# Mathematics

## Careers

Career preparation starts your first year at Western. Visit Career Services in Library 120 and online at western.edu/career to discover your interests, define your goals and land your dream job.

The data below is automatically collected by Burning Glass Technologies, a firm that sources job market data and provides analytics. The statistics illustrate general trends in U.S. careers, but do not precisely represent every job and salary.

## Courses

For required courses and degree plans, visit the official University Catalog. Below is a general overview of courses at Western Colorado University related to this area of study.

** CS 190 - Computer Science I (3 cred.)**

An introduction to software development taught in Python. Topics include control structures, I/O, functions, strings, lists, files, other data structures and basic algorithms that use them. Emphasis is placed on good problem-solving practices, testing and debugging.

** CS 191 - Computer Science II (3 cred.)**

A continuation of CS 190 taught in C++. Students develop applications of increasing sophistication. Topics include control structures, I/O, functions, strings, arrays, files, objects and classes, elementary searching and sorting algorithms. Emphasis is placed on software engineering and an introduction to object-oriented programming. Prerequisite: CS 190 with a minimum grade of “C-”.

** MATH 105 - Mathematics for the Liberal Arts (3 cred.)**

Topics may include practical applications such as personal finance and numbers in the media, along with aesthetic applications such as connections between mathematics and art or music. GT-MA1

** MATH 151 - Calculus I (4 cred.)**

A study of differential calculus, including limits, continuous functions, Intermediate Value Theorem, tangents, linear approximation, inverse functions, implicit differentiation, extreme values and the Mean Value Theorem. This course also introduces Integral calculus including anti-derivatives, definite integrals, and the Fundamental Theorem of Calculus. Prerequisite: ACT math score of 27 or above; SAT math score of 630 or above; MATH 141 with a minimum grade of C-; or Accuplacer university-level mathematics test with a score of 95 or above. GT-MA1

** MATH 213 - Probability and Statistics (3 cred.)**

A course in the use of statistical techniques to draw knowledge from data. Topics include exploratory data analysis, descriptive statistics, t-procedures, ANOVA, chi squared procedures, regression, and non-parametric tests. Statistical software is used extensively to analyze real data sets. Prerequisite: MATH 141 with a minimum grade of C-, or Accuplacer university-level mathematics test score of 85 or above; or instructor permission. GT-MA1

** MATH 220 - Introduction to Advanced Mathematics (3 cred.)**

Students develop and use elementary logic and set theory to construct deductive proofs with relations, functions, and some algebraic structures. Topics include indexing, equivalence relation theory, and cardinality. Prerequisite: MATH 151 with a minimum grade of "C-."

** MATH 251 - Calculus II (4 cred.)**

Topics include techniques of integration, area computations, improper integrals, infinite series and various convergence tests, power series, Taylor's Formula, polar coordinates, and parametric curves. Prerequisite: MATH 151 with a minimum grade of "C-."

** MATH 252 - Calculus III (4 cred.)**

Topics include calculus of functions of several variables, differentiation and elementary integration, vectors in the plane and space. Prerequisite: MATH 251 with a minimum grade of "C-."

** MATH 260 - Applied Linear Algebra (3 cred.)**

A course in the techniques and applications of linear algebra. The core topics include solving systems of linear equations, eigenvalues and eigenvectors, matrix decomposition, the pseudoinverse and least squares approximations, and the singular value decomposition. The theory is supplemented with extensive applications and computer programming. Prerequisite: MATH 141.

** MATH 300 - Introduction to Mathematical Modeling (3 cred.)**

Designed to teach the basic principles of mathematical modeling and applied mathematics. Techniques from calculus, statistics, and probability are utilized to model real-world problems. Analytic and numeric tools are used to implement the models, obtain predictions and investigate underlying mechanisms. Topics include dimensional analysis, curve fitting, simulations, differential and difference equations. Prerequisites: MATH 251 and MATH 213 with minimum grades of "C-."

** MATH 313 - Statistical Modeling and Simulation (3 cred.)**

A study of statistical techniques used to model and simulate stochastic processes. The core topics include linear and nonlinear multivariate models, generalized additive models, time series models with auto-correlated error, and mixed effects models. Emphasis is placed on computational techniques appropriate to large data sets and data visualization. Prerequisites: MATH 213 or ECON 216, MATH 260, CS190.

** MATH 314 - Applied Probability (3 cred.)**

A study of the basic principles of probability theory and their applications. Topics include combinational analysis, conditional probabilities, discrete and continuous random variables, and measures of centrality and variance. Emphasis is placed on applications using probability distributions (including binomial, geometric, Poisson, uniform, exponential, and normal distributions) to assess and manage risk in the fields of finance, insurance, medicine, and quality control. Prerequisite: MATH 251 with a grade C- or better.

