# Graduate Programs

The Department of Applied Mathematics and Statistics (AMS) prepares the next generation of mathematical and statistical scientists to be leaders in a world driven by increasingly complex technology and challenges. Our department is at the forefront of research in mathematical and statistical methods that are used to address the opportunities and challenges of the future.

AMS offers Master of Science and Doctor of Philosophy degrees in Computational and Applied Mathematics and Statistics. The department prides itself on being highly interdisciplinary with ties to on-campus and national research centers and laboratories.

Our faculty engages in research in a range of areas including:

- Uncertainty Quantification
- Mathematical Biology
- Data Science
- Scientific Computing
- Spatial and Multivariate Statistics
- Machine Learning
- Computational PDEs and Integral Equations
- Wave Phenomena
- Computational Statistics
- Multiscale Analysis and Simulation

Employment of Mathematicians is projected to grow 21% from 2014-2024, much faster than the average for all occupations (11%), according to the Bureau of Labor Statistics.

## Alumni Statistics

### Mean number of years for PhD Graduation

%

### Placement rate for 2016-17 Master's graduates

# $78,413

### Average Starting Salary for Grads

### Mean number of years for MS Graduation

Graduates of the MS and PhD programs generally pursue careers in industry, government, or academia. Recent graduates have accepted positions at

- ) Technological and data-oriented companies – Fast Enterprises, Hitachi, and Google
- ) Energy, Aerospace, and Defense companies – Lockheed Martin, Northrop Grumman, Tallgrass Energy, and Raytheon
- ) Financial corporations – Oppenheimer Funds
- ) Governmental laboratories – the National Renewable Energy Laboratory, Los Alamos National Laboratory, and the United States Geological Survey
- ) Colleges and universities – the University of Colorado Boulder and the Virginia Military Institute

##### Computational and Applied Mathematics

The MS program in Computational and Applied Mathematics (CAM) provides the opportunity for students to pursue 30 specialized credits through either a thesis or non-thesis degree program. All MS candidates pursuing CAM complete the following six courses:

- MATH 500 Linear Vector Spaces
- MATH 501 Applied Analysis
- MATH 514 Applied Mathematics I
- MATH 515 Applied Mathematics II
- MATH 550 Numerical Solutions to PDEs
- MATH 551 Computational Linear Algebra

All MS candidates pursuing CAM will take at least two courses from the following list:

- MATH 454 Complex Analysis
- MATH 455 Partial Differential Equations
- MATH 484 Mathematical and Computational Modeling – capstone
- MATH 503 Functional Analysis
- MATH 506 Complex Analysis II
- MATH 510 ODEs and Dynamical Systems
- MATH 540 Parallel Scientific Computing
- MATH 557 Integral Equations
- MATH 572 Mathematical and Computational Neuroscience
- MATH 598 Special Topics

The above courses account for at least 24 credit hours of required course work for all students.

- For non-thesis MS students, an additional 6 course credits are required. These courses can be taken from any of the MATH 500 electives, or from another 400-500 level course in another department at Mines.
- An MS-thesis degree requires the student to complete a minimum of six research credits, in lieu of two additional electives.
- Minors are also an option for both non-thesis and thesis students.

##### Statistics

The MS program in Statistics provides the opportunity for students to pursue 30 specialized credits through either a thesis or non-thesis degree program. All MS candidates pursuing Statistics will complete the following five courses:

- MATH 500 Linear Vector Spaces
- MATH 530 Statistical Methods I
- MATH 531 Statistical Methods II
- MATH 534 Mathematical Statistics I
- MATH 535 Mathematical Statistics II

All MS candidates pursuing Statistics will take at least two courses from the following list:

- MATH 532 Spatial Statistics
- MATH 536 Advanced Statistical Modeling
- MATH 537 Multivariate Analysis
- MATH 538 Stochastic Models
- MATH 539 Survival Analysis
- MATH 582 Statistics Practicum

The above courses account for at least 21 credit hours of required course work for all students.

- For non-thesis MS students, an additional 9 course credits are required. These courses can be taken from any of the MATH 500 electives, or from another 400-500 level course in another department at Mines.
- Thesis students will complete a minimum of six credits as research credits towards the required 30 credits.
- Minors are also an option for both non-thesis and thesis students.

