# 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.

**The Bachelor of Science Degree in physics is offered with several emphasis areas:**

For the Physics emphasis the recommended sequences of courses presume that the student is ready to begin MATH 126 Calculus and Analytic Geometry I (5 c.h.) in the first term of the freshman year. If not, MATH 124 Pre-calculus Math (5 c.h.) should be taken in the fall and MATH 126 Calculus and Analytic Geometry I (5 c.h.) in the spring of the freshman year concurrently with PHYS 221 General Physics I (4 c.h.). Otherwise it may not be possible to complete the requirements for a physics degree within four years. Students, especially transfers, who do not strictly adhere to the plan of study, may find that the term of attendance at CSU Pueblo will be extended beyond four years.

### Physics Secondary Certification Emphasis

This emphasis provides students with the knowledge and skills necessary to obtain Colorado Department of Education certification as science teachers with an emphasis in physics.

Students completing a major in Physics with an emphasis in Secondary Certification are required to complete a minor in education and meet all other requirements outlined by the Teacher Education Program.

### Physical Science Secondary Certification Emphasis

This emphasis provides students with the knowledge and skills necessary to obtain Colorado Department of Education certification as science teachers with an emphasis in physics and chemistry.

Students completing a major in Physics with an emphasis in Secondary Certification are required to complete a minor in education and meet all other requirements outlined by the Teacher Education Program.

### Double Majors

A Math and Physics double major is also available. See Math Program for details.

A double major with Chemistry, Biology, or Engineering, for example, is possible. Please consult your advisor and the department chair.

### Minors

A minor is available in physics, and is an especially attractive addition to majors in chemistry, engineering or mathematics. See the course requirements below.

### 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

- Computational Mathematics, Minor
- Math/Physics Double Major, Bachelor of Science
- Mathematics, Bachelor of Art
- Mathematics, Bachelor of Art: Secondary Certification Emphasis
- Mathematics, Bachelor of Science
- Mathematics, Minor
- Physics, Bachelor of Science: Physical Science Secondary Certification Emphasis
- Physics, Bachelor of Science: Physics Emphasis
- Physics, Bachelor of Science: Physics Secondary Certification Emphasis
- Physics, Minor

## Mathematics (MATH)

### Undergraduate Courses

**MATH 91**

**Special Topics**

**(1-4 V)**

Special topics are offered to students in areas where regular course offerings are not available. This course does not count toward graduation. Prerequisite: Satisfactory placement exam score. (AN) Repeatable (99).

**MATH 96**

**College Prep Math 1**

**3(3-0)**

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: Satisfactory placement exam score. (F, S)

**MATH 97**

**College Prep Math 2**

**3(3-0)**

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: Satisfactory placement exam score or MATH 096 or equivalent. (F, S)

**MATH 101**

**Introductory College Mathematics**

**3(3-0)**

Solving systems of linear equations. Introduction to functions. Operations with radical expressions. Solving radical equations. Exponential and logarithmic functions with applications. Prerequisite: Satisfactory placement exam score or MATH 097 or equivalent. (F, S) (Gen Ed: M, GT-MA1)

**MATH 109**

**Mathematical Explorations**

**(3.0 V)**

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: Satisfactory placement exam score or Math 097 or equivalent. (F,S) (Gen Ed: M, GT-MA1)

**MATH 120**

**Pre-Calculus Algebra**

**3(3-0)**

Solutions of algebraic equations, graphs of rational functions, exponential and logarithmic functions. Prerequisite: Satisfactory placement exam score or Math 101 or equivalent. (F, S) (Gen Ed: M, GT-MA1)

**MATH 122**

**College Trigonometry**

**(3.0 V)**

Trigonometric and circular functions, identities, inverse functions, vectors, complex numbers. Prerequisite: MATH 120 or equivalent. (F,S,SS,E,O)

**MATH 124**

**Pre-calculus Math**

**5(5-0)**

Polynomial, rational, exponential and logarithmic functions; solution of systems of equations; trigonometric, circular and certain special functions. Prerequisite: Satisfactory placement exam score or MATH 120 or equivalent. (F,S) (Gen Ed: M, GT-MA1)

**MATH 126**

**Calculus and Analytic Geometry I**

**5(5-0)**

Introduction to limits, continuity, differentiation and integration with selected applications. Prerequisite: Satisfactory placement exam score or MATH 124 or equivalent. (F, S) (Gen Ed: M, GT-MA1)

**MATH 156**

**Introduction to Statistics**

**3(3-0)**

Introduction to data analysis. Binomial and normal models. Sample statistics, confidence intervals, hypothesis tests, linear regression and correlation, and chisquare tests. Prerequisite: Satisfactory placement exam score or Math 101 or equivalent. (F,S) (Gen Ed: M, GT-MA1)

**MATH 191**

**Special Topics**

**(1-5 V)**

Special topics suitable for entry level math students. Available in S/U grading. Prerequisite: Permission of instructor or approval of the department chair. (AN) Repeatable (99).

