2025 Fall Course Syllabus - Mathematics 3131.001

Course Title:

Real Analysis

Course Credits:

4

Course Mode:

In person

Course Days and Time:

TTh 11:40 am - 1:20 pm

Course Room:

Wachman 213

Course Instructor:
Luke Peilen
Instructor Email:
luke.peilen@temple.edu
Instructor Office:

Wachman 544

Instructor Phone:

Please contact me via email at luke.peilen@temple.edu. You can expect a response of time of under 3 hours during the week and by the next week day on weekends

 

Office Hours:

TBD. I will also be available to meet by appointment



 

Course Materials:
  • The course textbook is"Understanding Analysis " by Stephen Abbott, 2015 (ISBN-13: 978-1-4939-2712-8). The e-book is freely available through SpringerLink; sign into your TU Library account and follow the link there.

     

    All course readings will be assigned from this textbook.

  •  
  • The following open source book is also fabulous and has great exercises: Jiří Lebl, "Basic Analysis". 
    • There are many other fabulous classic texts out there as well (Rudin, Beals, etc.) that I encourage you to check out for more reading as well!



 



 

Course grading scheme:

The course grading will be based on the following scheme:

 

Reading and Problem Quizzes: 10%

Portfolio Problems: 30%

Midterm Exams (in class): 30%

Final Exam (in class): 30%


Your reading and portfolio problem grades will be assessed as discussed below




 

Course prerequisites:

Minimum grade of C- in Calculus III (MATH 2043 or MATH 2943) and Basic Concepts of Math (MATH 2111)

Course goals:

The course aims to introduce students to the theoretical underpinnings of calculus. Students will develop their skills in mathematical reasoning and writing, both as individuals and as a team, as well as honing their critical thinking and problem solving skills. Students will develop an understanding of analytical techniques that will be prepare them well for more advanced courses in analysis, differential equations, geometry and topology, probability, applied math and more, while also developing analytical reasoning skills that will prepare them well to approach important questions in the sciences and humanities

Topics covered:

Sets and functions, ordered fields and the real numbers, sequences and series, metric spaces and elementary topology with a focus on the real numbers, continuity, differential and integral calculus, sequences of functions

Exam dates:

Midterm 1 (tentative): in class, 10/16. Midterm 2 (tentative): in class, 11/20. Final Exam: Tuesday 12/16, 12:30 pm

Attendance policy:

Attendance is strongly encouraged, since a critical aspect of your learning is engaging with the class. Much of the course design will be active, and a fundamental learning goal of the course is learning to engage with the material with your peers. Attendance will consequently be linked to your grade by completion of the various reading and problem quizzes, see below

Technology Specifications for this Course:
Access to a computer for accessing the canvas page is essential
Homework and Portfolio Problems:

Your homework grade will be determined via completion of a series of ``portfolio problems", which are already posted on the canvas page. Each of these problems requires understanding of a critical concept of the course.

 

Each problem will be graded on a 2 point scale: 2 for correct, 1 for needs revision, and 0 for incomplete. You can submit each problem at any point during the semester. If you initially receive a grade of 1, you can revise the problem two times for full credit, incorporating my comments and your discussions with me and your peers. Your grade in the category will be assigned on an A-F scale based on the following cutoffs:

 

A : 33-36 points

B : 30-32 points

C : 24-29 points

 

I will post additional weekly homework throughout the semester. This will not be collected, but it is critical that you complete them to develop mastery of the course material for the exams . The portfolio problems will appear on them as we progress through the course, and I am happy to discuss any and all problems in office hours

Reading and Problem Quizzes:

Reading will be assigned throughout the semester. Since reading mathematical literature and engaging in course discussion are fundamental learning goals, each non-exam day we will either have a reading quiz at the beginning of class or a problem quiz at the end of class. The reading quiz will be graded based on completion, and will ask you a discussion prompting question based on that class's reading. The problem quiz will also be based on completion, and will ask you a discussion prompting question based on that day's material. There are 25 total: you must complete the following amount to receive a grade in the category.

 

A: 22-25

B: 18-22

C: 15-18



 

Canvas:

This is a registered Canvas course. Please check Canvas daily for important announcements!



