Mathematics  

MATH #300 - College Algebra
Credits:
Review of functions and topics in algebra. Functional domains and ranges, composition of functions, inverse functions. Algebraic fractions, exponential expressions, roots, and radicals, logarithmic, and exponential functions. Cr/F.

MATH 301 - Elementary Math I
Credits: 4.00
Beginning algebra including integer operations, solving linear equations, graphing linear functions, solving linear inequalities, systems of linear equations, polynomials, rational expressions and equations, and exponents and radicals. May not be taken for credit toward a bachelor's degree.

MATH 302 - Elementary Math II
Credits: 4.00
Review of elementary algebra, exponents, polynomials, factoring, rational exponents, and absolute value. Solving linear and quadratic equations and inequalities; systems of equations; radical equations. Linear functions and related notions; quadratic functions. May not be taken for credit toward a bachelor's degree. Prereq: MATH 301 or the equivalent.

MATH 305 - Elementary Functions
Credits: 4.00
Properties of elementary functions, including exponential and logarithmic, trigonometric and inverse trigonometric functions. May not be taken for credit toward a bachelor's degree. Prereq: MATH 302 or the equivalent.

MATH 418 - Analysis and Applications of Functions
Credits: 4.00
Analysis and applications of algebraic and transcendental functions, with special emphasis on exponential, logarithmic, and trigonometric functions. Graphical analysis. Written projects will be required on some or all of the following topics: rates of change, optimization, logarithmic or exponential modeling, and trigonometric functions. Intended for students planning to take MATH 425. Prereq: MATH 302 or equivalent. Cannot receive credit if taken after receiving credit for MATH 424A or B or MATH 425.

MATH #419 - Evolution of Mathematics
Credits: 4.00
Mathematics form antiquity to the present; origins of the various methods and branches. How and why such concepts as number and geometry evolved. Prereq: MATH 302 or the equivalent. Not offered for credit to mathematics majors.

MATH 420 - Finite Mathematics
Credits: 4.00
Topics selected from probability, systems of linear equations, matrix algebra, linear programming, mathematics of finance. Not a preparation for calculus. Prereq: MATH 302 or the equivalent. Not offered for credit to mathematics majors.

MATH 424A - Calculus for Social Sciences
Credits: 4.00
Real-valued functions and their graphs; derivatives and their applications; antiderivatives and areas; exponentials and logarithms; introduction to multivariable calculus and partial derivatives. CEPS majors not allowed. Primarily intended for majors in College of Liberal Arts and the Whittemore School. Prereq: MATH 418 or equivalent.

MATH 424B - Calculus for Life Sciences
Credits: 4.00
Real-valued functions and their graphs; derivatives and their applications; antiderivatives and areas; exponentials and logarithms; introduction to multivariable calculus and partial derivatives. CEPS majors not allowed. Primarily intended for majors in College of Life Sciences and Agriculture. Prereq: MATH 418 or equivalent.

MATH 425 - Calculus I
Credits: 4.00
Calculus of one variable covering limits, derivatives of algebraic, trigonometric, exponential, and logarithmic functions; applications include curve sketching, max-min problems, related rates, and volume and area problems. Enrollment in MATH 425H requires concurrent enrollment in PHYS 407H. Prereq: completing MATH 418 with a grade of C or better or successfully passing the calculus placement test. (Not offered for credit if credit is received for MATH 424.)

MATH 425H - Honors/Calculus I
Credits: 4.00
See description for MATH 425.

MATH 426 - Calculus II
Credits: 4.00
Second course in calculus of one argument, techniques and applications of integration, polar coordinates, and series. Enrollment in MATH 426H requires concurrent enrollment in PHYS 408H. Prereq: MATH 425. Pre-or Coreq: PHYS 408.

MATH 426H - Honors/Calculus II
Credits: 4.00
See description for MATH 426.

MATH 525 - Linearity I
Credits: 6.00
Examination of the fundamental role that linear models play in science and engineering; and the role of linearization in understanding nonlinear phenomena. Models are considered along several conceptual axes: discrete to continuous, one-dimensional to multi-dimensional, and static to dynamic, with an emphasis on the former. Mathematical areas of coverage include matrix algebra, concepts from calculus of several variables, difference equations, and linear transformations. Prereq: MATH 426, permission. Lab.

