This course is designed to enhance students’ understanding of calculus through active and collaborative learning. Participants will work in small groups to explore concepts and problem-solving strategies under the guidance of peer leaders. Through guided inquiry, discussion, and practice, students will develop critical thinking, communication, and teamwork skills while deepening their knowledge of calculus. The workshop format fosters a supportive learning environment where students can ask questions, share ideas, and learn from their peers.
This is the laboratory portion of MATH 1434, Precalculus Mathematics.
This is the laboratory portion of MATH 1451, Calculus I.
This is the laboratory portion of MATH 1452, Calculus II.
This course is designed to help students review and strengthen mathematical skills needed for success in MATH 1313.
Topics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included. This course may be repeated for credit.
A review of arithmetic and algebraic skills needed for success in college-level mathematics. Students take assessments and will study and practice topics needed to strengthen their math skills as identified by their personal assessment. Topics may include fractions, signed arithmetic, order of operations, signed and fractional exponents, solving linear equations and inequalities, absolute value, quadratic equations, polynomials, rational functions, algebraic fractions, exponentials and radicals. This course is offered to aid students needing to strengthen their basic mathematical skills. Students who already have credit for a higher-level mathematics course will not be given credit for this course. This course may not be counted as part of the mathematics major or the mathematical studies major.
Mathematical topics needed for the critical evaluation of quantitative information and arguments, including set theory, counting, logic, and the critical appraisal of graphs and tables, including the use of some simple mathematical models, and an introduction to probability and statistics. Additional topics may be selected from finance, graph theory, number theory, geometry and matrix theory. This course may not be counted as part of a mathematics major or a mathematical studies major.
Evaluating and manipulating algebraic expressions, the laws of exponents, polynomials, factoring, rational expressions, radicals, the quadratic formula, solving equations and inequalities, systems of linear equations, an introduction to graphing, and applications. Students with no previous exposure to algebra should take MATH 1302 before MATH 1313. MATH 1313 may not be counted as part of a mathematics major. It may not be counted as part of a mathematical studies major except by students with a specialization in middle grades.
A study of trigonometric functions, exponentials, logarithms, and applications for students needing a more comprehensive background than the accelerated coverage given in MATH 1434. This course may not be counted as part of the mathematics major.
Sets, relations, functions, roots of polynomial equations, trigonometry, and analytic geometry. This course may not be counted as part of the mathematics major. This course includes one semester hour credit for laboratory sessions.
Limits, continuity, differentiation and integration of elementary and transcendental functions, L’Hôpital’s Rule. Applications, including rates of change, max/min problems, and area between curves. This course includes one semester hour credit for laboratory sessions.
A continuation of MATH 1451. Topics include: Techniques and applications of integration, improper integrals, parametric representations of curves, polar coordinates, L’Hôpital’s Rule, numerical approximation of integrals, an introduction to differential equations, and infinite series. This course includes one semester hour credit for laboratory sessions.
This is the laboratory portion of MATH 2451, Calculus III.
Topics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. This course may be repeated for credit.
Topics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included. This course may be repeated for credit.
This course is a mathematically rigorous introduction to fundamental concepts required for higher-level mathematics. Topics include logic, sets, relations, functions, and algebraic structures, with an emphasis on formal mathematical proof techniques. It is required for the mathematics major.
A study, from an advanced perspective, of the concepts and skills involved in arithmetic and numeration. Topics include sets, rational numbers (whole numbers and place value, fractions, integers and decimals), number theory, properties and algebraic reasoning, arithmetic operations, percents, ratios, and proportions. Problem solving is emphasized. This course, designed for education majors, may not be counted as part of the mathematics major or minor or meet the Liberal Arts Core Curriculum, math proficiency requirement.
A study, from an advanced perspective, of the basic concepts and methods of geometry, measurement, probability and statistics. Topics include: representation and analysis of data; discrete and conditional probability; measurement; and geometry as approached through similarity and congruence, through coordinates, and through transformations. Problem solving is emphasized. This course, designed for education majors, may not be counted as part of the mathematics major or minor or meet the Liberal Arts Core Curriculum, math proficiency requirement.
Introduction to linearity in mathematics. Topics include: matrices, determinants, abstract vector spaces, linear dependence, bases, eigenvalues and eigenvectors, and linear transformations.
A continuation of MATH 1452. Topics include: three-dimensional coordinate systems, quadric surfaces, cylindrical and spherical coordinates, vector calculus in three dimensions, partial derivatives, the total differential, multiple integrals, line integrals, surface integrals, vector fields, Green’s Theorem, Stokes’ Theorem, the Divergence Theorem, and applications. This course includes one semester hour credit for laboratory sessions.
This is a seminar style course covering topics related to computer science and cybersecurity that are not covered in MATH 2323, MATH 3311, and MATH 3314. Topics may include, but are not limited to, cryptography, graph theory, probability and statistics, discrete mathematics, and numerical methods and their implementation.
A study of classical Euclidean geometry using both analytic and synthetic techniques, with an emphasis on the formal development of geometry. Topics include: axiomatic systems, congruence and similarity, transformations, area and volume, Euclidean construction, finite geometries, and a brief introduction to non-Euclidean geometry. This course is required for the mathematical studies major but may not be counted as part of a mathematics major.
