2007-2008 Catalog (PDF) - Colorado State University-Pueblo
2007-2008 Catalog (PDF) - Colorado State University-Pueblo 2007-2008 Catalog (PDF) - Colorado State University-Pueblo
CSU-Pueblo MATH 122 College Trigonometry 3(3-0) Trigonometric and circular functions, identities, inverse functions, vectors, complex numbers. Prerequisites: MATH 121 or equivalent. (*) 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. Prerequisites: Satisfactory placement exam score. Two years of high school algebra or equivalent. (F,S) MATH 126 Calculus and Analytic Geometry I 5(5-0) Introduction to limits, continuity, differentiation and integration with selected applications. Prerequisites: Satisfactory placement exam score. MATH 124 or equivalent. (F,S) 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. Prerequisites: Satisfactory placement exam score. Math 099 or one year of high school algebra or equivalent. (F,S,SS) MATH 207 Matrix and Vector Algebra with Applications 2(2-0) Systems of equations, matrix representation of systems, solution of systems, inverses, determinants, and Cramer’s Rule. Vectors, scalar and cross-products, applications to two- and three- dimensional geometry. Prerequisite: MATH 124 or equivalent. Corequisite: Majors and minors should take this course concurrently with MATH 224 or MATH 325. (F,S) MATH 209 Symmetry 3(3-0) Liberal arts course exploring the mathematical world of symmetry. Topics include isometrics, Euclidean geometry, tiling theory, group theory, and fractals. Prerequisite: Satisfactory placement exam score. One year of high school geometry or permission of instructor. (*) MATH 220 Quantitative Analysis for Business 4(4-0) An introduction to quantitative methods required for business studies, includes a brief introduction to the Calculus. Prerequisites: Satisfactory placement exam score. MATH 121 or equivalent. (F,S,SS) MATH 221 Applied Calculus: 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. Prerequisites: Satisfactory placement exam score. MATH 121 or equivalent. (F,S) MATH 224 Calculus and Analytic Geometry II 5(5-0) Differentiation and integration of trigonometric, logarithmic, and other transcendental functions. Infinite sequences and series, parametric representation of curves, and selected applications. Prerequisite: MATH 126. Corequisite: Majors and minors should take this course concurrently with MATH 207. (F,S) MATH 242 Introduction to Computation with MATLAB 4(3-2) Introduction to mathematical computation using MATLAB. Includes projects in numerical, graphical and symbolic computation. Loops, conditionals, functions, scripts, recursion, errors, program testing and documentation. Prerequisites: MATH 124 required 207 recommended. (S) MATH 256 Probability for Engineers and Scientists 3(3-0) A calculus-based introduction to applied probability and stochastic processes. An intuitive study of random variables, special distributions, expectations, and limit theorems. Prerequisite: MATH 224 or permission of instructor. (S) MATH 291 Special Topics (1-3 VAR) Prerequisites: permission of instructor and approval of the department chair. (F,S) Repeatable MATH 295 Independent Study (1-3 VAR) Prerequisite: permission of instructor. (F,S) Repeatable MATH 307 Introduction to Linear Algebra 4(4-0) A rigorous development of vector spaces and linear transformations. Prerequisites: MATH 207 and MATH 224 and knowledge of a programming language. (F,S) 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. Prerequisites: a grade of C or better in MATH 224 and MATH 207. (*) MATH 325 Intermediate Calculus 3(3-0) Continuation of MATH 224. Vector valued functions and multivariable calculus. Prerequisites: MATH 224 or equivalent. Corequisite: Majors and minors who have not yet completed MATH 207 must enroll in MATH 207 concurrently with MATH 325. (F) MATH 327 Abstract Algebra 4(4-0) Introduction to groups, rings, and fields and their elementary properties. Prerequisites: MATH 307 and 3 additional upper division mathematics courses. (S) MATH 330 Introduction to Higher Geometry 3(3-0) Euclidean, hyperbolic, finite, and