MATH 526 - Linearity II
Credits: 6.00
Continuation of study of linear models and the process of linearization begun in MATH 525, with an emphasis on models of dynamic phenomena. Additional mathematical areas of coverage include differential equations, eigenvalue and eigenvector analysis, phase plane analysis, and additional concepts from vector calculus. Prereq: MATH 525, permission. Lab.

MATH 527 - Differential Equations with Linear Algebra
Credits: 4.00
Fundamental methods of solving first-order equations, essentials of matrix algebra; higher-order linear equations, and linear systems; series solutions; Laplace transforms; selected applications. Prereq: MATH 426.

MATH 527H - Honors/Differential Equations with Linear Algebra
Credits: 4.00
See description for MATH 527.

MATH 528 - Multidimensional Calculus
Credits: 4.00
Partial differentiation; composite functions and chain rules; maximum and minimum; transformations; vector algebra; vector functions; gradient, divergence, and curl; curves and surfaces; multiple, line, and surface integrals; divergence, Green's and Stoke's theorem. Prereq: MATH 426.

MATH 531 - Mathematical Proof
Credits: 4.00
Introduction to reading and writing proofs in mathematics. The basic language of mathematics common to all branches of the subject, especially set theory and basic logic. Prereq: MATH 426. Writing intensive.

MATH 532 - Discrete Mathematics
Credits: 4.00
Counting principles, (including permutations, combinations, pigeonhole principle, inclusion-exclusion principle); big-O relation; graphs, trees, and related topics. Prereq: MATH 531.

MATH 545 - Introduction to Linear Algebra and Mathematical Proof
Credits: 4.00
Introduction to mathematical writing and proof in the context of basic linear algebra. Designed to reinforce ideas seen throughout the mathematics curriculum. Centered on an intense study of vector spaces and linear systems, beginning with a brief study of linear system equations, progressing to a discussion of linear transformation and vector spaces. No credit if credit has been received for MATH 645. Prereq: MATH 426. Writing intensive.

MATH 601 - Exploring Mathematics for Teachers I
Credits: 4.00
This course will provide prospective elementary teachers with the opportunity to explore and master concepts involving number systems, and operations, data analysis and probability. Mathematical reasoning, problem solving and the use of appropriate manipulatives and technology will be integrated throughout the course. Readings, class discussions, and assignments will focus on mathematics content as well as applicable theories of learning, curriculum resources, and state and national recommendations. The course will model instructional techniques that can be adapted to the elementary curricula. Prereq: EDUC 500. No credit if credit is earned for MATH 621, 623, 721, and/or 723. CEPS majors not allowed.

MATH 602 - Exploring Mathematics for Teachers II
Credits: 4.00
This course will provide prospective elementary teachers with the opportunity to explore and master concepts involving geometry, measurement, and algebraic thinking. Mathematical reasoning, problem solving and the use of appropriate manipulatives and technology will be integrated throughout the course. Readings, class discussions, and assignments will focus on mathematics content as well as applicable theories of learning, curriculum resources, and state and national recommendations. The course will model instructional techniques that can be adapted to the elementary curricula. Prereq: EDUC 500. No credit if credit earned for MATH 621, 721, 622, and/or 722. CEPS majors not allowed.

MATH 619 - Historical Foundations of Mathematics
Credits: 4.00
Historical development of number theory, geometry, probability, algebra, and analysis. Study of the significant mathematical contributions to these topics made by prominent mathematicians spanning several historical periods. Prereq: MATH 531 or 545.

MATH 621 - Number Systems for Teachers
Credits: 4.00
Problem solving; counting and set concepts, number systems (whole numbers, integers, rational, and real numbers); number theory; estimation and mental calculation techniques; and applications requiring calculators and computers. Manipulatives and models are used in a lab setting to illustrate the concepts and properties of the number systems and teach number sense. No credit offered toward mathematics major except for B.S. mathematics education-elementary and middle school options. Prereq: permission.

MATH 622 - Geometry for Teachers
Credits: 4.00
Properties of plane and space figures; tessellations; symmetry; LOGO computer language; nonstandard, English, and metric units of measure; area and perimeter; volume and surface area; estimations and approximations of measurements; constructions; congruence and similarity mappings; problem solving using geometric and algebraic skills, and applications requiring calculators and computers. Manipulatives and models are used in a lab setting to illustrate concepts and properties of geometry. No credit offered toward mathematics major except for B.S. mathematics education-elementary and middle school options. Prereq: MATH 621 or permission.

