A quantitative reasoning course which includes topics from college algebra ( such as functions, linear, exponential and logarithmic models), statistics, and probability. Emphasizes modeling, problem-solving and applications. Designed for students whose programs do not require further coursework in pre-calculus or calculus. Appropriate for students majoring and minoring in areas such as the arts, humanities, social sciences, and education.
QUANTITATIVE REASONING - Waiver
Designed to give students a broad understanding and appreciation of mathematics. Includes topics not usually covered in a traditional algebra course. Topics encompass some algebra, problem solving, counting principles, probability, statistics, and consumer mathematics. This course is designed to meet the University Proficiency Requirement for students who do not wish to take any course having MATH 141 as a prerequisite.
A functional approach to algebra with emphasis on applications to different disciplines. Topics include linear, exponential, logarithmic, quadratic, polynomial and rational equations and functions, systems of linear equations, linear inequalities, radicals and rational exponents, complex numbers, variation. Properties of exponents, factoring, and solving linear equations are reviewed.
Mathematical preparation for the understanding of quantitative methods in management and social sciences. Topics include sets, relations, linear functions, interest, annuities, matrices, solution of linear systems by graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability. College of Business and Economics majors must take this course on a conventional grade basis.
A study of topics in early childhood mathematics, including sets, numbers, operations, measurement, data, and geometry. The focus is on increasing conceptual understanding of mathematics, highlighting connections, and developing the ability to communicate mathematical knowledge. Problem-solving methods used by children will also be explored. Manipulatives, cooperative learning activities, and problem solving strategies are used throughout the course.
A study of sets, whole numbers, fractions, integers, decimals and real numbers, basic arithmetic operations and their properties, standard and alternative algorithms and estimations strategies; problem-solving, proportional reasoning and algebraic thinking. Manipulatives and cooperative learning activities are used throughout the course. For elementary education majors.
Topics in probability and statistics, with emphasis on descriptive techniques. Investigations in geometric figures, measurement, construction, transformations, congruent and similar geometric figures. Problem solving strategies, manipulatives, and cooperative learning activities are emphasized throughout the course.
Study of polynomial, radical, rational, piecewise, exponential, and logarithmic functions, including basic graphs, transformations, inverses, and combining functions; solving equations and inequalities both algebraically and graphically is explored. The course also includes an introduction to vectors.
Study of trigonometric functions including basic graphs, transformations, and inverses; trigonometric functions are studied through the unit circle and right triangle approaches. Also studied are trigonometric identities, equations, and applications, including Law of Sines and Law of Cosines, as well as polar coordinates.
Study of polynomial, radical, rational, piecewise, exponential, logarithmic, and trigonometric functions, including basic graphs, transformations, inverses, and combining functions; solving equations and inequalities both algebraically and graphically is explored. In addition, trigonometric functions are studied through the unit circle and right triangle approaches. Also studied are vectors, trigonometric identities, trigonometric equations, and polar coordinates.
A study of logic particularly as it is used in the game of chess and, most particularly, in chess strategy and the end game of chess. The rules are taught to those who are not already acquainted with the game.
A course on the principles, procedures and concepts surrounding the production, summarization and analysis of data. Emphasis on critical reasoning and interpretation of statistical results. Content includes: probability, sampling, and research design; statistical inference, modeling and computing; practical application culminating in a research project.
A general survey of the calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, and integration. Business and social science applications are stressed.
An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, exponential and logarithmic functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included. A student may earn credit for only one of MATH 243, MATH 250, and MATH 253.
Review of algebraic and trigonometric functions, transcendental functions, limits, study of the derivative, techniques of differentiation, continuity, applications of the derivative, L' Hopital's Rule and indeterminate forms, the Riemann integral, Fundamental Theorem of Calculus, and substitution rule.
Techniques of integration, applications of the integral, introduction to differential equations, polar coordinates and conic sections, infinite sequences and series. This course includes a writing component.
Solid analytic geometry, vectors and vector functions, functions of several variables, multiple integrals and their applications.
This course will cover basic topics in R, a statistical computing framework. Topics include writing R functions, manipulating data in R, accessing R packages, creating graphs, and calculating basic summary statistics.