##### Data Science

The non-thesis MS program in Data Science is designed to give candidates a foundation in statistics and computer science and also provide knowledge in a particular application domain of science or engineering. All MS candidates pursuing Data Science will follow a 3 × 3 + 1 design: three modules each consisting of three, 3-credit courses, and a mini-module, comprising 3-credit hours.

Modules:

- Data modeling and statistical learning
- Machine learning, data processing and algorithms, and parallel computing
- Individualized and domain specific coursework

Mini-Module:

Professional skills and career development

For further information about the Data Science Master’s Program, please visit the website here.

We also offer combined BS/MS degree programs in either Computational and Applied Mathematics or in Statistics. These programs offer an expedited application process and allow students to begin graduate coursework while still finishing their undergraduate degree requirements.

- This is an option for students who are currently in the process of completing, or have already completed, a BS degree at Mines within the past 5 years.
- For students with a bachelors in AMS, the department will waive letters of recommendation, GRE scores, and the Statement of Purpose.
- Students with a bachelors outside of the AMS department will have the GRE score waived, but the department still requires letters of recommendation and a Statement of Purpose.
- To apply, students are required to have completed a minimum of five AMS courses past MATH 225 Differential Equations.
- Cost to apply is $25 for all Mines students

Additional information about the Master’s program can be found in the “MS” tab to the left.

##### Computational and Applied Mathematics

The Doctor of Philosophy requires 72 credit hours beyond the bachelor’s degree. At least 24 of these hours must be thesis hours. Doctoral students must pass the comprehensive examination (a qualifying examination and thesis proposal), complete a satisfactory thesis, and successfully defend their thesis.

All PhD candidates pursuing CAM complete the following six courses, with two more required for specific students as noted:

- MATH 500 Linear Vector Spaces
- MATH 501 Applied Analysis
- MATH 514 Applied Mathematics I
- MATH 515 Applied Mathematics II
- MATH 550 Numerical Solutions to PDEs
- MATH 551 Computational Linear Algebra
- SYGN 502 Introduction to Research Ethics *
- MATH 589 Applied Mathematics and Statistics Teaching Seminar **

* Required only for students receiving federal support.

** Required only for students employed by the department as graduate teaching assistants and student instructor/lecturers.

##### Statistics

The Doctor of Philosophy requires 72 credit hours beyond the bachelor’s degree. At least 24 of these hours must be thesis hours. Doctoral students must pass the comprehensive examination (a qualifying examination and thesis proposal), complete a satisfactory thesis, and successfully defend their thesis.

All PhD candidates pursuing Statistics will complete the following five courses, with two more reqired for specific students as noted:

- MATH 500 Linear Vector Spaces
- MATH 530 Statistical Methods I
- MATH 531 Statistical Methods II
- MATH 534 Mathematical Statistics I
- MATH 535 Mathematical Statistics II
- SYGN 502 Introduction to Research Ethics*
- MATH 589 Applied Mathematics and Statistics Teaching Seminar **

* Required only for students receiving federal support.

** Required only for students employed by the department as graduate teaching assistants and student instructor/lecturers.

All PhD candidates pursuing Statistics will take at least two courses from the following list:

- MATH 532 Spatial Statistics
- MATH 536 Advanced Statistical Modeling
- MATH 537 Multivariate Analysis
- MATH 538 Stochastic Models
- MATH 539 Survival Analysis
- MATH 582 Statistics Practicum

The AMS Graduate Committee reviews applications for admission for the Fall and Spring semesters only. Applicants must submit a completed application to the Graduate School by the posted admission deadlines in order to be considered for admission and funding.

We strongly encourage applicants to meet the Fall admission priority deadline of December 15th, if applying to a thesis-based degree and seeking funding. Fall admission decisions with funding decisions are typically determined by the **end of January**.

The minimum requirements for admission to the MS and PhD programs are:

- A baccalaureate degree with a grade-point average of 3.0 or better on a 4.0 scale.
- Graduate Record Examination (Quantitative section) score of 151 or higher (or 650 on the old scale). Applicants who have graduated from the Colorado School of Mines within the past five years are not required to submit GRE scores.
- For International applicants or applicants whose native language is not English: TOEFL score of 79 or higher (or 550 for the paper-based test or 213 for the computer-based test). In lieu of a TOEFL score, an IELTS score of 6.5 or higher will be accepted.
- For PhD applicants, prior research experience is desired but not required.

