# Applied Mathematics & Statistics

# Program Description

The Applied Mathematics and Statistics Department (AMS) offers an undergraduate degree in which students are exposed to a breadth of coursework in computational mathematics, applied mathematics, and statistics. In the senior year, students may choose an area of emphasis in either Computational and Applied Mathematics (CAM) or Statistics (STAT). Both of these options emphasize technical competence, problem solving, teamwork, projects, relation to other disciplines, and verbal, written, and graphical skills.

In a broad sense, these programs stress the development of practical applications and techniques to enhance the overall attractiveness of applied mathematics and statistics majors to a wide range of employers in industry and government. More specifically, AMS utilizes a summer field session program to introduce concepts and techniques in advanced mathematics and the senior capstone experiences in Computational and Applied Mathematics and Statistics to engage high-level undergraduate students in problems of practical applicability for potential employers. These courses are designed to simulate an industrial job or research environment. The close collaboration with potential employers and professors improves communication between our students and the private sector as well as with sponsors from other disciplines on campus.

Applied Mathematics and Statistics majors are encouraged to use free elective courses to gain knowledge in another discipline and incorporate either an Area of Special Interest (ASI) or a minor. This adds to the flexibility of the program and qualifies students for a wide variety of careers.

In addition to offering undergraduate and graduate degree programs, the Department provides the teaching skills and technical expertise to develop capabilities in computational mathematics, applied mathematics, and statistics for all Colorado School of Mines (CSM) students.

#### Primary Contact

Jaime Bachmeier

303 273-3860

jbachmeier@mines.edu

### Department Head

Greg Fasshauer, Professor

### Professors

Bernard Bialecki

Mahadevan Ganesh

Paul A. Martin

William C. Navidi

Doug Nychka

### Associate Professor

Soutir Bandyopadhyay

Luis Tenorio

Stephen Pankavich

### Assistant Professors

Cecilia Diniz Behn

Karin Leiderman

### Teaching Professors

G. Gustave Greivel

Debra Carney

Mike Nicholas

Scott Strong

Rebecca Swanson

### Teaching Associate Professors

Terry Bridgman

Holly Eklund

Mike Mikucki

Ashlyn Munson

Jennifer Strong

### Emeriti Professors

William R. Astle

Norman Bleistein

Ardel J. Boes

Austin R. Brown

John A. DeSanto

Graeme Fairweather

Raymond R. Gutzman

Frank G. Hagin

Donald C.B. Marsh

Willy Hereman

Steven Pruess

### Emeriti Associate Professors

Barbara B. Bath

Ruth Maurer

# Program Educational Objectives

### (Bachelor of Science in Applied Mathematics and Statistics)

In addition to contributing toward achieving the educational objectives described in the CSM Graduate Profile and the Accreditation Board for Engineering and Technology's (ABET) accreditation criteria, the Applied Mathematics and Statistics Program at CSM has established the following program educational objectives:

Students will demonstrate technical expertise within mathematics and statistics by:

- Designing and implementing solutions to practical problems in science and engineering; and,
- Using appropriate technology as a tool to solve problems in mathematics.

Students will demonstrate a breadth and depth of knowledge within mathematics by:

- Extending course material to solve original problems,
- Applying knowledge of mathematics to the solution of problems,
- Identifying, formulating and solving mathematics problems, and
- Analyzing and interpreting statistical data.

Students will demonstrate an understanding and appreciation for the relationship of mathematics to other fields by:

- Applying mathematics and statistics to solve problems in other fields,
- Working in cooperative multidisciplinary teams, and
- Choosing appropriate technology to solve problems in other disciplines.

Students will demonstrate an ability to communicate mathematics effectively by:

- Giving oral presentations,
- Completing written explanations,
- Interacting effectively in cooperative teams, and
- Understanding and interpreting written material in mathematics.

## Curriculum

The calculus sequence emphasizes mathematics applied to problems students are likely to see in other fields. This supports the curricula in other programs where mathematics is important, and assists students who are under prepared in mathematics. Priorities in the mathematics curriculum include: applied problems in the mathematics courses and ready utilization of mathematics in the science and engineering courses.

This emphasis on the utilization of mathematics continues through the upper division courses. Another aspect of the curriculum is the use of a spiraling mode of learning in which concepts are revisited to deepen the students’ understanding.

The applications, teamwork, assessment and communications emphasis directly address ABET criteria and the CSM graduate profile. The curriculum offers the following two areas of emphases:

### Degree Requirements (Applied Mathematics and Statistics)

#### Computational and Applied Mathematics (CAM) EMPHASIS

Freshman | ||||
---|---|---|---|---|

Fall | lec | lab | sem.hrs | |

CHGN121 | PRINCIPLES OF CHEMISTRY I | 3.0 | 3.0 | 4.0 |

CSCI101 | INTRODUCTION TO COMPUTER SCIENCE, CBEN 110, CHGN 122, or CHGN 125 | 3.0 | 3.0 | |

CSM101 | FRESHMAN SUCCESS SEMINAR | 0.5 | 0.5 | |

HASS100 | NATURE AND HUMAN VALUES | 4.0 | 4.0 | |

MATH111 | CALCULUS FOR SCIENTISTS AND ENGINEERS I | 4.0 | 4.0 | |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

16.0 | ||||

Spring | lec | lab | sem.hrs | |

EBGN201 | PRINCIPLES OF ECONOMICS | 3.0 | 3.0 | |

EDNS151 | INTRODUCTION TO DESIGN | 3.0 | ||

MATH112 | CALCULUS FOR SCIENTISTS AND ENGINEERS II | 4.0 | 4.0 | |

PHGN100 | PHYSICS I - MECHANICS | 3.0 | 3.0 | 4.5 |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.0 | ||||

Sophomore | ||||

Fall | lec | lab | sem.hrs | |

CSCI261 | PROGRAMMING CONCEPTS | 3.0 | 3.0 | |

MATH213 | CALCULUS FOR SCIENTISTS AND ENGINEERS III | 4.0 | 4.0 | |

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 | 3.0 | |

PHGN200 | PHYSICS II-ELECTROMAGNETISM AND OPTICS | 3.0 | 3.0 | 4.5 |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.0 | ||||

Spring | lec | lab | sem.hrs | |

HASS200 | GLOBAL STUDIES | 3.0 | 3.0 | |

MATH201 | PROBABILITY AND STATISTICS FOR ENGINEERS | 3.0 | 3.0 | |

MATH332 | LINEAR ALGEBRA or 342 | 3.0 | 3.0 | |

CSCIxxx | COMPUTER ELECTIVE^{1} | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.5 | ||||

Summer | lec | lab | sem.hrs | |

MATH310 | INTRODUCTION TO MATHEMATICAL MODELING | 3.0 | 3.0 | 4.0 |

4.0 | ||||

Junior | ||||

Fall | lec | lab | sem.hrs | |

MATH300 | FOUNDATIONS OF ADVANCED MATHEMATICS | 3.0 | 3.0 | |

MATH307 | INTRODUCTION TO SCIENTIFIC COMPUTING | 3.0 | 3.0 | |

MATH331 | MATHEMATICAL BIOLOGY | 3.0 | 3.0 | |

MATH334 | INTRODUCTION TO PROBABILITY | 3.0 | 3.0 | |

HASS/EBGN | HASS MID-LEVEL ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Spring | lec | lab | sem.hrs | |

MATH301 | INTRODUCTION TO ANALYSIS | 3.0 | 3.0 | |

MATH335 | INTRODUCTION TO MATHEMATICAL STATISTICS | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM ELECTIVE^{2} | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM ELECTIVE^{2} | 3.0 | 3.0 | |

HASS/EBGN | HASS MID-LEVEL ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Senior | ||||

Fall | lec | lab | sem.hrs | |

MATH408 | COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 3.0 | 3.0 | |

MATH455 | PARTIAL DIFFERENTIAL EQUATIONS | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