This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. Topics covered will include sets, logic, Boolean algebra and switching circuits, combinatorics, probability, graphs, trees, recursion, and algorithm analysis. Expressing mathematical ideas and writing proofs will be emphasized.
Preparation for the William Lowell Putnam Competition. Includes advanced problem solving techniques in pure mathematics. Review of previous examination problems and related material. May be repeated for a total of four credits. Satisfactory/No Credit only.
Study of a selected topic or topics under the direction of a faculty member. Repeatable. Department Consent required.
A first course in real analysis. Topics include properties of the real numbers, convergence of sequences, monotone and Cauchy sequences, continuity, differentiation, the Mean Value Theorem, and the Riemann integral. Emphasis is placed on proof-writing and communicating mathematics.
This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, and the use of computers to analyze statistical problems. This course contains a writing component.
Sets and counting, probability spaces, discrete and continuous random variables, mathematical expectation, discrete and continuous distributions with applications and probabilistic computing using R.
This course will cover the topics of interest theory listed in the Society of Actuaries/Casualty Actuarial Society syllabus for Exam FM/2. Topics include the time value of money, annuities, loans, bonds, general cash flows and portfolios, and immunization schedules.
This course is primarily for pre-service elementary and middle school teachers. Students will be introduced to the concepts of calculus, which include infinite precesses, limits, and continuity. In addition, dirivatives and integrals, and their relationship to area and change will be covered.
The topics included in this course are foundations of Euclidean geometry, Euclidean transformational geometry, modern synthetic geometry that builds on Euclidean geometry, selected finite geometries, and an introduction to non-Euclidean and projective geometry, including their relationship to Euclidean geometry. Although the course is adapted to the prospective teacher of geometry, it will also meet the needs of those in other majors needing a background in geometry. Standards and guidelines of appropriate national and local bodies will be implemented.
Systems of linear equations, matrices and determinants, finite dimensional vector spaces, linear dependence, bases, dimension, linear mappings, orthogonal bases, and eigenvector theory. Applications stressed throughout.
An introduction to probability and statistics for teachers. Topics covered include counting techniques, basic probability theory, exploratory data analysis, simulation, randomization, and statistical inference. This course contains a writing component.
Ordinary differential equations: general theory of linear equations, special methods for nonlinear equations including qualitative analysis and stability, power series and numerical methods, and systems of equations. Additional topics may include transformation methods and boundary value problems. Applications stressed throughout.
This course covers theory and applications of commonly used distribution-free tests such as the sign test and the Wilcoxon signed rank test. Other topics include: the Kruskal-Wallis and Friedman tests for analysis of variance, nonparametric regression, and nonparametric bootstrapping.
This course is primarily for pre-service elementary and middle school teachers. Students will learn a variety of problem solving strategies applicable in elementary and middle school. The applications will cover many different areas of mathematics.
A study of the development of mathematical notation and ideas from prehistoric times to the present. Periods and topics will be chosen corresponding to the backgrounds and interests of the students.
Modeling involving formulation of deterministic, stochastic and rule-based models and computer simulation in order to make predictions. Topics may include unconstrained and constrained growth models, equilibrium and stability, force and motion, predator-prey model, enzyme kinetics, data-driven models, probability distributions, Monte Carlo simulations, random walk, diffusion, cellular automaton simulations, and high performance computing.
A course for students who need a review of basic mathematics or who lack the computational skills required for success in algebra and other University courses. Topics include fractions, decimals, percent, descriptive statistics, English and metric units of measure, and measures of geometric figures. Emphasis is on applications. A brief introduction to algebra is included at the end of the course. This course does count toward the semester credit load and will be computed into the grade point average. It will not be included in the 120 credits required for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Not available to students who have satisfied the University Proficiency requirement in mathematics. ACT Math subscore 14 or below (SAT 340 or below) Arithmetic skills test required.
A course for those who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational and radical expressions, and systems of linear equations. The course credits count towards the semester credit load and GPA, but are not included in the 120 credit graduation requirement.
An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics from logic, sets, algebraic structures, and number theory.
A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tessellations, transformations, problem solving, symmetries of polygons and polyhedra, and use of geometry computer software.
A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, module arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.
This is a second course in regression analysis and its applications. Topics include correlation, simple and multiple linear regression, model assumptions, inference of regression parameters, regression diagnostics and remedial measures, categorical predictors, multicollinearity,and model selection. Real data re emphasized and analyzed using statistical software such as R or SAS.