transformation geometries, models, and constructions. Prerequisite: MATH 224 or permission of instructor. (S) MATH 337 Differential Equations I 3(3-0) First order differential equations, homogeneous and nonhomogenous linear differential equations, introduction to the Laplace transform, applications. Prerequisite: MATH 224 or equivalent. (S) MATH 338 Differential Equations II 3(3-0) 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: recommend MATH 325. (*) MATH 342 Introduction to Numerical Analysis 3(3-0) Numerical solutions of polynomial, differential, integral, and other equations using the computer. Prerequisites: MATH 207 and a programming language, or permission of instructor. (*) MATH 345 Algorithms and Data Structures 4(3-2) An introduction to data structures, sorting, searching, recurrence relations and performance measures. Algorithms will be studied analytically and through computer implementation. Prerequisites: MATH 207, MATH 224 and CIS 253. (*) MATH 348 Numerical Methods 3(3-0) Linear and non-linear systems of equations, systems of differential equations and boundary value problems, rational function approximations. Prerequisites: MATH 307 and a programming language. (*) 228
Course Descriptions 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 256 or MATH 350. (S) MATH 360 Elementary Concepts of Mathematics I 3(3-0) Development of the real number system and related concepts, including sets, numeration systems, whole numbers, integers, fractions, rational numbers, number theory and algorithms. Prerequisites: Intermediate Algebra, or equivalent. Recommend MATH 156. (F,S) MATH 361 Elementary Concepts of Mathematics II 3(3-0) Conceptual development of fractions, rational numbers, geometry, measurement, probability and statistics. Prerequisite: C or better in MATH 360. Recommend MATH 156. (F,S,SS) 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. Prerequisites: C or better in both MATH 156 and MATH 361, or their equivalents. (F,S) MATH 411 Introduction to Topology 3(3-0) An introduction to topological spaces, homeomorphisms, topological properties, and separation axioms. Prerequisite: MATH 320. (*) MATH 419 Number Theory 3(3-0) Divisibility, prime numbers, linear congruences, multiplicative functions, cryptology, primitive roots, and quadratic residues. Prerequisite: MATH 307 or MATH 320. (*) MATH 421 Advanced Calculus I 4(4-0) An introductory course in real analysis providing a rigorous development of the concepts of elementary calculus. Prerequisites: MATH 307 and 3 additional upper division mathematics courses. (F) MATH 422 Advanced Calculus II 3(3-0) Additional topics from elementary real analysis, theory of multivariable calculus, Stieltjes and line integrals. Prerequisite MATH 421. (*) 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. (*) MATH 445 Discrete Mathematics 3(3-0) Topics selected from mathematical reasoning, combinatorial techniques, set theory, binary relations, functions and sequences, algorithm analysis, and discrete analysis. Prerequisites: MATH 224, 307 and knowledge of a programming language. (*) MATH 456 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. (*) MATH 463 History of Mathematics 3(3-0) Survey of the origins of important mathematical concepts and of the mathematicians responsible for these discoveries. Prerequisites: MATH 307 or MATH 320. (F/O) MATH 477 Materials and Techniques of Teaching Secondary School Mathematics 4(4-0) Topics and current issues in secondary mathematics education, including materials development, learning theories, instructional and assessment strategies, curriculum, planning and standards. Field experience required. Prerequisites: Acceptance into Teacher Education Program and Math 307 or Math 320. (F/E) MATH 480 Tutoring Practicum (1-2 VAR) Participation in tutoring mathematics in the MLC under the guidance of the MLC Director. May be repeated for a maximum of two credits. Prerequisites: C or better in MATH 224 and permission of MLC Director. (S/U grading) (F,S,SS) Repeatable (2) MATH 491 Special Topics (1-3 VAR) Prerequisite: permission of instructor. (F,S) Repeatable MATH 492 Research (1-3 VAR) Research project selected by student and supervised by a regular mathematics faculty member. Prerequisite: department approval. (F/S) Repeatable MATH 493 Seminar (1-3 VAR) Prerequisites: senior standing and permission of instructor. (F,S) Repeatable MATH 495 Independent Study (1-3 VAR) Prerequisites: senior standing and permission of instructor. (F,S) Repeatable MATH 498 Internship (1-6 VAR) 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. (S/U grading) (F,S,SS) Repeatable GRADUATE COURSES MATH 501 Foundations of Mathematics 3(3-0) Sets, logic, axiomatics, mappings and the various subsystems of the reals for beginning graduate students. Prerequisite: permission of instructor. (*) MATH 507 Linear Algebra 3(3-0) Vector spaces, linear transformations, matrix representation, canonical form. Prerequisite: permission of instructor. (*) 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. (*) MATH 527 Abstract Algebra 3(3-0) Groups, rings, integral domains, quotient rings, ideals, fields, homomorphisms and related topics. Prerequisite: permission of instructor. (*) MATH 530 Advanced Geometry 3(3-0) Foundations of geometry, geometric transformations, and applications. Prerequisite: permission of instructor. (*) MATH 541 Computers 3(3-0) The use of the computer in mathematical investigations, including sophisticated comprehensive computer programs such as Mathematica. Prerequisite: permission of instructor. (*) 229
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CSU-<strong>Pueblo</strong><br />
MATH 122 College Trigonometry 3(3-0)<br />
Trigonometric and circular functions, identities, inverse<br />
functions, vectors, complex numbers. Prerequisites:<br />
MATH 121 or equivalent. (*)<br />
MATH 124 Pre-calculus Math 5(5-0)<br />
Polynomial, rational, exponential and logarithmic<br />
functions; solution of systems of equations; trigonometric,<br />
circular and certain special functions. Prerequisites:<br />
Satisfactory placement exam score. Two years of high<br />
school algebra or equivalent. (F,S)<br />
MATH 126 Calculus and Analytic Geometry I 5(5-0)<br />
Introduction to limits, continuity, differentiation and<br />
integration with selected applications. Prerequisites:<br />
Satisfactory placement exam score. MATH 124 or<br />
equivalent. (F,S)<br />
MATH 156 Introduction to Statistics 3(3-0)<br />
Introduction to data analysis. Binomial and normal<br />
models. Sample statistics, confidence intervals, hypothesis<br />
tests, linear regression and correlation, and chisquare<br />
tests. Prerequisites: Satisfactory placement exam score.<br />
Math 099 or one year of high school algebra or equivalent.<br />
(F,S,SS)<br />
MATH 207 Matrix and Vector Algebra with Applications<br />
2(2-0)<br />
Systems of equations, matrix representation of systems,<br />
solution of systems, inverses, determinants, and Cramer’s<br />
Rule. Vectors, scalar and cross-products, applications to<br />
two- and three- dimensional geometry. Prerequisite:<br />
MATH 124 or equivalent. Corequisite: Majors and minors<br />
should take this course concurrently with MATH 224 or<br />
MATH 325. (F,S)<br />
MATH 209 Symmetry 3(3-0)<br />
Liberal arts course exploring the mathematical world of<br />
symmetry. Topics include isometrics, Euclidean geometry,<br />
tiling theory, group theory, and fractals. Prerequisite:<br />
Satisfactory placement exam score. One year of high<br />
school geometry or permission of instructor. (*)<br />
MATH 220 Quantitative Analysis for Business 4(4-0)<br />
An introduction to quantitative methods required for<br />
business studies, includes a brief introduction to the<br />
Calculus. Prerequisites: Satisfactory placement exam<br />
score. MATH 121 or equivalent. (F,S,SS)<br />
MATH 221 Applied Calculus: An Intuitive Approach<br />
4(4-0)<br />
Non-rigorous introduction to calculus with emphasis on<br />
applications and modeling in the life sciences, social and<br />
behavioral sciences and business. Prerequisites:<br />
Satisfactory placement exam score. MATH 121 or<br />
equivalent. (F,S)<br />