MATH 623 - Topics in Mathematics for Teachers
Credits: 4.00
Logic (valid and invalid forms of reasoning); descriptive statistics (graphs, measures of central tendency, measures of variation); inferential statistics (samplings, distributions, measures of relative standing, simulations); probability (experimental, geometrical, and theoretical); permutations and combinations; probability simulations; problem solving using skills from statistics and probability; mathematical connections and communication review of computer software; and applications requiring calculators and computers. No credit offered toward mathematics major except for B.S. mathematics education-elementary and middle school options. Prereq: 621 or permission. (Offered in alternate years during spring semester.)

MATH 624 - Analysis for Secondary School Teachers
Credits: 4.00
Examines concepts from calculus and pre-calculus mathematics with an emphasis on connecting and logically refining the concepts of function, limit, sequences, series, and probability. Includes a deeper analysis of problems and topics drawn from secondary school mathematics with the kind of mathematical knowledge and sophistication that the student has gained from other collegiate mathemathics courses. Proofs for many of the theorems that are typically introduced in a non-rigorous fashion in calculus are studied. Prereq: MATH 425, 545 or equivalent, EDUC 500 or by permission.

MATH 639 - Introduction to Statistical Analysis
Credits: 4.00
A first course introducing concepts of probability and scientific methods for data analysis. Exploratory data analysis, survey sampling, probability, discrete and continuous distributions, confidence intervals, hypothesis testing, comparing samples, linear regression, analysis of variance. Statistical software, such as JMP or Minitab used. Offered primarily for mathematics majors at the sophomore level; engineering majors are urged to take MATH 644. No credit for students who have completed MATH 644. Prereq: MATH 426.

MATH 644 - Statistics for Engineers and Scientists
Credits: 4.00
Introduction to the design of controlled experiments and to the collection and analysis of scientific data. Use of a statistical software package is an integral part of the course; interpreting and drawing conclusions from standard software output is emphasized. Graphical data analysis, statistical process control, regression and correlation, multifactor experimental designs, confidence intervals, hypothesis testing. No credit for students who have completed MATH 639. Prereq: MATH 426.

MATH 645 - Linear Algebra for Applications
Credits: 4.00
Fundamental notions of vector space theory, linear independence, basis, span, scalar product, orthogonal bases. The course includes a survey of matrix algebra, solution of systems linear equations, rank, kernel, eigenvalues and eigenvectors, the LU- and QR-factorizations, and least squares approximation. Selected applications in mathematics, science, engineering and business. Prereq: MATH 426. (Not offered for credit if credit is received for MATH 762.)

MATH 645H - Honors/Linear Algebra for Applications
Credits: 4.00
See description for MATH 645.

MATH 646 - Introduction to Partial Differential Equations
Credits: 4.00
Introduction to the solution of partial differential equations. Models arising from initial-boundary-value problems of mathematical physics and Sturm-Liouville problems are examined; solution techniques include separation of variables, Bessel functions, series expansions by orthogonal functions, and numerical methods. Prereq: CS 410 or 415; MATH 527; 528; 645; /or permission.

MATH 647 - Complex Analysis for Applications
Credits: 4.00
Complex numbers, analytic functions, Cauchy-Riemann equations, conformal mapping, contour integration, Cauchy's integral formula, infinite series, residue calculus, Fourier and Laplace transforms. Prereq: MATH 528. (Not offered for credit if credit is received for MATH 788.)

MATH 656 - Introduction to Number Theory
Credits: 4.00
Unique factorization, arithmetic functions, linear and quadratic congruences, quadratic reciprocity law, quadratic forms, introduction to algebraic numbers. Prereq: MATH 531. (Offered in alternate years.)

MATH 657 - Geometry
Credits: 4.00
Advanced approach to fundamental properties of Euclidean and other geometries. Prereq: MATH 531. Writing intensive.

MATH 658 - Topics in Geometry
Credits: 4.00
Topics selected from among projective geometry, finite geometrics, convexity, transformational geometry, non-Euclidean geometry, and other areas of elementary geometry within the framework of modern mathematics. Prereq: MATH 657. (Offered in alternate years.)

