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MATH 6321:

Theory of Functions of Real Variables II

Spring 2023

Quizzes Calendar Exams Missed Class Prelim Exams

"If I had an hour to solve a problem, I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions."
Albert Einstein

All information on the website is subject to change if circumstances require it. I will communicate any changes during the class. Check back for the most up-to-date information.

If you haven't found here what you were looking for, please contact me using the contact information below. All your inputs are highly valued and appreciated.

Syllabus

Class syllabus can be found on Access UH. Due to the changing nature of the COVID-19 pandemic, please note that the instructor may need to make modifications to the course syllabus and may do so at any time. Notice of such changes will be announced as quickly as possible through UH email.

Class times

We will meet MWF 10:00-11:00am in S 115.

Technology requirements

You should have a scanner or certain smartphone apps that allow you to scan your handwritten homework into a pdf file. Alternatively, certain tablets and tablet apps allow you submit your written work directly from the tablet.

Recordings of class

Students may not record all or part of class, livestream all or part of class, or make/distribute screen captures without advanced written consent of the instructor. If you have or think you may have a disability such that you need to record class-related activities, please contact the Justin Dart Jr. Student Accessibility Center. If you have an accommodation to record class-related activities, those recordings may not be shared with any other students, whether in this course of not, or with any other person or on any other platform. Classes may be recorded by the instructor. Students may use instructor's recordings for their own studying or notetaking. Instructor's recordings are not authorized to be shared with anyone without the prior written approval of the instructor. Failure to comply with requirements regarding recordings will result in a disciplinary referral to the Dean of Students Office and may result in disciplinary action.

Contact

Dr. Vershynina (you should refer to me as either Doctor/Dr. or Professor/Prof. followed by my last name)

Email: anna@math.uh.edu

Please include "MATH 6321" in the subject, so that your email won't be regarded as spam. For security reasons I will reply only to emails sent from official UH emails (i.e. ending in "uh.edu").

When writing an email, make sure it adheres to the protocol of formality, which is standard in academia. Read more about it here, for example.

Normally, I answer urgent emails within one-two business days. Generally, I do not repeat information that can be found on this website or was communicated in class. If I do not respond to your email within two working days, please resend the email. If you again do not hear from me within one more working day, it is likely that your email is not coming through and you should speak with me before or after class. It is your responsibility to ensure that I am aware of issues you may have with the course; failure to effectively initiate timely communication is not a valid basis for a grade grievance and cannot be used as such.

Bring comments or complaints to my attention as soon as possible. Don't wait until the end of the semester to bring up a matter which we could deal with and solve early on.

UH Email

Email communications related to this course will be sent to your Exchange email account which each University of Houston student receives. The Exchange mail server can be accessed via Outlook, which provides a single location for organizing and managing day-to-day information, from email and calendars to contacts and task lists. Exchange email accounts can be accessed by logging into Office 365 with your Cougarnet credentials or through Acccess UH. They can also be configured on IOS and Android mobile devices. Additional assistance can be found at the Get Help page.

UH policy states that all required written notices shall be addressed to the student via their UH email. Notices properly addressed and so sent shall be presumed to have been received by the student. Thus, you are responsible for the content in emails sent to your UH account, regardless if your external (non-UH) email provider filters or blocks. Emails lost to external providers shall not be used as a justification to claim faculty are unresponsive, to appeal grades, etc.

Office Hours

Office hours will be done through Microsoft Teams on Wednesdays 11:15-12:15pm or by appointment. You are welcome and encouraged to make an appointment if you have any questions about material or issues that you would like to discuss. Please contact me by email to setup the meeting or let me know after the class. If Wednesdays 11:15am-12:15pm doesn't work for you, contact me at least two business days in advance to setup a different time.

Textbook

We will be using the following books:

R. Bass, "Real Analysis for Graduate Students"
G. B. Folland, "Real Analysis Modern Techniques and Their Application", Wiley Interscience, Somerset, NJ
W. Rudin, "Real and Complex Analysis" 3rd edition, McGraw-Hill, New York
Kenneth Davidson, Allan Donsig, "Real Analysis with Application: Theory in Practice", Springer 2010

Topics we cover each class are indicated in the calendar below. Here are some tips on how to read your textbook efficiently.

Prerequisites

6320

Grading

Your final grade will break down as follows:

Quizzes: 40% (lowest grade will be dropped)
Midterm: 25%
Final: 35%

Quizzes

Quiz will be held every couple of weeks, see calendar below. Changes can occur with an advance notice (at least 2 days). Most of the quizzes will consists of one/two problems not previously discussed in class, and will be 10-15 min long held during the class. One lowest grade will be dropped to accommodate any unforeseen life circumstances forcing you to miss the quiz. Excused absence of the second missed quiz will only be granted in accordance with the UH Absence Policy, with proper and timely provided documentation.

Quizzes will be graded using Gradescope system. Since this is an outside of the UH website, you are not required to use it. You must inform me during the first week if you opt out of using the system and alternative arrangements will be made for you. Information below is directed to those students wishing to use Gradescope system.

You have one week after your grade is posted to submit a regrade request if you believe there was a mistake with your grading. Along with your request in Gradescope, you must write me an email providing an explanation for a regrade (e.g. your solution was correct, but was marked as incorrect). Requests to change the rubrics will be ignored.

When enrolling yourself in Gradescope, use code: 4V5Y2B . When entering your name, please enter the first 3 letters of your LAST, then first 3 letters of your FIRST name. For example, for a name John Smith, a student should enter "Smi Joh". As your ID number, enter the last 3 digits of your student ID. You are free to use any email with Gradescope, it does not have to be your UH email.