** MATH 317 - Genome Analysis (3 cred.)**

This course introduces students to the appropriate mathematical techniques to answer questions about information contained in genetic sequences. These techniques may include dynamic programming, motif similarity, Bayesian models, hidden Markov models, principal component analysis, and clustering. Students use standard genome query tools to annotate genomic DNA. MATH 317 and BIOL 317 cannot both be taken for credit. Prerequisite: MATH 213 and either MATH 161 or CS 190.

** MATH 330 - Topics in Geometry (3 cred.)**

An introduction to modern geometries. Topics include synthetic, analytic, vector, and transformational approaches to geometry. Classification of geometries, axiomatics, and the application of geometry may also be included. Prerequisite: MATH 220 with a minimum grade of "C-."

** MATH 354 - Differential Equations (3 cred.)**

A study of the theory and methods for solving ordinary differential equations. Prerequisite: MATH 251 with a minimum grade of "C-."

** MATH 360 - Linear Algebra (3 cred.)**

A study of systems of linear equations, matrix operations, vector spaces, properties of determinants, eigenvalues, eigenvectors, orthogonality and least-squares. Emphasis is placed on theoretical aspects and general vector space properties with proof. Prerequisite: MATH 260, MATH 220 with a minimum grade of ÒC-.Ó

** MATH 370 - History of Mathematics (3 cred.)**

Acquaints the student with the historical development of mathematics. Includes an introduction to the proper methods and accepted formats of written, graphical, and oral communication in mathematics. Prerequisites: MATH 220 and MATH 251 with minimum grades of "C-."

** MATH 414 - Actuarial Mathematics (3 cred.)**

A study of mathematical concepts useful in risk management, including multivariate probability and interest theory. Topics include the Central Limit Theorem, joint distributions, combinations of distributions, conditional and marginal probabilities, time value of money, annuities, and loans. Emphasis is placed on solving problems from the actuarial field, including applications to insurance and business. Prerequisites: MATH 252 with a minimum grade of ÒC-Ò; MATH 314 with a minimum grade of ÒC-.Ó

** MATH 451 - Analysis I (3 cred.)**

An introduction to the theory of calculus. Topics include the usual topology of the reals, sequences, limits, continuity, differentiation, and Riemann integration. Prerequisites: MATH 220 and MATH 251 with minimum grades of C-.

** MATH 471 - Abstract Algebra I (3 cred.)**

An introduction to the theory of groups and rings. The fundamental group properties and concepts including cyclic groups, subgroups, direct products, symmetric groups, cosets, normal subgroups, and the group homomorphism theorems are discussed. Prerequisite: MATH 220 with a minimum grade of C-, and at least three upper-division mathematics credits.

** MATH 495 - Senior Seminar (3 cred.)**

A small group of graduating seniors pursue a practical project necessitating professional levels of problem solving, research, written and oral prowess, critical thinking, and familiarity with core curriculum. Final projects are of high quality, so they can be used by professionals and decision-makers in the field. Prerequisites: senior standing. Corequisite 490.

## Faculty & Staff

### Faculty

Professor of Mathematics, Chair of the Department of Mathematics & Computer Science Phone: 970.943.2111
Email: rcohen@western.edu
Office Location: Hurst Hall 210 |
Professor of Mathematics Phone: 970.943.3234
Email: kfix@western.edu
Office Location: Hurst Hall 216 |

Lecturer of Mathematics Phone: 970.943.2127
Email: ekjosness@western.edu
Office Location: Hurst Hall 108 |
Assistant Professor of Mathematics Phone: 970.943.7063
Email: fmannan@western.edu
Office Location: Hurst Hall 216 |

Assistant Professor of Mathematics Education Phone: 970.943.7061
Email: mmorgan@western.edu
Office Location: Crawford Hall 102 |
Associate Professor of Mathematics Phone: 970.943.3150
Email: jmuskat@western.edu
Office Location: Hurst Hall 112 |

Lecturer of Math Phone: 970.943.7009
Email: arasche@western.edu
Office Location: Hurst Hall 114 |
Mathematics Lecturer Phone: 970.943.7023
Email: sschaefer@western.edu
Office Location: Hurst Hall 106 |

Lecturer of Mathematics Phone: 970.943.2075
Email: ztreisman@western.edu
Office Location: Hurst Hall 110 |

## Scholarships

### Program-Based Scholarships

**Charlesworth, William Memorial Scholarship**

#### Eligibility

- Applied or accepted Western student
- Student is pursuing a major in Mathematics or related Natural Sciences
- Applicant has demonstrated a need for financial assistance
- Demonstrated an interest and is active in inter-collegiate athletics
- Preference should be given to entering freshmen, however all classes are eligible
- Preference should be given to applicants whose study time is limited by family obligations or the need to earn income
- No preference shall be given based on the sex of the applicant
- Preference will be given to applicant from Delta County, CO. or the Western Slope of Colorado

#### Description

Established with the Western Colorado University Foundation to perpetuate the memory of William Charlesworth, a 1954 graduate of Western Colorado University. The express purpose of the fund is to provide financial assistance to student-athletes pursuing majors in mathematics or related natural sciences.

