This course is designed to meet the needs of students who are unprepared to successfully complete a regular college mathematics course. It is remedial in nature, and is not applicable toward the Science/Math requirement. After successfully completing this course, a student would be prepared to take courses that will fulfill the requirement. No credit toward 120 s.h. needed for graduation.
A liberal arts course for students who will not be scheduling a technical/professional math course. This terminal course presents a survey of mathematics important to the history of Western civilization and to the modern world. Introductory modules covered usually include: number theory, geometry, topology, probability, statistics, computers, consumer mathematics and set theory. No credit in Math/Science Block for math and science majors.
For students who need to improve their algebraic skills before taking a higher level course such as MATH 160 or 161, this course focuses on algebraic topics deemed most important for success in college mathematics and its applications. Topics covered include the real number system, linear equations and inequalities, word problems, polynomials and factoring, rational algebraic expressions, exponents and radicals, quadratic equations, irrational equations, graphs of equations, systems of equations, and logarithmic and exponential functions. [syllabus]
A survey of mathematical ideas developed by non-European cultures including, but no limited to, those of Africans, Asians, and native North, Central and South Americans. Includes culture, specific examples from the following areas of mathematics: number theory, topology, probability, group theory and logic. No credit under block G2 for math or science majors. MATH 100 and MATH 102 may not both be taken for general education credit. Offered periodically.
This course examines the mathematics content which elementary and special education teachers of mathematics at any level need to know and understand before beginning to teach. It is designed to ensure that all such majors acquire sufficient knowledge and facility in mathematics to prepare them to teach mathematics effectively in contemporary schools. The course surveys many relevant topics including sets and logic, number systems, structure of algorithms, number theory, properties of integers, rational numbers and real numbers, and the beginning of geometry and measurement. Emphasis is given to problem solving and reasoning within each topic. Required of all elementary education and special education majors. [syllabus]
An extension of MATH 104, this course covers additional mathematical topics relevant to teaching elementary mathematics. Topics include algebra, additional study in geometry and measurement, probability and statistics, graphing, and further emphasis on problem solving and reasoning. Required of all elementary education majors. [syllabus]
For students preparing to take calculus who are deficient in trigonometry. Beginning with angles, numerical trigonometry and triangle-solving, this course develops the concepts and analytical skills required in calculus: identities, inverse functions, trigonometric equations, graphs and applications.
Derivation of basic formulas; measures of central tendency and variability; probability and normal curve; sampling and hypothesis testing; confidence intervals. No credit toward a math or four-year CSCI major nor under block G2 for majors in the School of Science and Mathematics except for nursing majors.[syllabus]
Elementary introduction to calculus and its applications in business, economics, life sciences and social sciences. Functions, limits and continuity. The derivative; applications in marginal analysis, related rates, extreme value problems, curve sketching, optimization, differentials and error estimation. Exponential and logarithm functions; applications to growth and decay problems. Elementary differential equations; bounded growth models. Improper integrals. This course will not count toward a major or minor in mathematics.
Designed to provide the student with an introductory survey of calculus as applied to the business, social, and life sciences. Frequent use of relevant and factual applications are used to demonstrate how calculus serves as an indispensable tool for problem solving in the real world. Intended for majors not in the School of Science and Mathematics. No credit for math requirement for any major in the School of Science and Mathematics.
Continuation of MATH 155. Extension of the calculus of functions of several variables with related applications in maxima and minima. Double integrals. Techniques of integration. Probability and calculus. Intended for non-science majors. No credit for math requirement for any major in the School of Science and Mathematics.
Designed for persons intending to continue into Calculus, this course is required only of those not adequately prepared to begin their mathematics sequence with Calculus I (MATH 161). Topics covered are those in which beginning calculus students are often deficient: elementary functions, curve sketching, theory of equations, inequalities, trigonometry and analytic geometry. Math placement testing/evaluation before registration is required.
