# Courses Satisfying Core Requirements for PhD in Computational Science/Engineering

## PhD Core Requirements

### Numerical Methods (Courses are 3 credits each)

MATH 2070 Numerical Methods in Scientific Computing 1

MATH 2071 Numerical Methods in Scientific Computing 2

MATH 2090 Numerical Solution of Ordinary Differential Equations

MATH 3071 Numerical Solution of Partial Differential Equations

ME 2060 Numerical Methods

### Scientific Computing/Programming (Courses are 3 credits each)

PHYS 2274 Computational Methods

CS 2010 Algorithm Design

CS 2045 Introduction to High Performance Computing Systems

CS 2150 Design and Analysis of Algorithms

CS 2450 Parallel Computing

CS 2620 Interdisciplinary Modeling and Visualization

## Concentration Areas

### Bioengineering

Students doing a concentration in Bioengineering need to take a minimum of 12 credits from the following list. All listed courses are 3 credits except MS CMP 3780 which is 2 credits and BIOE 2095 which can be for one, two or three credits.

BIOE 2035 Biomechanics Modeling of Movement

BIOE 2065 Biomechanics of Organs, Tissues, and Cells

BIOE 2067 Musculoskeletal Biomechanics

BIOE 2310 Hemodynamics and Biotransport

BIOE 2515 Cardiovascular System Dyanmics and Modeling

BIOE 2696 Control Theory inNeuroscience

MSCMP 3780 Systems Approach to Inflammation

BIOE 2095 Independent/Directed Study

### Biological Sciences

Students doing a concentration in Biological Sciences are required to take all of the following 2 credit courses. (BIOSC 2011-2013 are taken together in one term and BIOSC 2021-2023 are taken together in the following term.) Each of these courses is 3 credits.

BIOSC 2011 Current Topics in Molecular, Cell and Developmental Biology

BIOSC 2012 Current Topics in Molecular, Cell and Developmental Biology

BIOSC 2013 Current Topics in Molecular, Cell and Developmental Biology

BIOSC 2021 Current Topics in Molecular, Cell and Developmental Biology

BIOSC 2022 Current Topics in Molecular, Cell and Developmental Biology

BIOSC 2023 Current Topics in Molecular, Cell and Developmental Biology

### Chemical and Petroleum Engineering

Students doing a concentration in Chemical and Petroleum Engineering should take the following four courses. Each of these courses is 3 credits.

ChE 2101 Fundamentals of Thermodynamics

ChE 2201 Fundamentals of Reaction Processes

ChE 2301 Fundamentals of Transport Processes I

ChE 3902 Directed Study

### Chemistry

Students Doing a concentration in Chemistry must take two core courses, one additional 3-credit chemistry graduate course and 3 credits of directed study. Courses that meet the core course requirement are listed below. Each of these courses is 3 credits.

CHEM 2110 Physical Inorganic Chemistry

CHEM 2120 Inorganic Synthesis

CHEM 2210 Electrochemistry

CHEM 2220 Chemical Seporations

CHEM 2230 Analytical Spectroscopy

CHEM 2410 Mechanistic Organic Chemistry

CHEM 2420 Advanced Organic Synthesis

CHEM 2430 Quantum Mechanics and Kinetics

CHEM 2440 Thermodynamics and Statistical Mechanics

CHEM 2810 Biological Chemistry I

CHEM 2820 Biological Chemistry II

CHEM 3902 Directed Study

### Civil and Environmental Engineering

Students doing a concentration in Civil and Environmental Engineering should take four courses from the following list of courses. Each of these is 3 credits.

CEE 2100 Numerical Methods 3

CEE 2105 Advanced Civil Engineering Materials

CEE 2320 Advanced Mechanics of Materials 3

CEE 2322 Fatigue and Fracture of Metal Structures

CEE 2324 Computational Nanomechanics

CEE 2333 Fundamentals of the Finite Element Method

CEE 2330 Advanced Structural Analysis

CEE 2360 Dynamics of Structures

CEE 2408 Advanced Environmental Fluid Mechanics

CEE 3320 Continuum Mechanics

CEE 3321 Applied Plasticity

CEE 3322 Fracture Mechanics

CEE 3330 Structural Stability

CEE 3331 Plate and Shell Structures

CEE 3332 Energy Methods in Structural Analysis

CEE 3333 Advanced Finite Elements

CEE 3414 Advanced Hydrology

CEE 3420 Hydrologic Modeling

CEE 3997 Special Investigation

### Computer Science

Students doing a concentration in Computer Science should take four courses from the following list of courses. Each of these is 3 credits.

CS 2010 Introduction to Algorithms

CS 2150 Algorithms

CS 2045 Introduction to High Performance Computing Systems

CS 2450 Parallel Computing

CS 2620 Modeling and Visualization

CS 2410 Computer Architecture

CS 2210 Compilers

CS 2550 Database

CS 2510 Operating Systems

CS 2750 Machine Learning

### Economics

Students doing a concentration in Economics, should choose one fo the following course sequences. Each of these courses is 3 credits.

ECON 2100 Advanced Microeconomic Theory I

ECON 2120 Advanced Microeconomic Theory II

ECON 2600 Computational Methods in Economics

ECON 3902 Directed Study

or

ECON 2110 Advanced Macroeconomic Theory I

ECON 2130 Advanced Macroeconomic Theory II

ECON 2600 Computational Methods in Economics

ECON 3902 Directed Study

or

ECON 2260 Advanced Economectrics I

ECON 2270 Advanced Macroeconomic Theory II

ECON 2600 Computational Methods in Economics

ECON 3902 Directed Study

### Industrial Engineering

Students doing a concentration in Industrial Engineering should take the following two classes and two others from the elective list. Each of these courses is 3 credits.