*Award depends on funds available.*

**Selected By: **The chair of Mathematics and Computer Science and a representative from the Athletic Department appointed by the Athletic Director. A representative from the Natural Sciences Department shall be on the selection committee.

#### Application:

Contact the Mathematics & Computer Science Department or the Athletic Department for application and deadline information.**Mathematics & Computer Science Department:** 970.943.2015 | Hurst Hall 128**Athletic Department:** 970.943.2079 | Paul Wright Gym 201.

**Dorgan, William E. Memorial Math Scholarship**

#### Eligibility

- Full-time Western Students
- Must be a declared Mathematics major
- Must have a GPA 3.0 or greater

#### Description

This scholarship is provided by the estate and family to celebrate the memory of William E. Dorgan.

*Award depends on funds available*

**Selected by: **Western Mathematics faculty in consultation with the Office of Admissions and Financial Aid as needed.

#### Application:

Contact the Mathematics & Computer Information Science Department for application and deadline information.

970.943.2015 | Hurst Hall 128

**Mathematical Studies Scholarship**

#### Eligibility

- Students has successfully completed a minimum of 24 credits at Western (at least 6 apply towards their major)
- Must be a declared major in Mathematics
- Must have a GPA of 3.0 or higher in math at Westen that apply towards the major
- Must be enrolled for at least nine credits at Western during the semester of application
- Financial need and the student's contribution to the math program will be considered

#### Description

This scholarship is provided by the friends of the Mathematics program.

*Varies depending upon funds available.*

**Selected By: **Donor Scholarship Committee.

#### Application:

Contact the Mathematics & Computer Science Department for application and deadline information.

970.943.2015 | Hurst Hall 128

**Calkins-Barge Mathematics Scholarship**

#### Eligibility

Applicants for the Calkins-Barge Mathematics Scholarship:

- Must be a Mathematics major entering junior or senior year and having satisfactorily completed Mathematics 220, Introduction to Advanced Mathematics.
- Must have a GPA of 2.670 or higher.
- Preference will be given to a current student-athlete (NCAA sport) or a first responder.
- If a student-athlete (NCAA sport), preference will be given to members of the Wrestling Team.
- If a first responder, applicant must be an active member with a Gunnison Valley Service Provider and preference will be given to members of the Gunnison Volunteer Fire Department.
- Recipients may reapply unless they fail to maintain eligibility.

#### Description

The Calkins-Barge Mathematics Scholarship has been established by Glenn R. and Leila M. (Barge) Calkins to provide scholarship assistance to Western students majoring in mathematics. This scholarship serves to honor Western Graduates: Hazel, Glenn's mother (Elementary Education - 1932); Glenn (Mathematics and Physics -1962); Shane (Mathematics - 2016), Glenn and Leila's son. This Scholarship also honors Glenn and Leila, who taught in the Mathematics & Computer Science Department at Western. Glenn taught from 1978-2000, and Leila from 1986-2009. Finally, we honor William Calkins, Glenn's father who attended and was employed at Western, and Jesse and Mary Barge, Leila's parents, who fell in love with Western and the Gunnison Valley.

#### Application Procedures

Individuals interested in being considered for this scholarship must contact the Mathematics & Computer Science Department and the Financial Aid Office for scholarship application information.

The deadline for applying shall be April 1 to be considered for the following academic year.

The Mathematics faculty and Financial Aid staff will assemble those applications which meet the stated criteria. Recipients will be selected by Glenn and Leila Calkins, in consultation with the Director of Financial Aid.

## Get Involved

A college education is more than just taking courses. Meet new people, apply your skills and stretch beyond your comfort zone. Make your education an experience.

**Conferences:**Students and faculty travel to two conferences each year.

**Seminars:**Faculty show what they have been working on and students present their research projects.

**Tutoring Jobs:**Available to students interested in teaching others and mastering basic principles.

Mathematics students learn how to reason their way through unfamiliar territory, find familiar structures, make predictions and answer important questions. In a world saturated with big data, the ability to create meaning out of this information is increasingly relevant and desired in business, finance, engineering, medicine and the sciences. A major or minor in mathematics complements any degree that uses the scientific process.

### Learn More

Reach out for more information about the program.