Courses offered for mathematics majors and minors

Admission to Mathematics Major courses numbered 300 or above requires the successful completion of MA 171, 172, 271, 272, and 231 or permission of the Chair of the Department.

MA 171 Differential Calculus Functions; limits, continuity, and derivatives; applications; relative maxima, minima, and curve sketching; absolute maxima and minima; related rates; Rolle's Theorem and the Mean Value Theorem. Antidifferentiation; the definite integral and the Fundamental Theorem of Calculus. 4 semester hours

MA 172 Integral Calculus The definite integral; applications; area, volume, and arc length; exponential, logarithmic, trigonometric, and hyperbolic functions; integration techniques; indeterminate forms; Taylor's Theorem; and infinite series. 4 semester hours

MA 231 Discrete Mathematics Emphasis on logic and proofs; sets; functions; equivalence relations and partitions; factor sets; mathematical induction; isomorphisms; countability. Also listed as CS 231. 3 semester hours

MA 235 Linear Algebra Linear spaces and subspaces; linear independence and dependence;bases and dimension; linear operators; matrix theory; determinants and systems of linear equations; eigenvalues and eigenvectors. Prerequisite: MA 231. 3 semester hours

MA 271 Multivariable Calculus I Convergence tests, power series. Vectors in the plane and in 3-space. Arc length, curvature, equations of lines and planes. Vector functions, parametric equations. Functions of several variables, differentiability, gradient, directional derivatives. Tangent planes, normal lines. Total differential, extrema. Lagrange multipliers. Sequences and series. Prerequisite: MA 172 or the equivalent. 3 semester hours

MA 272 Multivariable Calculus II Multiple integration: volume and surface integrals in Cartesian, cylindrical and spherical coordinates. Line integrals, Green's theorem, divergence and curl, Jacobians, change of variables. Separation of variables and exact differential equations. Inverse functions, implicit function theorems. 3 semester hours

MA 334 Abstract Algebra Group theory and the Sylow Theorems; rings and ideals, integral domains, fields; vector spaces; algebras. 3 semester hours

MA 337 Number Theory A study of the integers including but not limited to the following topics: primes and theirdistribution, divisibility and congruences, Quadratic Reciprocity, special numerical functions such as Euler's 1-function, Diophantine equations. The influence number theory has had on the development of algebra and the interplay between the two will be considered. 3 semester hours

MA 341 Linear Programming and Operations Research Convex sets, extreme points, theoretical basis of the simplex method for linear programming, the simplex computational procedure, duality theory, sensitivity analysis. The transportation problem and network applications as time permits. Prerequisite: MA 235. 3 semester hours

MA 342 Theory of Computation Finite state machines, push-down automata, Turing machines and recursive functions. Formal languages: regular grammars, context-free grammars, context-sensitive grammars. Decidable vs. undecidable problems. Introduction to algorithm analysis. Also listed as CS 342. Prerequisite: CS 231. 3 semester hours

MA 351 Probability Theory I Counting techniques, axiomatic probability theory. Discrete and continuous sample spaces. Random variables, distribution functions, probability density and mass functions. Normal, binomial, Poisson distributions. Limit laws. 3 semester hours

MA 352 Probability and Statistics II Joint distribution and continuous distributions. Statistical application of probability. Theory of sampling. Variances of sums and averages . Estimation and hypothesis testing. Least squares, curve-fitting, and regression. Prerequisite: MA 351. 3 semester hours

MA 361 Topics in Algebra This course is designed to investigate a number of topics in greater depth than can be done in the first linear or abstract algebra course. Three topics will be selected from the following list: Canonical Forms for Matrices, Metric Linear Algebra, Ideal Theory, Finite Non-abelian Groups and Galois Theory. It is expected that at leastone topic from each of linearand abstract algebra will be selected. Prerequisites: MA 235, and MA 334. 3 semester hours

Polyhedra at Paris' Louvre

MA 365 Differential Geometry This course will provide a basic introduction to elementary differential geometry. Topics will include tangent vectors, vector fields, differentials and calculus as well as the basic properties of curves including the Seret-Frenent apparatus, and an introduction to surfaces and the role of Euclidean geometry. There will also be brief introductions to the concept of a manifold and to Riemannian geometry. Prerequisite: Multivariable Calculus i.e. MA 225, MA 227, or MA 272. 3 semester hours

MA 371 Real Analysis R as a complete, ordered, archimedian field; R as a linear vector space equipped with inner product and norm; metrics on R particularly the euclidean one, topological concepts: continuity, connectedness and compactness; the Intermediate Value, Extreme Value, Monotone Convergence, Bolzano/Weierstrass and Heine/Borel Theorems; convergence and uniform convergence of sequences of continuous functions; Differentiation: the Mean Value, Implicit and Inverse Function Theorems; Integration: The Riemann Integral and the Theorem of Lebesgue. 3 semester hours

