2021-2022 Academic Catalog

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Mathematics (MATH)

MATH 1010 -  Mathematics for the Liberal Arts  (3 Credits)  

Designed to give liberal arts students the skills required to understand and interpret quantitative information that they encounter in the news and in their studies, and to make quantitatively-based decisions in their lives. Topics include a survey of logic and analysis of arguments, identifying fallacies in reasoning, working with numbers and units, linear and exponential relations and essentials of probability and statistics. The emphasis is on applications with case studies in economics, finance, environmental sciences, health, music and science. Note: This course assumes that students have knowledge equivalent to three years of high school mathematics (two years of algebra). Requisite: In order to promote student success, any student who has an ACT MATH score less than 19 (or equivalently an SAT MATH score less than 520) AND a H.S. GPA of less than 3.25 will be required to enroll in the one credit hour co-requisite workshop MATH 1011. Term offered: fall, spring, summer. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1

Grading Basis: Letter Grade

In order to promote student success, any student who has an ACT MATH score less than 19 (or equivalently an SAT MATH score less than 520) AND a H.S. GPA of less than 3.25 will be required to enroll in the one credit hour co-requisite workshop MATH 1011.

Additional Information: Denver Core Requirement, Mathematics; GT courses GT Pathways, GT-MA1, Mathematics.

MATH 1011 -  Math for Liberal Arts Workshop  (1 Credit)  

Prepares students for college-level mathematics. Students receive one-on-one and small-group instruction on mathematics topics related to college level mathematics success. Coreq: MATH 1010. Term offered: fall, spring. Max hours: 1 Credit.

Grading Basis: Letter Grade

Coreq: MATH 1010

MATH 1060 -  Finite Mathematics  (3 Credits)  

This course is designed to introduce students to mathematics topics commonly encountered by business students. This course meets the universities CORE mathematics requirement. The topics include linear equations and inequalities, linear, quadratic, exponential and logarithmic functions, simple, compound and continuous interest, future and present value annuities, amortization, systems of equations, linear programming, logic, sets and probability. Graphing technology is used extensively and business applications are emphasized throughout. Terms offered: Fall and Spring. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Additional Information: Denver Core Requirement, Mathematics.

MATH 1070 -  College Algebra for Business  (3 Credits)  

Covers the same mathematical topics as College Algebra, MATH 1110, but with business applications. Note: Graphics calculator required. Note: Students may not receive credit for this course if they have already received credit for MATH 1110 or MATH 1130. Note: 24 on ACT-Math, 560 on SAT-Math or above average performance in intermediate algebra, algebraic literacy or integrated math are strongly recommended as preparation for this course. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics.

MATH 1080 -  Calculus for Social Sciences and Business  (3 Credits)  

A one-semester course in single-variable calculus. Topics include limits, derivatives, differentiation rules, integration and integration rules. Emphasis is on applications to business and social sciences. Note: No knowledge of trigonometry is required. Those planning to take more than one semester of calculus should take MATH 1401 instead of MATH 1080. MATH 1070 or MATH 1110 with a C- or higher is required for students to register for this course. No co-credit with MATH 1401. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 1070 or MATH 1110 with a C- or higher

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 1108 -  Stretch College Algebra-Part 1  (3 Credits)  

This course is the first half of a two-semester sequence (consisting of MATH 1108 followed by MATH 1109). The two-semester course sequence is equivalent to MATH 1110 (College Algebra). The topics in algebra are designed for students who intend to take the calculus sequence. An in-depth study of functions, linear and quadratic equations, circles, inequalities, domain & range, piecewise and transformation of functions, mathematical modeling and select other topics are explored. Desmos graphing technology is used extensively and students will review algebraic skills such as factoring and completing the square, graphing techniques and function properties where needed. Applications are emphasized. Note: No co-credit with MATH 1070, MATH 1110 or MATH 1130. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 1109 -  Stretch College Algebra-Part 2  (3 Credits)  

This course is the second half of a two-semester sequence (consisting of MATH 1108 followed by MATH 1109). The two semester course sequence is equivalent to MATH 1110 (College Algebra). The topics in algebra are designed for students who intend to take the calculus sequence. Data scatter plots and curve fitting, solving equations, polynomial functions, rational functions, exponential and logarithmic functions and selected other topics are explored. Desmos graphing technology is used extensively and students enrolled in MATH 1109 will review algebraic skills such as solving linear and quadratic equations, factoring and completing the square, graphing techniques and function properties where needed. Applications are emphasized. Note: No co-credit with MATH 1070, MATH 1110 or MATH 1130. Prerequisite: MATH 1108 with a C- or higher. Max hours: 3 Credits.