18.0 | ||||

Spring | lec | lab | sem.hrs | |

MATH484 | MATHEMATICAL AND COMPUTATIONAL MODELING (CAPSTONE) | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

HASS/EBGN | HASS 400-LEVEL ELECTIVE | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Total Semester Hrs: 128.5 |

^{1} | May be satisfied by CSCI262 or any other approved computationally intensive course. |

Mathematics-CAM elective list. CAM students must choose at least 2 electives from this list. ^{2} | ||

MATH440 | PARALLEL SCIENTIFIC COMPUTING | 3.0 |

MATH454 | COMPLEX ANALYSIS | 3.0 |

MATH457 | INTEGRAL EQUATIONS | 3.0 |

MATH458 | ABSTRACT ALGEBRA | 3.0 |

MATH459 | ASYMPTOTICS | 3.0 |

MATH472 | MATHEMATICAL AND COMPUTATIONAL NEUROSCIENCE | 3.0 |

MATH500 | LINEAR VECTOR SPACES | 3.0 |

MATH501 | APPLIED ANALYSIS | 3.0 |

MATH514 | APPLIED MATHEMATICS I | 3.0 |

MATH515 | APPLIED MATHEMATICS II | 3.0 |

MATH550 | NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS | 3.0 |

MATH551 | COMPUTATIONAL LINEAR ALGEBRA | 3.0 |

MATH | Department approval required for courses not on this list. |

Mathematics-STAT Elective List. CAM students may choose up to 4 electives from this list to satisfy CAM/STAT Elective requirements. ^{2} | ||

MATH424 | INTRODUCTION TO APPLIED STATISTICS | 3.0 |

MATH432 | SPATIAL STATISTICS | 3.0 |

MATH436 | ADVANCED STATISTICAL MODELING | 3.0 |

MATH437 | MULTIVARIATE ANALYSIS | 3.0 |

MATH438 | STOCHASTIC MODELS | 3.0 |

MATH439 | SURVIVAL ANALYSIS | 3.0 |

MATH482 | STATISTICS PRACTICUM | 3.0 |

MATH530 | STATISTICAL METHODS I | 3.0 |

MATH531 | STATISTICAL METHODS II | 3.0 |

MATH534 | MATHEMATICAL STATISTICS I | 3.0 |

MATH535 | MATHEMATICAL STATISTICS II | 3.0 |

CSCI303 | INTRODUCTION TO DATA SCIENCE | 3.0 |

CSCI403 | DATA BASE MANAGEMENT | 3.0 |

CSCI406 | ALGORITHMS | 3.0 |

MATH | Department approval required for courses not on this list. |

#### Statistics (STATS) EMPHASIS

Freshman | ||||
---|---|---|---|---|

Fall | lec | lab | sem.hrs | |

CSCI101 | INTRODUCTION TO COMPUTER SCIENCE, CBEN 110, CHGN 122, or CHGN 125 | 3.0 | 3.0 | |

CHGN121 | PRINCIPLES OF CHEMISTRY I | 3.0 | 3.0 | 4.0 |

CSM101 | FRESHMAN SUCCESS SEMINAR | 0.5 | 0.5 | |

HASS100 | NATURE AND HUMAN VALUES | 4.0 | 4.0 | |

MATH111 | CALCULUS FOR SCIENTISTS AND ENGINEERS I | 4.0 | 4.0 | |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

16.0 | ||||

Spring | lec | lab | sem.hrs | |

EBGN201 | PRINCIPLES OF ECONOMICS | 3.0 | 3.0 | |

EDNS151 | INTRODUCTION TO DESIGN | 3.0 | ||

MATH112 | CALCULUS FOR SCIENTISTS AND ENGINEERS II | 4.0 | 4.0 | |

PHGN100 | PHYSICS I - MECHANICS | 3.0 | 3.0 | 4.5 |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.0 | ||||