MA 373 Complex Variables Algebra of complex numbers, analytic functions, integration in the complex plane, Cauchy's Theorem and integral formula, Nonformal mapping, residue theory, applications. Prerequisite: MA 371. 3 semester hours

MA 375 Differential Equations and Dynamical Systems Theory of ordinary differential equations, transfomms, senes solutions, systems of equations with classical and modem applications. Prerequisites: MA 235, and MA 371.
3 semester hours

MA 377 Numerical Analysis Computer arithmetic, round-off errors, the solution of nonlinear equations, polynomial approximation, numerical differentiation and integration, and the solution of systems of linear equations will be investigated via student-written code to implement the algorithms and/or the use of available software. Also listed as CS 377. Prerequisite: MA 235 and proficiency in a computer language. 3 semester hours

MA 383 Modern Geometry Foundation for plane geometries. Theorems of Menelaus, Ceva, Desargues, Pascal, Brianchon, Feuerbach. Inversion and reciprocation transformations. Projective, Riemannian and Lobachevskian geometries. Poincare model. 3 semester hours

MA 385 Point Set Topology Topological spaces, continuous functions; product, metric and quotient spaces; countability and separation axioms; existence and extension of continuous functions; compactification; metrization theorems, complete metric spaces. Prerequisite: MA 371. 3 semester hours

Courses offered for Mathematics Minors

"Euclid alone hath looked on beauty bare."

MA 211 Applied Matrix Theory Techniques and applications of linear algebra; solutions of linear equations, determinants, linear geometry, eigenvalues and eigenvectors, for students majoring in the sciences, economics, and business. Not for mathematics majors. 3 semester hours

MA 225 Calculus III for non-physics majors Partial differentiation, multiple integrals, infinite series, and first order differential equations. Prerequisites: MA 21, 22. 3 semester hours

MA 227 Calculus III for Engineering and Physics Majors Infinite series, tests for convergence, power series, Taylor series. Geometry in 3-space. Partial differentiation of continuous functions. Chain rule, exact differentials, maxima and minima. Multiple integration. Application to volumes, center of gravity. Polar, cylindrical and spherical coordinates. Prerequisites: MA 25, MA 26 or equivalents. 3 semester hours

MA 228 Calculus IV for Engineering and Physics Majors Vector arithmetic and algebra, dot and cross products, parametric equations, lines and planes. Gradient, directional derivative, curl, divergence. Line integrals, work, Green's theorem, surface integrals. Stokes and divergence theorems. Prerequisites: MA 25, MA 26, MA 227 or equivalents. 3 semester hours

MA 241 Applications of Modern Geometry Axiomatic structures, undefined terms and axioms; centroid theorems, Ceva and Menelaus theorems, cross ratio. Transformation Geometry through inversion and reciprocation. Projective Geometry with complete quadrangles and quadrilaterals. Non-Euclidean Geometry theorems of Saccheri with limit triangles and Saccheri Quadrilaterals. Poincare model of Lobachevski's Hyperbolic geometry. Solution of triangles whose angle sum is less than 180. This course is meant for students seeking a minor in Mathematics. Prerequisite: MA 21, 22. 3 semester hours

MA 321 Ordinary Differential Equations Solutions of first and second order differential equations by formal methods. Linear equations are studied in detail. Systems of equations. Series solutions. Applications to geometry and physics. Prerequisite: MA 225 or the equivalent. 3 semester hours

MA 322 Partial Differential Equations Solution of first and second order partial differential equations by formal methods. Cauchy Problems. Fourier Series Solutions, Classical Theory of heat, wave and potential equations. Prerequisite: MA 321. 3 semester hours

MA 323 Special Functions of Mathematical Physics Orthogonality; Fourier Analysis; Bessel functions; Legendre, Hermite and Laguerre polynomials; Laplace and Fourier transforms; Calculus of Variations; Cauchy-Riemann equations; Conformal Mapping, Green's function. Prerequisite: MA 321. 3 semester hours

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The MACS Department

MACS Faculty
Some Occupations of Our MACS Graduates

Fairfield University's most interesting class of mathematicians - 1974

The two MACS Programs

Mathematics Minor
Descriptions of Mathematics Courses

For information about the MACS offerings
call chairman, Dr. Christopher Bernhardt: 203-256-2516
or email: cbernhardt@fair1.fairfield.edu

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Contact Information and Table of Contents for This Site
Mathematics Department Fairfield University Fairfield, CT 06430		email: macdonnell@fair1.fairfield.edu Voice mail - 203 256-7222 FAX 203-255-5947

These 13 polyhedra symbolize the 13 items of this page which is maintained by Joseph MacDonnell, S.J. They are the 13 Achimedean semiregular polyhedra.

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