Florian Pop: Math 203 (Proving things: Algebra)

Office/Phone/Fax: DRL 4E7A / 215-898-5971 / 215-573-4063

Office hours: Mo, We 3:00-4:00 PM and by appointment

See Penn Math course information

Teaching Assistant: Matthew Tai

E-mail: mtai AT math.upenn.edu

Office/Phone/Fax: DRL 3C15 / 617-642-7882 / 215-573-4063

Office Hours: Tuesday, Thursday, at 4:00-5:00 PM

General Information

• Lecture class on Mondays, Wednesdays and Fridays at 2-3 PM in DRL A2.
• Lab sessions are on Tuesday and Thursday at 6:30-8:30 PM in DRL 3C4. The lab is an integral part of this course, and attendance is required.
• This course is the Algebra part of an year long course on Proving things, but the two parts of the course are independent from each other. The emphasis in this course is on on discovery, reasoning, the necessity of proofs and effective communication in the mathematical language. At the same time we will learn more about arithmetic, and get acquainted with the basic algebra language and a few facts, like linear algebra, groups, rings and fields. The lecturing style is more informal, and take place in a discussion-type atmosphere, and often the entire class works together on a given problem. The students are expected to learn (some of) the language of rigorous mathematical argumentation and to be able to differentiate complete proofs from argumentation with gaps.
• Required background and Advice: It is expected that the students have a solid knowledge of the hight school mathematics, as well as the basic calculus skills.
• The Syllabus includes some of the following topics: the Peano Axioms for the integers, mathematical induction, basics of (first order) logic, congruences, primitive roots, quadratic reciprocity, basic algebraic structures like groups, rings, fields, linear algebra, applications to Cryptography.
  
  
• Main textbook: Number Theory with Applications by James. A. Anderson and James M. Bell
  
  
• Further suggested Reading:
  • Introduction to Number Theory by Peter D. Schumer.
    
  • Abstract Algebra by Michael Artin (a not too advanced text, with many exercises).
    
  • Algebra by Serge Lang, Springer Verlag (difficult for a beginner, but contains a very large amount of material).
    

Basic Rules:

Announcement, homework assignment, notes, sample problems, etc., will all be posted on web. No hard copies will be distributed. Please check this page frequently for the most updated information.

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The Final grade is based on: Two exams (20%+25%), regular homework and participation and performance in the lab sessions (35%), participation in a project (20%).

Exam dates (tentatively): Feb 24, 2012 / Apr 18, 2012.

Presentation of a project (tentatively): Towards the end of the Spring term 2012.

• Homework
  • Homework is intended to be thought-provoking, but also skill-sharpening. In oder to see the homework please follow the links under Homework Math 203.
  • It is recommended that your works contains complete, rigorous and logically correct proofs. (A reminder: Part of a rigorous and logically correct formulation of a proof is a grammatically correctly written proof!)
  • You are encouraged to work in groups and discuss/communicate as much as possible with each other. But it is recommended that the work you hand in IS YOUR OWN WRITE-UP.
  • It is expected that you submit the homework by the due day.
• Lab
  • The lab is an integral part of this course, and thus attendance is recommended and/or required. Your teaching assistant is ???, and I am convicted that you will enjoy working with him!
  • It is strongly recommended that the students actively participate in the lab. This is a part of the training to construct and communicate mathematical contents and mathematically correct proofs.
• Project
  • There will be some Projects to choose from, and I recommend that each of you eventually works with a group of other students on one of the subjects I propose or on a topic you find yourself. The task consists of doing the necessary research and finally present your findings in the class. This is a great opportunity for you to study a subject in more depth, and to try doing some research on your own!

Info pages for undergraduate math:

• General Mathematics Undergraduate Information
• Information and advice for current and prospective Mathematics Majors.
• A list of courses in other departments that can be counted as Mathematics Electives in the major.
• Biological Mathematics major
• Mathematics Minor requirements

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