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MATH Course Descriptions
Lower Division Level Courses
Information on the Math Placement Test is found at the Student Success Career Center
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MATH 090-1. Fundamentals of Algebra. A review
of basic algebra and arithmetic, including algebra of
polynomials, factorization of simple polynomials, arithmetic
operations on fractions and rational expressions, laws of
exponents, linear equations and inequalities in one variable,
quadratic equations using factoring. Administered through
Department of Mathematics. Pass/fail grading only. Does
not count toward BA or BS degree.
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MATH 104-3. College Algebra. An in-depth study of
algebraic equations and inequalities. Comprehension of the
underlying algebraic structure will be stressed as well as
appropriate algebraic skills. The study will include polynomials,
rational, exponential, and logarithmic functions as well as
systems of equations/inequalities. Prer., score 9 or more on algebra diagnostic exam.
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MATH 105-4 Elementary Functions of Calculus. An intensive study of the elementary funtions required for calculus.
These functions will include polynomial, rational, exponential,
logarithmic, and trigonometric functions. Emphasis is on their
algebraic structure and graphs. Analysis of conic sections
and analytic geometry will be included. Prer., MATH 104 or
score 20 or more on algebra diagnostic exam.
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MATH 111-3. Topics in Linear Algebra. For business and economics students. Systems of linear equations, matrix algebra, linear programming, probability, statistics. Prer., MATH 104 or score 17 or more on algebra diagnostic exam.
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MATH 112-3 Calculus
for Business & Economics. Calculus for
the business and economics students. Prer., MATH 104
or score 17 or more on algebra diagnostic exam.
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MATH 131-3. Calculus I with Precalculus, Part A. See MATH 135 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. MATH 131 and MATH 132 together are equivalent to MATH 135. The sequence MATH 131-132 is designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for MATH 135. Prer., 4 years high school math (algebra, geometry, trigonometry or their equivalents). Credit not granted for this course and MATH 135.
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MATH 132-3. Calculus I with Precalculus, Part B. Continuation of MATH 131. See MATH 135 for calculus topics covered. Algebraic and trigonometric topics are studied throughout, as needed. Prer., MATH 131. Credit not granted for this course and MATH 135.
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MATH 135-4. Calculus I. Selected topics in analytical
geometry and calculus. Rates of change of functions, limits,
derivatives of algebraic and transcendental functions, applications of derivatives,
and integration. Prer., MATH 105 or score 20 or more on the Algebra Placement Exam AND score 10 or more on the Calculus Readiness Exam.
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MATH 136-4. Calculus II. Continuation of MATH 135.
Transcendental functions, techniques and applications of integration, Taylor's
theorem, improper integrals, infinite series, analytic geometry,
polar coordinates. Prer., MATH 135.
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MATH 215-3 Discrete Mathematics. Introduction
to most of the important topics of discrete mathematics, including
set theory, logic, number theory, recursion, combinatorics,
and graph theory. Much emphasis will be focused on the ideas
and methods of mathematical proofs, including induction and
contradiction. Prer., MATH 135.
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MATH 235-4. Calculus III. Continuation of MATH 136.
Parametric curves, vector functions, partial differentiation,
multiple integrals, Green's Theorem and Stoke's Theorem. Prer., MATH 136.
300 Level Courses
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MATH 301-3. Mathematics for Elementary Teachers I.
Covers the whole number, integer, and rational number systems that are of prime importance to the elementary teacher. For students
planning on elementary
teacher certification.
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MATH 302-3. Mathematics for Elementary Teachers II.
Intuitive and logical development of the fundamental ideas
of geometry such as parallelism, congruence, and measurement.
Includes study of plane analytical geometry. For students
planning on elementary
teacher certification.
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MATH 310-3. Statistics for the Sciences. Descriptive
probability, hypothesis testing, non- parametric methods.
Discrete and continuous random variables, mean and variance,
confidence limits, correlation and regression. Prer., MATH 135.
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MATH 311-3. Theory of Numbers. A careful study, with
emphasis on proofs, of the following topics associated with
the set of integer: divisibility, congruences, arithmetic
functions, sums of squares, quadratic residues and reciprocity,
and elementary results on distributions of primes. Prer., MATH 136 and MATH 215.
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MATH 313-3. Introduction to Linear Algebra. Systems
of linear equations, matrices, vector spaces, linear independence,
basis, dimension, determinants, linear transformations and
matrices, eigenvalues and eigenvectors. Prer., MATH 135.
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MATH 340-3. Introduction to Differential Equations.
First order differential equations, linear differential equations,
the Laplace transform method, power series solutions, numerical
solutions, linear systems. Prer., MATH 235.
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MATH 341-3. Estimation, Convergence and Approximation.
Sequences, numerical series, and power series. Integrals
and the analysis of functions defined by integrals. This course provides a thorough introduction
to proofs in analysis, and is strongly recommended for students planning
to take MATH 431. Prer., MATH 235.
