Mathematics (MAT)

A course designed to reinforce and strengthen topics in algebra in order to improve arithmetic and algebra skills, as well as quantitative reasoning and analytical skills. It provides the foundation for the math skills that students will need to succeed in College Algebra. This course is not a stand-alone course, students will take this course together with the College Algebra course. This course is intended to allow some students placing into developmental math an opportunity to earn credit for college level math course while providing the additional time and support associated with developmental courses.

A course designed to reinforce and improve mathematical skills, as well as quantitative reasoning and analytical skills. It provides the foundation for the math skills that students will need to succeed in Math for Liberal Arts. This course is not a stand-alone course, students will take this course together with the Math for Liberal Arts course. This course is intended to allow some students placing into developmental math an opportunity to earn credit for college level math course while providing the additional time and support associated with developmental courses.

A liberal arts mathematics course for non-mathematics and non-science majors. Explores several ideas of mathematics to give the student an appreciation of the significance of mathematics. The course covers mathematical patterns and problem solving, numeration and mathematical systems, other number bases, the binary number system, modular arithmetic, the Fibonacci sequence and the Golden ration, and real numbers and their representation.

This course is designed for liberal arts majors who need to fulfill their math and general education requirements. The course covers an introduction to set theory, growth models, financial mathematics, probability, and statistics. The goal of this course is to help students develop into problem solvers and critical thinkers.

A review of topics in intermediate algebra and an extended treatment of some topics such as equations, inequalities, relations and functions, including polynomial, rational, exponential, and logarithmic functions and graphs. Additional topics include solving linear systems of equations by various methods. This course is designed to illustrate several ways in which mathematics is used in the real world. We will explore some topics or general interest which are not typically taught in a formal mathematics class. The goal is for you to see not only how useful mathematics is but also how beautiful and elegant it can be.

A course for mathematics and science majors designed to de-velop and strengthen those topics in algebra and trigonometry that a student should master before taking a first standard course in calculus. Basic concepts from analytic geometry such as circles, ellipses and other conic sections. Roots of polynomials, graphs and transformations of graphs. Graphs of polynomial, and rational functions. Trigonometric identities and equations. The trigonometric and inverse trigonometric functions and their graphs. Graphing calculator is optional.

Basic algebraic concepts such as factorization of polynomials, solving basic algebraic equations. Lines and parabolas. Maxima and minima. Exponentials and logarithms. Compound interest and other exponential models. The study of matrices and their application. Examples include inversion and the solution of systems in linear equations, linear inequalities and linear programming (graphical approach), dual problems, and economic interpretation.

Introduces the basic concepts of functional relationships, the basic skills of differentiation and integration, maxima and minima problems, and several other applications of calculus, especially models in business, exponential models, and mathematics of finance.

Differential Calculus. Functions, including polynomials, rational and radical functions. Exponential and logarithmic functions. Trigonometric and inverse trigonometric functions. Limits, continuity, differentiation of algebraic and transcendental functions. Applications of the derivative, Fermat's Theorem,, Rolle's Theorem, the Mean Value Theorem. Monotone functions, maxima and minima. Asymptotes, Convexity and Concavity and sketching graphs. L'Hopital's rule. course.

Integral Calculus. Antiderivatives and the indefinite integral. Riemann sums and the definite integral. Properties of the integral and the Fundamental Theorem of Calculus. The logarithm via an integral, exponential, hyperbolic and inverse hyperbolic functions. Methods of integration, including the substitution method and integration by parts. Trigonometric integral and trigonometric substitutions. Integration of rational functions and rationalizing substitutions. Applications of integration, area, length, surface area and volume. Polar coordinates. Improper integrals.

Organization, description, and interpretation of data. Probability and probability distributions. Sampling distributions and estimation of population parameters. Testing hypotheses, linear regression, correlation analysis, and index numbers.

The course explores several facets of Cryptography: historical, mathematical, as well as technological. Basic ciphers and their attack methods are presented, including the mathematics behind. The language of programming C++ is introduced, and used to implement cryptographic algorithms. The course will be held in a lab. Invited speakers who currently work in the field of Cryptography will have short conversations with the students via zoom.

Topics of higher Euclidean geometry and geometric constructions. Geometrical transformations and different kinds of geometries. Projective and hyperbolic geometries.

Sequences and Series of real numbers. Vectors and vector -valued functions. Functions of several variables. Limits and continuity. The derivative, directional and partial derivatives. Chain rule. Maxima, minima, Lagrange's multipliers. Double and triple integrals, cylindrical and spherical coordinates and change of variable formula. Applications.

A treatment of the basic notions of calculus using computer and mathematical software programs, for example, Derive 6, Mathematica, etc. The course covers problems involving limits, derivatives, graphs, approximation of solutions. and approximation of series and integrals. Lab Fee.

