MATH 228 - Algebra: Introduction to Ring Theory |
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The course introduces the concept of a ring. Beginning from the ring of integers and its main properties (prime factorization), the modular rings are constructed, and finally more abstract rings are considered. Along the way, the concepts of mathematical induction are introduced. |
MATH 324 - Elementary Number Theory |
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Number theory refers to the study of the natural numbers. Its main goal is to discover and describe (prove) interesting and unexpected relationships between numbers. |
MATH 326 - Rings and Modules |
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This class studies the theory of rings and modules in general, and fields, integral domains, polynomial rings, and Noetherian rings in particular. Emphasis is on the development of abstract concepts. |
MATH 328 - Algebra: Introduction to Group Theory |
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This course introduces the most fundamental algebraic concept in mathematics, namely groups. Their basic structures are studied, as well as group actions on sets, group homomorphisms, and the construction of quotient groups. |
MATH 422 - Coding Theory |
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Coding theory focuses on the problem of how to encode information that is to be transmitted over an unreliable channel such that the original information can be recovered as long as not too many errors occur during transmission, using so-called error-detecting or error-correcting codes. For this purpose, finite fields and polynomials over finite fields are introduced and their properties developed as pertaining to coding theory. |
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Web page with resources for MATH 422, including online lecture notes by Dr. John C. Bowman. |
MATH 424 - Algebra: Groups and Fields |
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The main focus of this course is the theory of automorphism groups of fields and field extensions, also known as Galois theory. Prominent topics include the insolvability of the quintic equation, and constructions with rules and compass. |
MATH 428 - Algebra: Advanced Ring Theory |
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Topics in this course will be chosen to illustrate the use of ring theory in another area of mathematics such as the theory of numbers, algebraic geometry, representations of groups, or computational algebra. |
MATH 429 - Algebra: Advanced Group Theory |
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This course covers more advanced topics in group theory, such as the Sylow theorems. |