Florian Pop: Teaching

## Florian Pop: Math 202 (Proofs -Analysis)

E-mail: `pop AT math.upenn.edu`
Office/Phone/Fax: DRL 4E7A / 215-898-5971 / 215-573-4063
Office hours: Mo, Fr 1:00-2:30 PM. Please make an appointment in advance (by email).
TA: Linbo Liu, Office/Phone/E-mail: DRL 1N1 / 267-982-9825 / linbo@sas.upenn.edu

### General Information

• See Undergrad Course Description
• Class: Tu 10:15-12:00(noon) in DRL 4C6, Th 10:30-12:00(noon) in DRL 3C6. First class on Tu, Aug 29, 2017.
• Lab: Mo, We 6:30-8:30 PM
• This course is about rigorous proofs in the context of Analysis. For a passing grade, the students are expected to:
• Understand rigorous mathematical argumentation/proofs and to be able to write coherent mathematical proofs.
• Understand and know the material and be able to solve related problems.
• Syllabus: Basic facts about an axiomatic approach to sets and operations with sets. Basic facts about construction of the domains of numbers: the natural, integer, rational numbers, and the usual operation with numbers. The real numbers and their definition, the basic operations with and properties of real numbers. The definition of continuity, differentiability, integrability, and basic properties (with proofs). Proof of Fundamental Thm of Calculus. The properties of the elementary functions, and of spaces of functions.
• Required background/prerequisites: The high school honors algebra, familiarity with proofs, e.g., proofs by induction and/or proofs in (Euclidean) geometry.
• Resources: There are several books you can use (and some course notes might/will be provided).
• J. P. D'Angelo - D. B. West, Mathematical Thinking: Problem-Solving and Proofs, 2nd Edition, Prentice Hall (2000).
• Serge Lang, Undergraduate Analysis (This is a more advanced text, and has a large amount of material.)

### Basic Rules:

• The final grade is based on midterms and a final exam (30%+35%) and everything else (35%). "Everything else" consists of regular homework, participation/performance in class and lab, etc.
• Exam dates (tentatively): Oct 12, Nov 16, Dec 14, 2017.
• Miscellania: Announcements, homework assignment, notes, etc., will all be posted on web. No hard copies will be distributed. Please check this page frequently for the most updated information. Remember to use to RELOAD button of your browser.
• Homework:
• Homework will be assigned each week, and in oder to see the homework please follow the links under Homework Math 202. The homework assignment of each week is tentatively due on Wednesday of the next week.
• Your works should contain complete solutions, and rigorous and logically correct proofs for theoretical problems. (Note: such a proof must be written in grammatically correct language.)
• You are encouraged to work in groups and discuss/communicate with each other as much as possible. But the work you hand in must be your own write-up.
• Late work will not be accepted.

• Grading Note: At the end of the semester, everyone who has not withdrawn from the class will get a grade. The grade "I" (Incomplete) will not be given to avoid the grade "F" (Fail).

### Info pages for undergraduate math:

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