# Undergraduate Programs

The Applied Mathematics and Statistics (AMS) department supports undergraduate students seeking degrees in Applied Mathematics and Statistics. Students choose an area of emphasis in either Computational and Applied Mathematics (CAM) or Statistics (STAT). Through extensive coursework, AMS students gain the knowledge and skills to succeed in a variety of career paths including computer information and software firms, energy systems firms, government agencies, consulting firms, engineering research labs and academic institutions, to name a few.

As an example, the senior capstone engages our students in solving problems of practical applicability for potential employers. This course is designed to simulate an industrial job or research environment; in small teams, students work for a client, make weekly reports and present final written and oral reports. The close collaboration with potential employers and professors improves students’ communication and time management skills and builds a sense of confidence.

Mathematics and Statistics are the building blocks for engineering and the sciences. Our faculty and students conduct research in scientific computing, multivariate analysis, numerical analysis, spatial statistics, wave theory, biostatistics, multi-scale simulation, partial differential equations, inverse problems, uncertainty quantification and bio-mathematics.

## Quick Links

- Computational and Applied Mathematics Emphasis Flowchart | Fact Sheet
- Statistics Emphasis Flowchart | Fact Sheet
- Mines Course Catalog

## BS in Computational and Applied Mathematics

Students pursuing a degree in Computational and Applied Mathematics gain experience in mathematical modeling, applied analysis, the development and analysis of numerical algorithms, and the use of mathematical software. Courses include Computational Methods for Differential Equations, Complex Analysis, Parallel Scientific Computing, Programming Concepts, to name a few. In addition to an in-depth mathematics curriculum, students have opportunities to incorporate a minor or area of special interest to delve into another discipline; from Biochemistry to Electrical Engineering to Physics.

Substantial focus is placed on the development of practical applications and techniques to enhance the competitiveness of our students to a wide range of employment opportunities including careers in computer programing, systems analytics, finance, national laboratories, academia, and in industry. Employment of Mathematicians is projected to grow 21% from 2014-2024, much faster than the average (11%) for all occupations, according to the Bureau of Labor Statistics.

## BS in Statistics

Statistics provides quantitative methods for analyzing and interpreting data, designing experiments and surveys, and determining informed decisions under uncertainty and modeling randomness and variability.

The undergraduate Statistics program provides a thorough foundation in applied statistics and probability through courses such as Intro to Mathematical Statistics, Intro to Probability, Mathematical Biology, Complex Analysis, to name a few. In addition to an in-depth mathematics curriculum, students have opportunities to incorporate a minor or area of special interest to delve into another discipline; from Biochemistry to Electrical Engineering to Physics.

Statistics can be applied almost anywhere, which is one of the reasons the employment is projected to grow 34% from 2014-2024, according to the Bureau of Labor Statistics. Opportunities are available for Statisticians in a wide range of industries including finance, insurance, pharmaceutical, medical, engineering, life sciences and internet search, among others.

## Combined BS-MS Program

Why earn just one degree when you could graduate with two?

Current Mines students have the opportunity to earn an undergraduate and graduate degree in Computational and Applied Mathematics or Statistics through our combined BS – MS degree program. Thesis and Non-thesis options are available for both degree programs.

This program provides an opportunity for students to work on the two degrees simultaneously and graduate with both degrees in 5 to 5.5 years.

Current Mines students typically apply to this program upon successful completion of five classes with a MATH prefix numbered 225 or higher.

More information can be found on the Mines Combined Undergraduate and Graduate Degrees page.

## Additional Information

##### Why Major in Math?

Mathematics is everywhere. It’s cliché, but it’s also true. A degree in mathematics will prepare you for jobs in statistics, actuarial sciences, mathematical modeling, cryptography, and mathematics education, as well as for graduate school leading to a research career in engineering, mathematics or statistics. Graduates from our program have found employment with many different types of companies including technology, engineering, and financial companies.

Here are some reasons/considerations you may want to major or minor in mathematics:

#### You like math and you’re good at it!

In the career you choose beyond Mines, you will be working 8 hours a day, 5 days a week, 50 weeks a year (at least!), so whatever you choose, be certain you enjoy it! When it comes to job satisfaction, you want to choose a career path that builds on your strengths and challenges you.

