![]() Linear Algebra (Formerly 92.523) Description Pre-req: MATH.2190 Discrete Structures I. Abstract Algebra I (Formerly 92.421/521) DescriptionĮlementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications. Effective strategies for incorporating problem solving in the curriculum will also be discussed. Mathematical Problem Solving (Formerly 92.420/520) Descriptionįocuses on: mathematical resources, ability to use heuristics, the student's beliefs about the use of mathematics to solve problems, and the student's self-confidence as a problem solver. Pre-req: MATH.2210 Linear Algebra I, and MATH.2190 Discrete Structures I. Study of primes, congruences, number-theoretic functions, Diophantine approximation, quadratic forms and quadratic number fields. Number Theory (Formerly 92.513) Description Complex Variables I (Formerly 92.411/511) DescriptionĪ first course in theory of analytic functions of one complex variable: complex differentiability and the Cauchy-Riemann equations, Cauchy Integral Theorem and Cauchy Integral Formula, Taylor and Laurent series, zeroes of analytic functions and uniqueness, the maximum modulus principle, isolated singularities and residues. Mathematics Masters degree credit for Teacher Option Only. Computers and Calculators in Classroom (Formerly 92.510) DescriptionĮxplores the roles of computers and calculators in instruction, examines some of the available software, and considers their use in a variety of areas of school mathematics, such as algebra, geometry (Euclidean and analytic) probability and statistics, and introductory calculus. Pre-req: MATH.2310 Calculus III, or Mathematics MS Students. ![]() The course covers the topics in probability models, random variables, expected values, important discrete and continuous distributions, limit theorems, and basic problems of statistical inference: estimation and testing. It is especially appropriate for students with an undergraduate science or engineering major who have not had a rigorous calculus-based probability and statistics course. This course provides a solid basis for further study in statistics and data analysis or in pattern recognition and operations research. Probability and Mathematical Statistics (Formerly 92.509) Description Pre-req: MATH.4030 Mathematical Analysis, or MATH.5010 Real Analysis, and MATH.2220 Linear Algebra II. Hilbert spaces, orthogonal sequences, weak sequential compactness, compact self-adjoint operators and their spectra, application to Sturm-Liouville theory. Banach spaces, dual spaces, weak v's strong convergence. ![]() Metric spaces, completeness, contractions, compactness, the Arzela-Ascoli theorem, Picard's theorem, Weierstrass's theorem. Applied Functional Analysis I (Formerly 92.507) Description This course is designed for graduate students in mathematics and undergraduate student interested in mathematics graduate school and college teaching. ![]() Students will have opportunities to observe classrooms, practice teaching short lessons with their peers, as well as design and teach lessons in real classrooms. Topics include equitable and inclusive teaching practices, assessing student work, lesson planning, inquiry-based learning, effective questioning in the classroom, and student engagement. The focus of the course is to help prospective college mathematics instructors develop pedagogical content knowledge in mathematics and specific math knowledge for teaching. This course will introduce students to various aspects of teaching undergraduate mathematics. Pre-req: MATH.1320 Calculus II, and MATH.2190 Discrete Structures I. Prerequisites: Calculus I-III or equivalent, Discrete Structures or equivalent. Bolzano-Weierstrass theorem Cauchy sequences and completeness Limit of a function Continuity of a function at a point and on a set Uniform continuity Open and closed sets, idea of compactness, compactness of a closed interval Sequences of functions, uniform convergence Riemann integration. Tentative topics are: Real numbers (algebraic, order and distance structures) Archimedean property Sequences and their limits. The main focus is given to rigorous proofs rather than computations. The class is aimed to give rigorous foundations to the basic concepts of Calculus such as limits of sequences and functions, continuity, Riemann integration. Real Analysis (Formerly 92.501) Description Masters degree credit for Teacher Option Only. The necessary background tools in set theory, logic, recursion, relations, and functions are also included. Discrete Structures (Formerly 92.500) DescriptionĪn introduction to discrete mathematics, including combinatorics and graph theory.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |