2025 Spring Course Syllabus - Mathematics 8042.001

Course Title:

Real Analysis II

Course Credits:

3

Course Mode:

In person

Course Days and Time:

Tu/Th 9:30-10:50am

Course Room:

Wachman 617

Instructor Office:

Wachman 614

Instructor Phone:

n/a

Office Hours:

Tu/Th 11:00am-12:00pm or by appointment

Course Materials:

"Measure and Integral: An Introduction to Real Analysis" 2nd ed. by Wheeden and Zygmund

Course grading scheme:

25% Homework

20% In Class Presentations

30% Midterms (2 exams, 15% each)

25% Final Exam

 

Homework

Homework will be due on (most) Fridays by noon and is to be submitted electronically via Canvas. There will be 8 homework assignments averaging around 6 or 7 problems per assignment. All problems on each assignment will be graded by the instructor.

 

In Class Presentations

Problem Set Presentations + Written Solution

There will be two assignments throughout the semester for which all solutions will be presented in class by the students. This is separate from the homework assignments. Each student will find out which problem they are to present during the class when presentations occur, so each student should come prepared to present any problem. Each student will present their problem in class then will have one week to submit a written solution. Student solutions will be compiled into a solution set and shared on Canvas. The problem set presentation days are scheduled for Thursday, January 30 and Thursday, March 20.

 

Lecture Presentations

Each student will be tasked with presenting part of the lecture content twice throughout the semester. The instructor will contact each student at least two days prior to their presentation (with a goal of contacting students a week prior) with instructions regarding the specific content they are to cover. Examples of content a student may be asked to present are proofs of theorems or explanations of examples given in the textbook.

 

Midterms

There will be two in-class, closed book midterms throughout the semester. They are scheduled for Thursday, February 20 and Thursday, April 10.

 

Final Exam

The final exam is scheduled for Thursday, May 1 8:00-10:00am in Wachman 617.

Course prerequisites:

Real Analysis I or knowledge of Lebesgue measure and integration in n-dimensional spaces.

Course goals:

Students will develop a deep working understanding of the core topics in (roughly) Chapters 7-12 of the text (see topics covered below for details). There will bean emphasis on developing students' proof writing skills.

Topics covered:

This is the second semester of a year-long course in Real Analysis. This semester will build on the ideas of Lebesgue integration developed in the first semester but move on to more abstract settings. Topics for this semester are:

  1. Abstract measures and integration
  2. Differentiation and maximal functions
  3. Lp-spaces
  4. Outer measures
  5. Basic functional analysis
  6. Fourier transform

 

Exam dates:

Midterm 1: Thursday, February 20

Midterm 2: Thursday, April 10

Final Exam: Thursday, May 1

 

Problem Set Presentations 1: Thursday, January 30

Problem Set Presentations 2: Thursday, March 20

Attendance policy:

Students are expected to attend every class unless they are sick or have a valid conflict.

Technology Specifications for this Course:
No specific technology is required for this course.
Canvas page:

https://templeu.instructure.com/courses/154523

Attendance and Your Health:

To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person  classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.

Expectations for Class Conduct :

It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse. 

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).

AI Policy:

The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

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.

Year
Semester
Course
Section
Course Extra
Title
Canvas page
Description

https://templeu.instructure.com/courses/154523

Title
Attendance and Your Health
Description

To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person  classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.

Title
Expectations for Class Conduct
Description

It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse. 

Title
Disability Statement
Description

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.

Title
Academic Freedom
Description

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).

Title
Add/Drop Policy
Description

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).

Title
AI Policy
Description

The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

Title
Incomplete Policy
Description

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).

Title
Student Support Services
Description

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.

Course title

Real Analysis II

Course credits

3

Course mode

In person

Course Days and Time

Tu/Th 9:30-10:50am

Course room

Wachman 617

Your office

Wachman 614

Your office hours

Tu/Th 11:00am-12:00pm or by appointment

Course materials

"Measure and Integral: An Introduction to Real Analysis" 2nd ed. by Wheeden and Zygmund

Course grading scheme

25% Homework

20% In Class Presentations

30% Midterms (2 exams, 15% each)

25% Final Exam

 

Homework

Homework will be due on (most) Fridays by noon and is to be submitted electronically via Canvas. There will be 8 homework assignments averaging around 6 or 7 problems per assignment. All problems on each assignment will be graded by the instructor.

 

In Class Presentations

Problem Set Presentations + Written Solution

There will be two assignments throughout the semester for which all solutions will be presented in class by the students. This is separate from the homework assignments. Each student will find out which problem they are to present during the class when presentations occur, so each student should come prepared to present any problem. Each student will present their problem in class then will have one week to submit a written solution. Student solutions will be compiled into a solution set and shared on Canvas. The problem set presentation days are scheduled for Thursday, January 30 and Thursday, March 20.

 

Lecture Presentations

Each student will be tasked with presenting part of the lecture content twice throughout the semester. The instructor will contact each student at least two days prior to their presentation (with a goal of contacting students a week prior) with instructions regarding the specific content they are to cover. Examples of content a student may be asked to present are proofs of theorems or explanations of examples given in the textbook.

 

Midterms

There will be two in-class, closed book midterms throughout the semester. They are scheduled for Thursday, February 20 and Thursday, April 10.

 

Final Exam

The final exam is scheduled for Thursday, May 1 8:00-10:00am in Wachman 617.

Course prerequisites

Real Analysis I or knowledge of Lebesgue measure and integration in n-dimensional spaces.

Course goals

Students will develop a deep working understanding of the core topics in (roughly) Chapters 7-12 of the text (see topics covered below for details). There will bean emphasis on developing students' proof writing skills.

Description of topics covered

This is the second semester of a year-long course in Real Analysis. This semester will build on the ideas of Lebesgue integration developed in the first semester but move on to more abstract settings. Topics for this semester are:

  1. Abstract measures and integration
  2. Differentiation and maximal functions
  3. Lp-spaces
  4. Outer measures
  5. Basic functional analysis
  6. Fourier transform

 

Exam dates

Midterm 1: Thursday, February 20

Midterm 2: Thursday, April 10

Final Exam: Thursday, May 1

 

Problem Set Presentations 1: Thursday, January 30

Problem Set Presentations 2: Thursday, March 20

Attendance Policy

Students are expected to attend every class unless they are sick or have a valid conflict.

Technology Specifications for this Course
No specific technology is required for this course.