MATH 696 - Independent Study
Credits: 1.00 to 4.00
Individual projects of study developed by the student and a faculty sponsor. Intended for students with superior scholastic achievement. May be repeated up to 8 credits. May be taken as writing intensive. Prereq: a written proposal, including goals and assessment, endorsed by a faculty sponsor and approved by the department chairperson.

MATH 696W - Independent Study
Credits: 1.00 to 4.00
See description for MATH 696. Writing intensive.

MATH 698 - Senior Seminar
Credits: 4.00
Exploration of mathematical topics beyond the student's previous coursework. Focus on problem solving, generation of problems, and oral and written communication of mathematics. Prereq: senior standing in mathematics or mathematics education.

MATH 700 - Introduction to Mathematics Education
Credits: 4.00
General background information about mathematics education, such as theories of learning and teaching mathematics, mathematics curricula, classroom management, and techniques the teaching, learning, and assessment of mathematics that are common to all levels of mathematics education. Prereq: MATH 426, EDUC 500 or equivalent, or by permission.

MATH 701 - Exploring Mathematics for Teachers I
Credits: 4.00
This course will provide perspective elementary teachers with the opportunity to explore and master concepts involving number systems, and operations, data analysis and probability. Mathematical reasoning, problem solving and the use of appropriate manipulatives and technology will be integrated throughout the course. Readings, class discussions, and assignments will focus on mathematics content as well as applicable theories of learning, curriculum resources, and state and national recommendations. The course will model instructional techniques that can be adapted to the elementary curricula Credit offered only to M.Ed. and M.A.T., certificate-only students, and in-service teachers. Prereq: EDUC 500. No credit if credit earned for MATH 621, 721, 623, and/or 723.

MATH 702 - Exploring Mathematics for Teachers II
Credits: 4.00
This course will provide prospective elementary teachers with the opportunity to explore and master concepts involving geometry, measurement, and algebraic thinking. Mathematical reasoning, problem solving and the use of appropriate manipulatives and technology will be integrated throughout the course. Readings, class discussions, and assignments will focus on mathematics content as well as applicable theories of learning, curriculum resources, and state and national recommendations. The course will model instructional techniques that can be adapted to the elementary curricula. Credit offered only to M.Ed. and M.A.T., certificate-only students, and in-service teachers. Prereq: EDUC 500. No credit if credit earned for MATH 621, 622, 721, and/or 722.

MATH 703 - Teaching of Mathematics, K-6
Credits: 4.00
Methods of teaching; uses of manipulatives, models, and diagrams in instruction; purposes and methods of assessment; curriculum standards and goals; review and evaluation of textbooks and computer software; uses of calculators and computers; teaching reading and writing in mathematics. Prereq: MATH 621 or 721; EDUC 500 or permission. (Offered in alternate years during the fall semester.)

MATH 721 - Number Systems for Teachers
Credits: 4.00
Problem solving; counting and set concepts, number systems (whole numbers, integers, rational, and real numbers); number theory; estimation and mental calculation techniques; and applications requiring calculators and computers. Manipulatives and models are used in a lab setting to illustrate the concepts and properties of the number systems. Credit offered only to M.Ed., M.A.T., certification-only students, and in-service teachers. Prereq: permission.

MATH 722 - Geometry for Teachers
Credits: 4.00
Properties of two- and three-dimensional figures; tessellations; symmetry; nonstandard, English, and metric units of measure; area and perimeter; volume and surface area; estimations and approximations of measurements; constructions; congruence and similarity mappings; applications requiring calculators and computers. Manipulatives and models are used in a lab setting to illustrate concepts and properties of geometry. Credit offered only to M.Ed., M.A.T., certification-only students, and in-service teachers. Prereq: 721 or permission.

MATH 723 - Topics in Mathematics for Teachers
Credits: 4.00
Descriptive statistics; inferential statistics; simulations; probability (experimental, geometrical, and theoretical); permutations and combinations; problem solving using skills from statistics and probability; applications requiring calculators and computers. Credit offered only to M.Ed., M.A.T., certification-only students, and in-service teachers. Prereq: 721 or permission. (Offered in alternate years during spring semester.)

