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Rings,Fields and Galois Theory (Adv)

MATH3962

This unit of study investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads naturally to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory.The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

Unit of study details

Unit of study level: Senior

Credit points: 6

Commencing semesters: 1

Further unit of study information

Unit of study handbook: MATH3962

Costs and scholarships information: Costs and Scholarships

Final dates to withdraw from units of study: Census Dates

Available for study abroad and exchange: Yes

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