Grading Basis: Letter Grade

Pre: MATH 1108 with C- or higher.

Additional Information: Denver Core Requirement, Mathematics.

MATH 1110 -  College Algebra  (4 Credits)  

Topics in algebra designed for students who intend to take the calculus sequence. Functions, domains, ranges, graphs, data scatter plots and curve fitting, solving equations and systems of equations, polynomial, rational, exponential and logarithmic functions and other topics. Applications are emphasized. Note: Students may not receive credit for this course if they have already received credit for MATH 1070 or MATH 1130. Prereq: MATH 1109 or MATH 1070 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA10 or MA30 or MA01 Student Group OR ALEKS PPL score 46-100. If you have any questions or concerns about this requisite, please notify MATH.Placement@ucdenver.edu. Term offered: fall, spring, summer. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

MATH 1109 or MATH 1070 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA10 or MA30 or MA01 Student Group OR ALEKS PPL score 46-100.

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 1111 -  First Year Seminar  (3 Credits)  

Restriction: Restricted to Freshman level students. Term offered: Fall. Max hours: 3 Credits.

Grading Basis: Letter Grade

Restriction: Restricted to Freshman level students

MATH 1120 -  College Trigonometry  (3 Credits)  

Topics in trigonometry, analytic geometry, and elementary functions designed for students who intend to take the calculus sequence. Angles and trigonometry functions of acute angles, analytic trigonometry, fundamental trigonometric functions and identities including hyperbolic trigonometry, parametric equations, and polar coordinate system. Graphic calculators and/or computer algebra systems are used extensively. Applications are emphasized. Prereq: MATH 1109 or MATH 1070 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100. If you have any questions or concerns about this requisite, please notify MATH.Placement@ucdenver.edu. Students with a grade of B- or better in MATH 1110 or MATH 1070 pass the course at a much higher rate. No co-credit with MATH 1130. Term offered: fall, spring, summer. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

MATH 1109 or MATH 1070 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100.

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 1130 -  Precalculus Mathematics  (4 Credits)  

Condensed treatment of the topics in MATH 1110 and 1120. Prereq: : MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100. If you have any questions or concerns about this requisite, please notify MATH.Placement@ucdenver.edu. No co-credit with MATH 1070, 1110 or 1120. Term offered: fall, spring, summer. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

MATH 1120 or MATH 1130 or MATH 1401 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100.

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 1376 -  Programming for Data Science  (3 Credits)  

The course introduces scientific computing using Python. Topics will include programming skills such as assignment, control statements, loops, and functions. Applications will focus on mathematical and data science topics. Prereq: MATH 1109 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 or MATH 2830 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 1109 or MATH 1110 or MATH 1120 or MATH 1130 or MATH 1401 or MATH 2830 with a C- or higher OR entry into the MA30 or MA01 Student Group OR ALEKS PPL score 61-100.

MATH 1401 -  Calculus I  (4 Credits)  

First course of a three-semester sequence (MATH 1401, 2411, 2421) in calculus. Topics covered include limits, derivatives, applications of derivatives, and the definite integral. Note: No co-credit with MATH 1080. Prereq:MATH 1109 or MATH 1070 or MATH 1110 with a C- or higher and MATH 1120 with a C- or higher or MATH 1130 with a C- or higher or MATH 1401 with a C- or higher OR entry into the MA01 Student Group OR ALEKS PPL score 76-100. If you have any questions or concerns about this requisite, please notify MATH.Placement@ucdenver.edu. Max Hours: 4 Credits.