Midterm

One midterm will be held during regular class time.

Final

Final will take place during the finals week period scheduled by the UH. It will cover ALL material from the beginning of the semester.

Regrade Requests

You have one week after your grade for Midterm or Quiz is posted to submit a regrade request if you believe there was a mistake with your grading. The deadline for the Final regrade will be communicated by email after the exam is graded.

Missed Class

If you miss class for whatever reason, you are responsible for all material covered, all lecture material presented in class, and all announcements made in class. When you miss a class, here are the steps to take to catch up with the material:

Check the calendar below to see what chapter was covered in class. Calendar is updated a few hours after the class.
Check Teams for any available notes covering this material. I will try to post some notes on Teams for each chapter, but they may not fully or accurately reflect what was done in class. If there are no notes on Teams, this means they are not available for this chapter/section/class.
Study the corresponding chapter in the textbook.
Contact your classmates for their lecture notes and to find our about any announcements made in class. Your classmates are the best resource for catching up with the material and for jointly solving homework problems.

Honor Code Statement

Students are expected to adhere to the University of Houston Graduate Academic Honesty Policy on all exams and tests. Academic honesty is taken very seriously and, in the cases of violations, penalties may include suspension or expulsion from the University of Houston."

Class Calendar
Topics listed in the calendar are tentative, and are subject to change without notice. I will update the topic we covered after each class.

Monday	Wednesday	Friday
	January 18 Lp spaces 15	January 20 Lp spaces 15 Quiz 1
January 23 Lp spaces 15	January 25 Lp spaces 15	January 27 Lp spaces 15
January 30 Lp spaces 15 Quiz 2	February 1 Lp spaces 15 Fourier transform 16	February 3 Fourier transform 16
February 6 Fourier transform 16	February 8 Fourier transform 16	February 10 Riesz representation 17
February 13 Riesz representation 17	February 15 Riesz representation 17 Quiz 3	February 17 Riesz representation 17
February 20 Banach spaces 18	February 22 Banach spaces 18	February 24 Banach spaces 18
February 27 Banach spaces 18 Quiz 4	March 1 Banach spaces 18	March 3 Banach spaces 18
March 6 Riesz representation 17.4	March 8 Review	March 10 MIDTERM
March 13 Spring Break	March 15 Spring Break	March 17 Spring Break
March 20 Hilbert spaces 19	March 22 Hilbert spaces 19	March 24 Hilbert spaces 19
March 27 Hilbert spaces 19	March 29 Hilbert spaces 19	March 31 Hilbert spaces 19
April 3 Topology 20 Quiz 5	April 5 Topology 20	April 7 Topology 20
April 10 Topology 20	April 12 Topology 20	April 14 Topology 20
April 17 Spectral Theory 25	April 19 Spectral Theory 25 Quiz 6	April 21 Spectral Theory 25
April 24 Spectral Theory 25	April 26 - NO CLASS Spectral Theory 25 self-study	April 28 Q&A
May 1 Q&A		May 05 FINAL 11:15am-1:15pm

COVID-19 information

Students are encouraged to visit the University's COVID-19 website for important information including on-campus testing, vaccines, diagnosis and symptoms protocols, campus cleaning and safety practices, report forms and positive cases on campus. Please check the website throughout the semester for updates.

Excused Absence Policy

Regular class attendance, participation, and engagement in coursework are important contributors to student success. Absences may be excused as provided in the University of Houston Graduate Excused Absence Policy for reasons including: medical illness of student or close relative, death of a close family member, legal or government proceeding that a student is obligated to attend, recognized professional and educational activities where the student is presenting, and University-sponsored activity or athletic competition. Under these policies, students with excused absences will be provided with an opportunity to make up any quiz, exam or other work that contributes to the course grade or a satisfactory alternative. Please read the full policy for details regarding reasons for excused absences, the approval process, and extended absences. Additional policies address absences related to military service, religious holy days, pregnancy and related conditions, and disability.

Religious Holy Days

Students whose religious beliefs prohibit class attendance or the completion of specific assignments on designated dates may obtain an excused absence. To do so, please make a written request for an excused absence and submit it to your instructor as soon as possible, to allow the instructor to make arrangements. For more information, seethe Student Handbook. http://catalog.uh.edu/index.

UH CAPS Statement

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach CAPS (www.uh.edu/caps) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus. http://www.uh.edu/caps/outreach/lets_talk.html

Reasonable Academic Adjustments/Auxiliary Aids
The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americas with Disabilities Act of 1900, pertaining to the provision of reasonable academic adjustments/Auxiliary aids for disabled students. In accordance with Section 504 and ADA guidelines, UH strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring and academic adjustment/auxiliary aid, please contact the Justin Dart Jr. Student Accessibility Center (formerly the Justin Dart, Jr. Center for Students with DisABILITIES).

Helpful Information

COVID-19 updates: https://uh.edu/covid-19/

Coogs Care: https://www.uh.edu/dsaes/coogscare/

Laptop Checkout Requests: https://www.uh.edu/infotech/about/planning/off-campus/index.php#do-you-need-a-laptop

Health FAQs: https://uh.edu/covid-19/faq/health-wellness-prevention-faqs/

Student Health Center: https://uh.edu/class/english/lcc/current-students/student-health-center/index.php

Preliminary Exams

Preliminary exam on the Theory of Real Variables is based on the material covered in two semesters of this class: 6320 and 6321. The exam mainly tests problem solving skills, which rely on the knowledge of definitions, statements and proofs of theorems covered in class. Full list of definition and theorems can be found here.