Successful applicants are generally expected to have completed the Calculus sequence, an introductory computer programming language course (featuring C, C++, Java, Python, or Matlab), and the following mathematics courses: Differential Equations, Linear Algebra, Probability and Statistics, and either Advanced Calculus/Mathematical Analysis or Introduction to Proofs. Completion of advanced mathematical coursework in Partial Differential Equations, Complex Analysis, Mathematical Modeling, Mathematical Biology, Mathematical Statistics, Numerical Analysis, or Scientific Computing is also preferred. As the graduate program is quite interdisciplinary, however, AMS also encourages applicants from other backgrounds including students with undergraduate degrees in Physics, Computer Science, Mechanical Engineering, Biology, and Chemical Engineering, among others.

For convenience, the application packet requirements listed by the Graduate School at Colorado School of Mines are provided below.

To learn more about the graduate admission requirements and the process for completing an online application, direct your questions to the Program Manager, Jaime Bachmeier, at jbachmeier@mines.edu, 303-273-3860, or by setting up a meeting via the scheduler below.

The AMS department is able to offer Teaching Assistantships (TAs) and Research Assistantships (RAs) to the overwhelming majority of enrolled doctoral students. Some graduate students are also sponsored by grants from governmental agencies, including the National Science Foundation and National Institutes of Health, to perform research with their advisors. Students who are supported by a TA position are typically responsible for leading recitations, grading, and holding tutoring and office hours for students enrolled in MATH 225: Differential Equations.

##### Department Colloquium

#### Department Colloquium

The AMS department hosts esteemed guest speakers to discuss their current and recent research in the fields of Applied Mathematics and Statistics. This event is typically held every other Friday afternoon at 3pm (alternating with the Graduate Student Colloquium) and features informative seminars by world-renowned researchers from around the globe. Refreshments are always available starting at 2:45pm, as well!

##### Graduate Student Colloquium

#### Graduate Student Colloquium

Current graduate students in the AMS department organize a student colloquium series, in which both undergraduate and graduate students can practice presenting their research to peers, without faculty involvement. This occurs every other Friday afternoon at 3pm (alternating with the AMS Colloquium) and serves as a creative outlet for students to hone their presentation and technical communication skills while receiving constructive feedback from their fellow student researchers.

##### Tea Time

#### Tea Time

The AMS department hosts a weekly Tea Time for faculty and students on Mondays from 3-4pm in the Chauvenet Hall Conference Room. This is a great opportunity to meet fellow AMS graduate students, chat with professors/advisors, and enjoy a break in the day.

##### SWiM

#### Society of Women in Math (SWiM)

The Society for Women in Mathematics (SWiM) is an organization focused on creating a community for women in mathematics at the Colorado School of Mines. The organization holds monthly meetings where members share food and conversation, listen to a faculty member or alumna tell her mathematical story, and hold a discussion over the presentation or other relevant topics.

If you want more information, join us on Mines Engage for regular communication about events.

**MATH500. LINEAR VECTOR SPACES .**

*3.0 Semester Hrs.*Finite dimensional vector spaces and subspaces: dimension, dual bases, annihilators. Linear transformations, matrices, projections, change of basis, similarity. Determinants, eigenvalues, multiplicity. Jordan form. Inner products and inner product spaces with orthogonality and completeness. Prerequisite: MATH301. 3 hours lecture; 3 semester hours.

**MATH501. APPLIED ANALYSIS.** *3.0 Semester Hrs.* Fundamental theory and tools of applied analysis. Students in this course will be introduced to Banach, Hilbert, and Sobolev spaces; bounded and unbounded operators defined on such infinite dimensional spaces; and associated properties. These concepts will be applied to understand the properties of differential and integral operators occurring in mathematical models that govern various biological, physical and engineering processes. Prerequisites: MATH301 or equivalent. 3 hours lecture; 3 semester hours.

**MATH503. FUNCTIONAL ANALYSIS.** *3.0 Semester Hrs.* Equivalent with MACS503, Properties of metric spaces, normed spaces and Banach spaces, inner product and Hilbert spaces. Fundamental theorems for normed and Banach spaces with applications. Orthogonality and orthonormal systems on Hilbert spaces with applications to approximation theory. Compact, bounded and unbounded operators. Duality, adjoint, self-adjoint, Hilbert-adjoint operators. Spectral analysis of linear operators. Applications to differential and integral equations. Prerequisites: MATH502. 3 hours lecture; 3 semester hours.