Grading Basis: Letter Grade

MATH 1109 or MATH 1070 or MATH 1110 with a C- or higher and MATH 1120 with a C- or higher or MATH 1130 with a C- or higher or MATH 1401 with a C- or higher OR entry into the MA01 Student Group OR ALEKS PPL score 76-100.

Additional Information: Denver Core Requirement, Mathematics; GT courses GT Pathways, GT-MA1, Mathematics.

MATH 1840 -  Independent Study.  (1-3 Credits)  

Repeatable. Max hours: 3 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 3.

MATH 2411 -  Calculus II  (4 Credits)  

The second of a three-semester sequence (MATH 1401, 2411, 2421) in calculus. Topics covered include exponential, logarithmic, and trigonometric functions, techniques of integration, indeterminate forms, improper integrals and infinite series. Prereq: C- or better in MATH 1401. Note: Students with a grade of B- or better in MATH 1401 pass this course at a much higher rate. Term offered: fall, spring, summer. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

Prereq: C- or better in MATH 1401

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 2421 -  Calculus III  (4 Credits)  

The third of a three-semester sequence in Calculus (MATH 1401, 2411 and 2421). Topics include vectors, vector-valued functions, partial differentiation, differentiation, multiple integration, and vector calculus. Prereq: C- or better in MATH 2411. Note: Students with a grade of B- or better in MATH 2411 pass this course at a much higher rate. Term offered: fall, spring, summer. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1

Grading Basis: Letter Grade

Prereq: C- or better in MATH 2411

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 2810 -  Topics  (1-3 Credits)  

Topics in mathematics with various subtitles reflecting course content. Prereq: permission of instructor. Repeatable. Max Hours: 6 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 6.

MATH 2830 -  Introductory Statistics  (3 Credits)  

Basic statistical concepts, summarizing data, probability concepts, distributions, confidence intervals, hypothesis testing. Note: This course assumes that students have knowledge equivalent to three years of high school mathematics (two years of algebra), intermediate algebra, or Algebraic Literacy at a Colorado Community College at the start of class. Students who have a grade of B- or better in one of these courses pass at a much higher rate. Term offered: fall, spring, summer. Requisite: In order to promote student success, any student who has an ACT MATH score less than 19 (or equivalently an SAT MATH score less than 520) AND a H.S. GPA of less than 3.25 will be required to enroll in the one credit hour co-requisite workshop MATH 2831. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1.

Grading Basis: Letter Grade

In order to promote student success, any student who has an ACT MATH score less than 19 (or equivalently an SAT MATH score less than 520) AND a H.S. GPA of less than 3.25 will be required to enroll in the one credit hour co-requisite workshop MATH 2831.

Additional Information: GT courses GT Pathways, GT-MA1, Mathematics; Denver Core Requirement, Mathematics.

MATH 2831 -  Introductory Statistics Workshop  (1 Credit)  

Prepares students for college-level mathematics. Students receive one-on-one and small-group instruction on mathematics topics related to college level mathematics success. Co-req: MATH 2830. Term offered: fall, spring. Max hours: 1 Credit.

Grading Basis: Letter Grade

Co-requisite: MATH 2830

MATH 2939 -  Internship  (1-3 Credits)  

Experiences involving application of specific, relevant concepts and skills in supervised employment situations. Note: students must work with the Experiential Learning Center advising to complete a course contract and gain approval. Prereq: 15 hours of 2.75 GPA. Repeatable. Max Hours: 9 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

MATH 3000 -  Introduction to Abstract Mathematics  (3 Credits)  

Students learn to prove and critique proofs of theorems by studying elementary topics in abstract mathematics, including logic, sets, functions, equivalence relations and elementary combinatorics. Coreq: MATH 2421 or MATH 3191. Note: This course assumes that students have taken MATH 2411 or equivalent. Students who have a grade of B- or better in MATH 2411 pass at a much higher rate. Term offered: fall, spring, summer. Max hours: 3 Credits.