Sophomore | ||||

Fall | lec | lab | sem.hrs | |

CSCI261 | PROGRAMMING CONCEPTS | 3.0 | 3.0 | |

MATH213 | CALCULUS FOR SCIENTISTS AND ENGINEERS III | 4.0 | 4.0 | |

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 | 3.0 | |

PHGN200 | PHYSICS II-ELECTROMAGNETISM AND OPTICS | 3.0 | 3.0 | 4.5 |

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.0 | ||||

Spring | lec | lab | sem.hrs | |

CSCI262 | DATA STRUCTURES | 3.0 | 3.0 | |

HASS200 | GLOBAL STUDIES | 3.0 | 3.0 | |

MATH201 | PROBABILITY AND STATISTICS FOR ENGINEERS | 3.0 | 3.0 | |

MATH332 | LINEAR ALGEBRA or 342 | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | ||

PAGN Elective | PHYSICAL ACTIVITY COURSE | 0.5 | ||

15.5 | ||||

Summer | lec | lab | sem.hrs | |

MATH310 | INTRODUCTION TO MATHEMATICAL MODELING | 3.0 | 3.0 | 4.0 |

4.0 | ||||

Junior | ||||

Fall | lec | lab | sem.hrs | |

MATH300 | FOUNDATIONS OF ADVANCED MATHEMATICS | 3.0 | 3.0 | |

MATH307 | INTRODUCTION TO SCIENTIFIC COMPUTING | 3.0 | 3.0 | |

MATH334 | INTRODUCTION TO PROBABILITY | 3.0 | 3.0 | |

MATH | MATHEMATICS-STAT ELECTIVE^{2} | 3.0 | 3.0 | |

HASS/EBGN | HASS MID-LEVEL ELECTIVE | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

18.0 | ||||

Spring | lec | lab | sem.hrs | |

MATH301 | INTRODUCTION TO ANALYSIS | 3.0 | ||

MATH335 | INTRODUCTION TO MATHEMATICAL STATISTICS | 3.0 | 3.0 | |

MATH | MATHEMATICS-STAT ELECTIVE^{2} | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

HASS/EBGN | HASS MID-LEVEL ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Senior | ||||

Fall | lec | lab | sem.hrs | |

CSCI403 | DATA BASE MANAGEMENT | 3.0 | ||

MATH424 | INTRODUCTION TO APPLIED STATISTICS | 3.0 | 3.0 | |

MATH | MATHEMATICS CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

HASS/EBGN | HASS 400-LEVEL ELECTIVE | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Spring | lec | lab | sem.hrs | |

MATH437 | MULTIVARIATE ANALYSIS | 3.0 | ||

MATH482 | STATISTICS PRACTICUM (STAT Capstone) | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

MATH | MATHEMATICS-CAM/STAT ELECTIVE^{2} | 3.0 | 3.0 | |

FREE | FREE ELECTIVE | 3.0 | 3.0 | |

15.0 | ||||

Total Semester Hrs: 128.5 |

Mathematics-STAT Elective List. STAT students must choose at least 2 electives from this list. ^{2} | ||

MATH432 | SPATIAL STATISTICS | 3.0 |

MATH436 | ADVANCED STATISTICAL MODELING | 3.0 |

MATH438 | STOCHASTIC MODELS | 3.0 |

MATH439 | SURVIVAL ANALYSIS | 3.0 |

MATH530 | STATISTICAL METHODS I | 3.0 |

MATH531 | STATISTICAL METHODS II | 3.0 |

MATH534 | MATHEMATICAL STATISTICS I | 3.0 |

MATH535 | MATHEMATICAL STATISTICS II | 3.0 |

MATH | Department approval required for courses not on this list. |

Mathematics-CAM Elective List. STAT students may choose up to 4 electives from this list to satisfy CAM/STAT Elective requirements. ^{2} | ||