**MATH 207**

**Matrix and Vector Algebra with Applications**

**3(3-0)**

Systems of equations, matrices, inverses, determinants, eigenvalues and eigenvectors, scalar and cross-product, selected applications. Prerequisite: MATH 124 (F, S)

**MATH 220**

**Quantitative Analysis for Business**

**4(4-0)**

An introduction to quantitative methods required for business studies, including linear programming, probablity and statistics. Prerequisite: Satisfactory placement exam score or Math 101 or equivalent. (F,S)

**MATH 221**

**Applied Calc: An Intuitive Approach**

**4(4-0)**

Non-rigorous introduction to calculus with emphasis on applications and modeling in the life sciences, social and behavioral sciences and business. Prerequisite: Satisfactory placement exam score or MATH 120 or equivalent. (F,S) (Gen Ed: M, GT-MA1)

**MATH 224**

**Calculus and Analytic Geometry II**

**5(5-0)**

Differentiation and integration of transcendental functions, infinite sequences and series, parametric curves, and applications. Prerequisite: MATH 126. (F, S)

**MATH 242**

**Introduction to Computation**

**4(3-2)**

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. (S)

**MATH 291**

**Special Topics**

**(1-5 V)**

Special Topics. Prerequisite: Permission of instructor and approval of the department chair. (AN) Repeatable (99).

**MATH 295**

**Independent Study**

**(1-5 V)**

Independent Study. Prerequisite: Permission of instructor. (AN) Repeatable (99).

**MATH 307**

**Introduction to Linear Algebra**

**4(4-0)**

**MATH 319**

**Number Theory**

**(3.0 V)**

Divisibility, prime numbers, linear congruences, multiplicative functions, cryptology, primitive roots, and quadratic residues. Prerequisite: MATH 224 (F,S,SS,E,O)

**MATH 320**

**Introductory Discrete Mathematics**

**3(3-0)**

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: A grade of C or better in MATH 224. (AN)

**MATH 325**

**Intermediate Calculus**

**4(4-0)**

**MATH 330**

**Introduction to Higher Geometry**

**(3.0 V)**

Euclidean, hyperbolic, finite, and transformation geometries, models, and constructions. Prerequisite: MATH 224 or permission of instructor. (F,S,SS,E,O)

**MATH 337**

**Differential Equations I**

**3(3-0)**

First order differential equations, homogeneous and non-homogenous linear differential equations, introduction to the Laplace transform, applications. Prerequisite: MATH 224 or equivalent. (F, S)

**MATH 338**

**Differential Equations II**

**3(3-0)**

**MATH 342**

**Introduction to Numerical Analysis**

**3(3-0)**

Numerical solutions of polynomial, differential, integral, and other equations using the computer. Prerequisite: MATH 224 and a programming language, or permission of instructor. (AN)

**MATH 345**

**Algorithms and Data Structures**

**4(3-2)**

**MATH 350**

**Probability**

**3(3-0)**

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. (F)

**MATH 356**

**Statistics for Engineers and Scientists**

**3(3-0)**

Calculus-based introduction to statistical methods. Sampling distributions, hypothesis testing, linear regression, design of experiments using ANOVA. Data analysis with Minitab. Prerequisite: MATH 350. (S)

**MATH 360**

**Elementary Mathematics Concepts I**

**3(3-0)**

Development of the real number system and related concepts, including sets, numeration systems, whole numbers, integers, number theory and algorithms. Recommended MATH 109. Prerequisite: Satisfactory placement score. (F)

**MATH 361**

**Elementary Mathematics Concepts II**

**3(3-0)**

Conceptual development of fractions, rational numbers, geometry, measurement, probability and statistics. Prerequisite: MATH 360 and satisfactory placement score. (S)

**MATH 362**

**Problem Solving for K-6 Teachers**

**3(3-0)**

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 and Liberal Studies General Education Mathematics requirement met. (F,S)

**MATH 411**

**Introduction to Topology**

**3(3-0)**

**MATH 421**

**Introduction to Analysis**

**4(4-0)**

An introductory course in real analysis providing a rigorous development of the concepts of elementary calculus. Prerequisite: MATH 307 and three approved upper division MATH courses. (F)

