Winter 2016 Course Syllabus

INSTRUCTOR: | Michael AndrewsOffice: MS 6322Office hours: Thursday 10:00am-12:00pm (Thursday office hours in ???); Friday 2:00pm-3:30pm (Friday office hours in ???)email: mjandr@math.ucla.edu |
---|---|

TA: |
Kevin CarlsonOffice: MS 2951Office hours: Thursday 2:00pm-3:00pm, Friday 12:00pm-1:00pmemail: kdcarlson@ucla.edu |

LECTURES: | MS 5138; MWF 1:00pm-1:50pm |

OFFICE HOURS: | I strongly encourage coming to mine or Kevin's office hours with any questions or concerns you have. If they are at inconvenient times for you throughout the quarter, please let me know. If you wish to meet at some other time, I will normally be happy to talk - just stop by my office or send me an email if I'm not there. |

DISCUSSION SECTION: | MS 5138; R 1:00pm-1:50pm
During the discussion section Kevin will try to address difficulties with the material covered in lectures and appearing on homeworks. This is a difficult class and so, while attendance of the discussions is not required, it is strongly recommended that you go. |

HOMEWORK: |
There will be eight homeworks. They will be collected in class on Mondays. The assignments are posted online.
Do not submit homework by e-mail. No late homework will be accepted. However, the lowest homework score will be dropped.
I encourage you to form study groups in the class with friends / people you like. When faced with a homework question, you should make sure that you understand the relevant material from lectures first. Discussing the lectures with others in your study group and/or talking to Kevin and myself can help. You should try to solve a problem BY YOURSELF FIRST. Only when you have enough thoughts about it, should you talk with others in your study group about it. Working in groups is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself and not copy off of others work. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment. You must also cite any sources you use other than the lecture or the textbook (other textbooks, a blog about algebra, etc.). |

EXAMS: | There will be in-class midterms on Friday, April 22 and Friday, May 13. There will be a final exam on Monday, June 6, 3:00pm-6:00pm. There will not be any make-up exams except in extreme and documented circumstances. In particular, note that university policy requires that a student, who has an undocumented absence from the final exam, be given a failing grade in the course.
The first midterm will cover lectures 1-9 inclusive, the second midterm will cover lectures 10-17 inclusive and the final will be comprehensive with more emphasis on lectures 18-25. The exams are closed book and closed notes. |

GRADES: | The course grade will be determined by the cumulative percentage of scores at the end of the quarter. This is calculated by taking the BETTER of the two schemes:
15% Homework, 20% Better Midterm, 65% Final. Any issues about grading for homeworks or exams must be addressed within two weeks of the turn-in date. After that time no score changes will be allowed. Grades will be available online through the myUCLA website. |

CONTENT: | This course is an introduction to abstract algebra with a view towards applications. We will discuss rings and fields. Our favorite examples will be the integers, polynomials over a field, and congruence classes in such rings. In particular, we will study division, gcds, the Euclidean algorithm, and factorization in the integers and polynomials rings over a field. This will allow us to calculate units in their congruence rings, prove the theorems of Euler and Fermat, and the Chinese Remainder theorem. Then we will look at applications such as error correcting codes, fast polynomial multiplication, and the fast Fourier transform. |

TEXTBOOK: | Lindsay N. Childs, A Concrete Introduction to Higher Algebra. Springer 2009. Third Edition. |

PREREQUISITES: | Math 33A, Math 33B. Math 115A and 131A are recommended but not required. |

CHEATING: | Cheating is stupid and a serious offense. Students caught cheating will be reported. Do NOT cheat!! |

Department of Mathematics | Math 117 |