MATH 737 - Statistical Methods for Quality Improvement
Credits: 4.00
Introduction to scientific data collection and analysis with an emphasis on industrial applications. Topics include statistical process control (SPC), engineering process control, failure modes and effects analysis (FMEA), Six-Sigma concepts and methods, and confidence intervals and hypothesis testing. Use of a statistical software package is an integral part of the course; graphical data analyses are emphasized. Prereq: MATH 644, permission.

MATH 739 - Applied Regression Analysis
Credits: 4.00
Statistical methods for the analysis of relationships between response and input variables: Simple linear regression, residual analysis and model selection, multicollinearity, nonlinear curve fitting, categorical predictors, introduction to analysis of variance and covariance. Students will be introduced to programming in SAS. Prereq: MATH 639 (or 644); or permission. Writing intensive.

MATH 740 - Industrial Statistics and Design of Experiments
Credits: 4.00
Emphasizes methods for solving complex problems, both in the industrial and research environments. Statistical process control, design of experiments, randomization and blocking, factorial designs, nested designs, fixed, random, and mixed effects models, fractional factorial designs, use of covariates, response surface methods. JMP software will be used extensively. Prereq: MATH 639 (or 644);/or permission.

MATH 741 - Biostatistics and Life Testing
Credits: 4.00
Explorations of models and data-analytic methods used in medical, biological, and reliability studies. Event-time data, censored data, reliability models and methods, Kaplan-Meier estimator, proportional hazards, Poisson models, loglinear models. SAS or JMP, and SPlus will be used. Prereq: MATH 639 (or 644);/or permission. (Offered in alternate years.)

MATH 742 - Multivariate Statistical Methods
Credits: 4.00
Issues dealing with multivariate response data. Random vectors and matrices, multivariate normal distribution, Hotelling's T2, multivariate analysis of variance (MANOVA), principal components, cluster analysis, factor analysis, longitudinal data and repeated measures. SAS or SPlus will be used. Prereq: MATH 639 (or 644);/or permission. (Offered in alternate years.)

MATH 744 - Design of Experiments II
Credits: 4.00
Experimental design strategies and issues that are often encountered in practice. Topics include: Complete and incomplete blocking, partially balanced incomplete blocking (BIB), confounding, intra and inter block information, split plotting and strip plotting, repeated measures, crossover design strategies, Latin squares and rectangles, Youden squares, crossed and nested treatment structures, variance components, mixed effects models, analysis of covariance, optimizations, missing responses. Prereq: MATH 740 or permission.

MATH 745 - Foundations of Applied Mathematics
Credits: 4.00
Basic concepts and techniques of applied mathematics intended for graduate students and advanced undergraduates in mathematics, engineering, and the sciences. Topics include computational linear algebra, nonlinear differential equations, and partial differential equations. Methods examined include Fourier expansions and transforms, Laplace transforms, optimization techniques, linear spaces, eigenvalue analysis, Sturm-Liouville systems, numerical methods, conformal mapping, and residue theory. Prereq: MATH 527; 528 or equivalent.

MATH 746 - Foundations of Applied Mathematics
Credits: 4.00
See description for MATH 745.

MATH 747 - Introduction to Nonlinear Dynamics and Chaos
Credits: 4.00
The mathematics of chaos and nonlinear dynamics. Topics include: Linear and nonlinear systems of ordinary differential equations; discrete maps; chaos; phase plane analysis; bifurcations and computer simulations. Prereq: MATH 527; 528; 645.

MATH 753 - Introduction to Numerical Methods I
Credits: 4.00
Introduction to mathematical algorithms and methods of approximation. Topics include a wide survey of approximation methods. Methods examined include polynomial interpolation, root finding, numerical linear algebra, numerical integration, and the approximation of differential equations. Included in each case is a study of the accuracy and stability of a given technique, as well as its efficiency. Prereq: MATH 426; CS 410.

MATH 754 - Introduction to Numerical Methods II
Credits: 4.00
Introduction to the tools and methodology of scientific computing through the examination of interdisciplinary case studies from science and engineering. Emphasis on numerical approaches to solving linear systems, eigenvalue-eigenvector Problems and ordinary and partial differential equations problems are solved on various hardware platforms using a combination of application software and data visualization packages. Prereq: CS 410 or 415; MATH 527, 645, 753 or permission.

