Math 421Modern AlgebraSpring 2005Instructor: Dr. John IskraOffice: 221 Miller HallOffice Phone: 6191Office Hours: MWF 1-2:30 Th 2-3e-mail: [email protected]: This course will serve as an introduction to so -called Modern Algebra: thestudy of groups, rings, fields and modules. I plan to approach these from the modernpoint of view. This viewpoint, which stresses general structure over specific calculationought to more quickly advance the mathematical maturity level of the student. She willthus find any other advanced mathematical courses easier to handle.Text: The primary text for this course will be notes which I author. They will beavailable on line and will be presented in class. In addition, I will place the followingbooks on reserve at E&H's library:Algebra by Saunders MacLane and Garrett Birkhoff: A synthesis of the traditional andmodern approach to Modern Algebra. MacLane is generally recognized as one of the twoto discover category theory. Contemporary Abstract Algebra by Gallian: A more traditional approach toundergraduate level abstract algebra. Lots of good graphics and fun historical notes.Introduction to Abstract Algebra by Moore: Like Gallian. A little more hard-nosed I'dsay, though.Categories for the Working Mathematician by Saunders Maclane: The classic. I wouldsay more mathematicians learned category theory on their own from this text than anyother. Does assume that you are a working mathematician and not one in training though.Also gives a thorough, yet accessible ( a relative term) treatment of foundational issues.Categories by Blyth: Just for a different treatment than MacLane's. These books may be taken out of the library for one day.Course Objectives: The successful student will, by the end of the semester, know thebasic definitions used in category theory and modern algebra. This student should beable to use these definitions to prove simple statements about those topics. In addition,this student will know the statements of some of the important basic theorems in thosesubjects: The three isomorphism theorems for rings, groups, and modules; the Galoiscorrespondence between fields and groups, the fundamental theorem of finitely generatedAbelian groups, and all others presented in class.Grade: The course grade will be determined by your performance in three areas:1. Daily, or near daily quizzes on definitions and statements of theorems2. Homework3. Final PresentationIn addition, points may be earned by correcting any mistakes in my notes. I will saymore about this as the course goes along.Each quiz will consist of one question and be worth one point.Each homework problem will be worth 2 points and may be resubmitted as many times asthe student wishes until 2 points are earned.The final presentation will be worth 10 points.Your final grade will be determined according to the following:A:>95 pointsA-:90-95 pointsB+: 87-89 pointsB: 83-86 pointsB-: 80-82 pointsC+: 77-79 pointsC:73-76 pointsC-:70-72 pointsD+: 67-69 pointsD: 63-66 pointsD-:60-62 pointsF:<59 pointsQuizzes: The quizzes will be based on assigned reading. This reading will be posted onthe web and consist of notes for the next class. The quizzes will ask you to correctly statea definition or theorem which we will be using or proving in class that day. Homework: The homework problems will be sprinkled throughout the text of my notes.I anticipate that there will be well over 100 problems to choose from. Problems may beresubmitted until a “2” is earned. The credit you earn for any given problem you attemptwill be the maximum number of points earned on that problem by the end of thesemester.Presentation: This will be on one of the homework problems you turn in for credit. I willchoose which. More details will be forthcoming.I view this course as an opportunity for both of us. For you I hope that you will learnmodern algebra. I also hope that this course will prepare you for other advanced mathcourses, and, that you emerge from this course with a better idea of how the wholediscipline is really a single entity. For myself, I look forward to your assistance andforbearance as I write the text for the