Course descriptions for Mathematics

An individually paced review of pre-college mathematics concepts and skills. Designed to prepare students for college-level mathematics. Focuses on basic concepts and skills and effective communication of quantitative information and concepts. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts. (Offered fall and spring semesters, and summer session.)

A continuation of Math 98 for those students who have not yet satisfied the ELM requirement. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts. (6 unit section of MATH 99 is offered only in the spring semesters) (Offered fall, spring, and summer sessions)

A continuation of Math 98 for those students who have not yet satisfied the ELM requirement. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts. (6 unit section of MATH 99 is offered only in the spring semesters) (Offered fall, spring, and summer sessions)

Covers linear, quadratic, exponential, and logarithmic functions; systems of equations and inequalities; simple and compound interest; annuities; loan; discrete probability; counting principles, frequency distributions, measures of central tendency; measures of dispersion, confidence intervals; areas; and volumes. Draws examples from applications in the social sciences, biological sciences, and business. Uses technology as a tool to acquire, visualize, and analyze data.

Trigonometric and inverse trigonometric functions; trigonometric identities and equations; applications involving right triangles illustrating the law of sines and cosines.

Mathematical modeling and data analysis applicable to the social sciences and business selected from the following: Linear functions, systems of linear equations, matrices, linear programming including the simplex method and the mathematics of finance.

Mathematical modeling and data analysis applicable to the social sciences and business selected from the following: logic, set theory, combinatorics, probability, probability distributions, statistics, Markov chains, graph theory, and game theory.

Develops student understanding of geometry by comparing and contrasting selected structures and theorems in Euclidean geometry with analogous or contrasting structures and theorems from at least two non-Euclidean geometries. Students emerge with greater insight into Euclidean geometry, increased spatial understanding, appreciation of geometry as an abstract system, and knowledge of applications of both Euclidean and non-Euclidean geometrical concepts. (Offered when enrollment warrants.)

Develops students' understanding of concepts needed in preparation for calculus. Intended for teachers of mathematics in grades 6-12. Students study linear, exponential, polynomial, and rational relations. Emphasizes general functional notation, graphing, data analysis, and modeling. Students complete projects involving a hands-on approach. (Offered when enrollment warrants.)

Build on knowledge of algebra using algebraic, graphical, and geometric reasoning to recognize patterns and structure, model information, and solve problems from various disciplines. Students use data from experiments; translate physical phenomena into equations; and analyze, solve, present, and interpret qualitative and numerical solutions. Students use a variety of representations, tools, and technologies to link modeling techniques and purely mathematical concepts, and to solve applied problems. (Offered when enrollment warrants.)

An in-depth look at algebra topics from grades 6-10 including algebraic operations, mathematical expressions, solving equations, and systems of equations and inequalities. The use of patterns and functions to represent and solve problems; connections among symbolic, graphic, and tabular representations; and selecting and applying appropriate technologies for problem solving. (Offered when enrollment warrants.)

For teachers of grades 6-12 who want to expand their knowledge of algebra and geometry. The Ancient Greeks did not distinguish between algebra and geometry as we do today. In fact, they understood much of what we now consider algebra as geometric statements about plane figures. Shows how these geometric interpretations can be used to develop understanding of beginning and intermediate algebra. (Offered when enrollment warrants.)

For teachers of mathematics. Traces the historical development of the real number system. Emphasizes the evolution of mathematical thought examined in a cultural and historical framework. Students gain enhanced insight into the real numbers and operations on the real numbers by contrasting our modern notation, techniques, and procedures with those used in earlier eras. (Offered when enrollment warrants.)

For middle and high school teachers of algebra or mathematics courses immediately preceding algebra. Focuses on developing students' ability to use algebra as a language to model real-world situations, and to use algebraic models to analyze and gain understanding of real-world situations. (Offered when enrollment warrants)

Functions and graphs, including polynomial, rational, exponential, logarithmic, and trigonometric functions. Applications, data analysis, mathematical modeling, and analytic trigonometry.

Includes limits, continuity, derivatives including trigonometric functions, chain rule, curve sketching, extremum problems, implicit differentiation, related rates, Mean Value Theorem, logarithmic and trigonometric functions, introduction to integration, fundamental theorem of calculus, substitution, and applications. (Offered every semester)

Includes the calculus of exponential and logarithmic functions, trigonometric and inverse trigonometric functions, techniques of integration, separable differential equations, Taylor polynomials, L'H?pital's rule, improper integrals, series, and introduction to partial derivatives. (Offered every semester)

Includes sets and sequences, elementary logic, relations, induction, counting principles, discrete probability, Boolean algebra, logic networks, matrices, graph theory, and trees. Applies these topics to real life and branches of science, particularly computer science. (Offered every semester)

Student and faculty member select topic of study and number of credits. (Offered when enrollment warrants.)

Vectors in three dimensions, solid analytic geometry, partial differentiation, multiple integration, differentiation under the integral sign, vector field theory. (Offered every semester)

Introduces matrices and systems of linear equations and covers topics such as determinants, vectors in two and three dimensions, vector spaces, linear transformations, and eigenvector eigenvalue decompositions. Emphasizes applications to real-world issues. Students use computing technology for the course. (Offered when enrollment warrants.)

First order ordinary differential equations including direction fields, separation of variables, first order linear equations, growth and decay, nonlinear models. Linear algebra including systems of linear equations, matrix inverses, determinants, vector spaces and subspaces, basis and dimension. (Credit/No Credit Available)

The capstone process begins in MATH 300. Students develop library research, scholarly reading, writing, and collaboration skills needed to develop, implement, and complete their capstone projects. Moreover, students investigate different philosophical viewpoints and notions of truth relating to mathematics and explore the utility of mathematics. Students also develop a learning plan that integrates their major concentration, capstone interests, and personal and professional goals.

Develops understanding of the power of mathematical abstraction and symbolism through the study of advanced algebraic structures. Studies matrices, groups, integral domains, rings, and fields and discusses their relationship to the pre-college algebra curriculum. Emphasizes problem solving and requires students to use a variety of algebraic representations and techniques to model and analyze problem situations and solutions. (Offered when enrollment warrants.)

Introduces Euclidean and non-Euclidean geometries as vehicles for studying axiomatic systems, for representing real world phenomena, and for visualizing mathematical ideas. Emphasizes aesthetic and practical applications of geometry and methods of proof. Students are required to do formal constructions and proofs using compass, straightedge, and computer software. (Offered when enrollment warrants.)

A careful analysis of methods of proof, axiomatic systems, consistency, the elaboration of mathematical structures from a minimal set of axioms and basic principals of symbolic logic. Students gain an understanding of the nature and purpose of axiomatic systems, and the ability to prove fundamental theorems utilizing various mathematical systems. (Offered when enrollment warrants.)

The first of a two-course sequence intended for future elementary teachers. Students develop an in-depth understanding of key concepts in K-8 mathematics and of students' learning of K-8 mathematics concepts. (Offered fall and spring semesters.)

Second in a sequence of courses intended for future elementary and middle school teachers. Students in this course will develop an in-depth understanding of additional key concepts in K-8 mathematics and further develop their understanding of children's learning processes in mathematics in general. (Offered fall and spring semesters.)

Concepts and applications of sample space, probability, random variable, expectation, moment, elementary combinatorial analysis, moment generating function, distribution, density function, estimation theory, hypothesis testing, regression, correlation, and an introduction to non-parametric statistics and statistical computing.

Introduces the tools, terminology, and symbols of advanced mathematics. Sets, infinite unions and intersections, index sets, functions, partially ordered and totally ordered sets, axiom of choice, and number systems from the natural numbers to the complex numbers. Formerly MATH 280.

Introduces the properties of integers. Topics include the division and Euclidean algorithms, mathematical induction, congruences, fundamental theorem of arithmetic, perfect numbers, number theoretic functions, and prime number theorem. (Offered every third semester)

The history of mathematics from ancient to modern times. Students learn to solve problems using only the tools of the past. Mathematics is developed in the context of its impact on the development of science and the interaction of mathematics with other fields of human endeavor such as philosophy, arts, and social values. (Offered every third semester)

The Hilbert postulates and axiomatic systems, isometries in the Euclidean Plane, non-Euclidean geometries, finite geometries, and the construction of geometries from fields. (Offered every third semster)

Linear equations and matrices, vector spaces, dual spaces and inner product spaces, linear transformations, determinants, eigenvalues and eigenvectors, systems of linear differential equations, and applications. (Offered fall semester)

Series solution of linear differential equations with variable coefficients, systems of differential equations, phase plane analysis, existence and uniqueness theorems, singular points, stability theory, transform analysis, and applications.

