. Smart clouds. Hadoop file system and Apache Spark. Storage management for big data. Machine learning and visualization with big data. Applications of big data. Big data and security, privacy, societal impacts.
Note: Not to be taken for credit with ICS 474
Prerequisite: Graduate Standing
MATH 557 Applied Linear Algebra (303)
Basics concepts from linear algebra and numerical analysis. Direct methods for large, sparse linear systems, Cholesky and LU factorizations. Regularization of illconditioned least squares problems. SVD and QR factorizations. Sensitivity and conditioning of linear systems and least square problems. Stationary and nonstationary iterative methods, multigrid methods. Matrix theory including spectral decompositions, and eigenvalue perturbation theory. Eigenvalue and QR algorithm, and computations of SVD. Applications.
Prerequisite: Graduate Standing
MATH 576 Applied Numerical Methods I (303)
This course introduces implementable numerical methods for solving initial value problems, stability and convergence. Onestep, multistep, and RungeKutta methods. Shooting and bisection methods. Finite difference methods and applications to equilibrium and nonequilibrium models including steadystate, heat, and wave problems.
Prerequisite: Graduate Standing
MATH 578 Applied Numerical Methods II (303)
This course introduces finite element, finite difference, and finite volume methods. Applications of these methods to steadystate, diffusion and wave models. Stability and convergence. Homogenization, upscale and multiscale methods. Implementations and computer labs.
Prerequisite: MATH 576, MATH 557 or Consent of the instructor
MATH 585 Computational Inverse Problem (303)
This course introduces students to fundamental concepts in linear and nonlinear inverse problems. Emphasis is placed on describing how to integrate various information sources from measured data and prior knowledge about the inverted model. Subjects studied will include topics and tools such as: Regression, Least squares, Maximum likelihood estimation, Rank deﬁciency, Illconditioning, Generalized and Truncated SVD solutions, regularizations (Tikohonov, spectral filtering), proximal and primaldual iterative schemes, Nonlinear inverse (gradientbased and global optimization methods), OCCAM method. Computer lab sessions will be organized to combine classroom learning with handson applications.
Prerequisite: MATH 557, MATH 576 or Consent of the instructor
MATH 619 Project (006)
A graduate student will arrange with a faculty member to conduct an industrial research project related to catalysis. Subsequently the students shall acquire skills and gain experiences in developing and running actual industrybased project. This project culminates in the writing of a technical report, and an oral technical presentation in front of a board of professors and industry experts.
Prerequisite: MATH 576, MATH 557, ICS 502 and PETE 547.
PETE 547 Computational Multiphysics Modeling (303)
Multiphysics is essential for many applications, it involves the analysis of multiple, simultaneous physical phenomena. This course exposes students to advanced concepts involving Multiphysics modeling. While concentrating more on Multiphysics modeling in fluid flow and heat transfer, Multiphysics modeling in other areas such as solid mechanics and electromagnetics will be covered as well. The course introduces the students to the derivations of the fundamental equations used in the various areas of modeling, detailing how and why the physical processes are coupled and briefly mentioning the approaches to solving such coupled problems.
Main topics: SinglePhase Flow, Reaction Advection Dispersion Equation, Conservation of Momentum in Fluid Flow, Nonisothermal Flow of Fluids, MP Phenomena in Solid Mechanics, Multiphysics Phenomena in Electromagnetic Waves.
Prerequisite: Graduate Standing