 



 

Make-up Policy:

There will be no regularly scheduled make up exams. In the case that you are unable to take an exam as scheduled, please contact me ASAP to make alternate arrangements!



 

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
Homework and Portfolio Problems
Description

Your homework grade will be determined via completion of a series of ``portfolio problems", which are already posted on the canvas page. Each of these problems requires understanding of a critical concept of the course.

 

Each problem will be graded on a 2 point scale: 2 for correct, 1 for needs revision, and 0 for incomplete. You can submit each problem at any point during the semester. If you initially receive a grade of 1, you can revise the problem two times for full credit, incorporating my comments and your discussions with me and your peers. Your grade in the category will be assigned on an A-F scale based on the following cutoffs:

 

A : 33-36 points

B : 30-32 points

C : 24-29 points

 

I will post additional weekly homework throughout the semester. This will not be collected, but it is critical that you complete them to develop mastery of the course material for the exams . The portfolio problems will appear on them as we progress through the course, and I am happy to discuss any and all problems in office hours

Title
Reading and Problem Quizzes
Description

Reading will be assigned throughout the semester. Since reading mathematical literature and engaging in course discussion are fundamental learning goals, each non-exam day we will either have a reading quiz at the beginning of class or a problem quiz at the end of class. The reading quiz will be graded based on completion, and will ask you a discussion prompting question based on that class's reading. The problem quiz will also be based on completion, and will ask you a discussion prompting question based on that day's material. There are 25 total: you must complete the following amount to receive a grade in the category.

 

A: 22-25

B: 18-22

C: 15-18



 

Title
Canvas
Description

This is a registered Canvas course. Please check Canvas daily for important announcements!



 



 

Title
Make-up Policy
Description

There will be no regularly scheduled make up exams. In the case that you are unable to take an exam as scheduled, please contact me ASAP to make alternate arrangements!



 

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

Course credits

4

Course mode

In person

Course Days and Time

TTh 11:40 am - 1:20 pm

Course room

Wachman 213

Your office

Wachman 544

Your office hours

TBD. I will also be available to meet by appointment



 

Course materials
  • The course textbook is"Understanding Analysis " by Stephen Abbott, 2015 (ISBN-13: 978-1-4939-2712-8). The e-book is freely available through SpringerLink; sign into your TU Library account and follow the link there.

     

    All course readings will be assigned from this textbook.

  •  
  • The following open source book is also fabulous and has great exercises: Jiří Lebl, "Basic Analysis". 
    • There are many other fabulous classic texts out there as well (Rudin, Beals, etc.) that I encourage you to check out for more reading as well!



 



 

Course grading scheme

The course grading will be based on the following scheme:

 

Reading and Problem Quizzes: 10%

Portfolio Problems: 30%

Midterm Exams (in class): 30%

Final Exam (in class): 30%


Your reading and portfolio problem grades will be assessed as discussed below




 

Course prerequisites

Minimum grade of C- in Calculus III (MATH 2043 or MATH 2943) and Basic Concepts of Math (MATH 2111)

Course goals

The course aims to introduce students to the theoretical underpinnings of calculus. Students will develop their skills in mathematical reasoning and writing, both as individuals and as a team, as well as honing their critical thinking and problem solving skills. Students will develop an understanding of analytical techniques that will be prepare them well for more advanced courses in analysis, differential equations, geometry and topology, probability, applied math and more, while also developing analytical reasoning skills that will prepare them well to approach important questions in the sciences and humanities

Description of topics covered

Sets and functions, ordered fields and the real numbers, sequences and series, metric spaces and elementary topology with a focus on the real numbers, continuity, differential and integral calculus, sequences of functions

Exam dates

Midterm 1 (tentative): in class, 10/16. Midterm 2 (tentative): in class, 11/20. Final Exam: Tuesday 12/16, 12:30 pm

Attendance Policy

Attendance is strongly encouraged, since a critical aspect of your learning is engaging with the class. Much of the course design will be active, and a fundamental learning goal of the course is learning to engage with the material with your peers. Attendance will consequently be linked to your grade by completion of the various reading and problem quizzes, see below

Technology Specifications for this Course
Access to a computer for accessing the canvas page is essential
Course Instructor
Luke Peilen
Instructor Email
luke.peilen@temple.edu