An introduction to the concepts and techniques of Calculus, beginning with limits. Major emphasis is on theory and application of derivatives, anti-derivatives and the definite integral. Introductory calculus of trigonometric, exponential and logarithm functions is included.[syllabus]
A more in-depth and enriched introduction to the concepts and techniques of elementary calculus than that provided in MATH 161.
Continuation of MATH 161. Transcendental functions, techniques of integration, applications of the definite integral, improper integrals, polar coordinates, and infinite series. [syllabus]
A survey of elementary probability theory, estimation, hypothesis testing and simple regression and correlation. Interpretation of statistical inference in the analysis of data. Emphasis on application in both behavioral and physical sciences. [syllabus]
An extension of MATH 235. Includes estimation, hypothesis testing, design of experiments with analysis of variance, regression analysis, covariance analysis and nonparametric approaches. Includes experiences using a variety of computing devices. A solid methods course for any major who needs to use statistical techniques. No credit toward math major. Offered in spring.
The evolution of mathematics from the empiricism of the Babylonians to the formalism of Hilbert--short developments of algebra, geometry, trigonometry, and calculus. The effect of culture on mathematics and conversely.
This course counts for Perspectives credit only, not toward a major in mathematics.
Emphasizes formal mathematical reasoning and communication of mathematical ideas both orally and in writing. Symbolic logic, techniques of mathematical proof. Algebra of sets, binary relations and functions. Infinite sets, both countable and uncountable. (This course counts as a Writing (W) course in the General Education curriculum).
Continuation of MATH 211. Vector calculus, functions of several real variables, partial differentiation, implicit functions, multiple integrals, line and surface integrals, and applications. [syllabus]
Specifically designed for the special education major; emphasizes the content, methods, strategies and materials for use in an effective educational program for LD, ED, EMR, TMR, SPMR and physically handicapped students. MATH 314 helps students become more competent and confident when working with mathematics in special education. Offered in fall.
An extension and synthesis of the calculus sequence that provides students with the problem solving skills emphasized in such examinations as the Society of Actuaries Exam 100, the Graduate Record Exam and the Advanced Placement Calculus Exams. Does not count as an upper division elective for the mathematics major or minor. Offered in spring.
A rigorous introduction to linear algebra for majors in mathematics and the sciences, essential for mathematics courses beyond calculus. Topics include systems of linear equations, matrix algebra, determinants, vector spaces, geometry in Rn, linear transformations, eigentheory, and diagonalization.
This course is designed for mathematics education majors to provide a rigorous one-semester study of probability, distribution theory and the basics of statistical inference. Topics to be covered include probability, expectation, discrete and continuous distributions, descriptive statistics and both estimation and hypothesis testing for one and two-sample problems. No credit for both MATH 333 and 235 or for both MATH 333 and MATH 335.
Probability, random variables and probability distributions, mathematical expectation, special probability distributions and probability densities. MATH 335 may be considered as an introductory course in probability theory.
Groups, rings, fields, integral domains. Emphasis on structure of algebra.
Various examples of axiom systems, brief exposition of Euclidean geometry using Hilbert's axioms. Growth and development of geometry, non-Euclidean geometries and projective geometry. More than half the semester is spent on elementary projective geometry from both the synthetic and analytic points of view.
The study of geometry from a transformational point of view. The group of affine transformations, with the subgroups of similarities and motions, is studied with investigation of invariant properties. There is some exposure to transformations in the complex plane.
The study of the following topics and some of their applications: (1) first order ordinary differential equations, (2) linear second order initial value problems, (3) power series solutions. In addition, at least one of the following topics: special functions of mathematical physics, Laplace transforms, systems of first order equations. [syllabus]
Principles of model building; examples from linear optimization, network analysis, dynamic programming, probabilistic decision theory, Markov chains, queuing theory, simulation and inventory models. Applications and theory will be examined.
Numerical methods for solving systems of linear equations, solving nonlinear equations, integration, interpolation, approximation, and least squares curve fitting. Error theory.
Number Theory is the study of the properties of integers with respect to the fundamental operations. The primary emphasis in this course in on the logical derivations of these properties. Topics covered include: induction, divisibility, congruences, theorems of Fermat and Euler, continued fractions, and quadratic reciprocity.
This course provides a mathematical foundation for the concepts and techniques used in combinatorics. Topics include recurrence relations, finite differences, generating functions, pigeonhole principle, special sequences of integers (such as Fibonacci, Sterling, and Bell sequences), principle of inclusion and exclusion, and an introduction to the theory of graphs. Applications will be indicated.
Place and function of mathematics in secondary education; evaluation and improvement of instruction; current trends in objectives, methods, and subject matter of junior and senior high school mathematics. A considerable portion of class time will be devoted to teaching mathematics to secondary school students. When offered only one time during the academic year, it will be offered during fall term. This course should be taken during the semester immediately preceding student teaching. [syllabus]
A continuation of MATH 322, emphasizing the algebra and geometry of linear transformation and their matrix representations. Change of bases, equivalence and similarity. Inner product spaces, orthogonal transformations and n-dimensional rigid motions. Bilinear and quadratic forms. Generalized inverses.
A continuation of Mathematical Statistics I. Functions of random variables, sampling distributions, point estimation, interval estimation, hypothesis testing theory and applications.
Continuation of MATH 345. Introduction to field theory, rings of polynomials, introduction to Galois theory.
Frenet frames; curvature and torsion of curves in 3 space. Calculus of vector fields; geodesics and curvature of surfaces in 3-space. Surface area and volume. The Euler characteristic of a surface and the Gauss-Bonnet theorem. Rigid motions and isometries. Riemannian metrics, parallelism, non-Euclidean geometries, and applications.
Rigorous development of the concepts and methods of calculus. The real number system and its topology; theory of limits and continuity; differentiable functions and their properties; the Riemann integral; infinite series.
Continuation of MATH 464. Topics chosen from the following: convergence and uniform convergence of infinite sequences and series of functions; topology of Euclidean n-space Rn; differential calculus of functions Rn->R and Rn->Rm; extreme values; implicit and inverse function theorems; Riemann integration in Rn; metric spaces; function spaces; Riemann-Stieltjes integration.
Study of techniques of applied mathematics utilized to solve linear partial differential equations of the first and second order involving two independent variables. D'Alembert's Formula, methods of separation of variables, Sturm-Liouville problems and eigenfunction expansions, Fourier Series and The Fourier Transform. Discussion of three prominent classical equations of mathematical physics, namely the wave equation, the heat equation, and Laplace's Equation.
Applications of mathematics to real-world problems drawn from industry, research laboratories, the physical sciences and engineering and the scientific literature. May include parameter estimation, curve fitting, elementary probability, optimization, computer programming, and ordinary and partial differential equations. Offered periodically.
Foundation course for extensive study in modern higher analysis and topology, and related areas. Infinite set theory, metric spaces, topological spaces, separation properties, continuous mappings, homeomorphisms, convergence theory, product spaces, quotient spaces, connectedness, compactness, function spaces, applications.
Topics courses are scheduled by arrangement with the instructor; semester hours of credit and meeting times for those courses are set by arrangement.
A survey of statistical methods currently used in research, education, behavioral science and biomedical application. Various experimental designs are discussed regarding advantages, disadvantages, sampling problems, analysis and conclusions. Regression and correlation analysis, analysis of variance and nonparametric approaches are included.
Continuation and extension of the statistical methods introduced in MATH 535 (Statistical Methods I). Advanced topics in analysis of variance, randomized block designs and experimental designs.
This is a capstone course, designed to serve as an outcome assessment for the for mathematics majors enrolled in the Actuarial Science/Statistics option. The course will involve problem solving, data analysis and statistical consulting. Materials for the course will be drawn from real-world problems encountered by local industry and the experience of the course instructor. Reading materials will be assigned from the literature related to statistical consulting. Students will work both individually and in teams.
A study of functions of a complex variable, complete enough to contain and illustrate the essential features of the subject. Applications are indicated.
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