IE 2082 Linear Optimization

IE 2088 Digital Systems Simulation

**Elective List **

IE 2081 Nonlinear Optimization

IE 3051 Computational Optimization

IE 3053 Global Optimization

IE 3071 Atomistic Simulations of Nanomaterials

IE 3072 Nanomechanics

IE 3076 Combinatorial Optimization

IE 3081 Numerical Optimization

IE 3087 Network-Based Optimization

IE 3088 Integer Programming

IE 3091 Heuristic Optimization

IE 3093 Stochastic Programming

IE 3094 Markov Decision Processes

IE 3097 Algorithms for Engineers

IE 3186 Approximate Dynamic Programming

### Mathematics

Students doing a concentration in Mathematics should choose four courses from the following list. Each of these courses is 3 credits.

MATH 2070 Numerical Methods in Scientific Computing I

MATH 2071 Numerical Methods in Scientific Computing II

MATH 2090 Numerical Solution of Ordinary Differential Equations

MATH 3071 Numerical Solution of Partial Differential Equations

MATH 2030 Iterative Methods for Linear and Nonlinear Systems

MATH 2950 Methods of Applied Mathematics

MATH 3072 The Finite Element Method

MATH 3380 Mathematical Biology

MATH 2960 Computational Fluid Mechanics

MATH 2601 Advanced Scientific Computing I

MATH 2602 Advanced Scientific Computing II

MATH 3375 Computational Neuroscience

MATH 2603 Advanced Scientific Computing III

MATH 2604 Advanced Scientific Computing IV

MATH 3040 Topics in Scientific Computing: High Performance Computing

MATH 3902 Directed Study

### Mechanical Engineering

Students doing a concentration in Mechanical Engineering should take four courses from the following list. Each of these courses is 3 credits.

ME 2027 Advanced Dynamics

ME 2033 Fracture Mechanics for Production Design & MFG

ME 2041 Experimental Mechanics ME 2045 Linear Congtrol Systems

ME 2046 Digital Control Systems ME 2050 Thermodynamics

ME 2055 Computer Aided Analysis in Transportation Phenomena

ME 2056 Introduction to Combustion Theory

ME 2064 Introduction to Cell Mechanobiology

ME 2067 Musculoskeletal Biomechanics (3)

ME 2080 Introduction to Micro Electric Mechanical Systems (MEMS)

ME 2082 Principles of Electromechanical Sensors & Actuators

ME 3003 Theory of Continuous Media ME 3004 Advanced Elasticity

ME 3006 Inelasticity ME 3007 Energetics

ME 3021 Mechamical Vibrations II

ME 3023 Composite

ME 3036 Advanced Fracture Mechanics

ME 3047 Advanced Finite Element Analysis

ME 3052 Conduction Heat Transfer

ME 3054 Convection Heat Transfer

ME 3055 Multiphase Flow

ME 3075 Hydrodynamic Stability

ME 3078 Viscous Fluids

ME 3079 Turbulence

ME 3081 Non-Newtonian Fluids

### Physics and Astronomy

Students choosing to do a concentration in Physics will choose from one of the following five thematic areas. Example course groupings within each thematic area are also listed. Exact courses taken by each student will be determined by the student an his/her advisor. In some cases the advisor may require more than four Physics courses to fulfill the concentration requirement. Each of these courses is 3 credits, with the exception of PHYS 2555, which is 4 credits. Computational Elementary Particle Physics

PHYS 2373 Mathematical Methods

PHYS 2555 Electricity and Magnetism

PHYS 2565 Quantum Mechanics I

PHYS 2566 Quantum Mechanics II

PHYS 3717 Partical Physics

PHYS 3718 Advanced Particle Physics

PHYS 3765 Relativistic Quantum Mechanics

PHYS 3766 Field Theory I Computational Cosmology and Extragalactic Astronomy

PHYS 2373 Mathematical Methods

PHYS 2555 Electricity and Magnetism

PHYS 3750 Galactic and Extragalactic Astronomy

PHYS 3785 Cosmology Computational Stellar Astronomy

PHYS 2373 Mathematical Methods

PHYS 2555 Electricity and Magnetism PHYS 3780 Stellar Structure

PHYS 3751 Interstellar Medium

PHYS 3784 Radiative Processes in Astrophysics Survey Astronomy

PHYS 3752 Astronomical Techniques PHYS 3750 Galactic and Extragalactic Astronomy

PHYS 3780 Stellar Structure

PHYS 3751 Interstellar Medium

PHYS 3784 Radiative Processes in Astrophysics Computational Nanoscience

PHYS 2373 Mathematical Methods

PHYS 2555 Electricity and Magnetism

PHYS 2565 Quantum Mechanics I PHYS

2566 Quantum Mechanics II

PHYS 3715 Solid-State Physics

Psychology

Students doing a concentration in Psychology need to complete the following courses. Eac of these courses is 3 credits.

PSYC 2476 Topics Seminar: Computational Modeling

PSYC 2450 Problem Solving and Reasoning

PSYC 2465 Perception and Attention

PSYC Skill Acquisition

### Statistics

Students doing a concentrations in Statistics need to complete the following courses. Each of these courses is 3 credits.

STAT 2270 Data Mining

STAT 3341 Advanced Modern Statistical Computing (Monte Carlo Methods)

STAT 3342 Advanced Modern Statistical Computing

STAT 3731 Topics in Stochastic Processes (Stochastic Differential Equations)

STAT 3732 Topics in Stochastic Processes

## About the Program

Our students pursue research in diverse areas including: