Course Offerings - MATHEMATICS
Prerequisite courses must be completed with a grade of "C" or above. The Mathematics Department recommendation for students entering their first course in mathematics is made on the basis of the student's high school record, ACT score, University objectives, and mathematics placement exam.
Basic concepts about numbers, fundamental operations of arithmetic, algebraic expressions, an introduction to linear equations, functions, and factoring. Only those students failing to meet the prerequisites for 67-103 will be recommended for this course. This course does not count toward the 120 credits necessary for graduation. A grade of "C" or above is required to remove mathematics deficiency.67-102 Introduction of Modern Mathematics and its Applications (MA) 4 cr. (Fall-Spring)
This is a course intended for students whose major program does not require algebra or calculus. Students will see that the connection between the mathematics presented and down-to-earth, concrete real-life problems is direct and immediate. Topics are selected from social choice (voting systems, fair division, apportionment), management science (graphs, networks, scheduling), growth and symmetry (growth, populations, patterns), statistics (data analysis, probability, distributions) and computer technology (algorithms, data storage, coding, graphics). Prerequisite: 67-100 with a grade of "C" or better or placement.67-103 Introduction to College Algebra (MA) 3 cr. (Fall-Spring)
The structure of the real numbers, open sentences in one variable (equalities and inequalities), systems of linear open sentences, functions and graphs, polynomials and factoring. Prerequisite: 67-100 with a "C" or above or placement. Not open to students who have completed 67-104 or higher.67-104 College Algebra 3 cr. (Fall-Spring)
Continuation of functions and graphs including logarithms, polynomials, induction, progressions, matrices and determinants, permutations, combinations, probability. Students may not receive credit for both 67-104 and 67-108. Prerequisite: 67-103 with a grade of C or above or placement.
A first course in trigonometry. Basic circular functions and their inverses. Trigonometric identities and equations. Triangle trigonometry. Law of Sines and Law of Cosines. Students may not receive credit for both 67-108 and 67-106. Prerequisite: 67-104 with a grade of C or better or placement.67-107 Introduction to Statistics (MA) 3 cr. (Fall-Spring)
Descriptive statistics/elementary probability/basic problems of statistical inference: estimation, confidence intervals, hypothesis testing, regression and correlation. Prerequisite: 67-100 with a "C" or above or placement. Not open to students who have completed 67-104 or higher.67-108 College Algebra and Trigonometry 5 cr. (Fall-Spring)
A functional approach to college algebra and trigonometry. Polynomial, exponential, logarithmic, circular, and trigonometric functions. Students may not receive credit from both 67-104 and 67-108. Prerequisite: 67-103 with a grade of C or placement test. The Mathematics Department recommendation for students entering their first course in mathematics is made on the basis of the student's high school record, ACT score, University objectives, and mathematics placement exam.67-110 Number Systems 3 cr. (Fall-Spring)
Exploring, conjecturing, communicating and reasoning within the content domain of the whole numbers, the integers, the rational numbers and the real numbers. Includes experiences with sets, number sense and numeration, number systems, number theory, concepts of operations on numbers, computational algorithms and estimation. Prerequisite: Open only to students in elementary and special education. Initial math placement above the remedial level or a C or better in 67-100.67-122 Introduction to Discrete Mathematics 3 cr.
Topics in discrete mathematics for majors and minors in mathematics, for computer science and for general education. Topics include propositional logic, predicate logic, induction, sets, counting strategies, graph theory and trees. Prerequisites: 67-104 or 67-108 with a grade of C or above or four years of college preparatory mathematics and recommended placement based on mathematics placement exam.67-171 Calculus I 4 cr. (Fall-Spring)
Real valued functions of a single variable. Concept of derivative, antiderivative, and definite integral. Differentiation and applications, including optimization and curve-sketching. Emphasis on problem solving, approximation, data analysis, visualization. A graphics programmable calculator is required. Prerequisite: 67-108 or 67-104 and 67-106 (with grade(s) of C or above) or 4 years of college preparatory mathematics and a satisfactory score on a placement examination.67-172 Calculus II 4 cr. (Fall-Spring)
Definite integration and applications, several techniques of integration, approximation, and improper integrals. Numerical differential equations, slope fields, Euler's method, and mathematical modeling. Taylor and Fourier Series. A graphics programmable calculator is required. Prerequisite: 67-171 with a grade of C or above.67-175 Honors: Calculus I 4 cr.
Covers the same subject matter as 67-171 (Calculus I), but with greater mathematical depth and emphasis on heuristic problem solving processes, computer or calculator graphics, and applications. Prerequisite: Enrollment in the University Scholars Program in addition to the prerequisites for 67-171.67-200 Minitab Statistical Computing 1 cr.
An introduction to the statistical computing package MINITAB. Descriptive techniques, graphical presentations of data, correlation and regression, random numbers and simulation, statistical tests. Prerequisite: 67-200. A statistics course at the level of 67-107 or higher or concurrent registration in such a statistics course.67-201 Applied Statistics 3 cr. (Fall-Spring)
An introduction to applied statistics using a statistical computing package such as MINITAB. Topics include: Descriptive statistics, elementary probability, discrete and continuous distributions, interval and point estimation, hypothesis testing, regression and correlation. Credit cannot be earned for both 67-107 and 67-201. Prerequisite: 67-104 or 67-108 with a grade of C or above.67-204 Mathematics for Business Analysis I 4 cr. (Fall-Spring)
This course is designed to acquaint business students with mathematical techniques which are useful in business and management. Topics include Functions, Matrix Algebra and Applications, Linear Programming, Probability, and Mathematics of Finance. Prerequisite: 67-103 or 67-108 with a grade of C or above.67-206 Mathematics for Business Analysis II 4 cr. (Fall-Spring)
This course follows 67-204. Topics include Logarithmic and Exponential Functions, Differential and Integral Calculus and their application to business problems. Prerequisite: 67-204 with a grade of C or above.67-207 Short Course in Calculus 4 cr.
A basic calculus course designed to give students a practical working knowledge of differential and integral calculus. Applications of algebraic, logarithmic and exponential functions will be presented in the areas of business, natural sciences, and the social sciences. Students may not get credit for both 67-206 and 67-207. Not open to students who have completed 67-171 or equivalent. Prerequisite: 67-104 or 67-108 with a grade of C or placement test. The Mathematics Department recommendation for students entering their first course in mathematics is made on the basis of the student's high school record, ACT score, University objectives, and mathematics placement exam.67-211 Fundamentals of Geometry and Measurement for Elementary and Special Education Programs (MA) 3 cr. (Fall-Spring)
Intuitive geometry and topology. Introduction to motion geometry. Measurement of length, area, volume and angle size. Includes a content foundation for teaching the geometry and measurement concepts recommended in the DPI K-8 guidelines. Prerequisite: 67-110.
This course uses activities and experiments to develop ideas about analyzing and reporting data, statistical techniques, probability and simulation. Most activities will involve data gathered from real life situations. Prerequisite: 67-110.67-222 Introduction to Abstract Mathematics 3 cr. (Fall)
Topics include proof strategies, elementary number theory, relations, functions and some algebraic structures. Proof strategies include conditional proof, proof by contradiction, proof by cases, existence proofs, mathematical induction, strong induction, over generalization and counter example. Relations emphasized are equivalence relations and partial order relations. Functions emphasized are isomorphisms and homomorphisms. Prerequisite: 67-122, 67-171 with a grade of C or above in each.67-256 Introduction to Linear Mathematics 3 cr. (Fall-Spring)
An introduction to linear algebra based on the study of matrices, with an emphasis on situations which can be interpreted geometrically in the plane or in space. Topics include: matrix operations, systems of linear equations, determinants, eigenevectors and eigenvalues, properties of Rn (with emphasis on R2 and R3), and applications of each of these topics. Most computation will be done on TI-85 or equivalent technology. Prerequisite: 67-171, 67-122 with a grade of "C" or above in each.67-273 Calculus III 4 cr. (Fall-Spring)
Vectors in two and three dimensions and vector functions. Multivariate differential and integral calculus, partial derivatives and multiple integrals. Line and surface integrals. Prerequisite: 67-172 with a grade of C or above.67-287 Elementary Topics in Mathematics 1 cr.
Elementary level topics from such areas as: decision theory, game theory, graphs and networks, linear programming, applications of calculus to biology, ecology, and the social sciences, mathematical modeling, and statistics. Prerequisite: 67-104 or 67-108.67-301 Introduction to Probability and Statistics 3 cr. (Fall-Spring)
Elementary probability models, discrete and continuous random variables, sampling and sampling distributions, estimation, and hypothesis testing. Prerequisite: 67-172, 67-122 with a grade of "C" or above in each.67-302 Intermediate Statistical Methods 3 cr. (Spring)
Emphasis on models & methods used in statistical applications. Topics covered include: two-sample procedures, linear regression and correlation, analysis of variance, goodness of fit tests. Prerequisites: 67-301, 67-200 (or concurrent registration in 67-200).67-304 Introduction to Nonparametric Methods 3 cr.
Statistical methods when the functional form of the population is unknown. Emphasis on applications and comparison of methods. One and two sample tests, contingency tables, tolerance limits, confidence intervals for means, tests of significance for some measures of correlation, and K-sample tests. Prerequisites: 67-200 and a statistics course at the level of 67-201 or higher.67-305/505 Statistics for Quality and Productivity 3 cr.
Statistical process control charts including Shewart and CUSUM. Design of experiments including factorials, fractional factorials and designs to explore response surfaces. The roles of blocking, confounding and randomization. The course will be about 25% statistical process control and about 75% design of experiments. Prerequisite: 67-302.67-317/517 Probability and Statistics for Elementary and Middle School Programs 4 cr.
An introduction to probability and statistics emphasizing problem solving and communication. Topics include sample spaces, permutations and combinations, random variables, expected value, probability distributions, hypothesis testing and statistical inference. This course will employ technology and contain a historical component. Prerequisite: 67-104 or equivalent, 67-211 and 67-217, each with a grade of C or better.67-319 Infinite Processes for Elementary and Middle School Programs 4 cr.
An introduction to infinite processes; this course emphasizes problem solving and communication. Topics include functions, continuity, limiting processes, rates of change, optimization, approximation of areas and volumes, sequences and series. This course will employ technology and will contain a historical component. (May not receive credit for both 67-319 and 67-171.) Prerequisite: 67-104 or equivalent, 67-211 and 67-217, each with a grade of "C" or better.
An introduction to the evolution of geometry, modern elementary geometry, transformation theory, and modern axiomatic Euclidean geometry. Prerequisite: 67-222.67-333 Synthetic Projective Geometry 2 cr.
Topics include duality, harmonic sequences, projective transformations, and conics. Prerequisite: 67-331.67-334 Hyperbolic Geometry 2 cr. (Spring)
This course will survey the history of non-Euclidean geometry and develop the basic properties of hyperbolic geometry. A consistency model will be constructed in the Euclidean plane and hyperbolic trigonometry developed by the use of this model. Prerequisite: 67-331.67-342/542 Abstract Algebra I 3 cr.
A survey course in modern algebra including such topics as: basic properties of the integers, a study of groups and their properties with examples and applications, other systems including rings and fields. Prerequisite: 67-222 with a grade of "C" or above.67-346/546 Linear Algebra 3 cr. (Fall)
An introduction to finite dimensional vector spaces, linear transformations, matrices and determinants (with applications to systems of linear equations) and characteristic values and characteristic vectors. Additional topics may include advanced work involving: characteristic values and characteristic vectors, Jordan canonical form, inner products, quadratic forms. Prerequisite: 67-256 with a grade of "C" or above.67-349/549 Elementary Number Theory 3 cr.
Divisibility, primes, congruences, quadratic reciprocity, number theoretic functions, Diophantine equations, continued fractions, and selected topics. Prerequisite: 67-222 with a grade of "C" or above.67-352/552 Computing Mathematics with Applications 3 cr.
An introduction to programming in Mathematica or a similar software package. The course begins by exploring the numerical, algebraic and graphical capabilities of the software. Topics include lists, functions and programming with applications to number theory, discrete mathematics, analysis and probability. Prerequisite: 67-122 and 67-172.67-355/555 Introduction to Numerical Analysis 3 cr. (Fall)
Topics in numerical computations selected from polynomial interpolation, solution of nonlinear equations, numerical integration, numerical solution of differential equations, and approximation. Prerequisites: 67-273, 34-151 or equivalent.67-356/556 Linear Numerical Analysis 3 cr. (Spring)
Topics in numerical linear algebra selected from: Gaussian elimination, matrix inversion, eigenvector and eigenvalue computations, error analysis, condition numbers and pivoting strategies. Prerequisites: 67-273, 67-256, 34-151 or equivalent.67-357 Linear Programming 3 cr.
Application and theory of linear programming. Primal and dual formulations, sensitivity analysis, simplex method, transportation algorithm, and the assignment problem. Students will learn modeling and how to apply linear programming to problems. Case studies are used. This course is appropriate for mathematics students as well as students from other fields. Prerequisite: 67-256.67-365 Math Modeling 2 cr. (Spring)
Research, analysis, and construction of mathematical models for "real world" problems. Application to areas within and outside mathematics. Oral group presentations and a written technical report are required. Prerequisite: completion of core plus 12 credits in math numbered above 300.67-371/571 Differential Equations 3 cr. (Spring)
An introductory course treating ordinary differential equations of the first and second order; linear equations with constant coefficients; solutions using series, the Laplace transform, and numerical methods. Prerequisite: 67-172.67-375/575 Applied Mathematical Analysis I 3 cr. (Fall)
Topics in mathematics applicable to the physical sciences: Vector analysis, Green's theorem and generalizations, analytic function theory. Prerequisite: 67-273.67-376/576 Applied Mathematical Analysis II 3 cr. (Spring)
Topics in mathematics applicable to the physical sciences: Solutions of certain classical differential equations (ordinary and partial), Fourier methods, and applied linear algebra. Prerequisite: 67-371.67-381/581 Stochastic Modeling 3 cr.
Condition probability and conditional expectation, Markov Chains, Poisson Processes, Branching Processes and Population Growth. Prerequisites: 67-256, 67-301.67-385/585 Applied Regression Analysis 3 cr.
A practical introduction to regression emphasizing applications rather than theory. Simple and multiple regression analysis, basic components of experimental design, and elementary model building. Both conventional and computer techniques will be used in performing the analyses. Prerequisites: 67-200, 67-256, 67-301.67-386/586 Linear Statistical Models 3 cr.
A unified approach to the application of linear statistical models in analysis of variance (ANOVA) and experimental design. In ANOVA topics from single-factor ANOVA and multifactor ANOVA will be considered. Experimental design will include randomized blocks, Latin squares, and incomplete block designs. Prerequisites: 67-256, 67-302.67-401/601 Mathematical Statistics I 3 cr. (Fall)
Probability and combinatorial methods. Discrete and continuous, univariate and multivariate distributions, expected values, moments, normal distributions and derived distributions. Prerequisites: 67-273, 67-301.67-402/602 Mathematical Statistics II 3 cr. (Spring)
Estimation, testing hypothesis, analysis of variance, comparison of means, least squares analysis, regression and correlation. Prerequisite: 67-401.67-403 Issues in Statistical Practice 2 cr. (Spring)
Selected readings and projects illustrating some of the special problems encountered by professional statisticians in their roles as consultants, educators and researchers. Prerequisites: 67-401 and at least two courses from 67-303, 67-305, 67-381, 67-385, 67-386.67-413/613 Modern Algebra for Elementary and Middle School Programs 4 cr.
An intuitive and investigative study of selected mathematical structures (groups, rings, integral domains, fields and vector spaces), sets, operations and functions including historical aspects. Emphasis is on problem solving. Prerequisite: 67-104 or equivalent, 67-211 and 67-217, each with a grade of "C" or better.67-415/615 Modern Geometry for Elementary and Middle School Programs 4 cr.
An informal approach to geometry. Topics are chosen from transformational (motion) geometry (reflections, rotations, translations and glide-reflections), symmetry, fractal geometry, spatial visualization, topology and graph theory including historical aspects. Emphasis is on problem solving and reasoning using technology and math manipulative. The course will contain a historical component. Prerequisite: 67-104, or equivalent, 67-211 and 67-217, each with a grade of "C" or better..67-446 Independent Study 1-3 cr.
See Independent Study under Course and Academic Advisement Policies information for general course description, general prerequisites, and proper contract form requirements.67-467/667 Advanced Calculus 3 cr.
Real number properties and the topology of the real numbers. Limits, continuity, differentiation, and integration. Sequences and infinite series. Prerequisite: 67-273 with a grade of "C" or above.67-474 Honors: Thesis 1-6 cr.
Honors thesis projects include any advanced independent endeavor in the student's major field of study: e.g. a written thesis, scientific experiment or research project, or creative arts exhibit or production. Proposals (attached to Independent Study contract) must show clear promise of honors level work and be approved by a faculty sponsor. Course title for transcript will be "Honors Thesis." Completed projects will be announced and presented to interested students and faculty. Prerequisites: Enrollment in University scholar program, junior standing.67-480/680 Elementary Topology 3 cr.
Historical introduction, continuity, open sets, closed sets, neighborhoods, homeomorphism, construction of topologies, separation, compactness, connectedness, uniform spaces, subspaces, and completeness. Prerequisite: 67-273.67-485/685 Seminar in Mathematical Problem Solving 2 cr. (Spring)
General heuristic strategies applied to non-routine mathematical problems. Interactive problem solving and analysis by participants. Designed for communicators of mathematics. Prerequisite: completion of core plus 67-222 plus nine credits in math numbered above 300.
Seminar emphasizing problem solving and mathematical modeling in Elem/Middle School programs. Survey and study of research literature on the teaching and learning of mathematics, connections between the other courses in the mathematics minor. Experience with units from demonstration projects in middle school curriculum materials. Prerequisite: senior status with major in elementary education and completion of 17 credits toward a minor in mathematics.
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Last Updated July 1, 1999