### Computational Modeling and Data Analytics

**Division Leader:** M. Embree

**Program Manager:** C. Conley

**Principle Faculty:** N. Abaid, C. Beattie, J. Chung, M. Chung, E. de Sturler, X. Deng, F. Faltin, R. Gramacy, S. Gugercin, A. Habibnia, P. Haskell, R. Hewett, D. Higdon, L. House, L. Johnson, I. Kim, S. Leman, C. Lucero, E. Martin, G. Matthews, J. P. Morgan, C. North, L. Pillonen, M. Pleimling, N. Ramakrishnan, C. Ribbens, E. Smith, E. Ufferman, 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 during the academic year of admission to Virginia Tech apply. Requirements for graduation are listed on checksheets. Students must satisfactorily complete all requirements and university obligations for degree completion. The university reserves the right to modify requirements in a degree program.

Please visit the University Registrar's website at https://www.registrar.vt.edu/graduation-multi-brief/checksheets.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 https://www.registrar.vt.edu/graduation-multi-brief/checksheets.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 o r 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), (CMDA 2006 or STAT 3104 or STAT 4105 or STA T 4714). (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.