#### You want to pursue graduate school.

Professional graduate schools in medicine, law, business and engineering consider a mathematics degree great preparation because it develops problem-solving and analytical skills. Students who major in mathematics receive substantially higher than average scores on the GMAT and LSAT, according to a study by the National Institute of Education that compared the scores of 550,000 college students who took the LSAT or DMAT over a period of eighteen years.

#### You want to stand out in your specific field of engineering.

Having a double-major with mathematics allows you to apply the theories and systems of mathematics to a specific field. Even a minor in mathematics or statistics provides you with a stronger foundation than most of your peers. Students who pursue a minor or double major in mathematics still have a choice between Statistics or Computational and Applied Mathematics. These students are in high demand in the final years of their program, as research and internships call for students who understand the logical structure that underlies all scientific inquiry.

#### You want a job that pays well with lots of options.

Every year Career Cast ranks jobs according to the work environment, income, stress, and projected growth. Careers in mathematics and statistics have consistently ranked at the top. Whether you want to develop models and interpret their results or develop algorithms to expedite known processes, or work in the biotech industry, a strong background in mathematics will serve you well!

##### Course Offerings

MATH100. INTRODUCTORY TOPICS FOR CALCULUS. 2.0 Semester Hrs.

An introduction and/or review of topics which are essential to the background of an undergraduate student at Mines. This course serves as a preparatory course for the Calculus curriculum and includes material from Algebra, Trigonometry, Mathematical Analysis, and Calculus. Topics include basic algebra and equation solving, solutions of inequalities, trigonometric functions and identities, functions of a single variable, continuity, and limits of functions. Does not apply toward undergraduate degree or g.p.a. Prerequisite: none. 2 hours lecture, 2 semester hours.

MATH111. CALCULUS FOR SCIENTISTS AND ENGINEERS I. 4.0 Semester Hrs. Equivalent with MACS111, First course in the calculus sequence, including elements of plane geometry. Functions, limits, continuity, derivatives and their application. Definite and indefinite integrals; Prerequisite: precalculus. 4 hours lecture; 4 semester hours. Approved for Colorado Guaranteed General Education transfer. Equivalency for GT-MA1.

MATH112. CALCULUS FOR SCIENTISTS AND ENGINEERS II. 4.0 Semester Hrs Equivalent with MACS112, MATH122, Vectors, applications and techniques of integration, infinite series, and an introduction to multivariate functions and surfaces. Prerequisite: Grade of C or better in MATH111. 4 hours lecture; 4 semester hours. Approved for Colorado Guaranteed General Education transfer. Equivalency for GT-MA1.

MATH113. CALCULUS FOR SCIENTISTS AND ENGINEERS II – SHORT FORM. 1.0 Semester Hr. This is a bridge course for entering freshmen and new transfer students to CSM who have either a score of 5 on the BC AP Calculus exam or who have taken an appropriate Calculus II course at another institution (determined by a departmental review of course materials). Two, three and n-dimensional space, vectors, curves and surfaces in 3-dimensional space, cylindrical and spherical coordinates, and applications of these topics. Prerequisites: none. 1 hour lecture; 1 semester hour.

MATH122. CALCULUS FOR SCIENTISTS AND ENGINEERS II HONORS. 4.0 Semester Hrs. Equivalent with MATH112, Same topics as those covered in MATH112 but with additional material and problems. Prerequisite: none. 4 hours lecture; 4 semester hours.

MATH198. SPECIAL TOPICS. 1-6 Semester Hr. Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once. Prerequisite: none. Variable credit; 1 to 6 credit hours. Repeatable for credit under different titles.

MATH199. INDEPENDENT STUDY. 1-6 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; 1 to 6 credit hours. Repeatable for credit.

MATH201. PROBABILITY AND STATISTICS FOR ENGINEERS. 3.0 Semester Hrs. Equivalent with MATH323, This course is an introduction to Probability and Statistics, including fundamentals of experimental design and data collection, the summary and display of data, elementary probability, propagation of error, discrete and continuous probability models, interval estimation, hypothesis testing, and linear regression with emphasis on applications to science and engineering. Prerequisites: MATH112, MATH122 or concurrent enrollment in MATH113. 3 hours lecture; 3 semester hours.