Grading Basis: Letter Grade

Coreq: MATH 2421 or MATH 3191

MATH 3041 -  Fundamental Mathematics: Algebra, Probability and Data Analysis  (3 Credits)  

This course is particularly pertinent to prospective elementary teachers, involving algebra, probability and data analysis from a modern approach. Its primary emphasis is asking and answering questions intelligently about our world through the use of algebra, probability, and data analysis. Explorations focus on representing, analyzing, generalizing, formalizing, and communicating patterns and the chances of future events. Mathematics content will be presented in a problem solving and exploratory context, using appropriate instructional tools. This course will not satisfy the requirements for a major in Mathematics. Prereq: MTED 3040 with a C- or higher. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MTED 3040 with a C- or higher.

Additional Information: Denver Core Requirement, Mathematics.

MATH 3191 -  Applied Linear Algebra  (3 Credits)  

Topics include systems of equations, Gaussian elimination with partial pivoting, LU--decomposition of matrices, matrix algebra, determinants, vector spaces, linear transformations, eigen values and applications. Note: No co-credit with MATH 3195. Prereq: C- or better in MATH 2411. Term offered: fall, spring, summer. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: C- or better in MATH 2411

MATH 3195 -  Linear Algebra and Differential Equations  (4 Credits)  

Presents the essential ideas and methods of linear algebra and differential equations, emphasizing the connections between and the applications of both subjects. The course is designed for students in the sciences and engineering. Note: No co-credit with MATH 3200 and MATH 3191. Prerequisite: MATH 2411 with a C- or higher. Term offered: fall, spring, summer. Max hours: 4 Credits.

Grading Basis: Letter Grade

Prereq: C- or better in MATH 2411

MATH 3200 -  Elementary Differential Equations  (3 Credits)  

First and second order differential equations, Laplace transforms, systems of equations, with an emphasis on modeling and applications. Note: No co-credit with MATH 3195. Prerequisite: MATH 2411 with a C- or higher, Co-requisite MATH 3191. Term offered: fall, spring, summer. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prerequisite: MATH 2411 with a C- or higher, Co-requisite MATH 3191.

MATH 3210 -  Higher Geometry I  (3 Credits)  

Studies the foundations of modern geometry by examining axiomatic systems for various geometrics, with an emphasis on non-Euclidean hyperbolic geometry. Prereq: C- or better in MATH 3000. Cross-listed with MCKE 5210. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: C- or better in MATH 3000

MATH 3301 -  Introduction to Optimization  (3 Credits)  

Introduces a mathematical approach for decision-making in practice based on optimization. Students will learn to model, analyze and solve a variety of problems from deterministic operations using both continuous and discrete mathematical programming algorithms and software. Note: this course assumes that students have taken MATH 3191 or MATH 3195 or equivalent. Students who have received a grade of B- or better in MATH 3191 or 3195 pass this course at a much higher rate. Term offered: fall. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 3302 -  Simulation in Operations Research  (3 Credits)  

Elementary stochastic processes and standard nondeterministic operations research models solved by simulation: Markov chains, Poisson process, Monte Carlo and discrete-event simulation, queuing theory, and inventory models. Note: This course assumes that students have programming experience (e.g. MATLAB), and have taken MATH 3191 and MATH 3800 or 4810 or equivalent. Students who have a grade of B- or better in MATH 3191 and MATH 3800 or 4810 pass this course at a much higher rate. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 3376 -  Data Wrangling & Visualization  (3 Credits)  

The course provides an introduction to obtaining, restructuring, and visualizing complex data sets. Students will learn to manipulate many data types, store data in a variety of structures, and construct static and dynamic plots in a variety of contexts. Students earning a B- or better in Math 1376 or 4387 are more likely to be successful in this course than students earning lower grades. Prereq: MATH 1376 or MATH 4387 with a C- or higher and MATH 2830 or MATH 3382 with a C- or higher. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prerequisite: MATH 1376 or MATH 4387 with a C- or higher and MATH 2830 or MATH 3382 with a C- or higher

MATH 3382 -  Statistical Theory  (3 Credits)  

Probability, random variables, properties of distributions, bootstrap methods, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing. Prereq: MATH 2421 with a C- or higher. Term offered: fall, spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 2421 with a C- or higher.

