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Course Criteria
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3.00 Credits
Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Enrollment Requirement: Twelve (12) units of upper-division in Mathematics. Enrollment restricted to students who have obtained consent of instructor.
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3.00 Credits
Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Enrollment Requirement: Twelve (12) units of upperdivision mathematics. Enrollment restricted to students who have obtained consent of instructor.
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3.00 Credits
Mathematics studied through the reading, analysis and discussion of original papers. May be repeated once for credit with consent of instructor. Enrollment requirements to be determined by instructor.
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3.00 Credits
Selected topics in advanced mathematics chosen to demonstrate appropriate use of technology and effective organization and presentation of mathematics in oral and written form. Includes three aspects of mathematical writing: writing expository mathematics, writing formal mathematics, and writing as a tool to learn; preparation of mathematical lectures; development software modules/notebooks. Prerequisite for undergraduates and enrollment requirement for graduate students: MATH 350. Additional enrollment requirement for all students: At least nine (9) other units of upper-division mathematics.
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3.00 Credits
Review and continuation of the study of algebra begun in MATH 470. Covers some of the following: the theory of finite group theory including the Sylow Theorems, polynomial ring, unique factorization, number fields, and finite fields. The latter half of the course will cover field extensions and Galois Theory, including the classic theorems on the unsolvability of the general quintic and the impossibility of certain ruler and compass constructions, such as trisecting an angle. Prerequisite for undergraduate students and enrollment requirement for graduate students: MATH 470.
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3.00 Credits
Introduction to algebraic tools and ideas that have applications in such fields as cryptography, coding theory, number theory, algebraic geometry, integer programming, computing modeling, and robotics. Includes some of the following: finite fields, Gr?ner bases, resultants, algebraic curves and their codes. Prerequisite for undergraduate students and enrollment requirement for graduate students: MATH 470.
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3.00 Credits
Introduction to number theory from the algebraic and/or analytic point of view. Includes some of the following: congruences, finite fields and rings, and quadratic reciprocity; quadratic forms and Diophantine equations; elliptic curves; the Gaussian integers, the Eisenstein integers, and unique factorization in these rings; other quadratic and cyclotomic fields and ideal factorization; introduction to analytic number theory, primes in arithmetic progressions, and the prime number theorem. Prerequisite for undergraduate students and enrollment requirement for graduate students: MATH 470.
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3.00 Credits
Algorithms for factorization and primality testing: pseudo-primes, quadratic sieve, Lucas Test, continued fractions, factorization using elliptic curves, public key cryptosystems such as RSA, which is widely used for secure transfer of data on the internet. Additional background material (such as the rudiments of elliptic curves) will be introduced as needed. Combines theoretical ideas with computer lab experimentation and implementation. Some familiarity with a computer language is useful but not required. Prerequisite for undergraduates and enrollment requirement for graduate students: MATH 350 or 370.
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3.00 Credits
Vector spaces; dual spaces; linear transformations, bilinear forms and their matrix representations; Jordan and other canonical forms; finite-dimensional spectral theory; connections to other branches of mathematics. Prerequisite for undergraduates and enrollment requirement for graduate students: MATH 374.
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3.00 Credits
Lebesgue measure, measurable functions, the Lebesgue integral, Fubini's Theorem, Lpspaces, and differentiation. Prerequisite for undergraduates and enrollment requirement for graduate students: MATH 430.
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