# Mathematics & Physics Department

## Mathematics Program

The program’s mission is to foster students’ development in quantitative and analytical reasoning skills, powerful mathematical problem-solving strategies, effective techniques for the communication of results and the capacity for lifelong independent learning. The major in mathematics leads to either a Bachelor of Arts (BA) or a Bachelor of Science (BS) degree. The program’s flexible curriculum prepares students for diverse professional careers and for graduate studies. Faculty advisors work directly with majors and minors to design individual programs of study. Students who are potential majors or minors should consult with a faculty advisor as early as possible. Appointments with a faculty advisor can be made anytime by calling the department office.

### Co-Curricular Requirements

Students have the opportunity to broaden and reinforce the academic experience through participation in a variety of co-curricular activities. All students are encouraged to join the CSU Pueblo Math Club. Many students serve as tutors in the Math Learning Center.

## Physics/Physical Science Program

The major in physics leads to a Bachelor of Science (BS) Degree. In addition, supporting courses and general education courses in physics and astronomy are available for students with a wide spectrum of interests, backgrounds and needs. Physics majors must consult with a program advisor as early as possible and must file a departmentally approved plan of study by the beginning of the junior year. A degree plan may be designed based on the student’s interests through consultation with the advisor and the department chair.

### Co-Curricular Requirements

The program faculty believes that students should have co-curricular experiences that complement and reinforce their academic experiences. Therefore, the faculty encourages students to join and participate in events sponsored by the department and the Society of Physics Students (SPS), Sigma Pi Sigma initiations, physics expositions, picnics, graduation dinners, potluck dinners, etc. to foster a spirit of camaraderie.

## Academic Programs

### Mathematics

##### Majors

- Mathematics, Bachelor of Arts
- Mathematics, Bachelor of Science
- Mathematics: Secondary Certification Concentration, Bachelor of Arts
- Math/Physics Double Major, Bachelor of Science

##### Minors

##### Certificates

### Physics

##### Majors

- Physics, Bachelor of Science
- Physics: Physical Science Secondary Certification Concentration, Bachelor of Science
- Physics: Physics Secondary Certification Concentration, Bachelor of Science
- Math/Physics Double Major, Bachelor of Science

##### Minors

## Mathematics (MATH)

**MATH 091**

**Special Topics**

**(1-4 V)**

As Needed.

Special topics are offered to students in areas where regular course offerings are not available. This course does not count toward graduation.

Prerequisite: None.

Corequisite: None.

Registration Information: Satisfactory placement exam score.

**MATH 096**

**College Prep Math 1**

**3(3-)**

Fall, Spring.

Operations with real numbers. Solving and graphing linear equations with applications. Polynomial addition, subtraction, multiplication and division. This course does not count toward graduation.

Prerequisite: None.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

**MATH 097**

**College Prep Math 2**

**3(3-)**

Fall, Spring.

Factoring polynomials, solving polynomial equations. Rational expressions and equations with applications. Inequalities and absolute value. Quadratic functions with applications. This course does not count towards graduation.

Prerequisite: MATH 096.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

**MATH 101**

**Introductory College Mathematics (GT-MA1)**

**3(3-0)**

Fall, Spring, Summer.

Solving systems of linear equations. Introduction to functions. Operations with radical expressions. Solving radical equations. Exponential and logarithmic functions with applications.

Prerequisite: MATH 096.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 109**

**Mathematical Explorations (GT-MA1)**

**(3 V)**

Fall, Spring.

Emphasis on quantitative reasoning and problem solving. Topics chosen from: logic, sets, algebra, linear programming, probability, statistics, number theory, geometry, voting theory and graph theory.

Prerequisite: MATH 097.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 120**

**College Algebra (GT-MA1)**

**3(3-0)**

Fall, Spring.

Solutions of algebraic equations, graphs of rational functions, exponential and logarithmic functions.

Prerequisite: MATH 101.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 122**

**College Trigonometry**

**(3 V)**

As Needed.

Trigonometric and circular functions, identities, inverse functions, vectors, complex numbers.

Prerequisite: MATH 120.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

**MATH 124**

**Pre-Calculus (GT-MA1)**

**5(5-0)**

Fall, Spring.

Polynomial, rational, exponential and logarithmic functions; solution of systems of equations; trigonometric, circular and certain special functions.

Prerequisite: MATH 120.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 126**

**Calculus and Analytic Geometry I (GT-MA1)**

**5(5-0)**

Fall, Spring.

Introduction to limits, continuity, differentiation and integration with selected applications.

Prerequisite: MATH 124.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 156**

**Introduction to Statistics (GT-MA1)**

**3(3-0)**

Fall, Spring, Summer.

Introduction to data analysis. Binomial and normal models. Sample statistics, confidence intervals, hypothesis tests, linear regression and correlation, and chi-square tests.

Prerequisite: MATH 101.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 191**

**Special Topics**

**(1-5 V)**

As Needed.

Special topics suitable for entry level math students.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor or department chair.

**MATH 207**

**Matrix and Vector Algebra with Applications**

**3(3-0)**

Fall, Spring.

Systems of equations, matrices, inverses, determinants, eigenvalues and eigenvectors, scalar and cross-product, selected applications.

Prerequisite: MATH 124.

Corequisite: None.

Registration Information: None.

**MATH 220**

**Quantitative Analysis for Business**

**4(4-0)**

Fall, Spring, Summer.

An introduction to quantitative methods required for business studies, including linear programming, probability and statistics.

Prerequisite: MATH 101.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

**MATH 221**

**Applied Calc: An Intuitive Approach (GT-MA1)**

**4(4-0)**

Fall, Spring.

Non-rigorous introduction to calculus with emphasis on applications and modeling in the life sciences, social and behavioral sciences and business.

Prerequisite: MATH 120.

Corequisite: None.

Registration Information: Satisfactory placement exam score or equivalent.

(GT-MA1)

**MATH 224**

**Calculus and Analytic Geometry II**

**5(5-0)**

Fall, Spring.

Differentiation and integration of transcendental functions, infinite sequences and series, parametric curves, and applications.

Prerequisite: MATH 126.

Corequisite: None.

Registration Information: None.

**MATH 242**

**Introduction to Computation**

**4(3-2)**

Spring.

Computer programming and computation with applications. Loops, conditionals, data types and structores, I/O, functions debugging, testing, and documentation. Numerical, graphical, symbolic computation issues and projects.

Prerequisite: MATH 126.

Corequisite: None.

Registration Information: None.

**MATH 291**

**Special Topics**

**(1-5 V)**

As Needed.

Special Topics.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor and approval of the department chair.

**MATH 295**

**Independent Study**

**(1-5 V)**

As Needed.

Independent Study.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 307**

**Introduction to Linear Algebra**

**4(4-0)**

**MATH 319**

**Number Theory**

**(3 V)**

Spring, Odd.

Divisibility, prime numbers, linear congruences, multiplicative functions, cryptology, primitive roots, and quadratic residues.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: None.

**MATH 320**

**Introductory Discrete Mathematics**

**3(3-0)**

Spring.

Introduction to discrete structures with emphasis on logic and proof. Topics selected from graph theory, boolean algebra, combinatorics, binary relations, set theory, functions and sequences.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: None.

**MATH 325**

**Intermediate Calculus**

**4(4-0)**

**MATH 330**

**Introduction to Higher Geometry**

**(3 V)**

Spring, Even.

Euclidean, hyperbolic, finite, and transformation geometries, models, and constructions.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 337**

**Differential Equations I**

**3(3-0)**

Spring.

First order differential equations, homogeneous and non-homogenous linear differential equations, introduction to the Laplace transform, applications.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: None.

**MATH 338**

**Differential Equations II**

**3(3-0)**

Fall, Odd.

Linear systems, existence and uniqueness of solutions, non-linear equations, series solutions, orthogonal sets of functions. Fourier series, boundary value problems, partial differential equations and applications.

Prerequisite: MATH 337.

Corequisite: None.

Registration Information: MATH 325 is recommended as prerequisite.

**MATH 342**

**Introduction to Numerical Analysis**

**3(3-0)**

Spring, Even.

Numerical solutions of polynomial, differential, integral, and other equations using the computer.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: Programming language recommended. Permission of instructor.

**MATH 345**

**Algorithms & Data Structures**

**4(3-2)**

**MATH 350**

**Probability**

**3(3-0)**

Fall.

Introduction to probability theory and stochastic processes. Probability spaces, random variables and their distributions, exponential and Poisson processes, limit theorems and applications.

Prerequisite: MATH 325.

Corequisite: None.

Registration Information: None.

**MATH 356**

**Statistics for Engineers and Scientists**

**3(3-0)**

Spring.

Calculus-based introduction to statistical methods. Sampling distributions, hypothesis testing, linear regression, design of experiments using ANOVA. Data analysis with Minitab.

Prerequisite: MATH 350.

Corequisite: None.

Registration Information: None.

**MATH 360**

**Elementary Mathematics Concepts I**

**3(3-0)**

Fall.

Development of the real number system and related concepts, including sets, numeration systems, whole numbers, integers, number theory and algorithms.

Prerequisite: None.

Corequisite: None.

Registration Information: MATH 101 or MATH 109 recommended as prerequisite. Satisfactory placement score.

**MATH 361**

**Elementary Mathematics Concepts II**

**3(3-0)**

Spring.

Conceptual development of fractions, rational numbers, geometry, measurement, probability and statistics.

Prerequisite: MATH 360.

Corequisite: None.

Registration Information: Satisfactory placement score.

**MATH 362**

**Problem Solving for K-6 Teachers**

**3(3-0)**

Fall.

This course focuses on the process of mathematical problem solving. Students will develop and implement useful heuristics, and reflect on problem solving strategies.

Prerequisite: MATH 361.

Corequisite: None.

Registration Information: Liberal Studies General Education Mathematics requirement met.

**MATH 411**

**Introduction to Topology**

**3(3-0)**

**MATH 421**

**Introduction to Analysis**

**4(4-0)**

Fall.

An introductory course in real analysis providing a rigorous development of the concepts of elementary calculus.

Prerequisite: MATH 307.

Corequisite: None.

Registration Information: Three approved upper division MATH courses.

**MATH 425**

**Complex Variables**

**3(3-0)**

Fall, Even.

An introduction to complex function theory. Complex numbers, sequences and series, the calculus of complex functions, analytic functions, and conformal mappings.

Prerequisite: MATH 325.

Corequisite: None.

Registration Information: None.

**MATH 427**

**Abstract Algebra**

**4(4-0)**

Spring.

Introduction to groups, rings and fields and their elementary properties.

Prerequisite: MATH 307.

Corequisite: None.

Registration Information: Three approved upper division MATH courses.

**MATH 442**

**Machine Learning for Data Analytics**

**3(2-2)**

As Needed.

Implementation of algorithms for supervised and unsupervised learning, to include linear/logistic regression, random forests, naïve Bayes, neural networks, clustering, support vector machines, hidden markov models.

Prerequisite: MATH 242.

Corequisite: None.

Registration Information: None.

**MATH 445**

**Discrete Mathematics**

**3(3-0)**

**MATH 463**

**History of Mathematics**

**3(3-0)**

**MATH 477**

**Methods for Teaching Secondary Math**

**4(3-2)**

Fall, Even.

Topics and issues in secondary mathematics education, including materials development, learning theories, instructional and assessment strategies, curriculum, planning and standards. Sixty hours field experience required.

Prerequisite: MATH 307 or MATH 320.

Corequisite: None.

Registration Information: Acceptance into Teacher Education Program.

**MATH 480**

**Tutoring Practicum**

**(1-2 V)**

As Needed.

Participation in tutoring mathematics in the MLC under the guidance of the MLC Director.

Prerequisite: MATH 224.

Corequisite: None.

Registration Information: Permission of Math Learning Center Director.

**MATH 491**

**Special Topics**

**(1-3 V)**

As Needed.

Special Topics.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 492**

**Research**

**(1-3 V)**

As Needed.

Research project selected by student and supervised by a regular mathematics faculty member.

Prerequisite: None.

Corequisite: None.

Registration Information: Approval of department.

**MATH 493**

**Seminar**

**(1-3 V)**

As Needed.

Seminar.

Prerequisite: None.

Corequisite: None.

Registration Information: Senior standing. Permission of instructor.

**MATH 495**

**Independent Study**

**(1-3 V)**

As Needed.

Independent Study.

Prerequisite: None.

Corequisite: None.

Registration Information: Senior standing. Permission of instructor.

**MATH 498**

**Internship**

**(1-6 V)**

As Needed.

Work experience using the discipline of mathematics under the direction of the selected organization and a faculty member.

Prerequisite: None.

Corequisite: None.

Registration Information: Junior or senior standing. Permission of department chair.

**MATH 501**

**Foundations of Mathematics**

**3(3-0)**

As Needed.

Sets, logic, axiomatics, mappings and the various sub-systems of the reals for beginning graduate students.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 507**

**Linear Algebra**

**3(3-0)**

As Needed.

Vector spaces, linear transformations, matrix representation, canonical form.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 521**

**Intermediate Analysis**

**3(3-0)**

As Needed.

Point set theory, including the Bolzano-Weierstrass and the Heine-Borel theorems, theory of differentiation and Riemann integration, and sequences and series of functions.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 527**

**Abstract Algebra**

**3(3-0)**

As Needed.

Groups, rings, integral domains, quotient rings, ideals, fields, homomorphisms and related topics.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 530**

**Advanced Geometry**

**3(3-0)**

As Needed.

Foundations of geometry, geometric transformations, and applications.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 550**

**Statistical Methods**

**3(3-0)**

As Needed.

Statistical modeling as a framework for the analysis of experimental data. Emphasis on use of statistical software. Regression, ANOVA, variance components, and chisquare tests.

Prerequisite: MATH 156.

Corequisite: None.

Registration Information: None.

**MATH 556**

**(EN 556)**

**Design and Analysis of Experiments**

**3(3-0)**

Summer.

Foundations of experimental design, outline efficient methods to implement experiments, develop statistical methods to sort signal from noise, and analyze information derived from the experiment.

Prerequisite: MATH 256 and MATH 356.

Corequisite: None.

Registration Information: None.

**MATH 577**

**Concepts in Secondary School Mathematics**

**(1-4 V)**

As Needed.

Problems of teaching secondary school mathematics; the slow learner, methods, gifted students, evaluation.

Prerequisite: None.

Corequisite: None.

Registration Information: Permission of instructor.

**MATH 591**

**Special Topics**

**(1-3 V)**

As Needed.

Special Topics.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**MATH 595**

**Independent Study**

**(1-2 V)**

As Needed.

Independent Study.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**MATH 598**

**Graduate Internship**

**(1-4 V)**

As Needed.

Volunteer or paid work experience under the combined supervision of the selected organization and a faculty member.

Prerequisite: None.

Corequisite: None.

Registration Information: Graduate standing.

**MATH 599**

**Thesis Research**

**(1-6 V)**

As Needed.

Thesis Research.

Prerequisite: None.

Corequisite: None.

Registration Information: Graduate standing.

## Physics/Physical Science (PHYS)

**PHYS 110**

**Astronomy (GT-SC2)**

**3(3-0)**

Fall, Spring.

Solar system, including motions of the planets, eclipses, and satellite exploration; classification and evolution of stars; clusters, nebulae, galaxies and the expanding universe.

Prerequisite: MATH 096.

Corequisite: None.

Registration Information: Satisfactory placement score.

(Gen Ed: ST, GT-SC2)

**PHYS 110L**

**Astronomy Lab (GT-SC1)**

**1(0-2)**

**PHYS 140**

**Light, Energy, & the Atom (GT-SC2)**

**3(3-0)**

As Needed.

A non-mathematical approach to light, energy sources, conservation, atoms, nuclei and nuclear radiation. Emphasis on phenomena encountered in everyday life or that affect public policy.

Prerequisite: MATH 096.

Corequisite: None.

Registration Information: Satisfactory placement score.

(Gen Ed: ST, GT-SC2)

**PHYS 140L**

**Light, Energy and the Atom Lab (GT-SC1)**

**1(0-2)**

As Needed.

Optional laboratory to accompany PHYS 140. Experiments in light, solar energy, atomic and nuclear physics with emphasis on qualitative understanding of observations.

Prerequisite: None.

Corequisite: None.

Registration Information: PHYS 140 strongly recommended as co-requisite.

(Gen Ed: ST, GT-SC1)

**PHYS 150**

**(CHEM 150)**

**Elementary Concepts in Phys & Chem**

**4(3-2)**

Spring.

Hands-on standards-based approach to understanding basic concepts of physics and chemistry. Integrated lecture, lab and discussion periods.

Prerequisite: None.

Corequisite: None.

Registration Information: Acceptance into Teacher Education Program.

**PHYS 201**

**Principles of Physics I (GT-SC2)**

**3(3-0)**

Fall, Spring, Summer.

Motion, forces, conservation of energy and momentum, wave motion, sound and heat. For engineering, technology, life sciences, and other interested students.

Prerequisite: MATH 120.

Corequisite: None.

Registration Information: Satisfactory math placement exam score. PHYS 201L strongly recommended as co-requisite.

(Gen Ed: ST, GT-SC2)

**PHYS 201L**

**Principles of Physics Lab I (GT-SC1)**

**1(0-2)**

Fall, Spring, Summer.

Principles of Physics Lab I.

Prerequisite: None.

Corequisite: None.

Registration Information: PHYS 201 strongly recommended as corequisite.

(Gen Ed: ST, GT-SC1)

**PHYS 202**

**Principles Of Physics II (GT-SC2)**

**3(3-0)**

Fall, Spring.

Electrostatics, electromagnetism, light, atomic and nuclear physics.

Prerequisite: None.

Corequisite: None.

Registration Information: PHYS 201L strongly recommended as corequisite.

(Gen Ed: ST, GT-SC2)

**PHYS 202L**

**Principles Of Physics II Lab (GT-SC1)**

**1(0-2)**

Fall, Spring.

Principles Of Physics II Lab.

Prerequisite: None.

