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 Computational_Analytics

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 real-world 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, multi-physics, 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 #TitleLTLBCR
Fall Semester   
ICS502Machine Learning303
MATH557Applied Linear Algebra303
MATH576Applied Numerical Methods I303
PETE547Computational Multiphysics Modeling303
   12012
Spring Semester   
COE588Modeling and Simulations303
ICS574Big Data Analytics303
MATH578Applied Numerical Methods II303
MATH619Project00IP
   909
Summer Term   
MATH585Computational Inverse Problem303
MATH619Project006
   309
  Total Credit Hours  30

 

Course Descriptions

COE 588 Modeling and Simulations (3-0-3)

Approaches to the simulation problem (event scheduling, process-based, 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 (3-0-3)

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 (3-0-3)

Introduction and foundation of big data and big-data 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 (3-0-3)

Basics concepts from linear algebra and numerical analysis. Direct methods for large, sparse linear systems, Cholesky and LU factorizations. Regularization of ill-conditioned least squares problems. SVD and QR factorizations. Sensitivity and conditioning of linear systems and least square problems. Stationary and non-stationary 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 (3-0-3)

This course introduces implementable numerical methods for solving initial value problems, stability and convergence. One-step, multistep, and Runge-Kutta methods. Shooting and bisection methods. Finite difference methods and applications to equilibrium and non-equilibrium models including steady-state, heat, and wave problems. 

Prerequisite: Graduate Standing

MATH 578 Applied Numerical Methods II (3-0-3)

This course introduces finite element, finite difference, and finite volume methods. Applications of these methods to steady-state, 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 (3-0-3)

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, Ill-conditioning, Generalized and Truncated SVD solutions, regularizations (Tikohonov, spectral filtering), proximal and primal-dual iterative schemes, Nonlinear inverse (gradient-based and global optimization methods), OCCAM method. Computer lab sessions will be organized to combine classroom learning with hands-on applications.

Prerequisite: MATH 557, MATH 576 or Consent of the instructor

MATH 619 Project (0-0-6)

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 industry-based 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 (3-0-3)

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: Single-Phase 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

635