MATH 755 - Probability and Stochastic Processes with Applications
Credits: 4.00
Introduction to the theory, methods, and applications of randomness and random processes. Probability concepts, random variable, expectation, discrete and continuous distributions, stochastic processes, Markov chains, Poisson processes, moment-generating functions, convergence of random variables. Prereq: MATH 528 and 639; (or 644);/or permission.

MATH 756 - Principles of Statistical Inference
Credits: 4.00
Introduction to the basic principles and methods of statistical estimation and model fitting. One- and two-sample procedures, consistency and efficiency, likelihood methods, confidence regions, significance testing, Bayesian inference, nonparametric and resampling methods, decision theory. Prereq: MATH 755; or 528, 639, (or 644), and permission.

MATH 761 - Abstract Algebra
Credits: 4.00
Basic properties of groups, rings, fields, and their homomorphisms. Prereq: MATH 531 or 545. Writing intensive.

MATH 762 - Linear Algebra
Credits: 4.00
Vector spaces over arbitrary fields, linear transformations and their relationship with matrices, eigenvalues and eigenvectors, the rational and Jordan canonical forms for linear transformations. Prereq: MATH 761.

MATH 764 - Advanced Algebra
Credits: 4.00
Topics selected from rings, modules, algebraic fields, and group theory. Prereq: MATH 761. (Offered in alternate years.)

MATH 767 - One-Dimensional Real Analysis
Credits: 4.00
Theory of limits, continuity, differentiability, integrability. Prereq: MATH 531, or 545.

MATH 776 - Logic
Credits: 4.00
Examination of the basic notions of soundness and completeness, first for sentential and then for propositional logic. Turning to the question of decision procedures for logical formulae, the concept of recursive function, which emerges in the work of Church and Turning, provides the essential link between logic and theory of computation. The course culminates with Godel's Incompleteness Theorems, which demonstrate the intrinsic limitations of the logical method. Prereq: MATH 531. (Offered in alternate years.)

MATH 780 - Teaching MIddle School Mathematics
Credits: 4.00
Teaching and learning of middle school mathematics. Students examine the major mathematical concepts presented in the middle school curriculum and learn techniques for planning, designing, and evaluating procedures for helping students to learn these concepts. Prereq: MATH 426, 700, and EDUC 500 or equivalents, or by permission.

MATH #783 - Set Theory
Credits: 4.00
Axiomatic set theory, including its history. Cantor's theory of infinite cardinal and ordinal numbers seemed laden with contradictions and paradoxes. A satisfactory treatment of these difficulties came with the axiomatic set theory of Zermelo and Fraenkel. This course develops the Zermelo-Fraenkel axioms and examines cardinal and ordinal arithmetic in the context they provide. The course then investigates the consequences of various additional axioms extending Zermelo-Fraenkel, such as the Axiom of Choice, the Continuum Hypothesis, large cardinal axioms of determinacy. Prereq: MATH 531. (Offered in alternate years.)

MATH 784 - Topology
Credits: 4.00
Open sets, closure, base, and continuous functions; connectedness, compactness, separation axioms, and metrizability. Prereq: MATH 531.

MATH 788 - Complex Analysis
Credits: 4.00
Complex functions, sequences, limits, differentiation and Cauchy-Riemann equations, elementary functions, Cauchy's theorem and formula, Taylor's and Laurent's series, residues, conformal mapping. Prereq: MATH 767. (Not offered for credit if credit is received for MATH 647.)

MATH 791 - Teaching of Mathematics, 7-12
Credits: 4.00
Methods for teaching middle and secondary school mathematics; survey of instructional materials; uses of models, calculators, and computers; integrating reading, writing, and problem solving into mathematics curricula; methods of assessment; theories of learning mathematics; review and evaluation of curriculum materials, software and instructional resources; and introduction to professional organizations and publications. Prereq: EDUC 500 or equivalent; MATH 426;/or permission.

MATH 796 - Topics
Credits: 4.00
New or specialized courses not covered in regular course offerings. Prereq: permission. May be repeated up to 8 credits.

MATH 799 - Senior Thesis
Credits: 2.00 or 4.00
Students work under the direction of a faculty sponsor to plan and carry out independent research resulting in a written thesis. Required for honors-in-major. Prereq: senior standing; a written proposal endorsed by a faculty sponsor and approved by the department chairperson (or designee). May be repeated up to 4 credits. Writing intensive.