Corequisite: None.

Registration Information: PHYS 202 strongly recommended as corequisite.

(Gen Ed: ST, GT-SC1)

**PHYS 221**

**General Physics I**

**4(4-0)**

Spring.

Newtonian mechanics, including linear and rotational dynamics, momentum, energy, gravitation, fluid mechanics, wave motion and thermodynamics. Uses the calculus and vector notation.

Prerequisite: MATH 126.

Corequisite: None.

Registration Information: PHYS 221L strongly recommended as corequisite.

(Gen Ed: ST, GT-SC2)

**PHYS 221L**

**General Physics I Lab**

**1(0-2)**

**PHYS 222**

**General Physics II**

**4(4-0)**

**PHYS 222L**

**General Physics II Lab (GT-SC1)**

**1(0-2)**

Fall, Spring.

General Physics II Lab.

Prerequisite: None.

Corequisite: PHYS 222.

Registration Information: None.

(Gen Ed: ST, GT-SC1)

**PHYS 291**

**Special Topics**

**(1-4 V)**

As Needed.

Special Topics.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**PHYS 293**

**Seminar**

**1(1-0)**

As Needed.

The student attends at least 11 Physics Seminar presentations or other approved presentations and then presents a public seminar presentation on some approved physics-related topic.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**PHYS 301**

**Analytical & Orbital Mechanics**

**4(4-0)**

Fall, Even.

Statics & dynamics of particles & rigid bodies. Conservation principles, minimum principles, accelerated coordinate systems, Lagrangian & Hamiltonian methods. Applications to astrodynamics & oscillations applications.

Prerequisite: MATH 325 and MATH 337 and PHYS 221.

Corequisite: None.

Registration Information: None.

**PHYS 321**

**Thermodynamics**

**3(3-0)**

Spring, Odd.

Introduction to thermodynamic laws and principles, entropy, kinetic theory and statistical mechanics.

Prerequisite: PHYS 221.

Corequisite: None.

Registration Information: None.

**PHYS 322**

**Advanced Laboratory - Thermo**

**1(0-2)**

**PHYS 323**

**General Physics III**

**4(4-0)**

**PHYS 323L**

**General Physics III Lab**

**1(0-2)**

Spring.

Teaches how and why experimental physics is done through representive experiments related to PHYS 323 topics; techniques of good record keeping, data analysis, modeling, instrumentation and presentation of results.

Prerequisite: MATH 242.

Corequisite: None.

Registration Information: PHYS 323 strongly recommended as corequisite.

**PHYS 341**

**Optics**

**3(3-0)**

**PHYS 342**

**Advanced Laboratory-Optics**

**1(0-2)**

**PHYS 431**

**Electricity & Magnetism**

**4(4-0)**

**PHYS 432**

**Advanced Laboratory-Electricity and Magnetism**

**1(0-2)**

Spring, Even.

Develops skills, experience and independence in experimental research design, modeling, data analysis, instrumentation and presentation of results through representative experiments related to PHYS 431.

Prerequisite: MATH 242 and PHYS 431.

Corequisite: None.

Registration Information: None.

**PHYS 441**

**Quantum Mechanics**

**4(4-0)**

**PHYS 480**

**Practicum in Laboratory Instruction**

**1(0-2)**

As Needed.

Participation in laboratory instruction under the guidance of a staff member. Includes instruction on laboratory safety.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**PHYS 491**

**Special Topics**

**(1-4 V)**

As Needed.

Special Topics.

Prerequisite: None.

Corequisite: None.

Registration Information: None.

**PHYS 492**

**Research**

**1(0-2)**

As Needed.

Research.

Prerequisite: None.

Corequisite: None.

Registration Information: Eight credits in upper-division PHYS courses.

**PHYS 493**

**Seminar**

**1(1-0)**

As Needed.

Class members report on recently published work or on their own research in physics or applied physics.

Prerequisite: None.

Corequisite: None.

Registration Information: Advanced standing with a major or minor in physics.

**PHYS 495**

**Independent Study**

**(1-2 V)**

As Needed.

Independent Study.

Prerequisite: None.

Corequisite: None.

Registration Information: Junior or senior standing. Permission of department chair.

**PHYS 498**

**Internship**

**(1-6 V)**

As Needed.

Work experience using the discipline of physics under the direction of the selected organization and a faculty member.

Prerequisite: None.

Corequisite: None.

Registration Information: Junior or senior standing. Permission of department chair.

**PHYS 499**

**Thesis Research**

**1(1-0)**

As Needed.

Students write a research paper describing their own research.

Prerequisite: None.

Corequisite: None.

Registration Information: Senior standing.