MATH331 | MATHEMATICAL BIOLOGY | 3.0 |

MATH408 | COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 3.0 |

MATH440 | PARALLEL SCIENTIFIC COMPUTING | 3.0 |

MATH454 | COMPLEX ANALYSIS | 3.0 |

MATH455 | PARTIAL DIFFERENTIAL EQUATIONS | 3.0 |

MATH457 | INTEGRAL EQUATIONS | 3.0 |

MATH458 | ABSTRACT ALGEBRA | 3.0 |

MATH459 | ASYMPTOTICS | 3.0 |

MATH472 | MATHEMATICAL AND COMPUTATIONAL NEUROSCIENCE | 3.0 |

MATH484 | MATHEMATICAL AND COMPUTATIONAL MODELING (CAPSTONE) | 3.0 |

MATH500 | LINEAR VECTOR SPACES | 3.0 |

MATH501 | APPLIED ANALYSIS | 3.0 |

MATH514 | APPLIED MATHEMATICS I | 3.0 |

MATH515 | APPLIED MATHEMATICS II | 3.0 |

MATH550 | NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS | 3.0 |

MATH551 | COMPUTATIONAL LINEAR ALGEBRA | 3.0 |

CSCI303 | INTRODUCTION TO DATA SCIENCE | 3.0 |

CSCI406 | ALGORITHMS | 3.0 |

MATH | Department approval required for courses not on this list. |

### Major GPA

During the 2016-2017 Academic Year, the Undergraduate Council considered the policy concerning required major GPAs and which courses are included in each degree’s GPA. While the GPA policy has not been officially updated, in order to provide transparency, council members agreed that publishing the courses included in each degree’s GPA is beneficial to students.

The following list details the courses that are included in the GPA for this degree:

- CSCI100 through CSCI799 inclusive
- MACS100 through MACS799 inclusive (Previous subject code)
- MATH100 through MATH799 inclusive

# Overview

The CSM guidelines for Minor/ASI can be found in the Undergraduate Information section of the CSM Bulletin.The Department of Applied Mathematics and Statistics offers the following:

### ASIs are available in:

Computational and Applied Mathematics (CAM) | ||

Required Courses | ||

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 |

or MATH235 | DIFFERENTIAL EQUATIONS HONORS | |

MATH307 | INTRODUCTION TO SCIENTIFIC COMPUTING | 3.0 |

MATH332 | LINEAR ALGEBRA | 3.0 |

or MATH342 | HONORS LINEAR ALGEBRA | |

Plus 3 hours of elective courses listed below. |

Statistics (STAT) | ||

Required Courses | ||

MATH201 | PROBABILITY AND STATISTICS FOR ENGINEERS | 3.0 |

MATH334 | INTRODUCTION TO PROBABILITY | 3.0 |

MATH335 | INTRODUCTION TO MATHEMATICAL STATISTICS | 3.0 |

MATH424 | INTRODUCTION TO APPLIED STATISTICS | 3.0 |

Plus 3 hours of elective courses from the list below. |

Mathematical Sciences | ||

Required Courses | ||

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 |

Plus 9 hours of upper division or graduate level MATH courses. 3 of which must be at the 400-level. |

### Minors are available in:

Computational and Applied Mathematics (CAM) | ||

Required Courses | ||

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 |

or MATH235 | DIFFERENTIAL EQUATIONS HONORS | |

MATH307 | INTRODUCTION TO SCIENTIFIC COMPUTING | 3.0 |

MATH332 | LINEAR ALGEBRA | 3.0 |

or MATH342 | HONORS LINEAR ALGEBRA | |

Plus 9 hours of electives from the list below. |

Statistics (STAT) | ||

Required Courses | ||

MATH201 | PROBABILITY AND STATISTICS FOR ENGINEERS | 3.0 |

MATH334 | INTRODUCTION TO PROBABILITY | 3.0 |

MATH335 | INTRODUCTION TO MATHEMATICAL STATISTICS | 3.0 |

MATH424 | INTRODUCTION TO APPLIED STATISTICS | 3.0 |

Plus 9 hours of electives from the list below |

Mathematical Sciences | ||

Required Courses | ||

MATH225 | DIFFERENTIAL EQUATIONS | 3.0 |

Plus 15 hours of upper division or graduate level MATH courses. 3 of which must be at the 400-level. |

To complete a Minor/ASI in Computational and Applied Mathematics (CAM), students must choose 9 credits(Minor) or 3 credits(ASI) from the following elective list | ||

