CS 203B: Abstract Algebra

Course description:

Abstract algebra is the study of algebraic structures (sets with operations on them). The algebraic structures we will study are Groups, Rings and Fields. The course will focus on teaching the definitions and basic properties of these algebraic strucutres. On the way, we will see applications of group theory in mathematics and computer science which makes it such a useful topic. For more information please read the following wikipedia link,

http://en.wikipedia.org/wiki/Abstract_algebra .

CS 203B: Notes

Course notes:

Topic Link
Introduction to abstract algebra Introduction
Groups, examples, Properties and Homomorphisms. Groups
Subgroups, cosets and Lagrange's theorem Subgroups
Group action, orbits and Burnside lemma Orbits
Quotient group, normal subgroup and homomorphisms. Quotient
Rings, Chinese remaindering, integral domains and fields Rings
Polynomials over rings and fields Polynomials
Finite fields and applications. Finite fields
Complete notes Full notes

CS 203B: References

Linear Algebra

Abstract algebra

Quantum computing

  • Quantum computation and quantum information, Nielsen and Chuang.

Primes is in P