An introduction to elementary probability and statistics with applications to the life sciences. Topics include: frequency distributions, measures of central tendency and spread, probability concepts, discrete and continuous distributions, point and interval estimation, hypothesis testing, analysis of variance, and an introduction to linear correlation and regression. This course includes one semester hour credit for laboratory sessions. May not be counted as part of a math major or a math studies major. Students may not receive credit for both MATH 3304 and MATH 3404.
This course introduces students to elements of combinatorics, number theory, and discrete structures. Topics covered include: permutations, combinations, prime factorizations, the Euclidean Algorithm, relations, the pigeonhole principles, inclusion and exclusion, and finite state machines. It exposes students to areas of mathematics of current practical interest and involves the use of proof and algorithmic thinking.
A mathematical development of the basic concepts of probability and statistics, emphasizing the theory of discrete and continuous random variables, with applications in science and engineering. Topics include descriptive statistics, probability theory, random variables, expected value, probability density functions, probability distributions, correlation and regression, and an introduction to statistical inference. Students may not receive credit for both MATH 3304 and MATH 3314.
An introduction to dynamical systems. This course develops the theory for normal forms, structural stability of solutions, robust behavior, transversality, and local bifurcations.
A first course. Topics include: existence and uniqueness of solutions, solutions of linear equations, solutions of higher order linear equations with constant coefficients, infinite series solutions, numerical solutions, solutions of linear systems, an introduction to nonlinear differential equations, and application.
An introduction to the basic properties of partial differential equations, including ideas and techniques that have proven useful in analyzing and solving them. Topics include: vibrations of solids, fluid flow, molecular structure, photon and electron interactions, and radiation of electromagnetic waves, with emphasis on the role of partial differential equations in modern mathematics, especially in geometry and analysis.
An introduction to algebraic structures. Topics include: sets, operations, relations, groups, subgroups, equivalence classes, Lagrange’s Theorem, homomorphisms, rings, and ideals.
An introductory course in computer programming with applications to mathematics. The programming language used will vary; possible choices include but are not restricted to Java, C++, C#, Maple, and MATLAB. Topics include: design of algorithms, structured programming, data types, control structures, functions and procedures, and mathematical problem solving. This course may be repeated for credit provided a different computer programming language is used.
An introduction to complex analysis and the study of complex-valued functions of a single complex variable. Topics include: the complex number system; the Cauchy-Riemann conditions; analytic functions including linear, exponential, logarithmic and trigonometric transformations; differentiation and integration of complex-valued functions; line integrals; and Taylor and Laurent Series expansions.
Advanced techniques in applied mathematics for students of science and engineering, with topics chosen from partial differential equations, Laplace transforms, Fourier series, complex analysis, and vector analysis. (Offered also as PHYS 3383.)
A review of mathematical topics of special interest to students obtaining teacher certification in mathematics, including material from algebra, geometry, probability, statistics, linear algebra, discrete math, and others. This course includes instruction on technology used in teaching mathematics, both graphing calculators and computer software. Required for the mathematical studies major, but may not be counted as part of a mathematics major.
A rigorous introduction to mathematical analysis. Topics covered include: the real and complex number systems, basic topology, numerical sequences and series, continuity of functions, and differentiation.
A continuation of MATH 4301. Further study of mathematical analysis. Topics covered include: Riemann integration, sequences and series of functions, functions of several variables, and integration of differential forms.
An introduction to modern approximation techniques. This course shows how, why, and when numerical techniques can be expected to work and fail. It demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. Topics covered include: approximating solutions to equations in one variable, interpolation and approximation of polynomials, numerical differentiation and integration, applications to differential equations, and solutions of both linear and nonlinear systems of equations.
Further study of enumerative techniques and discrete structures including generating functions, recurrence relations, graph theory, spanning trees, optimization, and Boolean algebras.
An introduction to topology and its applications. Topics include: a review of basic abstract algebra; the definition of a topological space, interior, closure, and boundary of sets; subspace, product, and quotient topologies; continuity and homeomorphisms; metrics and metric spaces; connectedness; and compactness.
A continuation of MATH 4311. Topics include: dynamical systems and chaos, homotopy and degree theory, fixed point theorems, embeddings, knots, graphs, and manifolds.
Introduction to the theory of equilibrium solutions of nonlinear equations. Presentation of the theory of bifurcations includes the analysis of the nonlinear ordinary and algebraic equations that arise from the methods of reduction by projections.
Introduction to modeling in biology and genetics. Some of the models covered include populations models; host-parasite models; and gene spread models as described by difference equations, differential equations, and partial differential equations. The emphasis of this course will be to familiarize students with the selection of models and predictions based on the models chosen.
A continuation of MATH 3353. The focus of this course is on rings, domains, fields, polynomials, Galois theory, Boolean algebra, and modules. Other topics may be covered if time permits.
Further study of differentiable complex-valued functions of a single complex variable. Topics include: residue theory and contour integrals, z-transforms, conformal mapping, harmonic functions and their applications, Fourier Series, and Laplace transforms.
An introduction to diffeomorphisms and smooth manifolds. Topics covered include: tangent spaces, orientation of manifolds, vector fields, homotopy, and the index of a map.
