Mathematics 431 and 731 (Section 02 and Section 03), Fall 2024
Section 02, Time: TuTh 1:25PM - 2:40PM, Location: Physics 235
Section 03, Time: TuTh 3:05PM - 4:20PM, Location: Physics 235
Instructor: Saman Habibi Esfahani, saman.habibiesfahani (at) duke (dot) edu
Text: Fundamental Ideas of Analysis, M. Reed, Wiley
431 vs 731. The course content is identical for undergraduates (Math 431) and graduate students (Math 731), with the exception that graduate students must complete one additional assignment. Another section of this course is taught by Mike Reed (section 01), but all three sections cover the same material.
Lectures and the Flipped Classroom. We will use a flipped classroom format, meaning lectures (by Mike Reed) are prerecorded and posted online. These lectures align with the book sections as outlined in the syllabus. Each lecture is divided into two 25-minute parts, typically totaling six such segments per week. These are labeled by week, lecture, part, and book section covered. For example, w1-L2-1(1.4) indicates the first part of the second lecture in week 1, covering Section 1.4. The URL for the lectures is available on Sakai in the file w0-Lectures. Note that minor adjustments to the syllabus may occur throughout the course.
Intellectual Goals. The course aims to introduce you to mathematical analysis and teach you how to create and write logical, clear proofs.
Class Time. In-class sessions will provide further examples of proofs, with opportunities for questions and assistance. Students will often work on proofs together or in small groups during class.
The Problems. The course is problem-centric, with problems listed for most days and weeks on the syllabus. Most problems require proofs, and collaboration with fellow students is encouraged. Quizzes will largely consist of proving problems similar to those from the previous week's homework, but may also include definitions, theorems, book proofs, or new proof challenges. There will be 11 quizzes (including one makeup quiz), with the lowest quiz grade dropped and the remaining 10 quizzes counted.
Writing. This is a writing-intensive course. Evaluation questions will typically ask for proofs, which must be written in complete sentences with proper grammar and punctuation. Special mathematical symbols like ⇒ for "implies" and ∃ for "there exists" are not allowed, except for ≥, ≤, and for "contained in."
Evaluation
Grades will be based on:
- Quizzes (100 points)
- 1st Midterm (100 points)
- 2nd Midterm (100 points)
- Final Exam (200 points)
This totals 500 points. Weekly homework will be assigned, collected via Gradescope, and feedback will be provided. Homework is not mandatory and does not count toward the final grade, but collaboration is highly encouraged.
Graduate Students. The extra assignment will constitute 8% of the course grade, or 40 points. For graduate students, the final score will be calculated as (.92)P + score on the graduate student assignment. The assignment will be given before Thanksgiving and due by 5pm on December 8. Late submissions will incur a penalty of 5 points per day.
Missed Evaluations.
Legitimate reasons for missing an evaluation include:
1. Significant illness (submit form before evaluation)
2. Religious observance (inform both me and your Dean before evaluation)
3. Varsity athletic participation (submit form before evaluation)
4. Personal or family emergency (Dean must email requesting a makeup)
5. Required legal appearance (Dean must email requesting a makeup)
Except for these, makeups are not allowed. One makeup quiz will be available in the last week of class, and the lowest quiz grade will be dropped.
Academic Assistance. The Mathematics Department maintains a list of tutors available for hire. Contact Laurie Triggiano in the Mathematics Department Office: laurie.triggiano@duke.edu. Additionally, the Academic Resource Center (ARC) offers free services to all undergraduate students at Duke. Contact the ARC at 211 Academic Advising Center Building, East Campus – behind Marketplace. Email: theARC@duke.edu, 919-684-5917.