# Courses

## Mathematics Courses

### MTH101 Calculus I

#### [3–0, 3 cr.]

The course is an intuitive approach to the techniques of calculus and analytic geometry. Topics include functions, graphs, trigonometric functions, rates of change, limits and continuity, the derivative function, the derivative as a rate of change, differentiation rules, derivatives of trigonometric functions, the chain rule, implicit differentiation, extreme values of a function, the Mean Value and Intermediate Value Theorems, curve sketching, optimization, linearization and differentials, L’Hopital’s rule, and an introduction to anti-derivatives.

### MTH102 Calculus II

#### [3–0, 3 cr.]

This course covers integration. Topics include indefinite integrals, integral rules, integration by substitution, estimating with finite sums, Riemann sums and definite integrals, the Fundamental Theorem of Calculus, substitution in definite integrals, applications of integrals (areas between curves and volumes by slicing, volumes by cylindrical shells, and lengths of plane curves), transcendental functions (logarithms, exponential functions, inverse trigonometric functions), and some basic techniques of integration (integration by parts, and trigonometric integrals). In addition, the course covers differential equations and modeling (first order separable differential equations, linear first order differential equations), vectors in the plane and in space, as well as dot and cross products, lines and planes in space, and conics (ellipse, hyperbola, parabola).

*Prerequisite: MTH101 Calculus I*

### MTH201 Calculus III

#### [3–0, 3 cr.]

This course covers hyperbolic functions, integration techniques and improper integrals. The course covers also infinite sequences and series: limits of sequences of numbers, bounded sequences, integral test for series, comparison tests, ratio and root tests, alternating series test, absolute and conditional convergence, power series, Taylor and MacLaurin series, and applications of power series. Polar functions, polar coordinates, and graphing of polar curves are also covered. In addition, topics from multivariable calculus are introduced: functions of several variables, partial derivatives, double integrals, applications to double integrals, and double integrals in polar form.

*Prerequisite: MTH102 Calculus II*

### MTH206 Calculus IV

#### [3–0, 3 cr.]

This course covers the Fourier series, cylinders and quadric surfaces, vector-valued functions, arc length and the unit tangent vector, curvature and the unit normal vector, torsion and the binormal vector, partial derivatives and applications, the chain rule, directional derivatives, gradient vectors, tangent planes, linearization and differentials, extreme values and saddle points, Lagrange multipliers, triple integrals, triple integrals in cylindrical and spherical coordinates, integration in vector fields, line integrals, circulation and flux, potential functions and conservative fields, the Fundamental Theorem of Line Integrals, Green’s theorem, surface integrals, parametric surfaces, Stokes and divergence theorems.

*Prerequisite: MTH201 Calculus III*

### MTH207 Discrete Structures I

#### [3–0, 3 cr.]

This course covers the foundations of discrete mathematics as they apply to computer science. The course is an introduction to propositional logic, logical connectives, truth tables, normal forms, validity, predicate logic, universal and existential quantification, and the limitations of predicate logic. Also, the following topics are covered: the number system, the Euclidean algorithm, proof techniques, mathematical induction, counting arguments, permutations and combinations, binomial coefficients, sets, functions, relations, matrices, and Boolean Algebra.

*Co-requisite: MTH 102 Calculus II*

### MTH301 Linear Algebra

#### [3–0, 3 cr.]

This is an introductory course in linear algebra where students are exposed for the first time to a balance of computation, theory, and applications. Topics include the systems of linear equations, vector spaces, linear dependence, bases, linear transformations, matrices, determinants, eigenvalues, and eigenvectors.

*Prerequisite: MTH201 Calculus III*

### MTH302 Geometry

#### [3–0, 3 cr.]

This course presents an investigation of the axiomatic foundations of modern geometry. More specifically, Euclidean geometry is discussed in detail. Less emphasis is also placed on spherical, and/or hyperbolic geometries.

*Prerequisite: Junior standing*

Note: This course has not been taught since Fall 2017 and will not be taught in the academic year 2020-2021.

### MTH303 Numerical Methods

#### [3–0, 3 cr.]

This course compares and contrasts various numerical analysis techniques, in addition to error definition, stability, the machine precision concepts, inexactness of computational approximations, the design, code, test, and debug programs that implement numerical methods, floating-point arithmetic, convergence, iterative solutions for finding roots (Newton’s Method), curve fitting, function approximation, numerical differentiation and integration, explicit and implicit methods, differential equations (Euler’s Method), and finite differences.

*Prerequisite: MTH201 Calculus III*

### MTH304 Differential Equations

#### [3–0, 3 cr.]

This course covers the topics of first order ordinary differential equations and applications, linear higher order differential equations and applications, systems of linear differential equations, series solutions of differential equations and solutions, and Laplace transforms.

*Prerequisite: MTH201 Calculus III*

### MTH305 Probability and Statistics

#### [3–0, 3 cr.]

This course covers essentially the distribution theory, estimation and tests of statistical hypotheses. More specifically, the topics of this course include: Random variables, discrete probability, conditional probability, independence, expectation, standard discrete and continuous distributions, regression and correlation, point and interval estimation. Also included are illustrations from various fields.

*Prerequisite: MTH 201 Calculus III*

### MTH306 Non-Linear Dynamics Chaos

#### [3–0, 3 cr.]

This course covers the topics of iteration, fixed and periodic points, graphical analysis of iteration, stable and unstable orbits, attracting and repelling periodic points, iterations of a quadratic family, Julia sets, Mandelbrot sets, fractals, and chaos.

Course Learning Outcomes:

- Students will be able to iterate functions, identify the orbits of seed values and analyze graphically such orbits.
- Students will be able to find fixed points and identify them as repelling, attracting, or neutral. Students will also understand bifurcations.
- Students will have a complete understanding of the real and complex quadratic families.
- Students will be able to construct the Cantor Set and measure its length, construct the Sierpinski Triangle and measure its area, construct the Koch Curve and measure its perimeter.
- Students will learn about the Julia and Manderbolt Sets.

### MTH307 Discrete Structures II

#### [3–0, 3 cr.]

This course covers computational complexity and order analysis, recurrence relations and their solutions, graphs and trees, elementary computability, classes P and NP problems, NP-completeness (Cook’s theorem), NP-complete problems, reduction techniques, automata theory including deterministic and nondeterministic finite automata, equivalence of DFAs and NFAs, regular expressions, the pumping lemma for regular expressions, context-free grammars, Turing machines, nondeterministic Turing machines, sets and languages, uncomputable functions, the halting problem, implications of uncomputability, Chomsky hierarchy, and the Church-Turing thesis.

*Prerequisites: MTH207 Discrete Structures I, and MTH201 Calculus III*

### MTH308 Number Theory

#### [3–0, 3 cr.]

Topics covered are: The history of number representation systems, divisibility, greatest common divisor and prime factorization, linear Diophantine equations, congruences, and condition congruences.

### MTH309 Graph Theory

#### [3–0, 3 cr.]

This course covers the fundamental concepts and methods of graph theory, and their applications in various areas of computing. Topics include graphs as models, representation of graphs, trees, distances, matching, connectivity, and flows in networks, graph colorings, Hamiltonian cycles, traveling salesman problem, and planarity.

*Prerequisite: MTH201 Calculus III*

### MTH310 Set Theory

#### [3–0, 3 cr.]

This course covers operations on sets and families of sets, ordered sets, transfinite induction, axiom of choice and equivalent forms, and ordinal and cardinal numbers.

*Prerequisite: MTH207 Discrete Structures I*

Note: This course has not been taught since Fall 2017 and will not be taught in the academic year 2020-2021.

### MTH311 Abstract Algebra

#### [3–0, 3 cr.]

This course studies the algebra of sets, the definition and basic properties of groups, rings, and fields, and the divisibility theorems for integers and polynomials.

*Prerequisite: MTH207 Discrete Structures I, and Co-requisite: Junior standing*

### MTH400 Advanced Linear Algebra

#### [3–0, 3 cr.]

A thorough treatment of vector spaces and linear transformations over an arbitrary field; the Hamilton-Cayley Theorem, similarity, the Jordan Normal form, the dual of a linear transformation, direct sums, canonical forms, orthogonal and unitary transformations, normal matrices, and selected applications of linear algebra.

*Prerequisite: MTH 301 Linear Algebra*

### MTH401 Real Analysis I

#### [3–0, 3 cr.]

Topics covered include metric spaces, basic topics in topology, numerical sequences and series, continuity and uniform continuity of functions, differentiation, the mean-value theorem, Taylor’s theorem, and the Riemann-Stieljes integral.

*Prerequisites: MTH207 Discrete Structures I and MTH 301 Linear Algebra*

### MTH402 Theory of Interest

#### [3–0, 3 cr.]

This course is an intensive study of interest including the measurement of interest, the accumulation and discount of money, the present value of a future amount, the forces of interest and discount, equations of value, annuities (simple and complex), perpetuities, amortization and sinking funds, yield rates, bonds, and other securities, installment loans, depreciation, depletion and capitalized cost.

*Prerequisite: MTH102, and Co-requisite: Junior standing*

### MTH403 Introduction to Complex Analysis

#### [3–0, 3 cr.]

Topics covered include the algebra of complex numbers, analytic functions, complex integration, Cauchy’s integral formula, singularities, residues, poles, Taylor and Laurent series.

*Prerequisite: MTH 401 Real Analysis I*

### MTH407 Actuarial Mathematics

#### [3–0, 3 cr.]

This course covers survival functions, complete and curtate future lifetime random variables, life tables, select and ultimate survival functions, valuation of insurance benefits, mathematics of life annuities, future loss random variables, premium calculations, policy values calculation, multiple state models and mathematics of pension plans and retirement benefits.

*Prerequistes: MTH305 and either MTH402 or FIN301*

### MTH409 Introduction to Topology

#### [3–0, 3 cr.]

Topics covered include general topological spaces, connectedness, and compactness, continuity, and product spaces.

*Prerequisite: MTH401 Real Analysis I*

### MTH410 Real Analysis II

#### [3–0, 3 cr.]

This course will continue to cover the fundamentals of real analysis, concentrating on the Riemann integral, convergence of sequences and series of functions, functions of several variables, integration of differential forms, curl, divergence and Stoke’s theorem.

*Prerequisites: MTH206 Calculus IV and MTH401 Real Analysis I*

### MTH411 Advanced Topics in Abstract Algebra

#### [3–0, 3 cr.]

This course is a continuation of Abstract Algebra and topics covered include ring theory, Galois Theory, unique factorization, Principal Ideal Domain, Unique Factorization Domain, and some Diophantine Equations.

*Prerequisite: MTH311 Abstract Algebra*

### MTH498 Topics in Mathematics

#### [3–0, 3 cr.]

This course covers selected topics in mathematics. It may be repeated for credit.