**MATH506. COMPLEX ANALYSIS II.** *3.0 Semester Hrs.* Analytic functions. Conformal mapping and applications. Analytic continuation. Schlicht functions. Approximation theorems in the complex domain. Prerequisite: MATH454. 3 hours lecture; 3 semester hours.

**MATH510. ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS.** *3.0 Semester Hrs.* Equivalent with MACS510, Topics to be covered: basic existence and uniqueness theory, systems of equations, stability, differential inequalities, Poincare-Bendixon theory, linearization. Other topics from: Hamiltonian systems, periodic and almost periodic systems, integral manifolds, Lyapunov functions, bifurcations, homoclinic points and chaos theory. Prerequisite: MATH225 or MATH235 and MATH332 or MATH 342 or equivalent courses. 3 hours lecture; 3 semester hours.

**MATH514. APPLIED MATHEMATICS I.** *3.0 Semester Hrs.* The major theme in this course is various non-numerical techniques for dealing with partial differential equations which arise in science and engineering problems. Topics include transform techniques, Green’s functions and partial differential equations. Stress is on applications to boundary value problems and wave theory. Prerequisite: MATH455 or equivalent. 3 hours lecture; 3 semester hours.

**MATH515. APPLIED MATHEMATICS II.** *3.0 Semester Hrs.* Topics include integral equations, applied complex variables, an introduction to asymptotics, linear spaces and the calculus of variations. Stress is on applications to boundary value problems and wave theory, with additional applications to engineering and physical problems. Prerequisite: MATH514. 3 hours lecture; 3 semester hours.

**MATH530. STATISTICAL METHODS I.** *3.0 Semester Hrs.* Introduction to probability, random variables, and discrete and continuous probability models. Elementary simulation. Data summarization and analysis. Confidence intervals and hypothesis testing for means and variances. Chi square tests. Distribution-free techniques and regression analysis. Prerequisite: MATH213 or equivalent. 3 hours lecture; 3 semester hours.

**MATH531. STATISTICAL METHODS II.** *3.0 Semester Hrs.* Equivalent with MACS531, Continuation of MATH530. Multiple regression and trend surface analysis. Analysis of variance. Experimental design (Latin squares, factorial designs, confounding, fractional replication, etc.) Nonparametric analysis of variance. Topics selected from multivariate analysis, sequential analysis or time series analysis. Prerequisite: MATH201 or MATH530 or MATH535. 3 hours lecture; 3 semester hours.

**MATH532. SPATIAL STATISTICS.** *3.0 Semester Hrs.* Modeling and analysis of data observed on a 2 or 3-dimensional surface. Random fields, variograms, covariances, stationarity, nonstationarity, kriging, simulation, Bayesian hierarchical models, spatial regression, SAR, CAR, QAR, and MA models, Geary/Moran indices, point processes, K-function, complete spatial randomness, homogeneous and inhomogeneous processes, marked point processes, spatiotemporal modeling. MATH424 or MATH531.

**MATH534. MATHEMATICAL STATISTICS I.** *3.0 Semester Hrs.* The basics of probability, discrete and continuous probability distributions, sampling distributions, order statistics, convergence in probability and in distribution, and basic limit theorems, including the central limit theorem, are covered. Prerequisite: none. 3 hours lecture; 3 semester hours.

**MATH535. MATHEMATICAL STATISTICS II.** *3.0 Semester Hrs.* Equivalent with MACS535, The basics of hypothesis testing using likelihood ratios, point and interval estimation, consistency, efficiency, sufficient statistics, and some nonparametric methods are presented. Prerequisite: MATH534 or equivalent. 3 hours lecture; 3 semester hours.

**MATH536. ADVANCED STATISTICAL MODELING.** *3.0 Semester Hrs.* Modern extensions of the standard linear model for analyzing data. Topics include generalized linear models, generalized additive models, mixed effects models, and resampling methods. Prerequisite: MATH 335 and MATH 424. 3 hours lecture; 3.0 semester hours.

**MATH537. MULTIVARIATE ANALYSIS.** *3.0 Semester Hrs.* Introduction to applied multivariate representations of data for use in data analysis. Topics include introduction to multivariate distributions; methods for data reduction, such as principal components; hierarchical and model-based clustering methods; factor analysis; canonical correlation analysis; multidimensional scaling; and multivariate hypothesis testing. Prerequisites: MATH 530 and MATH 332 or MATH 500. 3 hours lecture; 3.0 semester hours.

**MATH538. STOCHASTIC MODELS.** *3.0 Semester Hrs.* An introduction to the mathematical principles of stochastic processes. Discrete- and continuous-time Markov processes, Poisson processes, Brownian motion. Prerequisites: MATH 534. 3 hours lecture and discussion; 3 semester hours.

**MATH539. SURVIVAL ANALYSIS.** *3.0 Semester Hrs.* Basic theory and practice of survival analysis. Topics include survival and hazard functions, censoring and truncation, parametric and non-parametric inference, the proportional hazards model, model diagnostics. Prerequisite: MATH335 or MATH535.

**MATH540. PARALLEL SCIENTIFIC COMPUTING.** *3.0 Semester Hrs.* This course is designed to facilitate students’ learning of parallel programming techniques to efficiently simulate various complex processes modeled by mathematical equations using multiple and multi-core processors. Emphasis will be placed on the implementation of various scientific computing algorithms in FORTRAN/C/C++ using MPI and OpenMP. Prerequisite: MATH407, CSCI407. 3 hours lecture, 3 semester hours.

**MATH542. SIMULATION.** *3.0 Semester Hrs.* Equivalent with MACS542, Advanced study of simulation techniques, random number, and variate generation. Monte Carlo techniques, simulation languages, simulation experimental design, variance reduction, and other methods of increasing efficiency, practice on actual problems. Prerequisite: CSCI262 (or equivalent), MATH323 (or MATH530 or equivalent). 3 hours lecture; 3 semester hours.

**MATH544. ADVANCED COMPUTER GRAPHICS.** *3.0 Semester Hrs.* Equivalent with CSCI544, This is an advanced computer graphics course in which students will learn a variety of mathematical and algorithmic techniques that can be used to solve fundamental problems in computer graphics. Topics include global illumination, GPU programming, geometry acquisition and processing, point based graphics and non-photo-realistic rendering. Students will learn about modern rendering and geometric modeling techniques by reading and discussing research papers and implementing one or more of the algorithms described in the literature.

**MATH547. SCIENTIFIC VISUALIZATION.** *3.0 Semester Hrs.* Equivalent with CSCI547, Scientific visualization uses computer graphics to create visual images which aid in understanding of complex, often massive numerical representation of scientific concepts or results. The main focus of this course is on techniques applicable to spatial data such as scalar, vector and tensor fields. Topics include volume rendering, texture based methods for vector and tensor field visualization, and scalar and vector field topology. Students will learn about modern visualization techniques by reading and discussing research papers and implementing one of the algorithms described in the literature.

**MATH550. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS.** *3.0 Semester Hrs.* Equivalent with MACS550, Numerical methods for solving partial differential equations. Explicit and implicit finite difference methods; stability, convergence, and consistency. Alternating direction implicit (ADI) methods. Weighted residual and finite element methods. Prerequisite: MATH225 or MATH235, and MATH332 or MATH342. 3 hours lecture; 3 semester hours.

**MATH551. COMPUTATIONAL LINEAR ALGEBRA.** *3.0 Semester Hrs.* Equivalent with MACS551, Numerical analysis of algorithms for solving linear systems of equations, least squares methods, the symmetric eigenproblem, singular value decomposition, conjugate gradient iteration. Modification of algorithms to fit the architecture. Error analysis, existing software packages. Prerequisites: MATH332, CSCI407/MATH407. 3 hours lecture; 3 semester hours. M

**MATH556. MODELING WITH SYMBOLIC SOFTWARE.** *3.0 Semester Hrs.* Case studies of various models from mathematics, the sciences and engineering through the use of the symbolic software package MATHEMATICA. Based on hands-on projects dealing with contemporary topics such as number theory, discrete mathematics, complex analysis, special functions, classical and quantum mechanics, relativity, dynamical systems, chaos and fractals, solitons, wavelets, chemical reactions, population dynamics, pollution models, electrical circuits, signal processing, optimization, control theory, and industrial mathematics. The course is designed for graduate students and scientists interested in modeling and using symbolic software as a programming language and a research tool. It is taught in a computer laboratory. Prerequisites: none. 3 hours lecture; 3 semester hours.