MATH213. CALCULUS FOR SCIENTISTS AND ENGINEERS III. 4.0 Semester Hrs. Equivalent with MACS213,MATH214, Multivariable calculus, including partial derivatives, multiple integrals, and vector calculus. Prerequisites: Grade of C or better in MATH112 or MATH122 or Concurrent Enrollment in MATH113. 4 hours lecture; 4 semester hours. Approved for Colorado Guaranteed General Education transfer. Equivalency for GT-MA1.

MATH214. CALCULUS FOR SCIENTIST AND ENGINEERS III – SHORT FORM. 1.0 Semester Hr. Equivalent with MATH213, This is a bridge course for entering freshmen and new transfer students to CSM who have taken an appropriate Calculus III course at another institution (determined by a departmental review of course materials). Vector Calculus including line and surface integrals with applications to work and flux, Green’s Theorem, Stokes’ Theorem and the Divergence Theorem. Prerequisites: none. 1 hour lecture; 1 semester hour.

MATH222. INTRODUCTION TO DIFFERENTIAL EQUATIONS FOR GEOLOGISTS & GEOLOGICAL ENGINEERS. 2.0 Semester Hrs. An introduction to differential equations with a special emphasis on problems in the earth related fields. Topics include first and second order ordinary differential equations, Laplace Transforms, and applications relevant to the earth related fields. Prerequisites: MATH112 or MATH122. Student must also be a declared major in Geology and Geological Engineering. 2 hours lecture; 2 semester hours. **Note: Only one of MATH222 and MATH225 can be counted toward graduation in GE. Any student who completes MATH222 and then changes majors out of Geology and Geological Engineering, will be expected to complete MATH225 to meet graduation requirements. (In this case, MATH222 cannot be counted toward graduation in any manner even as a free elective.

MATH223. CALCULUS FOR SCIENTISTS AND ENGINEERS III HONORS. 4.0 Semester Hrs. Equivalent with MACS223, Same topics as those covered in MATH213 but with additional material and problems. Prerequisite: Grade of C or better in MATH122. 4 hours lecture; 4 semester hours.

MATH224. CALCULUS FOR SCIENTISTS AND ENGINEERS III HONORS. 4.0 Semester Hrs. Early introduction of vectors, linear algebra, multivariable calculus. Vector fields, line and surface integrals. Prerequisite: none. 4 hours lecture; 4 semester hours.

MATH225. DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs. Equivalent with MACS225,MACS315, Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase-plane and stability analysis of non-linear equations and systems. Applications from physics, mechanics, electrical engineering, and environmental sciences. May not also receive credit for MATH222. Prerequisites: Grade of C or better in MATH112 or MATH122 or Concurrent Enrollment in MATH113. 3 hours lecture; 3 semester hours.

MATH235. DIFFERENTIAL EQUATIONS HONORS. 3.0 Semester Hrs. Equivalent with MACS325, Same topics as those covered in MATH225 but with additional material and problems. Prerequisite: none. 3 hours lecture; 3 semester hours.

MATH298. SPECIAL TOPICS. 1-6 Semester Hr. Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once. Prerequisite: none. Variable credit; 1 to 6 credit hours. Repeatable for credit under different titles.

MATH299. INDEPENDENT STUDY. 1-6 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; 1 to 6 credit hours. Repeatable for credit.

MATH300. FOUNDATIONS OF ADVANCED MATHEMATICS. 3.0 Semester Hrs. This course is an introduction to communication in mathematics. This writing intensive course provides a transition from the Calculus sequence to theoretical mathematics curriculum in CSM. Topics include logic and recursion, techniques of mathematical proofs, reading and writing proofs. Prerequisites: MATH112 or MATH122. 3 hours lecture; 3 semester hours.