MATH 3440 -  Introduction to Symbolic Logic  (3 Credits)  

Covers truth functional and quantificational logic through polyadic first order predicate calculus and theory of identity. Attention is given to such problems in metatheory as proofs of the completeness and consistency of systems of logic. Cross-listed with PHIL 3440. Term offered: spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Typically Offered: Spring.

MATH 3511 -  Mathematics of Chemistry  (4 Credits)  

Multivariate functions, probability and statistics for chemistry, matrices and vectors, mathematics of reaction kinetics and symmetry point groups. Course covers mathematics needed for CHEM 4511 and 4521. Can also be an elective for the mathematics minor. Prereq: MATH 2411, CHEM 2031 or CHEM 2081, CHEM 2061 or CHEM 2091. Term offered: fall. Max hours: 4 Credits.

Grading Basis: Letter Grade

Prereq: MATH 2411, CHEM 2031 or CHEM 2081, CHEM 2061 or CHEM 2091

Typically Offered: Fall.

MATH 3800 -  Probability and Statistics for Engineers  (3 Credits)  

Basic probability theory, discrete and continuous random variables, point and interval estimation, test of hypotheses, and simple linear regression. Note: no co-credit with MATH 4810. Note: This course assumes that students have taken MATH 2411 and have either previously taken MATH 2421 or are taking MATH 2421 the same semester as MATH 3800. Students who have a grade of B- or better in MATH 2411 pass this course at a much higher rate. Term offered: fall, spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 3939 -  Internship  (1-3 Credits)  

Designed experiences involving application of specific, relevant concepts and skills in supervised employment situations. Note: students must work with the Experiential Learning Center advising to complete a course contract and gain approval. Prereq: Junior standing or higher. Repeatable. Max Hours: 9 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Prereq: junior standing or higher

MATH 4010 -  History of Mathematics  (3 Credits)  

A history of the development of mathematical techniques and ideas from early civilization to the present, including the inter-relationships of mathematics and sciences. Prereq: MATH 2411 with a C- or higher. Coreq: MATH 3000 or 3191. Cross-listed with MATH 5010. Term offered: spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 2411 with a C- or higher Coreq: MATH 3000 or 3191

Typically Offered: Spring.

MATH 4015 -  Capstone Course for Secondary Teachers  (3 Credits)  

High school mathematics from an advanced perspective: analyses of alternative definitions, extensions and generalizations of familiar theorems; discussions of historical contexts in which concepts arose; applications of mathematics. Note: For undergraduate majors, this course only counts toward the mathematics education option. Note: this course assumes that students have taken MATH 3210, 4310 and 3140 or equivalent. Cross-listed with MATH 5015. Max Hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4027 -  Topics in Mathematics  (3 Credits)  

Special topics in mathematics will be covered; consult 'Schedule Planner' for current topics and prerequisites. Repeatable. Max hours: 12 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 12.

MATH 4110 -  Theory of Numbers  (3 Credits)  

Every other year. Topics include divisibility, prime numbers, congruencies, number theoretic functions, quadratic reciprocity, and special diophantine equations, with applications in engineering. Prereq: Grade of C- or better in MATH 3000. Note: Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MATH 5110. Term offered: spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: Grade of C- or better in MATH 3000

MATH 4140 -  Introduction to Modern Algebra  (3 Credits)  

Studies the fundamental algebraic structures used in modern mathematics. Topics include groups, rings, fields and polynomials. Note: This course assumes that students have taken MATH 3000 or equivalent and either MATH 3191 or MATH 3195. Students who have a grade of B- or better in these courses pass at a much higher rate. Cross-listed with MCKE 5140. Prereq: MATH 3000 with a C- or higher. Term offered: spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 3000 with a C- or higher.

MATH 4310 -  Introduction to Real Analysis I  (3 Credits)  

Calculus of one variable, the real number system, continuity, differentiation, integration theory, sequence and series. Prereq: Prereq: Grade of C- or better in MATH 2421 and 3000. Note: Students who have a grade of B- or better in MATH 2421 and 3000 pass this course at a much higher rate. Cross-listed with MCKE 5310. Term offered: fall, spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: Grade of C- (1.7) or better in MATH 2421 and 3000

Typically Offered: Fall.