MATH301 | INTRODUCTION TO ANALYSIS | 3.0 |

MATH310 | INTRODUCTION TO MATHEMATICAL MODELING | 4.0 |

MATH331 | MATHEMATICAL BIOLOGY | 3.0 |

MATH348 | ADVANCED ENGINEERING MATHEMATICS | 3.0 |

MATH406 | ALGORITHMS | 3.0 |

MATH408 | COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 3.0 |

MATH440 | PARALLEL SCIENTIFIC COMPUTING | 3.0 |

MATH441 | COMPUTER GRAPHICS | 3.0 |

MATH444 | ADVANCED COMPUTER GRAPHICS | 3.0 |

MATH447 | SCIENTIFIC VISUALIZATION | 3.0 |

MATH454 | COMPLEX ANALYSIS | 3.0 |

MATH455 | PARTIAL DIFFERENTIAL EQUATIONS | 3.0 |

MATH457 | INTEGRAL EQUATIONS | 3.0 |

MATH474 | INTRODUCTION TO CRYPTOGRAPHY | 3.0 |

MATH484 | MATHEMATICAL AND COMPUTATIONAL MODELING (CAPSTONE) | 3.0 |

MATH3xx/4xx/5xx | Approved upper division or graduate course |

To complete a Minor/ASI in Statistics (STAT), students must choose 9 credits(Minor) or 3 credits(ASI) from the following elective list | ||

MATH432 | SPATIAL STATISTICS | 3.0 |

MATH436 | ADVANCED STATISTICAL MODELING | 3.0 |

MATH438 | STOCHASTIC MODELS | 3.0 |

MATH439 | SURVIVAL ANALYSIS | 3.0 |

MATH498 | SPECIAL TOPICS | 1-6 |

MATH5XXX | Graduate Level Math Course | 3.0 |

### Courses

**MATH100. INTRODUCTORY TOPICS FOR CALCULUS. 3.0 Semester Hrs.**

(S) An introduction and/or review of topics which are essential to the background of an undergraduate student at CSM. 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 GPA. 3 hours lecture; 3 semester hours.

**MATH111. CALCULUS FOR SCIENTISTS AND ENGINEERS I. 4.0 Semester Hrs.**

Equivalent with MACS111,

(I, II, S) 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,

(I, II, S) 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.**

(I, II) 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,

(I, II) Same topics as those covered in MATH112 but with additional material and problems. Prerequisites: Grade of C- or better in MATH111. 4 hours lecture; 4 semester hours.

**MATH198. SPECIAL TOPICS. 6.0 Semester Hrs.**

(I, II) 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.**

(I, II) 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,

(I,II,S) 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.**

(I, II, S) 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.**

(I, II) 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. 1 hour lecture; 1 semester hour.

**MATH223. CALCULUS FOR SCIENTISTS AND ENGINEERS III HONORS. 4.0 Semester Hrs.**

Equivalent with MACS223,

(II) 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.**

(I) Early introduction of vectors, linear algebra, multivariable calculus. Vector fields, line and surface integrals. Prerequisite: Grade of C- or better in MATH122. 4 hours lecture; 4 semester hours.

**MATH225. DIFFERENTIAL EQUATIONS. 3.0 Semester Hrs.**

Equivalent with MACS225,MACS315,

(I, II, S) 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. 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,

(II) Same topics as those covered in MATH225 but with additional material and problems. Prerequisite: Grade of C- or better in MATH112 or MATH122 or Concurrent Enrollment in MATH113. 3 hours lecture; 3 semester hours.

**MATH298. SPECIAL TOPICS. 1-6 Semester Hr.**

(I, II) 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.**

(I, II) 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.**

(I) (WI) 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,

(II) 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: MATH300. 3 hours lecture; 3 semester hours.

**MATH307. INTRODUCTION TO SCIENTIFIC COMPUTING. 3.0 Semester Hrs.**

Equivalent with CSCI407,MATH407,

(I, II, S) 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 or MATH223 or MATH224. Co-requisites: MATH225 or MATH235. 3 hours lecture; 3 semester hours.

