The algebra you’re familiar with from high school is primarily concerned with equations over standard number systems, particularly the real numbers. Abstract algebra generalizes those ideas, focusing on the structure and properties of abstract algebraic structures, the most important of those being groups, rings, and fields. Group Theory (which we’ll study in fall quarter) offers us concrete tools for thinking about and working with symmetry; Ring Theory (which we’ll study in winter quarter) helps us fully understand the properties and applications of polynomials; and Field Theory (which we’ll study in spring quarter), also called Galois Theory, gives us ways to understand the power and limitations of algebra itself.
This sequence of courses is a standalone module in the Mathematical Systems program. Contact the faculty to take this as a 4 credits/quarter module in that program.
Strong algebra skills. Previous experience with proofs and/or Discrete Mathematics is helpful but not required.
Upper division science credit will be awarded for work in this course.