MATH 4320 -  Introduction to Real Analysis II  (3 Credits)  

Convergence, uniform convergence; Taylor's theorem; calculus of several variables including continuity, differentiation and integration; Picard's theorem in ordinary differential equations and Fourier series. Prereq: MATH 4310 with a C- or higher. Term offered: spring. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 4310 with a C- or higher.

Typically Offered: Spring.

MATH 4337 -  Intro to Statistical and Machine Learning  (3 Credits)  

This is an applied, hands-on course in statistical and machine learning. This course will introduce students to the general framework, best practices, model training, and assessment for machine learning methods from the viewpoint of statistics. Both supervised and unsupervised methods are covered including penalized regression, knearest neighbors, clustering, and neural networks. Additional machine learning topics such as random forests and support vector machines are included as time permits. Ultimately, students will learn how and why to use a particular method, how to validate and explain the results, and apply the methods to real data. Note: It is recommended that students are comfortable learning a statistical computing language such as R or Python as these will be taught alongside the course material. Students with minimal programming experience should expect to spend more time learning the programming language throughout the course. Prereq: MATH 4387 or MATH 5387 or MATH 4830 or MATH 5830 or BIOL 3763 with a C- or higher. Students who have completed a different statistics course that contains regression and computing may seek instructor permission to enroll. Cross-listed with MATH 5337. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 4387 or MATH 5387or MATH 4830 or MATH 5830 or BIOL 3763 with a C- or higher.

MATH 4387 -  Applied Regression Analysis  (3 Credits)  

Topics include simple and multiple linear regression, model diagnostics and remediation, and model selection. Emphasis is on practical aspects and applications of linear models to the analysis of data in business, engineering and behavioral, biological and physical sciences. Prereq: Grade of C- (1.7) or better in MATH 3191 and in MATH 3800 or 4820 or 3382. Note: Students who have a grade of B- or better in MATH 3191, an A in MATH 3800 or a B- or better in MATH 4820 pass this course at a much higher rate. Cross-listed with MATH 5387. Term offered: fall, spring, summer. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: Grade of C- (1.7) or better in MATH 3191 and in MATH 3800 or 4820 or 3382

Typically Offered: Fall.

MATH 4388 -  Machine Learning Methods  (3 Credits)  

Regression, neural networks, clustering, support vector machines, random forests, and other prediction/classification techniques will be used to solve supervised and unsupervised learning problems. This course will connect each topic with the underlying mathematical foundation such as optimization methods and statistical inference. A key focus is deriving the methods and their properties to guide proper application. Students will learn how to apply methods using standard libraries from Python, R, or Matlab. Prereq: MATH 1376 or MATH 3250 and MATH 3382 or MATH 3800 and MATH 3191 or MATH 3195, all with a C- or higher. Cross-listed with MATH 5388. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 1376 or MATH 3250 and MATH 3382 or MATH 3800 and MATH 3191 or MATH 3195, all with a C- or higher.

MATH 4390 -  Game Theory  (3 Credits)  

Zero-sum and non-zero-sum games; Nash equilibrium and the principle of indifference; Shapley value and other concepts of fair division; Evolutionary game theory, ESS, and evolutionary population dynamics. Applications in economics, business, and biology. Note: This course assumes that students have programming experience (e.g. MATLAB), and have taken MATH 2421, 3191 and 3200 or MATH 3195, MATH 3800 or 4810, or equivalent. Students who have a grade of B- or better in these courses pass this course at a much higher rate. Cross-listed with MATH 5390. Max hours: 3 Credits.

Grading Basis: Letter Grade

Typically Offered: Fall, Spring, Summer.

MATH 4394 -  Experimental Designs  (3 Credits)  

Designs covered will include: completely randomized, complete block, split plot, incomplete block, factorial and fractional factorial designs. Additionally, power and study design for non-experimental studies will be covered. Prereq: Grade of C- or better in MATH 4387 or 5387. Cross-listed with MATH 5394. Term offered: spring of even years. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: Grade of C- or better in MATH 4387 or 5387

MATH 4408 -  Applied Graph Theory  (3 Credits)  

Introduces discrete structures and applications of graph theory to computer science, engineering, operations research, social science, and biology. Topics include connectivity, coloring, trees, Euler and Hamiltonian paths and circuits, matching and covering problems, shortest route and network flows. Prereq: MATH 2511 or CSCI 2511 or MATH 3000 with a C- or higher. Note: This course assumes that students have taken MATH/CSCI 2511 or MATH 3000. Students who have a grade of B- or better in MATH/CSCI 2511 or MATH 3000 pass this course at a much higher rateCross-listed with CSCI 4408 and MCKE 5408. Term offered: spring. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 2511 or CSCI 2511 or MATH 3000 with a C- or higher.

Typically Offered: Spring.

MATH 4409 -  Applied Combinatorics  (3 Credits)  

Every other year. Major emphasis is on applied combinatorics and combinatorial algorithms, with applications in computer science and operations. Topics include general counting methods, generating functions, recurrence relations, inclusion-exclusion, and block designs. Prereq: MATH 3000 with a C- or higher. Note: This course assumes that students have taken MATH 3000. Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MCKE 5409. Term offered: fall. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prerequisite: MATH 3000 with a C- or higher.

Typically Offered: Fall.

MATH 4450 -  Complex Variables  (3 Credits)  

Infrequent. Topics include complex algebra, Cauchy-Riemann equations, Laurent expansions, theory of residues, complex integration, and introduction to conformal mapping. Note: This course assumes that students have taken MATH 2421 and MATH 3000. Students who have a grade of B- or better in MATH 2421 and MATH 3000 pass this course at a much higher rate. Term offered: spring of even years. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4650 -  Numerical Analysis I  (3 Credits)  

Methods and analysis of techniques used to resolve continuous mathematical problems on the computer. Solution of linear and nonlinear equations, interpolation and integration. Prereq: MATH 3191 or MATH 3195 with a C- or higher. Cross-listed with CSCI 4650, 5660, and MATH 5660. Term offered: fall, spring. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 3191 or MATH 3195 with a C- or higher.

MATH 4660 -  Numerical Analysis II  (3 Credits)  

Numerical differentiation and integration, numerical solution of ordinary differential equations, and numerical solutions of partial differential equations as time allows. Prereq: MATH 3191 or MATH 3195 with a C- or higher and MATH 3200 with a C- or higher.. Cross-listed with MATH 5661, CSCI 4660 and 5661. Term offered: spring of odd years. Max Hours: 3 Credits.

Grading Basis: Letter Grade

Prerequisite: MATH 3191 or MATH 3195 with a C- or higher and MATH 3200 with a C- or higher.

Typically Offered: Spring.

MATH 4733 -  Partial Differential Equations  (3 Credits)  

Infrequent. Initial/Boundary value problems for first-order, wave, heat and Laplace Equations; maximum principles; Fourier Series and applications. Note: This course assumes that students have taken MATH 2421 and MATH 3200, and either have taken MATH 3000 or have experience with partial differential equations in engineering or physics. Students who have a grade of B- or better in MATH 2421 and MATH 3200 pass this course at a much higher rate. Cross-listed with MATH 5733. Term offered: spring of odd years. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4779 -  Math Clinic  (3 Credits)  

The clinic is intended to illustrate the applicability and utility of mathematical concepts. Research problems investigated originate from a variety of sources--industry, government agencies, educational institutions, or nonprofit organizations. Prereq: consult Schedule Planner or instructor. Cross-listed with MATH 5779. Term offered: fall, spring. Repeatable. Max Hours: 99 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 99.

