Time and Place: MWF 12:30–1:20 in UNIV 103

Instructor: Arshak Petrosyan

Office Hours: MWF 11:30–12:30, or by appointment, in MATH 610

Textbook:

[SS] E.M. Stein, R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis)

Additional Textbooks:

[R] H.L. Royden, Real Analysis
[WZ] R.L. Wheeden, A. Zygmund, Measure and Integral: An Introduction to Real Analysis

Syllabus: Construction of Lebesgue measure and integral, abstract measure spaces and integral, properties of measurable functions, $L^p$- spaces, Fubini-Tonelli theorem, convolutions in $\mathbb{R}^n$. Differentiation: Bounded variation and Helly Selection Theorem, Vitali Covering Theorem, differentiation of monotone functions, absolute continuity, Lebesgue Differentiation Theorem. (This roughly corresponds to Chap 1–4 and 6 (partially) in [SS])

Homework will be collected weekly; the day of the week may vary. The assignments will be posted on the Homework page at least one week prior to the due date. The homework will be collected at the beginning of class on the due date. No late homeworks will be accepted, however the lowest homework score will be dropped.

Exams: There will be two midterm exams (most likely evening exams) and a comprehensive final exam (covering all material). The exact time and place will be specified at least two weeks in advance. The appropriate information will be posted on the Exams page.

Grading: Your final score will be computed according to the scheme

Final Score = (1/3)FE + (7/30)ME1 + (7/30)ME2 + (1/5)HW,

where FE, MEi, HW are the scores (in %) for the Midterm Exam i, Final Exam, and the Homework, respectively.

Academic Integrity: As a reminder, all students must comply with Purdue’s policy for academic integrity:

https://www.purdue.edu/odos/osrr/academic-integrity/

Students with Disabilities: Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247.

In this mathematics course accommodations are managed between the instructor, student and DRC Testing Center. Students should see instructors outside class hours – before or after class or during office hours – to share your Accommodation Memorandum for the current semester and discuss your accommodations as soon as possible.

Emergencies: In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted onto the course website or can be obtained by contacting the instructor via email or phone. You are expected to read your @purdue.edu email on a frequent basis.