Complex numbers; analytic functions, Cauchy-Riemann equations; linear fractional transformations; construction and geometry of the elementary functions; Green's theorem, Cauchy's theorem; Jordan curve theorem, Cauchy's formula; Taylor's theorem, Laurent expansion; analytic continuation; isolated singularities, Liouville's theorem; Abel's convergence theorem and the Poisson integral formula.The fundamental theorem of algebra. (Credit/No Credit Available)

Study of teaching techniques and pedagogies involving tutoring mathematics. Overview of the mathematics program, techniques for providing feedback to students, assessing student performance in the classroom, and cultivating math study skills Primarily for students concurrently tutoring for Mathematics department. Course may be repeated for credit up to eight times.

Service learning placements in middle or high schools help students deepen their understanding of mathematical principles, techniques, and methodologies for effective instruction. Students also study how issues of social justice and equity affect mathematical literacy and why it is important for everyone to be mathematically literate.

Service learning component of Math 362S which may include aiding or tutoring in mathematics classes or facilitating mathematics activities in after-school programs. (Offered when enrollment warrants.)

Service learning placements in local non-profit organizations, school districts and community organizations help students deepen their understanding of mathematical and statistical principles, techniques, and methodologies for effective consulting. Students will also study how the need for mathematical and statistical analysis can influence issues of social justice and equity within the local and global community.

An advanced study of logic and discrete structures that have application in computer science. Includes logic, propositional and predicate calculus, proof structures, algorithms, and complexity. Emphasizes applications to core areas of computer science, such as computer architecture, programming languages, the theory of computation, artificial intelligence, software engineering, and relational databases.

Topics include tempering of scales, harmony and the overtone series, intervals, the chromatic scale and modular arithmetic, algebraic properties of diatonic harmony, Fourier series and timbre, polyrhythms and metric modulation and an exploration of connections with set theory. The course will incorporate listening to a wide variety music, including western classical, jazz and music from various parts of the world.

The construction of mathematical models to solve real world problems. Model types include continuous, discrete, deterministic and stochastic. The entire modeling process from construction of the model, fitting data to the model, analysis of the model including model selection, and verification of the model covered. Examples from a variety of disciplines including biology, physics, economics and finance.

Methods of numerical approximation of the value of functions, polynomials, systems of equations and integrals using a programming language such as R, C++ or Mathematica. Topics may include accuracy of approximate calculations, root finding methods, interpolation, numerical differentiation and integration, numerical solutions to ordinary differential equations, regression, optimization and Monte Carlo methods.

Derivation of partial differential equations; separation of variables; equilibrium solutions and Laplace's equation; Fourier series; method of characteristics for the one dimensional wave equation. Solutions of non-homogeneous equations. (Credit/ No Credit Available)

An introduction to basic notions and techniques in Enumerative Combinatorics. Basic structures of enumeration including enumerative families like binomial coefficients, Catalan numbers, Fibonacci numbers, Eulerian numbers, Bell numbers, and Stirling numbers; compositions and partitions; recurrences; permutations and permutation statistics; generating functions; partially ordered sets; applications to Symmetric functions.

Introductory graph theory with applications. Graphs and digraphs. Eulerian and Hamiltonian graphs. The traveling salesman problem, connectivity, trees, planarity, colorings, scheduling, minimal cost networks and graph models. (Credit/No Credit Available)

Studies a particular topic in Mathematics. May be repeated for credit when topics vary. (Offered only as interest warrants.) (Credit/No Credit Available)

Student and faculty member select topic of study and number of credits. (Offered when enrollment warrants.)

Under the guidance of a faculty member, students complete a formal write up and present research in an area of their interest.

Detailed study of the theory of basic algebraic systems, groups, and rings. Topics include subgroups, permutation groups, homomorphisms, subrings, ideals, and quotient rings.

A rigorous treatment of rings and fields. Examples from many branches of mathematics. Ideals and quotient rings, categorization of rings, Euclidean domains, polynomial rings and fields, unique factorization domains, extension fields, and Galois theory.

A rigorous introduction to the n-dimensional real number system. Topics include construction of the real numbers, topology of real numbers, continuity, derivatives and integration in multiple dimensions, sequences and series, and sequences and series of functions.

A continuation of MATH 420. Topics include implicit function theory, conformal mappings, Lagrange multipliers, special functions, transforms, uniform convergence of integrals, calculus of variations, Fourier series, and Lebesgue integration.

Under the guidance of a faculty member, students complete Capstone projects. Provides one-on-one guidance for students' research in mathematics, statistics, or mathematics education. To be taken concurrently with MATH 401. Course may be repeated up to three times.

Student and faculty member select topic of study and number of credits. (Offered when enrollment warrants.)

Student and faculty member select topic of study and number of credits. (Offered when enrollment warrants.)