**MATH 425**

**Complex Variables**

**3(3-0)**

An introduction to complex function theory. Complex numbers, sequences and series, the calculus of complex functions, analytic functions, and conformal mappings. Prerequisite: MATH 325. (AN)

**MATH 427**

**Abstract Algebra**

**4(4-0)**

Introduction to groups, rings and fields and their elementary properties. Prerequisite: MATH 307 and three approved upper division MATH courses. (S)

**MATH 442**

**Machine Learning for Data Analytics**

**3(2-2)**

**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)**

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: Acceptance into Teacher Education Program and MATH 307 or MATH 320. (F, E)

**MATH 480**

**Tutoring Practicum**

**(1-2 V)**

Participation in tutoring mathematics in the MLC under the guidance of the MLC Director. Prerequisite: MATH 224 and permission of MLC Director. (F, S, SS) Repeatable (2).

**MATH 491**

**Special Topics**

**(1-3 V)**

Special Topics. Prerequisite: Permission of instructor. (AN) Repeatable (99).

**MATH 492**

**Research**

**(1-3 V)**

Research project selected by student and supervised by a regular mathematics faculty member. Prerequisite: Department approval. (AN) Repeatable (99).

**MATH 493**

**Seminar**

**(1-3 V)**

Seminar. Prerequisite: Senior standing and permission of instructor. (AN) Repeatable (99).

**MATH 495**

**Independent Study**

**(1-3 V)**

Independent Study. Prerequisite: Senior standing and permission of instructor. (AN) Repeatable (99).

**MATH 498**

**Internship**

**(1-6 V)**

Work experience using the discipline of mathematics under the direction of the selected organization and a faculty member. Prerequisite: Junior or senior standing and permission of the department chair. (AN) Repeatable (99).

### Graduate Courses

**MATH 501**

**Foundations of Mathematics**

**3(3-0)**

Sets, logic, axiomatics, mappings and the various sub-systems of the reals for beginning graduate students. Prerequisite: Permission of instructor. (AN)

**MATH 507**

**Linear Algebra**

**3(3-0)**

Vector spaces, linear transformations, matrix representation, canonical form. Prerequisite: Permission of instructor. (AN)

**MATH 521**

**Intermediate Analysis**

**3(3-0)**

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: Permission of instructor. (AN)

**MATH 527**

**Abstract Algebra**

**3(3-0)**

Groups, rings, integral domains, quotient rings, ideals, fields, homomorphisms and related topics. Prerequisite: Permission of instructor. (AN)

**MATH 530**

**Advanced Geometry**

**3(3-0)**

Foundations of geometry, geometric transformations, and applications. Prerequisite: Permission of instructor. (AN)

**MATH 550**

**Statistical Methods**

**3(3-0)**

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 or equivalent within the last five years. (AN)

**MATH 556**

**(EN 556)**

**Design and Analysis Of Experiments**

**3(3-0)**

Foundations of experimental design, outline efficient methods to implement experiments, develop statistical methods to sort signal from noise, analysis of variance and response surface models. Prerequisite: Permission of instructor. (AN)

**MATH 577**

**Concepts in Secondary School Mathematics**

**(1-4 V)**

Problems of teaching secondary school mathematics; the slow learner, methods, gifted students, evaluation. Prerequisite: Permission of instructor. (AN)

**MATH 591**

**Special Topics**

**(1-3 V)**

Special Topics. (AN) Repeatable (99).

**MATH 595**

**Independent Study**

**(1-2 V)**

Independent Study. (AN) Repeatable (99).

**MATH 598**

**Graduate Internship**

**(1-4 V)**

Volunteer or paid work experience under the combined supervision of the selected organization and a faculty member. Prerequisite: Graduate standing. (AN) Repeatable (99).

**MATH 599**

**Thesis Research**

**(1-6 V)**

Thesis Research. Prerequisite: Graduate student status. (AN) Repeatable (99).

