**MATH 110A-1-Algebra-Winter 2019-UCLA**

**Lecture:** MWF, 12:00pm-12:50pm, at Bunche Hall Room 2160.

**Professor:** Wenhao Ou (wenhaoou-at-math.ucla.edu, MS 5346).

**Office Hours:** M 2:00pm-5:00pm, or e-mail me to make an appointment.

**Teaching assistant:** Weiyi Liu， (liuweiyi-at-ucla.edu).

**Textbooks: **Hungerford, *Abstract Algebra*, 3rd Ed., Brooks Col.

**Description.** This course provides an introduction to the theory of rings, which can be regarded as generalizations of the set of integers, with multiplication and summation.

**Schedule.** This course consists of two parts and about 25 lectures. We will start by recalling some arithmetic in the set of integers. The first part will end up with the definition of abstract rings. In the second part, we will focus on the study of rings of polynomials.

Weeks |
Sections | Topics |

1 |
1.1, 1.2, 1.3 | Arithmetic in the set of integers |

2 |
2.1, 2.2, 2.3 | Congruence and Modular Arithmetic |

3 |
3.1, 3.2 | Rings: Definition and Basic Properties |

4 |
3.3 | Homomorphisms and Isomorphisms |

5 |
4.1, 4.2, 4.3 | Arithmetic in Rings of Polynomials |

6 |
4.4, 4.5 | Midterm, Roots of Polynomial Functions, Polynomials with Rational Coefficients |

7 |
5.1 | Congruence in Rings of Polynomials |

8 |
5.2, 5.3 | Congurence-Class Arithmetic, Quotient Polynomial Rings by a Single Polynomial |

9 |
6.1, 6.2, 6.3 | Ideal and Quotient Rings |

10 |
Review of Course |

**Holidays:**

- Martin Luther King, Jr, holiday, Monday, January 21

- Presidents’ Day holiday, Monday, February 18

**Homework.** Homework is assigned weekly and collected at the beginning of class on Wednesday. There is no make-up homework. The lowest score is dropped from the computation of your grade. Please click here for the homework list.

**Exam Dates:**

- Midterm 1: Monday of week6, Feb 11,

- Final Exam: Thursday, Mar 21, 3pm-6pm.

**Grading.**

- 10% Homework + 30% Midterm + 60%Final Exam.

**Academic integrity.** Please review the regulations at the following website: http://www.deanofstudents.ucla.edu/Student-Conduct

**Notes.**

- Textbooks, Calculators, laptops and cell phones are prohibited during the Midterms and the Final Exam.

- There will be no make-up test. A missed test will count for a zero for that test.

- Students may work together to solve homework problems, but each student must write down his/her own solutions on separate copy. One should also write down the names of his/her collaborators.

- Exam grading complaint should be submitted to the instructor, no later than two weeks after the exam, and before the last lecture.