The algebra and calculus of vectors, scalar and vector product, coordinate systems, space geometry, vector differential operators, divergence and curl of vector fields, curvilinear coordinates, line and surface integrals. Green's theorem, Stokes' theorem, and divergence theorem.

The algebra of propositions and quantifiers; sets, relations, functions, equivalence relations, partial and total orders, and product sets; Cantor hypothesis, cardinal and ordinal numbers, and well-ordered sets; Axiom of Choice, Zorn's dilemma, and well ordering axiom.

Systems of linear equations, vector spaces, linear independence basis and dimension; matrices and determinants, rank and nullity; eigenvalues and eigenvectors; diagonalizable matrices; linear transformations and matrices.

Methods of solving ordinary differential equations with applications. Linear differential equations of first-, second-, and higher-order applications. Systems of linear differential equations.

An introductory course dealing with divisibility, number theorems, theory and congruences, quadratic residues, and Diophantine equations. Quadratic residues and quadratic reciprocity law. Fermat's theory, Chinese remainder theorem, Euler's theorme, and Wilson's theorme.

faculty member in the Mathematics department. For students majoring in Mathematics Education, the independent study is on the history of mathematics.

The course explores basic types of attack; ciphers such as substitution ciphers, Hill ciphers, as well as Number Theory related problems such as congruence equations and modular exponentiation.

Fourier series and Laplace transformations: applications. Series solution of differential equations. Lengendre's and Bessel's equations. Partial differential equations.

Real numbers, axiom of continuity, least upper bounds, and greatest lower bounds; open and closed sets; continuity differentiation; maxima and minima for functions of two or more variables; the method of Lagrange; implicit function theorems; and general theorems of partial differentiation.

The theory of Riemann integration in one and many variables. Multiple integrals, Fubini's Theorem, the change of variable theorem. Improper multiple integrals. Integrals depending on a parameter, the Gamma and Beta functions. Sequences and Series of functions, uniform convergence, power series.

Sets and mappings; theory of groups, rings, and fields; homomorphisms, isomorphisms, and the first isomorphism theorem for groups and rings; the field of real/ complex numbers. Polynomials.

Complex numbers and the topology of the complex plane; analytic and elementary functions, contour integrals, conformal mappings, power series, Laurent series, Cauchy-Riemann partial differential equations; Cauchy-Goursat theorem.

Families of sets, countable and uncountable sets, metric spaces, the space of continuous functions on a compact set, the Stone-Weirstrass theorem, measure and measurable functions, the Lebesgue Integral, and dominated and monotone convergence theorem, _Lp Spaces_.

Advanced course in linear algebra examining linear transformations and matrices, the characteristics and minimal polynomials, Caley-Hamilton theorem, diagonalization, unitary spaces, self-adjoint, normal matrices and the spectral theorem, Jordan canonical form, and quadratic form.

Set-theoretic preliminaries, metric spaces, topological spaces, continuity and homomorphism, compactness and connectedness, separation axioms, complete metric spaces, and covering spaces.

Discrete and continuous random variables and their probability distributions. Mathematical expectation and moments. Chebyshev's Theorem, the Bernoulli, Poisson, Geometric, and Hypergeometric distributions; the Uniform, Exponential, Gamma, Chi-Square, and Normal distribution. Multivariate probability distributions. Functions of random variables. Central Limit theorems.

Sampling distributions, methods of estimation and hypothesis, linear regression, and the method of least squares. Correlation and analysis of variance. Elements of decision theory, statistical games, and nonparametric tests.

Advanced problem-solving seminar for students interested in taking the GRE subject mathematics Exam for graduate studies or in taking the Examination given by the Society of Actuaries. According to the needs of the students, this seminar covers material from calculus, differential equations, complex variables and advanced calculus, or number theory, modern algebra and linear algebra or calculus, probability theory and mathematical statistics.

Students find internships through their own initiative, the Career Development Office, and occasionally through Faculty. Placements depend on the availability of suitable positions and must amount to a minimum of 45 hours for 1 credit, 90 hours for 2 credits, and 135 hours for 3 credits. The faculty internship coordinator, along with the site placement supervisor, will guide and evaluate the quality of the work. Internships must relate to mid or upper level mathematics or applied mathematics and will provide the student with an opportunity to apply their math skills. Requires approval of the departmental chairperson.

Independent study under the direction of a faculty member in the Mathematics department. For students majoring in Mathematics Education, the independent study is on the history of mathematics.

Cross-listed with: PHI-5402. The infinite is a rich and dynamic notion situated at the crossroads of several fields of study and reflection. This team-taught interdisciplinary seminar approaches the infinite from two distinct perspectives: that of philosophy, and that of mathematics.