The course revisits the high school curriculum from an advanced perspective. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes number systems, functions, equations, integers, and polynomials. Connections to geometry are emphasized throughout the course.
The course continues the exploration of the high school curriculum from an advanced perspective that was started in MATH 421. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes congruence, distance, similarity, trigonometry, area, and volume. Connections to algebra are emphasized throughout the course.
An introduction to applied experimental design with emphasis on the construction of causal knowledge, analytical techniques, and statistical publication requirements. Topics include single and multiple factor, randomized block, and repeated measure designs; model selection, underlying assumptions, inference, diagnostics, multiple comparison procedures, confidence intervals, effect sizes, and difficulties in applied research settings. The R computing platform will be used.
Practical issues in sampling, applied survey research, analysis of complex survey data, and professional reporting are emphasized. Topics include random and non-random sampling, parameter estimation, bias, questionnaire design and wording, psychology of participant response, data imputation, weighting, finite population correction, analysis of categorical data and hierarchical linear models. Students will conduct survey research and complete a data analysis project.
An introduction to point-set topology, including such topics as topological spaces, mappings, connectedness, compactness, separation axioms, metric spaces, complete spaces, product spaces and function spaces.
This course will cover moment generating functions; multivariate probability distributions including moments of linear combinations of random variables and conditional expectation; functions of random variables; sampling distributions and the Central Limit Theorem; the theory and properties of estimation; confidence intervals; and the Neyman-Pearson Lemma, likelihood ratio tests and common tests of hypotheses.
The course is designed to prepare students for Exam P/1, the first actuarial exam which tests students' knowledge of and ability to use and apply fundamental probability tools in assessing risk. Basic concepts from risk theory are introduced, probability theory is reviewed, and sample questions from previous exams are discussed.
This course is designed to prepare students for Exam FM/2, the second acturial exam which tests students' knowledge and understanding of the fundamental concepts of financial mathematics. Derivatives are introduced, interest theory is reviewed, and sample questions from previous exams and practice exams from other sources are discussed.
This course will examine basic concepts and applications of graph theory. Topics covered will be selected from trees, connectivity, paths and cycles, coloring, matching and covering problems, digraphs, and network flows.
An introductory survey of abstract algebra and number theory with emphasis on the development and study of the number systems of integers, integers mod n, rationals, reals, and complex numbers. These offer examples of and motivation for the study of the classical algebraic structures of groups, rings integral domains and fields. Applications to algebraic coding theory and crystallography will be developed if time allows.
This course is a continuation of MATH 452 with emphasis on ring and field theory. Topics include a review of group theory, polynomial rings, divisibility in integral domains, vector spaces, extension fields, algebraic extension fields, finite fields, etc.
Selected topics in ordinary differential equations: series solutions, stability, transform methods, special functions, numerical methods, vector differential calculus, line and surface integrals.
Fourier analysis, partial differential equations and boundary value problems, complex variables, and potential theory.
This course is a study of the algebra and geometry of complex numbers, the properties of analytic functions, contour integration, the calculus of residues and the properties of power series.
This course presents a rigorous treatment of the differential and integral calculus of single variable functions, convergence theory of numerical sequences and series, uniform convergence theory of sequences and series of functions, metric spaces, functions of several real variables, and the inverse function theorem. This course contains a writing component.
Emphasis on numerical algebra. The problems of linear systems, matrix inversion, the complete and special eigenvalue problems, solutions by exact and iterative methods, orthogonalization, gradient methods. Consideration of stability and elementary error analysis. Extensive use of microcomputers and programs using a high level language. This course contains a writing component.
An analytic, geometric, and intuitive study of continuous and discrete low-dimensional nonlinear dynamical systems. The basic notions of stability, bifurcations, chaotic systems, strange attractors, and fractals are examined. Specific applications will be taken from diverse fields such as Biology, Chemistry, Economics, Engineering, and Physics.
Variable credit course offering with a defined topic. Repeatable with a change of topic.
Variable topics. Group activity oriented presentations emphasizing `hands on` and participatory instructional techniques.
A study for which data is obtained or observations are made outside the regular classroom. Repeatable. Instructor Consent required.