**MATH310. INTRODUCTION TO MATHEMATICAL MODELING. 4.0 Semester Hrs.**

(S) 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,

(I, II) 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. Prerequisites: 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,

(I, II) 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,

(I) 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,

(II) 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.**

(I, II, S) (WI) 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,

(II) 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,

(I, II, S) 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.**

(I, II) 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, finite-state machines and regular languages. Prerequisite: MATH213 or MATH223 or MATH224. 3 hours lecture; 3 semester hours.

**MATH398. SPECIAL TOPICS. 6.0 Semester Hrs.**

(I, II) 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.**

(I, II) 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,

(I, II) 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-andbound 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.**

(I) 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.**

(I) 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 and MATH332 or MATH342. 3 hours lecture; 3 semester hours.

**MATH432. SPATIAL STATISTICS. 3.0 Semester Hrs.**

(I) 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.**

(II) 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.**

(II) 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 and MATH332 or MATH342. 3 hours lecture; 3 semester hours.

**MATH438. STOCHASTIC MODELS. 3.0 Semester Hrs.**

(II) 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.**

(I) 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,

(I) 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. Prerequisites: MATH307 or CSCI407. 3 hours lecture; 3 semester hours.

**MATH441. COMPUTER GRAPHICS. 3.0 Semester Hrs.**

Equivalent with CSCI441,

(I) 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,

(I, II) This is an advanced computer graphics course, focusing on modern rendering and geometric modeling techniques. Students will learn a variety of mathematical and algorithmic techiques that can be used to develop high-quality computer graphics software. In particular, the crouse will cover global illumination, GPU programming, geometry acquisition and processing, point based graphics and non-photorealistic rendering. Prerequistes: 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,

(I) 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,

(II) 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.**

(I, II) 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. Prerequisites: MATH225 or MATH235 and MATH213 or MATH223 or MATH224. 3 hours lecture; 3 semester hours.

**MATH457. INTEGRAL EQUATIONS. 3.0 Semester Hrs.**

(I) 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.**

(I) 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: MATH300. 3 hours lecture; 3 semester hours.

**MATH459. ASYMPTOTICS. 3.0 Semester Hrs.**

Equivalent with MATH559,

(I) Asymptotic methods are used to find approximate solutions to problems when exact solutions are unavailable or too complicated to be useful. A broad range of asymptotic methods is developed, covering algebraic problems, integrals and differential equations. Prerequisites: MATH213 and MATH225. 3 hours lecture; 3 semester hours.

**MATH472. MATHEMATICAL AND COMPUTATIONAL NEUROSCIENCE. 3.0 Semester Hrs.**

(II) This course will focus on mathematical and computational techniques applied to neuroscience. Topics will include nonlinear dynamics, hysteresis, the cable equation, and representative models such as Wilson-Cowan, Hodgkin-Huxley, and FitzHugh-Nagumo. Applications will be motivated by student interests. In addition to building basic skills in applied math, students will gain insight into how mathematical sciences can be used to model and solve problems in neuroscience; develop a variety of strategies (computational, theoretical, etc.) with which to approach novel mathematical situations; and hone skills for communicating mathematical ideas precisely and concisely in an interdisciplinary context. In addition, the strong computational component of this course will help students to develop computer programming skills and apply appropriate technological tools to solve mathematical problems. Prerequisite: MATH331. 3 hours lecture; 3 semester hours.

**MATH474. INTRODUCTION TO CRYPTOGRAPHY. 3.0 Semester Hrs.**

Equivalent with CSCI474,

(II) 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.**

(II) 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.**

(II) 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 MACS491,

(I) (WI) Individual investigation under the direction of a department faculty member. Written report required for credit. Variable - 1 to 3 semester hours. Repeatable for credit to a maximum of 12 hours.

**MATH492. UNDERGRADUATE RESEARCH. 1-3 Semester Hr.**

(II) (WI) 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.**

**MATH499. INDEPENDENT STUDY. 1-6 Semester Hr.**