2023 Spring Course Syllabus - Mathematics 8042.001

Course: Mathematics 8042.001.

Course Title: Real Analysis II.

Credits: 3 credits.

How this course will be taught: in-person.

Time: MW 1:00 PM - 2:20 PM.

Place: WCHMAN 1036.

Instructor: Irina Mitrea.

Instructor Office: WCHMAN 1020.

Instructor Email: imitrea@temple.edu

Instructor Phone: (215) 204-6741.

Course Web Page: N/A

Office Hours: Wednesdays 2:30 PM - 3: 50 PM; Tuesdays 1:30 PM - 2:50 PM on zoom; and by appointment.

Prerequisites: Math 8041, Real Analysis I.

Course Materials: Textbook: W. Rudin, Real and Complex Analysis, McGraw-Hill, 3rd edition, 1987.

Course Goals: Course goals include building the foundational background in Lebesgue Integration Theory. Focus will be placed on understanding advanced definitions, understanding and constructing proofs using the measure theoretic concepts introduced, analyzing conjectures and finding counterexamples to false statements. After completing this course, students will:

(1) Have gained a thorough grounding in modern Real Analysis (2) Be able to comprehend and critically reflect on mathematical statements and their proofs and to write their own formal proofs of mathematical results (3) Have developed a higher capacity for abstract and rigorous mathematical reasoning (4) Be well-equipped to study advanced applications of Real Analysis in other disciplines.

Topics Covered: The construction of the Lebesgue measure via the Riesz Representation Theorem; regularity properties of Borel measures; The Lebesgue measure in euclidean spaces; Lusin's Theorem; the Vitali-Caratheodory Theorem; Jensen's Inequality; Holder's Inequality; Minkowski's Inequality; Lebesgue spaces and convergence (pointwise, in measure, and in norm); Egoroff's Theorem; Lebesgue's Differentiation Theorem; the Vitali Covering Lemma; the Hardy-Littlewood Lemma; functions of bounded variation.

Course Grading: Prelims count for 25% each, the final counts for 25%, homework counts for 15%, and mini-presentations count for 10%. The grading scale is A: 90-100; B: 80-89; C: 70-79; D 60-69; F: 60.

Exam Dates: Midterm I: Wednesday, March 1st

Midterm II: Wednesday, April 19th (take home)Final: May 3rd, 10:30 AM - 12:30 PM.

Attendance Policy: You are expected to attend class. If you have an excuse for missing a class, please let me know. If you have 4 or more unexcused absences, your grade will drop half a notch (e.g. B to B-) for each 4 classes you miss.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.