MATH301. INTRODUCTION TO ANALYSIS. 3.0 Semester Hrs. Equivalent with MATH401, This course is a first course in real analysis that lays out the context and motivation of analysis in terms of the transition from power series to those less predictable series. The course is taught from a historical perspective. It covers an introduction to the real numbers, sequences and series and their convergence, real-valued functions and their continuity and differentiability, sequences of functions and their pointwise and uniform convergence, and Riemann-Stieltjes integration theory. Prerequisite: MATH213, MATH223 or MATH224, and MATH332 or MATH342. 3 hours lecture; 3 semester hours.

MATH307. INTRODUCTION TO SCIENTIFIC COMPUTING. 3.0 Semester Hrs. Equivalent with CSCI407,MATH407, This course is designed to introduce scientific computing to scientists and engineers. Students in this course will be taught various numerical methods and programming techniques to solve basic scientific problems. Emphasis will be made on implementation of various numerical and approximation methods to efficiently simulate several applied mathematical models. Prerequisites: MATH213, MATH223, or MATH224 and MATH225 or MATH235. 3 hours lecture; 3 semester hours.

MATH310. INTRODUCTION TO MATHEMATICAL MODELING. 4.0 Semester Hrs. An introduction to modeling and communication in mathematics. A writing intensive course providing a transition from the core math sequence to the upper division AMS curriculum. Topics include a variety of mathematical and statistical modeling techniques. Students will formulate and solve applied problems and will present results orally and in writing. In addition, students will be introduced to the mathematics software that will be used in upper division courses. Prerequisites: MATH201 and MATH225. 3 hours lecture; 3 hours lab; 4 semester hours.

MATH331. MATHEMATICAL BIOLOGY. 3.0 Semester Hrs. Equivalent with BELS331,BELS433,MACS433,MATH433, This course will discuss methods for building and solving both continuous and discrete mathematical models. These methods will be applied to population dynamics, epidemic spread, pharmacokinetics and modeling of physiologic systems. Modern Control Theory will be introduced and used to model living systems. Some concepts related to self-organizing systems will be introduced. Prerequisite: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture, 3 semester hours.

MATH332. LINEAR ALGEBRA. 3.0 Semester Hrs. Equivalent with MACS332, Systems of linear equations, matrices, determinants and eigenvalues. Linear operators. Abstract vector spaces. Applications selected from linear programming, physics, graph theory, and other fields. Prerequisite: MATH213, MATH223 or MATH224. 3 hours lecture; 3 semester hours.

MATH334. INTRODUCTION TO PROBABILITY. 3.0 Semester Hrs. Equivalent with MACS334,MACS434, An introduction to the theory of probability essential for problems in science and engineering. Topics include axioms of probability, combinatorics, conditional probability and independence, discrete and continuous probability density functions, expectation, jointly distributed random variables, Central Limit Theorem, laws of large numbers. Prerequisite: MATH213, MATH223 or MATH224. 3 hours lecture, 3 semester hours.

MATH335. INTRODUCTION TO MATHEMATICAL STATISTICS. 3.0 Semester Hrs. Equivalent with MACS435, An introduction to the theory of statistics essential for problems in science and engineering. Topics include sampling distributions, methods of point estimation, methods of interval estimation, significance testing for population means and variances and goodness of fit, linear regression, analysis of variance. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.

MATH340. COOPERATIVE EDUCATION. 3.0 Semester Hrs. Supervised, full-time engineering-related employment for a continuous six-month period (or its equivalent) in which specific educational objectives are achieved. Prerequisite: Second semester sophomore status and a cumulative grade point average of at least 2.00. 0 to 3 semester hours. Cooperative Education credit does not count toward graduation except under special conditions. Repeatable.

MATH342. HONORS LINEAR ALGEBRA. 3.0 Semester Hrs. Equivalent with MACS342, Same topics as those covered in MATH332 but with additional material and problems as well as a more rigorous presentation. Prerequisite: MATH213, MATH223 or MATH224. 3 hours lecture; 3 semester hours.

MATH348. ADVANCED ENGINEERING MATHEMATICS. 3.0 Semester Hrs. Equivalent with MACS348, Introduction to partial differential equations, with applications to physical phenomena. Fourier series. Linear algebra, with emphasis on sets of simultaneous equations. This course cannot be used as a MATH elective by MCS or AMS majors. Prerequisite: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture; 3 semester hours.