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MATH 350-3. Graph Theory. Standard material on the
theory of both directed and undirected graphs, including the
concepts of isomorphism, connectivity, trees, traversability,
planar graphs, coloring problems, relations and matrices.
Prer., MATH 215.
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MATH 351-3. Topics in Combinatorial Analysis. A survey
of important areas of combinatorics. Topics may include enumeration
techniques, recurrence relations, combinatorial designs, graph
theory, matching and optimization. Prer., MATH 215.
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MATH 381-3. Introduction to Probability and Statistics. The axioms of probability and conditional probability will be studied as well as the development, applications and simulation of discrete and continuous probability distributions. Also, expectation, variance, correlation, sum and joint distributions of random variables will be studied. The Law of Large Numbers and the Central Limit Theorem will be developed. Applications to statistics will include regression, confidence intervals, and hypothesis testing. Prer., MATH 235.
400/500 Level Courses
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MATH 405/505-1 to 3. Topics in Mathematics Secondary
Classroom. The topics covered will vary from one offering to the next. Topics will be chosen to meet the needs of secondary mathematics teachers for additional training to teach to the Colorado Model Content Standards. Prer., one semester of calculus, or instructor approval.
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MATH 410/510-3. Technology in Mathematics Teaching and
Curriculum. Methodology for using technology as a teaching/learning tool for high school and college math courses.
Use of graphing calculators, computer algebra systems, computer geometry systems and the internet will
be emphasized. Students are required to develop and present
a portfolio of in-depth projects. Prer., MATH 136.
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MATH 413/513-3. Linear Algebra I. Vector spaces,
Linear transformation and matrices, determinants, eigenvalues,
similarity transformations, orthogonal and unitary transformations,
normal matrices and quadratic forms. Prer., MATH 313.
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MATH 414-3. Modern Algebra I. A careful study of
the elementary theory of groups, rings, and fields. Mappings
such as homomorphisms and isomorphisms are considered. The
student will be expected to prove theorems. Prer., MATH 215 and MATH 313. One of MATH 311, MATH 350, or MATH 351 (preferably MATH 311) is strongly recommended.
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MATH 415/515-3. Modern Algebra II. Continuation of
MATH 414 through Galois theory. Prer., MATH 414.
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MATH 421/521-3. Higher Geometry. Axiomatic systems.
The foundations of Euclidean and Lobachevskian geometries.
Prer., MATH 311 or MATH 313.
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MATH 423/523-3. Fractal Geometry. Introduction to
iterated function systems and mathematical aspects of fractal
sets. Includes metric spaces and the space fractals live in,
transformations, contraction mapping and Collage Theorem,
chaotic dynamics, shadowing theorem, fractal dimension, fractal
interpolation, and measures on fractals. Prer., MATH 235 and MATH 313.
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MATH 425/525-3. Introduction to Chaotic Dynamical Systems.
Introduction to dynamical systems or processes in motion,
that are defined in discrete time by iteration of simple functions,
or in continuous time by differential equations. Emphasis
on understanding chaotic behavior that occurs when a simple
non-linear function is iterated. Topics include orbits, graphical
analysis, fixed and periodic points, bifurcations, symbolic
dynamics, chaos, fractals, and Julia sets. Prer., MATH 235.
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MATH 431-3. Modern Analysis I. Calculus of one variable,
the real number system, continuity, differentiation, integration.
Prer., MATH 215 and MATH 235, MATH 341 is strongly recommended.
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MATH 432/532-3. Modern Analysis II. Sequence and
series, convergence, uniform convergence; Taylor's theorem;
calculus of several variables including continuity, differentiation,
and integration. Prer., MATH 431.
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MATH 442/542-3. Optimization. Linear and nonlinear
programming, the simplex algorithm and other approaches to
linear optimization, minimax theorems, convex functions, introduction
to calculus of variations. Prer., MATH 313 and MATH 340.
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MATH 443/543-3 Ordinary Differential Equations. Linear systems of differential equations, existence and uniqueness theorems, stability, periodic solutions, eigenvalue
problems, and analysis of equations important for applications.
Prer., MATH 313 and MATH 340.
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MATH 445/545-3. Complex Variables. Theory of functions
of one complex variable including integrals, power series,
residues, conformal mapping, and special functions. Prer., MATH 235.
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MATH 447/547-3. Methods of Applied Mathematics. Boundary
value problems for the wave, heat, and Laplace equations,
separation of variables method, eigenvalue problems, Fourier
series, orthogonal systems. Prer., MATH 235, MATH 313 and MATH 340.
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MATH 448/548-3. Mathematical Modeling. The
use of diverse mathematical techniques to analyze and solve
problems from science and engineering, particularly problems
likely to arise in nonacademic settings such as industry or
government. Converting a problem to a mathematical model.