MATH 4791 -  Continuous Modeling  (3 Credits)  

Every other year. Surveys mathematical problems that arise in natural sciences and engineering. Topics may include population models, epidemic models, mechanics, heat transfer and diffusion, tomography, pharmaco-kinetics, traffic flow, fractal models, wave phenomena, and natural resource management. Most models discussed are based on differential and integral equations. Emphasis is formulation and validation of models as well as methods of solution. Note: This course assumes that students have taken MATH 3191 and MATH 3200. Students who have a grade of B- or better in MATH 3191 and MATH 3200 pass this course at a much higher rate. Cross-listed with MATH 5791. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4792 -  Probabilistic Modeling  (3 Credits)  

Every other year. Markov chains; Poisson processes, continuous time Markov chains, elementary topics in queuing theory, and some mathematical aspects of Monte Carlo simulation, including random variate generation, variance reduction, and output analysis. Note: This course assumes that students have taken MATH 4810 or 5310 and have some programming experience. Students who have a grade of B- or better in MATH 4810 or 5310 pass this course at a much higher rate. Cross-listed with MATH 5792. Term offered: fall. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4793 -  Discrete Math Modeling  (3 Credits)  

Every other year. Focuses on the use of graph theory and combinatorics to solve problems in a wide variety of disciplines. Applications are selected from computer science, communication networks, economics, operations research, and the social, biological and environmental sciences. Note: This course assumes that students have taken MATH 3191 and MATH 4408. Students who have a grade of B- or better in MATH 3191 and MATH 4408 pass this course at a much higher rate. Cross-listed with MATH 5793. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4794 -  Optimization Modeling  (3 Credits)  

Every other year. Principles of model formulation and analysis are developed by presenting a wide variety of applications, both for natural phenomena and social systems. Examples of optimization models to represent natural phenomena include principles of least time and energy. Examples in social systems include resource allocation, environmental control and land management. Specific applications vary, but are chosen to cover a wide scope that considers dichotomies, such as discrete vs. continuous, static vs. dynamic, and deterministic vs. stochastic. Some computer modeling language (like GAMS) is taught. Note: This course assumes that students have taken MATH 2421 and MATH 3191. Students who have a grade of B- or better in MATH 2421 and MATH 3191 pass this course at a much higher rate. Cross-listed with MATH 5794. Max hours: 3 Credits.

Grading Basis: Letter Grade

MATH 4810 -  Introduction to Probability  (3 Credits)  

The course covers axioms of probability, combinatorial probability, conditional probability, random variables (discrete, continuous, and multivariate), expected value (mean, moments, variance, covariance, etc.), limit theorems (laws of large numbers, Central Limit Theorem). Note: No co-credit with MATH 3800. Coreq: MATH 2421. Term offered: fall, spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Coreq: MATH 2421.

MATH 4820 -  Introduction to Mathematical Statistics  (3 Credits)  

Sampling distributions, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing, simple linear regression. Prereq: Grade of C- or better in MATH 3800 or MATH 4810 (preferred). Note: Students who have a grade of A in MATH 3800 or a B- or better in MATH 4810 pass this course at a much higher rate. Term offered: spring. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: Grade of C- or better in MATH 3800 or MATH 4810

Typically Offered: Spring.

MATH 4830 -  Applied Statistics  (3 Credits)  

Review of estimation, confidence intervals and hypothesis testing; Anova; categorical data analysis; non-parametric tests; linear and logistic regression. No co-credit with MATH 4387 or 5387 and doesn't count for Math degrees. Cross-listed with MATH 5830. Prereq: MATH 2830 with a C- or higher. Term offered: fall, spring, summer. Max hours: 3 Credits.

Grading Basis: Letter Grade

Prereq: MATH 2830 with a C- or higher.

Typically Offered: Spring.

MATH 4840 -  Independent Study  (1-3 Credits)  

Variable credit depending on the student's needs. Offered for the advanced student who desires to pursue a specific topic in considerable depth. Note: Supervision by a full-time faculty member is necessary, and the dean's office must concur. Students may register for this course more than once with departmental approval. Repeatable. Max Hours: 12 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 12.

MATH 4880 -  Directed Research  (1-6 Credits)  

Students will engage in original research projects supervised and mentored by faculty. Students must work with faculty prior to registration to develop a proposal for their project and receive permission to take this course. Repeatable. Max Hours: 6 Credits.

Grading Basis: Letter Grade

Repeatable. Max Credits: 6.