MATH358. DISCRETE MATHEMATICS. 3.0 Semester Hrs. Equivalent with CSCI358,MACS358, This course is an introductory course in discrete mathematics and algebraic structures. Topics include: formal logic; proofs, recursion, analysis of algorithms; sets and combinatorics; relations, functions, and matrices; Boolean algebra and computer logic; trees, graphs, finitestate machines and regular languages. Prerequisite: MATH213, MATH223 or MATH224. 3 hours lecture; 3 semester hours.

MATH398. 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. Prerequisite: none. Variable credit; 1 to 6 credit hours. Repeatable for credit under different titles.

MATH399. INDEPENDENT STUDY. 1-6 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; 1 to 6 credit hours. Repeatable for credit.

MATH406. ALGORITHMS. 3.0 Semester Hrs. Equivalent with CSCI406,MACS406, Divide-and-conquer: splitting problems into subproblems of a finite number. Greedy: considering each problem piece one at a time for optimality. Dynamic programming: considering a sequence of decisions in problem solution. Searches and traversals: determination of the vertex in the given data set that satisfies a given property. Techniques of backtracking, branch-and bound techniques, techniques in lower bound theory. Prerequisite: CSCI262 and (MATH213, MATH223 or MATH224, and MATH358/CSCI358). 3 hours lecture; 3 semester hours.

MATH408. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs. This course is designed to introduce computational methods to scientists and engineers for developing differential equations based computer models. Students in this course will be taught various numerical methods and programming techniques to simulate systems of nonlinear ordinary differential equations. Emphasis will be on implementation of various numerical and approximation methods to efficiently simulate several systems of nonlinear differential equations. Prerequisite: MATH307. 3 hours lecture, 3 semester hours.

MATH424. INTRODUCTION TO APPLIED STATISTICS. 3.0 Semester Hrs. Linear regression, analysis of variance, and design of experiments, focusing on the construction of models and evaluation of their fit. Techniques covered will include stepwise and best subsets regression, variable transformations, and residual analysis. Emphasis will be placed on the analysis of data with statistical software. Prerequisites: MATH201 or MATH335. 3 hours lecture; 3 semester hours.

MATH432. SPATIAL STATISTICS. 3.0 Semester Hrs. Modeling and analysis of data observed in a 2- or 3-dimensional region. 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. Prerequisite: MATH335. Corequisite: MATH424. 3 hours lecture; 3 semester hours.

MATH436. ADVANCED STATISTICAL MODELING. 3.0 Semester Hrs. Modern methods for constructing and evaluating statistical models. Topics include generalized linear models, generalized additive models, hierarchical Bayes methods, and resampling methods. Time series models, including moving average, autoregressive, and ARIMA models, estimation and forecasting, confidence intervals. Prerequisites: MATH335 and MATH424. 3 hours lecture; 3 semester hours.

MATH437. MULTIVARIATE ANALYSIS. 3.0 Semester Hrs. Introduction to applied multivariate techniques for data analysis. Topics include principal components, cluster analysis, MANOVA and other methods based on the multivariate Gaussian distribution, discriminant analysis, classification with nearest neighbors. Prerequisites: MATH335 or MATH201. 3 hours lecture; 3 semester hours.

MATH438. STOCHASTIC MODELS. 3.0 Semester Hrs. An introduction to stochastic models applicable to problems in engineering, physical science, economics, and operations research. Markov chains in discrete and continuous time, Poisson processes, and topics in queuing, reliability, and renewal theory. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.

MATH439. 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, hypothesis testing, the proportional hazards model, model diagnostics. Prerequisite: MATH335. 3 hours lecture; 3 semester hours.

MATH440. PARALLEL SCIENTIFIC COMPUTING. 3.0 Semester Hrs. Equivalent with CSCI440, 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 implementation of various scientific computing algorithms in FORTRAN 90 and its variants using MPI and OpenMP. Prerequisite: MATH307/CSCI407. 3 hours lecture; 3 semester hours.