**MATH557. INTEGRAL EQUATIONS.** *3.0 Semester Hrs.* This is an introductory course on the theory and applications of integral equations. Abel, Fredholm and Volterra equations. Fredholm theory: small kernels, separable kernels, iteration, connections with linear algebra and Sturm-Liouville problems. Applications to boundary-value problems for Laplace’s equation and other partial differential equations. Prerequisite: MATH332 or MATH342, and MATH455.

**MATH574. THEORY OF CRYPTOGRAPHY.** *3.0 Semester Hrs.* Equivalent with CSCI574, Students will draw upon current research results to design, implement and analyze their own computer security or other related cryptography projects. The requisite mathematical background, including relevant aspects of number theory and mathematical statistics, will be covered in lecture. Students will be expected to review current literature from prominent researchers in cryptography and to present their findings to the class. Particular focus will be given to the application of various techniques to real life situations. The course will also cover the following aspects of cryptography: symmetric and asymmetric encryption, computational number theory, quantum encryption, RSA and discrete log systems, SHA, steganography, chaotic and pseudo-random sequences, message authentication, digital signatures, key distribution and key management, and block ciphers. Prerequisites: CSCI262 plus undergraduate-level knowledge of statistics and discrete mathematics. 3 hours lecture, 3 semester hours.

**MATH582. STATISTICS PRACTICUM.** *3.0 Semester Hrs.* This is the capstone course in the Statistics Option. The main objective is to apply statistical knowledge and skills to a data analysis problem, which will vary by semester. Students will gain experience in problem-solving; working in a team; presentation skills (both orally and written); and thinking independently. Prerequisites: MATH 201 or 530 and MATH 424 or 531. 3 hours lecture and discussion; 3 semester hours.

**MATH589. APPLIED MATHEMATICS AND STATISTICS TEACHING SEMINAR.** *1.0 Semester Hr.* An introduction to teaching issues and techniques within the AMS department. Weekly, discussion-based seminars will cover practical issues such as lesson planning, grading, and test writing. Issues specific to the AMS core courses will be included. 1 hour lecture; 1.0 semester hour.

**MATH598. SPECIAL TOPICS.** *6.0 Semester Hrs.* Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once, but no more than twice for the same course content. Prerequisite: none. Variable credit: 0 to 6 credit hours. Repeatable for credit under different titles.

**MATH599. INDEPENDENT STUDY.** *0.5-6 Semester Hr.* Individual research or special problem projects supervised by a faculty member, also, when a student and instructor agree on a subject matter, content, and credit hours. Prerequisite: Independent Study form must be completed and submitted to the Registrar. Variable credit: 0.5 to 6 credit hours. Repeatable for credit under different topics/experience and maximums vary by department. Contact the Department for credit limits toward the degree.

**MATH610. ADVANCED TOPICS IN DIFFERENTIAL EQUATIONS.** *3.0 Semester Hrs.* Topics from current research in ordinary and/or partial differential equations; for example, dynamical systems, advanced asymptotic analysis, nonlinear wave propagation, solitons. Prerequisite: none. 3 hours lecture; 3 semester hours.

**MATH614. ADVANCED TOPICS IN APPLIED MATHEMATICS.** *3.0 Semester Hrs.* Topics from current literature in applied mathematics; for example, wavelets and their applications, calculus of variations, advanced applied functional analysis, control theory. Prerequisite: none. 3 hours lecture; 3 semester hours.

**MATH616. INTRODUCTION TO MULTI-DIMENSIONAL SEISMIC INVERSION.** *3.0 Semester Hrs.* Introduction to high frequency inversion techniques. Emphasis on the application of this theory to produce a reflector map of the earth’s interior and estimates of changes in earth parameters across those reflectors from data gathered in response to sources at the surface or in the interior of the earth. Extensions to elastic media are discussed, as well. Includes high frequency modeling of the propagation of acoustic and elastic waves. Prerequisites: partial differential equations, wave equation in the time or frequency domain, complex function theory, contour integration. Some knowledge of wave propagation: reflection, refraction, diffraction. 3 hours lecture; 3 semester hours.

