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MATH 6320:

 Theory of Functions of Real Variables I

Fall 2022

Class times   

We will meet MWF 10:00-11:00am in CBB 214.

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

Contact

Email: anna@math.uh.edu

Please include "MATH 6320" 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.

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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 by appointment only. 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 at least two days in advance to setup the meeting. Generally, I will be available to meet on Mondays 12:15-2:15pm, even on short notice.

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.

• graduate standing and knowledge of material covered in 6312/6313
  

• Homework: 35%
  
• Midterm:  30%
• Final: 35%

Homework will be handled using Gradescope system. Since this is an outside of the UH website, you are not required to use. 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.

Homework sheets can be downloaded in Gradescope. You will write solutions by hand on a blank piece of paper, scan it and upload to Gradescope indicating pages where solution to each problem is located. You are required to upload your paper to Gradescope before 11:00PM of the day indicated on the sheet and in the calendar below. Deadline extension may be granted only in case of a prolonged illness or emergency described in the UH Absence Policy, with proper and timely provided documentation. Try to complete homework at lest two days before the deadline expires, in case you encounter any issues with your technology.

When uploading your paper to Gradescope, make sure your copy is of high quality (contrast, resolution,...). Your handwriting must be clear and easy to read. Solution must be written neatly from top to bottom in a logical way.

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: V5G7JE . 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.

Homework may be graded selectively.

Here is an extensive and very good article on how to write and how not to write a good proof. And here is another one.

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One midterm will be held during regular class times.

Regrade Requests

You have one week after your grade for Midterm or Homework 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.

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:

1. Check the calendar below to see what chapter was covered in class. Calendar is updated a few hours after the class.
2. 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.
   
3. Study the corresponding chapter in the textbook.
4. 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 may be asked to sign an honor code statement as part of their submission of any graded work including but not limited to projects, quizzes, and exams: "I understand and agree to abide by the provisions in the University of Houston Undergraduate Academic Honesty Policy (or University of Houston Graduate Academic Honesty Policy). I understand that academic honesty is taken very seriously and, in the cases of violations, penalties may include suspension or expulsion from the University of Houston."

Monday	Wednesday	Friday
August 22 Introduction Notations 1	August 24 Algebras 2.1	August 26 Monotone Class Theorem 2.2
August 29 Measures 3	August 31 Measures 3	September 2 Construction of Measures 4
September 5 Labor Day	September 7  Construction of Measures 4	September 9 Construction of Measures 4 Homework 1 Due
September 12 Construction of Measures 4	September 14 Measurable Functions 5	September 16 Measurable Functions 5
September 19 Measurable Functions 5	September 21   Measurable Functions 5	September 23   Lebesgue Integral 6 Homework 2 Due
September 26 Limit Theorems 7	September 28 Limit Theorems 7	September 30 Limit Theorems 7   Properties of Lebesgue Integrals 8
October 3 Properties of Lebesgue Integrals 8	October 5 Riemann Integrals Davidson&Donsing book	October 7 Riemann Integrals 9  Homework 3 Due
October 10 Midterm prep	October 12   Midterm prep	October 14 MIDTERM
October 17   Types of Convergence 10	October 19 Types of Convergence 10	October 21 Product Measures 11
October 24 Fubini Theorem 11	October 26 Signed Measures 12	October 28 Hahn Decomposition Theorem Jordan Decomposition Theorem 12
October 31 The Radon-Nikodym Theorem 13	November 2 The Radon-Nikodym Theorem 13	November 4 Lebesgue Decomposition Theorem 13
November 7   CAMPUS CLOSED ASTROS PARADE	November 9 Differentiation 14	November 11 Differentiation 14 Homework 4 Due
November 14   Differentiation 14	November 16 Bounded Variation 14	November 18   Bounded Variation 14
November 21   Absolutely continuous functions 14	November 23	November 25 THANKSGIVING
November 28 Absolutely continuous functions 14	November 30 Review	December 2 In-class Final

COVID-19 information

Vaccinations

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.

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