MATH441. COMPUTER GRAPHICS. 3.0 Semester Hrs. Equivalent with CSCI441, Data structures suitable for the representation of structures, maps, three-dimensional plots. Algorithms required for windowing, color plots, hidden surface and line, perspective drawings. Survey of graphics software and hardware systems. Prerequisite: CSCI262. 3 hours lecture, 3 semester hours.

MATH444. ADVANCED COMPUTER GRAPHICS. 3.0 Semester Hrs. Equivalent with CSCI444, This is an advanced computer graphics course, focusing on modern rendering and geometric modeling techniques. Students will learn a variety of mathematical and algorithmic techniques that can be used to develop high-quality computer graphics software. In particular, the course will cover global illumination, GPU programming, geometry acquisition and processing, point based graphics and non-photorealistic rendering. Prerequisites: Basic understanding of computer graphics and prior exposure to graphics-related programming, for example, MATH441. 3 lecture hours, 3 credit hours.

MATH447. SCIENTIFIC VISUALIZATION. 3.0 Semester Hrs. Equivalent with CSCI447, 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 modern visualization techniques applicable to spatial data such as scalar, vector and tensor fields. In particular, the course will cover volume rendering, texture based methods for vector and tensor field visualization, and scalar and vector field topology. Basic understanding of computer graphics and analysis of algorithms required. Prerequisites: CSCI262 and MATH441. 3 lecture hours, 3 semester hours.

MATH454. COMPLEX ANALYSIS. 3.0 Semester Hrs. Equivalent with MACS454, The complex plane. Analytic functions, harmonic functions. Mapping by elementary functions. Complex integration, power series, calculus of residues. Conformal mapping. Prerequisite: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture, 3 semester hours.

MATH455. PARTIAL DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs. Linear partial differential equations, with emphasis on the classical second-order equations: wave equation, heat equation, Laplace’s equation. Separation of variables, Fourier methods, Sturm-Liouville problems. Prerequisite: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture; 3 semester hours.

MATH457. 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. Prerequisites: MATH332 or MATH342, and MATH455. 3 hours lecture; 3 semester hours.

MATH458. ABSTRACT ALGEBRA. 3.0 Semester Hrs. This course is an introduction to the concepts of contemporary abstract algebra and applications of those concepts in areas such as physics and chemistry. Topics include groups, subgroups, isomorphisms and homomorphisms, rings, integral domains and fields. Prerequisites: MATH213, MATH223 or MATH224, and MATH300. 3 hours lecture; 3 semester hours.

MATH474. INTRODUCTION TO CRYPTOGRAPHY. 3.0 Semester Hrs. Equivalent with CSCI474, This course is primarily oriented towards the mathematical aspects of cryptography, but is also closely related to practical and theoretical issues of computer security. The course provides mathematical background required for cryptography including relevant aspects of number theory and mathematical statistics. The following aspects of cryptography will be covered: 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. Many practical approaches and most commonly used techniques will be considered and illustrated with real-life examples. Prerequisites: CSCI262, MATH334/MATH335, MATH358. 3 credit hours.

MATH482. STATISTICS PRACTICUM (CAPSTONE). 3.0 Semester Hrs. This is the capstone course in the Statistics option. Students will apply statistical principles to data analysis through advanced work, leading to a written report and an oral presentation. Choice of project is arranged between the student and the individual faculty member who will serve as advisor. Prerequisites: MATH335 and MATH424. 3 hours lecture; 3 semester hours.

MATH484. MATHEMATICAL AND COMPUTATIONAL MODELING (CAPSTONE). 3.0 Semester Hrs. This is the capstone course in the Computational and Applied Mathematics option. Students will apply computational and applied mathematics modeling techniques to solve complex problems in biological, engineering and physical systems. Mathematical methods and algorithms will be studied within both theoretical and computational contexts. The emphasis is on how to formulate, analyze and use nonlinear modeling to solve typical modern problems. Prerequisites: MATH331, MATH307, and MATH455. 3 hours lecture; 3 semester hours.

MATH491. UNDERGRADUATE RESEARCH. 1-3 Semester Hr. Equivalent with CSCI491,MACS491, Individual investigation under the direction of a department faculty member. Written report required for credit. Prerequisite: none. Variable – 1 to 3 semester hours. Repeatable for credit to a maximum of 12 hours.