Commonly encountered classes of mathematical models, including
optimization problems, dynamical systems, probability models,
and computer simulations. Communication of results of mathematical
analysis. Prer., MATH 313, MATH 340, and MATH 310 or MATH 381 or ECE 3610.
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MATH 465/565-3. Numerical Analysis. Error analysis,
root finding, numerical integration and differentiation, numerical
methods for ordinary differential equations, numerical linear
algebra and eigenvalue problems. Prer., CS 115, MATH 313, and MATH 340.
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MATH 467/567-3. Scientific Computation.
Description and analysis of algorithms used for numerical
solutions of partial differential equations of importance in
science and engineering. The main emphasis is on
theoretical analysis, but some practical computations are
included. Prer., MATH 235, MATH 313, and CS 115 or equivalent.
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MATH 481/581-3. Mathematical Statistics I.
Exponential, Beta, Gamma, Student, Fisher and Chi-square
distributions are covered in this course, along with joint and conditional distributions, moment generating techniques, transformations of random variables and vectors. Prer., MATH 235 and MATH 313.
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MATH 482/582-3. Mathematical Statistics
II.
Point and confidence interval estimation, principles of maximum likelihood,
sufficiency and completeness; tests of simple and composite hypotheses. Linear models and multiple regression analysis. Other topics will be included. Prer., MATH 381 or MATH 310.
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MATH 483/583-3. Linear Statistical Models. Methods
and results of linear algebra are developed to formulate and
study a fundamental and widely applied area of statistics.
Topics include generalized inverses, multivariate normal distribution
and the general linear model. Applications focus on model
building, design models, and computing methods. The "Statistical
Analysis System" (software) is introduced as a tool for doing
computations. Prer., MATH 381 or ECE 3610, or MATH 310 and MATH 313.
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MATH 485/585-3. Stochastic Modeling. Mathematical
development of continuous and discrete time Markov chains,
queuing theory, reliability theory, and Brownian motion with
applications to engineering and computer science. Prer., MATH 381 or ECE 3610.
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MATH 511-1 to 3. Technology in Math Education Seminar. A follow-up to MATH 410/510. Students will present demonstrations, projects and/or laboratories they have developed for use in their math courses. Extended in-depth coverage of computer algebra or geometry systems and/or graphing calculators and internet. Basic familiarity with computer algebra or geometry systems and/or graphing calculators is required. Prer., MATH 510 or consent of instructor.
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MATH 517-3. Graduate Modern Algebra I. Groups, rings, modules, fields, algebraic systems and Galois theory. Prer., MATH 414.
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MATH 527-3. Algebraic Coding Theory. The basic ideas of the theory of error-correcting codes are presented. We will study some important examples and give applications. These codes are important for the digital transmission of data. Prer., MATH 414.
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MATH 533-3. Real Analysis I. Measure theory, metric and normed linear spaces, completions, continuous functions, Riemann-Stieltjes and Lebesgue integration. Prer., MATH 432/532
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MATH 535-3. Applied Functional Analysis. An introduction to the basic concepts, methods and applications of functional analysis. Topics covered will include metric spaces, normed spaces, Hilbert spaces, linear operators, spectral theory, fixed point theorems and approximation theorems. Prer., MATH 431.
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MATH 552-3. Perturbation Theory in Astrodynamics. Perturbation methods including Lagrange and Hamiltonian mechanics and the generalized method of averaging. Gravitational and atmosphere modeling. Prer., MAE 4410/5410 or PHYS 551.
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MATH 562-3. Complex Variables II. Homotopy, Global Cauchy Theorem, Residue Theory, conformal mapping, infinite products, analytic continuation, special functions, selected topics. Prer., MATH 445/545 and MATH 431.
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MATH 584-3. Computer Vision. Representation and manipulation of digital images; Fourier analysis of images; enhancement techniques in spatial and frequency domain; segmentation procedures; digital geometry, region and boundary representation; texture processing; pattern recognition and application to robotics. Prer., Graduate standing in mathematics, engineering or computer science. Meets with CS 584.
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MATH 590-1 to 3. Graduate Seminar. Various topics in mathematics at the graduate level. Prer., Consent of instructor.
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MATH 591-3. Theory of Probability. Theoretical approach to probability. Measure theory is given form within a large body of probabilistic examples, ideas and applications. Weak and strong laws of large numbers, central limit theory, recurrence, Martingales. Prer., MATH 431.
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600 - 900 Level Courses
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MATH 700-1 to 6. Master's Thesis.
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MATH 800-1 to 10. PhD Dissertation.
Enrollment is limited to those students who are in the PhD
program in Engineering, and have primary thesis advisor in
the Department of Mathematics. Prer., Consent of instructor.
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MATH 920-1 to 4. Independent Study Math
Undergraduate.
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MATH 940-1 to 3. Independent Study Math
Undergraduate.
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MATH 950-1 to 3. Independent Study Math,
Graduate.
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MATH 999-0. Candidate for Degree.
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