### Computational Modeling and Data Analytics

**Division Leader:** M. Embree

**Program Manager:** C. Conley

**Principle Faculty:** C. Beattie, J. Chung, M. Chung, E. de Sturler, X. Deng, R. Gramacy, S. Gugercin, A. Habibnia, P. Haskell, R. Hewitt, L. House, L. Johnson, I. Kim, S. Leman, C. Lucero, E. Martin, G. Matthews, C. North, L. Pillonen, M. Pleimling, N. Ramakrishnan, C. Ribbens, S. Sengupta, E. Smith, T. Warburton, J. Wilson, and L. Zeitsman

### Overview

The Computational Modeling and Data Analytics (CMDA) program is a joint effort of the departments of Mathematics, Statistics, and Computer Science. It resides in, and is organized as a division of, the College of Science's Academy of Integrated Science. CMDA courses impart the emerging concepts and techniques from mathematics and statistics, with a decidedly computational approach, that are most in demand by a data-driven world. They prepare students as quantitative scientists ready to engage data and modeling problems wherever they may occur. CMDA is Virginia Tech's Big Data degree.

### Bachelor of Science in Computational Modeling and Data Analytics

#### Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html for degree requirements.

### Satisfactory Progress

University policy requires that students who are making satisfactory progress toward a degree meet minimum criteria toward the General Education (Curriculum for Liberal Education or Pathways to General Education) (see "Academic Policies") and toward the degree.

Satisfactory progress requirements toward the B.S. in Computational Modeling and Data Analytics can be found on the major checksheet by visiting the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html.

### Computer Literacy

Most CMDA courses involve the use of statistical and/or mathematical software, primarily (but not limited to) MATLAB, R, C. Java, and Python. Experience with the software is not expected, but students should have familiarity with either the Windows or Macintosh operating system.

### Undergraduate Course Descriptions (CMDA)

1984: SPECIAL STUDY

Variable credit course.

2005-2006: INTEGRATED QUANTITATIVE SCIENCES

2005: Integrated topics from quantitative sciences that
prepare students for advanced computational modeling and
data analytics courses. Topics include: probability and
statistics, infinite series, multivariate calculus, linear
algebra. 2006: Intermediate linear algebra, regression,
differential equations, and model validation.
Pre: MATH 1226 for 2005; 2005, MATH 2114 or MATH 2114H, CMDA 2206 for 2006.
Co: MATH 2114 for 2005.
(6H,6C)

2014: DATA MATTER

This course develops fundamental analytical and programming
skills to complete the \034analytic pipeline\035, including
specifying research questions, selecting/collecting data
ethically and responsibly, processing and summarizing
datasets, and stating findings, while considering all
assumptions made. Students will identify vulnerabilities in
analyses, including sources of bias and ethical
implications. Some programming skills recommended, but not
required. Some prior use of data recommended, but not
required.
Pre: MATH 1014.
(3H,3C)

2984: SPECIAL STUDY

Variable credit course.

2984E: SPECIAL STUDY

Variable credit course.

2994: UNDERGRADUATE RESEARCH

Variable credit course.

3605-3606: MATHEMATICAL MODELING: METHODS AND TOOLS

3605: Mathematical modeling with ordinary differential
equations and difference equations. Numerical solution and
analysis of ordinary differential equations and difference
equations. Stochastic modeling, and numerical solution of
stochastic differential equations. 3606: Concepts and
techniques from numerical linear algebra, including
iterative methods for solving linear systems and least
squares problems, and numerical approaches for solving
eigenvalue problems. Ill-posed inverse problems such as
parameter estimation, and numerical methods for computing
solutions to inverse problems. Numerical optimization.
Emphasis on large-scale problems.
Pre: CS 1114 or MATH 3054, MATH 2114 or MATH 2114H or MATH 2405H, MATH 2204 or MATH 2
204H or MATH 2406H or CMDA 2006, MATH 2214 or MATH 2214H or MATH 2406H or CMDA 2006 f
or 3605; 3605 for 3606.
(3H,3C)

3634 (CS 3634): COMPUTER SCIENCE FOUNDATIONS FOR COMPUTATIONAL MODELING & DATA ANALYTICS

Survey of computer science concepts and tools that enable
computational science and data analytics. Data structure
design and implementation. Analysis of data structure and
algorithm performance. Introduction to high-performance
computer architectures and parallel computation. Basic
operating systems concepts that influence the performance of
large-scale computational modeling and data analytics.
Software development and software tools for computational
modeling. Not for CS major credit.
Pre: CS 2114.
(3H,3C)

3654 (CS 3654) (STAT 3654): INTRODUCTORY DATA ANALYTICS & VISUALIZATION

Basic principles and techniques in data analytics; methods
for the collection of, storing, accessing, and manipulating
standard-size and large datasets; data visualization; and
identifying sources of bias.
Pre: CS 1114 or CS 1044 or CS 1054 or CS 1064, MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H or CMDA 2005, STAT 3006 or STAT 4705 or STAT 4714 or CMDA
2006.
(3H,3C)

4604: INTERMEDIATE TOPICS IN MATHEMATICAL MODELING

Introduction to partial differential equations, including
modeling and classification of partial differential
equations. Finite difference and finite elements methods
for the numerical solution of partial differential equations
including function approximation, interpolation, and
quadrature. Numerical solution of nonlinear systems of
equations. Uncertainty quantification, prediction.
Pre: 3606.
(3H,3C)

4654 (CS 4654) (STAT 4654): INTERMEDIATE DATA ANALYTICS AND MACHINE LEARNING

A technical analytics course. Covers supervised and
unsupervised learning strategies, including regression,
generalized linear models, regularization, dimension
reduction methods, tree-based methods for classification,
and clustering. Upper-level analytical methods shown in
practice: e.g., advanced naive Bayes and neural networks.
Pre: (STAT 3654 or CMDA 3654 or CS 3654), (STAT 3104 or STAT 4706 or CMDA 2006).
(3H,3C)

4664 (STAT 4664): COMPUTATIONAL INTENSIVE STOCHASTIC MODELING

Stochastic modeling methods with an emphasis in computing
are taught. Select concepts from the classical and Bayesian
paradigms are explored to provide multiple perspectives for
how to learn from complex, datasets. There is particular
focus on nested, spatial, and time series models.
Pre: (STAT 4106 or CMDA 3605), (CS 1114 or CS 1064 or STAT 2005).
(3H,3C)

4864: COMPUTATIONAL MODELING AND DATA ANALYTICS CAPSTONE PROJECT

Capstone research project for Computational Modeling and
Data Analytics majors. Cultivates skills including reviewing
the literature, creative problem solving, teamwork, critical
thinking, and oral, written, and visual communications.
Quantitative and computational thinking, informed throughout
by ethical reasoning.
Pre: 3605, 3634 or CS 3634, CMDA 3654 or CS 3654 or STAT 3654.
(3H,3C)

4964: FIELD STUDY

Variable credit course.

4974: INDEPENDENT STUDY

Variable credit course.

4984: SPECIAL STUDY

Variable credit course.

4994: UNDERGRADUATE RESEARCH

Variable credit course.