MATH492. UNDERGRADUATE RESEARCH. 1-3 Semester Hr. Individual investigation under the direction of a department faculty member. Written report required for credit. Prerequisite: none. Variable – 1 to 3 semester hours. Repeatable for credit to a maximum of 12 hours.

MATH498. SPECIAL TOPICS. 1-6 Semester Hr. Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once. Prerequisite: none. Variable credit; 1 to 6 credit hours. Repeatable for credit under different titles.

MATH499. INDEPENDENT STUDY. 1-6 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; 1 to 6 credit hours. Repeatable for credit.

##### Student Groups

Colorado School of Mines has over 180 student groups across campus, offering something for everyone. As you grow at Mines, you will discover that the more involved you become, the more you will benefit from your educational experiences inside and outside the classroom. The Department of Applied Mathematics & Statistics has three active student groups: the Math Club, the Society of Women in Mathematics (SWiM), and the Actuarial Club. In addition, AMS hosts Tea Time most Mondays at 3 p.m., with coffee, cookies and conversation in Chauvenet 156.

#### Math Club

The Math Club of Colorado School of Mines is actually a consolidation of two chapters of national mathematics organizations: Kappa Mu Epsilon (KME) and the Society of Industrial & Applied Mathematics (SIAM). The Math Club helps build the undergraduate and graduate math community by hosting guest speakers from industry and academia, and fun events such as the annual Pie Mile Run and the Math Club-Physics Club challenge.

VIDEO: Mines Math Club Pi Day Celebration

#### 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.

#### Actuarial Science Club

The Actuarial Science Club’s mission is to increase awareness of the actuarial profession on campus and provide a bridge between students and the actuarial industry. Industry speakers are invited to help inform students about careers in actuarial science, skills needed and opportunities available. In addition, students form study groups to prepare for the actuarial exams, getting them one step closer to starting an enjoyable and lucrative career upon graduation.

##### Scholarships and Awards

#### Ryan Sayers Memorial Scholarship and Ryan Sayers Memorial Award

In memory of Ryan Sayers, 1982-2003

Ryan Sayers was born in Colorado Springs on July 20, 1982. Before his sophomore year of high school, Ryan earned a perfect score on the math section of the SAT. Ryan attended Colorado School of Mines, and planned to graduate with degrees in both mathematics and physics. In June 2003, while climbing in the Wind River Mountain of Wyoming, Ryan was hit and killed by a lightning strike. He was twenty years old.

The Sayers family continues Ryan’s legacy at Mines, as he is remembered in the annual Ryan Sayers Memorial Pi Mile Fun Run each spring, in the computer laboratory named in his honor, and in the lives of the outstanding students who have received the Ryan Sayers Memorial Award or the Ryan Sayers Memorial Scholarship.

The **Ryan Sayers Memorial Scholarship** is awarded to a student majoring in Engineering Physics and/or Applied Mathematics or Statistics, while demonstrating excellence in coursework and creativity in undergraduate research.

Previous recipients:

- 2015-2016: Mollie Murray
- 2014-2015: Jacob Neumann
- 2013-2014: Eric Jones
- 2012-2013: Eric Jones
- 2011-2012: Scott Deibert
- 2010-2011: William Anthony McCollum
- 2009-2010: William Anthony McCollum

The **Ryan Sayers Memorial Award** recognizes the outstanding academic achievements of a graduating student, majoring in engineering physics and/or applied mathematics and statistics, who has performed significant undergraduate research.

Previous recipients:

- 2015-2016: Kerrek Stinson
- 2014-2015: Eric Jones
- 2013-2014: Andrew Colin Cook
- 2012-2013: Linnea K. Jones
- 2011-2012: Sara M. Clifton
- 2010-2011: Janeen Marie Neri
- 2009-2010: Kelly Anne Commeford
- 2008-2009: Benjamin James Jones
- 2007-2008: Rachel Renee Miller
- 2006-2007: Dimitri Robert Dounas-Frazer
- 2005-2006: Ann Hermundstad
- 2004-2005: Robert “Scott” Danford
- 2003-2004: Maxine von Eye