MATH 224 Calculus and Analytic Geometry II 5(5-0)<br />
Differentiation and integration of trigonometric, logarithmic,<br />
and other transcendental functions. Infinite sequences<br />
and series, parametric representation of curves,<br />
and selected applications. Prerequisite: MATH 126.<br />
Corequisite: Majors and minors should take this course<br />
concurrently with MATH 207. (F,S)<br />
MATH 242 Introduction to Computation with MATLAB<br />
4(3-2)<br />
Introduction to mathematical computation using MATLAB.<br />
Includes projects in numerical, graphical and symbolic<br />
computation. Loops, conditionals, functions, scripts,<br />
recursion, errors, program testing and documentation.<br />
Prerequisites: MATH 124 required 207 recommended. (S)<br />
MATH 256 Probability for Engineers and Scientists<br />
3(3-0)<br />
A calculus-based introduction to applied probability and<br />
stochastic processes. An intuitive study of random<br />
variables, special distributions, expectations, and limit<br />
theorems. Prerequisite: MATH 224 or permission of<br />
instructor. (S)<br />
MATH 291 Special Topics (1-3 VAR)<br />
Prerequisites: permission of instructor and approval of the<br />
department chair. (F,S) Repeatable<br />
MATH 295 Independent Study (1-3 VAR)<br />
Prerequisite: permission of instructor. (F,S) Repeatable<br />
MATH 307 Introduction to Linear Algebra 4(4-0)<br />
A rigorous development of vector spaces and linear<br />
transformations. Prerequisites: MATH 207 and MATH 224<br />
and knowledge of a programming language. (F,S)<br />
MATH 320 Introductory Discrete Mathematics 3(3-0)<br />
Introduction to discrete structures with emphasis on logic<br />
and proof. Topics selected from graph theory, boolean<br />
algebra, combinatorics, binary relations, set theory,<br />
functions and sequences. Prerequisites: a grade of C or<br />
better in MATH 224 and MATH 207. (*)<br />
MATH 325 Intermediate Calculus 3(3-0)<br />
Continuation of MATH 224. Vector valued functions and<br />
multivariable calculus. Prerequisites: MATH 224 or<br />
equivalent. Corequisite: Majors and minors who have not<br />
yet completed MATH 207 must enroll in MATH 207<br />
concurrently with MATH 325. (F)<br />
MATH 327 Abstract Algebra 4(4-0)<br />
Introduction to groups, rings, and fields and their<br />
elementary properties. Prerequisites: MATH 307 and 3<br />
additional upper division mathematics courses. (S)<br />
MATH 330 Introduction to Higher Geometry 3(3-0)<br />
Euclidean, hyperbolic, finite, and transformation geometries,<br />
models, and constructions. Prerequisite: MATH 224<br />
or permission of instructor. (S)<br />
MATH 337 Differential Equations I 3(3-0)<br />
First order differential equations, homogeneous and nonhomogenous<br />
linear differential equations, introduction to<br />
the Laplace transform, applications. Prerequisite: MATH<br />
224 or equivalent. (S)<br />
MATH 338 Differential Equations II 3(3-0)<br />
Linear systems, existence and uniqueness of solutions,<br />
non-linear equations, series solutions, orthogonal sets of<br />
functions. Fourier series, boundary value problems, partial<br />
differential equations and applications. Prerequisite:<br />
recommend MATH 325. (*)<br />
MATH 342 Introduction to Numerical Analysis 3(3-0)<br />
Numerical solutions of polynomial, differential, integral,<br />
and other equations using the computer. Prerequisites:<br />
MATH 207 and a programming language, or permission of<br />
instructor. (*)<br />
MATH 345 Algorithms and Data Structures 4(3-2)<br />
An introduction to data structures, sorting, searching,<br />
recurrence relations and performance measures.<br />
Algorithms will be studied analytically and through<br />
computer implementation. Prerequisites: MATH 207,<br />
MATH 224 and CIS 253. (*)<br />
MATH 348 Numerical Methods 3(3-0)<br />
Linear and non-linear systems of equations, systems of<br />
differential equations and boundary value problems,<br />
rational function approximations. Prerequisites: MATH<br />
307 and a programming language. (*)<br />
228