The Catholic University for Independent Thinkers
Phone: 972-721-5175
Fax: 972-721-4148
1301. Euclidean and Non-Euclidean Geometries. Development of the mathematical way of thinking through firsthand experience. Emphasis on the student’s strengthening of his or her imagination, deductive powers, and ability to use language precisely and efficiently. Study of Euclid’s geometry; Hilbert’s axioms; neutral geometry; hyperbolic geometry (non-Euclidean geometry of Gauss, Bolyai, Lobachevsky); the axiomatic method; and consistency, independence and completeness of axiom systems. Historical perspective and philosophical implications are included. Students must prove a significant number of theorems on their own. Fall and Spring.
1303. Precalculus. Advanced algebra and trigonometry needed for Calculus. Solving equations and inequalities; polynomials; functions; trigonometry on the unit circle; parametric and polar coordinates; conic sections; arithmetic and geometric sequences; math induction. Prerequisite: successful placement in algebra. Fall.
1404. Calculus I. Limits, derivatives, applications of derivatives, integration, logarithmic and exponential functions. Prerequisite: Grade of C (2.0) or better in Mathematics 1303, or satisfactory placement. Fall and Spring.
1411. Calculus II. L’Hôpital’s Rule, inverse trigonometric and hyperbolic functions, methods of integration, analytic geometry, applications of integrals, sequences and series. Prerequisite: Grade of C (2.0) or better in Mathematics 1404, or satisfactory placement. Fall and Spring.
2107. Mathematics Colloquium. A forum for exposing students to the rich and deep areas of mathematics and its applications not normally seen in the first two years of undergraduate studies. Oral presentations are selected for their interest and accessibility. Speakers include faculty members, visiting lecturers, and students. Highly recommended for majors. Visitors are welcome. Public announcements of speakers will be made. Graded Pass/No Pass. May be repeated. Fall and Spring.
2304. Discrete Mathematics. Introduction to the mathematical foundation of computer science with two co-equal components: a study of combinatorics and graph theory including topics from the theory of computer science, and a development of the imagination and analytical skills required in mathematics and computing science. Students are required to do proofs. Prerequisite: MCS 2410. Offered as needed.
2305. Introduction to Statistics. Statistics may be broadly defined as the science of making rational decisions in the face of quantifiable uncertainty. Emphasis on a deep understanding of the fundamental elements of so-called "statistical thinking", including randomness, uncertainty, modeling, and decision processes. The superstructure of statistical methodology, including hypothesis testing, inference, and estimation, using the logical methods of mathematics. A significant amount of instruction is computer-based. Prerequisite: Successful demonstration of abilities in algebra. Fall and Spring.
2412. Calculus III. Vectors, vector calculus, functions of several variables, multiple integrals. Prerequisite: Grade of C (2.0) or better in Mathematics 1411, or satisfactory placement. Fall.
3107. Mathematics Colloquium. This course is similar to 2107 except that extra work is required to earn junior-level credit. Each student is expected to write a paper and present a talk based on it in addition to fulfilling the other requirements. Graded Pass/No Pass. May be repeated. Fall and Spring.
3159. Junior Workshop. This course is designed to improve the student's ability to "do math at the board" and to encourage a willingness to engage mathematical problems creatively. Emphasis is on generating ideas for solving problems and then testing those ideas to see if they bear fruit. Problems given are often open-ended and may lack a published solution so as to encourage creative approaches. Fall.
3190. Problem Solving. This course presents many problem-solving techniques not typically found in other mathematics courses. Emphasis is on problems from competitions, but the techniques have broad application for creatively thinking through many sorts of problems. Problems are drawn from many different fields of mathematics, yet very accessible to any student with an interest in math. Prerequisite: MAT 1404 or consent of instructor. Fall. Repeatable for credit.
3310. Linear Algebra. Geometry of R^{2} and R^{3} including the dot product and parametric equations of lines and planes. Systems of linear equations, matrices, determinants, vector spaces, and linear transformations. Applications to the sciences and economics are included. Prerequisite: Mathematics 1411 or consent of instructor. Fall.
3320. Foundations of Geometry. A systematic development of topics selected from metric and nonmetric geometries, comparison of postulate systems. Prerequisite: Mathematics 1411 or consent of instructor. Offered as needed.
3321. Linear Point Set Theory. Limit points, convergent sequences, compact sets, connected sets, dense sets, nowhere dense sets, separable sets. Prerequisite: Consent of chairman. Fall.
3322. History and Philosophy of Mathematics. The history of the development of mathematics, the lives and ideas of noted mathematicians. Prerequisite: Consent of instructor. Offered as needed.
3324. Differential Equations. First order equations, existence and uniqueness of solutions, differential equations of higher order, Laplace transforms, systems of differential equations. Prerequisite: Mathematics 1411 or consent of instructor. Fall, even years.
3326. Probability. Axioms and basic properties, random variables, univariate probability functions and density functions, moments, standard distributions, law of large numbers, and central limit theorem. Prerequisite: Mathematics 1411. Fall, odd years.
3327. Statistics. Sampling, tests of hypotheses, estimation, linear models, and regression. Prerequisite: Mathematics 3326. Spring, even years.
3331. Number Theory. A study of the properties of the integers. Topics include divisibility and primes, congruences, Euler’s theorem, primitive roots, and quadratic reciprocity. Prerequisite: Mathematics 3321 or consent of instructor. Spring, even years.
3338. Numerical Analysis. Zeros of polynomials, difference equations, systems of equations, numerical differentiation and integration, numerical solution of differential equations, eigenvalues and eigenvectors. Prerequisite: Mathematics 3310 and knowledge of a programming language. Offered as needed.
3V50. Special Topics. Gives the student an opportunity to pursue special studies not otherwise offered. Topics have included chaos, fractals, cellular automata, surreal numbers, and dynamical systems. May be repeated for credit. Prerequisite: consent of chairman.
4314. Advanced Multivariable Analysis. Continuous and differential functions from R^{m} into R^{n}, integration, differential forms, Stokes’s theorem. Prerequisite: Mathematics 2412 and 3310,or consent of instructor. Offered as needed.
4315. Applied Mathematics. Symmetric linear systems, equilibrium equations of the discrete and continuous cases, Fourier series, complex analysis and initial value problems. Prerequisite: Math 2412. Spring, odd years.
4332-4333. Abstract Algebra I, II. Group theory, ring theory including ideals, integral domains and polynomial rings, field theory including Galois theory, field extensions and splitting fields, module theory. Prerequisite: Mathematics 3310, 3321, and junior standing, or consent of instructor. Fall, even years (I); Spring, odd years (II).
4334. Topology. Topological spaces, connectedness, compactness, continuity, separation, metric spaces, complete metric spaces, product spaces. Prerequisite: Mathematics 3321 or consent of instructor. Spring, odd years.
4341-4342. Analysis I, II. Real number system, topological concepts, continuity, differentiation, the Stieltjes integral, convergence, uniform convergence, sequences and series of functions, bounded variation. Prerequisite: Mathematics 1411 and 3321, or consent of instructor. Fall, odd years (I); Spring, even years (II).
4V43-4V44. Research. Under the supervision of a member of the faculty, the student involves himself or herself in the investigation and/or creation of some areas of mathematics. The research should be original to the student. A paper is required. Prerequisite: junior or senior standing.
4V61. Independent Studies. An opportunity for the student to examine in depth any topic within the field under the guidance of the instructor. For advanced students.