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

- Linear Algebra: An introductory approach, Charles W. Curtis (Chapter 1-4).
- Introduction to Linear Algebra, Gilbert Strang (Chapter 1-3,6)
- Linear Algebra, Hoffman and Kunze (Chapter 1-3).

### Abstract algebra

- Abstract Algebra, Dummit and Foote.
- Discrete Mathematics, Norman L. Biggs.
- Notes on Group Theory , Peter J. Cameron.

### Quantum computing

- Quantum computation and quantum information, Nielsen and Chuang.

### Primes is in P