#### AMS Honor Fund Award

The Job/McAuliffe Award recognizes and honors Carol Job and Sharon McAuliffe, both of whom put a tremendous amount of effort into supporting students who struggled in their initial coursework or student life at Mines and ultimately became successful students due to the effort and attention of caring faculty. The recipient of this award will receive a plaque, a monetary reward, and support for a dinner with a faculty member who was instrumental in turning around the student’s performance at Mines. The winner will be asked to name his/her most inspirational faculty member at Mines and to provide a short essay narrating his/her story of perseverance through initial difficulties at Mines. Through this award, we hope to collect a library of stories that might serve as inspiration to future students who struggle in their initial coursework at Mines.

#### Everett Award

The Professor Everett Award was established by 1942 petroleum engineering alumnus Frank Ausanka to honor the memory of James R. Everett, an outstanding former faculty member in mathematics at Mines. The award is given each semester to a graduating senior in mathematics who demonstrates scholarship, leadership, community service and potential for the innovative application of mathematics to mineral engineering. Recipients’ names are added to a display of the Madrid Codices of Leonardo da Vinci, located in the Rare Books Collection in Arthur Lakes Library. The Codices are also a gift of Ausanka to the school. In addition to the prestige attached to the Professor Everett Award, each winner receives a gift of $500 funded by Ausanka.

Nominees must display leadership skills and valued involvement with the K-12 outreach program.

Previous recipients:

- 2015-2016: John Wakefield
- 2015-2016: Kownoon Her
- 2014-2015: Sean Lopp
- 2014-2015: Sarah Verros
- 2013-2014: Anastasia Vladislavovna Shpurik
- 2012-2013: Karen M. Moxcey
- 2011-2012: Michael C. Firmin
- 2010-2011: Courtney H. Rohde
- 2007-2008: Teresa E. B. Davies
- 2007-2008: Sara Ellen McFarland
- 2007-2008: Bryan Alan Romero
- 2006-2007: Erin R. Griggs

#### Outstanding Graduating Senior Award

The Outstanding Graduating Senior Award recognizes a graduating senior with high scholastic achievements and active involvement in departmental and school activities. Two awards are given within the department – one for Computational and Applied Mathematics and one for Statistics. Recipients receive a plaque which is typically accompanied with a monetary award or special departmental gift.

Previous recipients:

- May 2016: Taylor Chott, John Wakefield
- December 2015: Kelsey Kalmbach
- May 2015: Carson Kent, Eric Jones
- December 2014: Abigail Branch
- May 2014: Andrew Colin Cook
- December 2013: Kyle Geyser
- May 2013: Dylan Garth Denning, Lindsey Sharon Parr
- December 2012: Shad Allen
- May 2012: Sara Clifton
- December 2011: Michael Kasberg
- May 2011: Mitchell Scott Dushina, Janeen Marie Neri, Daniel E. Pascua, Joshua A. Warner
- December 2010: Gary Dean Scheid
- May 2010: Thea Ashley Gab, Sam A. Geldhof
- December 2009: Daniel Jacob Pearson
- May 2009: Benjamin James Jones, Thomas A. Cullison
- December 2008: Jonathan P. Hendricks, Kari Lee Macklin
- May 2008: Alyson Lin Burchardt, Jonathan Albert Maack, Rachel Renee Miller
- December 2007: Marianne L. Graham
- May 2007: Nathan F. Ostrander

#### Waltman Award

The William D. Waltman, 1899, Award is presented to the graduating senior whose conduct and scholarship have been most nearly perfect and who has most nearly approached the recognized characteristics of an American gentleman and/or lady during the recipient’s entire collegiate career.

To be eligible for this award, the graduating senior must:

- Be in the upper 10% of the graduating class
- Be American-born
- Not be involved in disciplinary matters
- Have completed at least four years of courses
- Have been in-residence for six regular semesters

Students must write a letter to the Awards Committee addressing their school, community activities, interests and thoughts about attending CSM and future plans. They must also submit a current resume, letter of reference from advisor or professor in their major. If it’s a transfer student, they need to specify the college they previously attended and the number of semesters enrolled at Mines (excluding summer sessions). One award is given from the entire graduating senior pool during spring commencement.