## Physics/Physical Science (PHYS)

### Undergraduate Courses

**PHYS 110**

**Astronomy**

**3(3-0)**

Solar system, including motions of the planets, eclipses, and satellite exploration; classification and evolution of stars; clusters, nebulae, galaxies and the expanding universe. Prerequisite: Pre or corequisite: satisfactory placement score or MATH 096. (F,S) (Gen Ed: ST, GT-SC2)

**PHYS 110L**

**Astronomy Lab**

**1(0-2)**

**PHYS 140**

**Light, Energy, & the Atom**

**3(3-0)**

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: Pre or corequisite: satisfactory placement score or MATH 096.(F,S) (Gen Ed: ST, GT-SC2)

**PHYS 140L**

**Light, Energy and the Atom Lab**

**1(0-2)**

**PHYS 150**

**(CHEM 150)**

**Elementary Concepts in Phys & Chem**

**4(3-2)**

Hands-on standards-based approach to understanding basic concepts of physics and chemistry. Integrated lecture, lab and discussion periods. Recommended: enrollment in the Teacher Education Program. (S)

**PHYS 201**

**Principles of Physics I**

**3(3-0)**

**PHYS 201L**

**Principles of Physics Lab I**

**1(0-2)**

Principles of Physics Lab I. Prerequisite: Pre or corequisite: PHYS 201. (F, S) (Gen Ed: ST, GT-SC1)

**PHYS 202**

**Principles Of Physics II**

**3(3-0)**

Electrostatics, electromagnetism, light, atomic and nuclear physics. Prerequisite: Pre or corequisite: PHYS 201. (F, S) (Gen Ed: ST, GT-SC2)

**PHYS 202L**

**Principles Of Physics II Lab**

**1(0-2)**

Principles Of Physics II Lab. Prerequisite: Pre or corequisite: PHYS 202. (F, S) (Gen Ed: ST, GT-SC1)

**PHYS 221**

**General Physics I**

**4(4-0)**

Newtonian mechanics, including linear and rotational dynamics, momentum, energy, gravitation, fluid mechanics, wave motion and thermodynamics. Uses the calculus and vector notation. For majors in physics, mathematics, geoscience, engineering and chemistry. Prerequisite: MATH 126. Pre or corequisite: PHYS 221L. (F, S) (Gen Ed: ST, GT-SC2)

**PHYS 221L**

**General Physics I Lab**

**1(0-2)**

General Physics I Lab. Prerequisite: Pre or corequisite: PHYS 221. (F, S) (Gen Ed: ST, GT-SC1)

**PHYS 222**

**General Physics II**

**4(4-0)**

**PHYS 222L**

**General Physics II Lab**

**1(0-2)**

General Physics II Lab. Corequisite: PHYS 222. (F, S) (Gen Ed: ST, GT-SC1)

**PHYS 291**

**Special Topics**

**(1-4 V)**

Special Topics. (AN) Repeatable (99).

**PHYS 293**

**Seminar**

**1(1-0)**

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. (AN) Repeatable (99).

**PHYS 301**

**Analytical and Orbital Mechanics**

**4(4-0)**

**PHYS 321**

**Thermodynamics**

**3(3-0)**

Introduction to thermodynamic laws and principles, entropy, kinetic theory and statistical mechanics. Prerequisite: PHYS 221. (F, E)

**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)**

**PHYS 341**

**Optics**

**3(3-0)**

**PHYS 342**

**Advanced Laboratory-Optics**

**1(0-2)**

**PHYS 431**

**Electricity and Magnetism**

**4(4-0)**

**PHYS 432**

**Advanced Laboratory-Electricity and Magnetism**

**1(0-2)**

**PHYS 441**

**Quantum Mechanics**

**4(4-0)**

**PHYS 480**

**Practicum in Laboratory Instruction**

**1(0-2)**

Participation in laboratory instruction under the guidance of a staff member. Includes instruction on laboratory safety. (F, S) Repeatable (2).

**PHYS 491**

**Special Topics**

**(1-4 V)**

Special Topics. (AN) Repeatable (99).

**PHYS 492**

**Research**

**1(0-2)**

Research. Prerequisite: Eight credits in upper-division physics courses. (F, S) Repeatable (99).

**PHYS 493**

**Seminar**

**1(1-0)**

Class members report on recently published work or on their own research in physics or applied physics. Prerequisite: Advanced standing with a major or minor in physics. (S, O) Repeatable (2).

**PHYS 495**

**Independent Study**

**(1-2 V)**

Independent Study. Prerequisite: Junior or senior standing; permission of department chair. (AN) Repeatable (99).

**PHYS 498**

**Internship**

**(1-6 V)**

Work experience using the discipline of physics under the direction of the selected organization and a faculty member. Prerequisite: Junor or senior standing and permission of the department chair. (AN) Repeatable (99).

**PHYS 499**

**Thesis Research**

**1(1-0)**

Students write a research paper describing their own research. Prerequisite: Senior standing in the department. (F, S) Repeatable (99).