**MATH650. ADVANCED TOPICS IN NUMERICAL ANALYSIS.** *3.0 Semester Hrs.* Topics from the current literature in numerical analysis and/or computational mathematics; for example, advanced finite element method, sparse matrix algorithms, applications of approximation theory, software for initial value ODE?s, numerical methods for integral equations. Prerequisite: none. 3 hours lecture; 3 semester hours.

**MATH691. GRADUATE SEMINAR.** *1.0 Semester Hr.* Presentation of latest research results by guest lecturers, staff, and advanced students. Prerequisite: none. 1 hour seminar; 1 semester hour. Repeatable for credit to a maximum of 12 hours.

**MATH692. GRADUATE SEMINAR.** *1.0 Semester Hr.* Equivalent with CSCI692,MACS692, Presentation of latest research results by guest lecturers, staff, and advanced students. Prerequisite: none. 1 hour seminar; 1 semester hour. Repeatable for credit to a maximum of 12 hours.

**MATH693. WAVE PHENOMENA SEMINAR.** *1.0 Semester Hr.* Students will probe a range of current methodologies and issues in seismic data processing, with emphasis on under lying assumptions, implications of these assumptions, and implications that would follow from use of alternative assumptions. Such analysis should provide seed topics for ongoing and subsequent research. Topic areas include: Statistics estimation and compensation, deconvolution, multiple suppression, suppression of other noises, wavelet estimation, imaging and inversion, extraction of strati-graphic and lithologic information, and correlation of surface and borehole seismic data with well log data. Prerequisite: none. 1 hour seminar; 1 semester hour.

**MATH698. SPECIAL TOPICS.** *6.0 Semester Hrs.* Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once, but no more than twice for the same course content. Prerequisite: none. Variable credit: 0 to 6 credit hours. Repeatable for credit under different titles.

**MATH699. INDEPENDENT STUDY.** *0.5-6 Semester Hr.* Individual research or special problem projects supervised by a faculty member, also, when a student and instructor agree on a subject matter, content, and credit hours. Prerequisite: Independent Study form must be completed and submitted to the Registrar. Variable credit: 0.5 to 6 credit hours. Repeatable for credit under different topics/experience and maximums vary by department. Contact the Department for credit limits toward the degree.

**MATH707. GRADUATE THESIS / DISSERTATION RESEARCH CREDIT.** *1-15 Semester Hr.* Research credit hours required for completion of a Masters-level thesis or Doctoral dissertation. Research must be carried out under the direct supervision of the student’s faculty adviser. Variable class and semester hours. Repeatable for credit.

## Current Graduate Students |
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## Laura AlbrechtPhD, STAT |
## Kai BartlettePhD, CAM |
## Lewis BlakePhD, STAT |
## Jake ChambersPhD, CAM |
## Alicia ColclasurePhD, CAM |

## James CurtisPhD, CAM |
## Nicholas DanesPhD, CAM |
## Erica Dettmer-RadtkeMS, STAT |
## Davis EnglerMS, CAM |
## Nicholas FisherPhD, CAM |

## Caitlyn HannumPhD, STAT |
## Joshua HoskinsonMS, STAT |
## Michael KelleyPhD, CAM |
## David KozakPhD, STAT |
## John Luke LustyMS, CAM |

## Justice MartinezMS, CAM |
## Katy MartinezPhD, CAM |
## Jenifer McClaryMS, STAT |
## David MontgomeryPhD, CAM |
## Abigail ParksMS, CAM |

## Jared PopelarPhD, CAM |
## Brett PowersPhD, CAM |
## Aaron PruntyMS, CAM |
## Brandon ReyesPhD, STAT |
## Ross Ring-JarviMS, STAT |

## Ariel ScheinerMS, STAT |
## Michael SchmidtPhD, CAM |
## Peter SimonsonPhD, STAT |
## Nora StackPhD, CAM |
## Nhat Thanh TranMS, CAM |

## Alexander VidalMS, STAT |
## Andrew WiegersMS, STAT |
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## GRADUATE TEACHING FELLOWS |
||||

## Justin GarrishPhD, CAM |
## Todd YoderPhD, CAM |