Home

MATH 4331/6312:

 Introduction to Real Analysis I

Fall 2021

Class times   

This course is being offered in the In-Person format. We will meet MWF 9:00-10:00am in SEC 104.

• Are NOT exhibiting any Coronavirus Symptoms that makes you think that you may have COVID-19
• Have NOT tested positive or been diagnosed for COVID-19
• Have NOT knowingly been exposed to someone with COVID-19 or suspected/presumed COVID-19
  

Face covering policy

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

Contact

Email: anna@math.uh.edu

Please include "MATH 4331/6312" 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.

back to top

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.

We will be using the following book: 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.

• MATH 3325
  
• MATH 3333 or 3334
  

• Homework: 25%
  
• Two Midterms:  40%
• 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: RW6PZZ . 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 will be graded selectively. Students in 6312 might receive additional problems, and it's possible that different problems will be graded for 4331 and 6312. In 6312 class, students will be held up to a higher standards for writing solutions in logical professional way.

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.

back to top

Two midterms will be held during regular class times. Midterm will consists of two problems from homework, two problems from the list of theorems/statements covered in class, and one new problem. The list of theorems will be uploaded to Teams no later than two weeks before the exam.

To give you an opportunity to improve your final grade you may take a Grade Improvement Test held right after Midterm 2 (before it is graded). The test will cover material from the beginning of the semester. You may take the test during the class time and at the end of the class decide wither you would like to turn it in or not. Here are the rules for the test:
- With this grade you may replace the grade for one of the following: Midterm 1, Midterm 2 or all of Homework 1-6.
- You may replace only a non-zero grade for the exams, and you may replace homework only if you wrote all six homework assignments with a nonzero grade each.
- Once you turn in your Grade Improvement Test, it will be graded, and this grade will replace the grade you indicated, even if the new grade is lower.

Regrade Requests

You have one week after your grade for Midterms, GIT or Homework 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. explain why your solution was correct, but was marked as incorrect). Requests to change rubrics will be ignored. Before you make a regrade request, read the following article explaining when and how to do that (all views and opinions expressed in that article are solely of the author).

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 23 Introduction	August 25 Proofs	August 27 Proofs; Topology of R^n 4.1 Homework 0 Due
August 30 Topology of R^n: 4.1	September 1 Topology of R^n: 4.1	September 3 Topology of R^n: convergence and completeness 4.2 Homework 1 Due
September 6 Labor Day	September 8  Homework 1 Solutions	September 10 Homework 1 Solutions Topology of R^n: 4.2 Homework 2 Due
September 13 Topology of R^n: open, closed sets 4.3	September 15 Topology of R^n: open, closed sets 4.3	September 17 Topology of R^n: open, closed sets 4.3 Homework 3 Due
September 20 Topology of R^n: compact sets 4.4	September 22 Topology of R^n: compact sets 4.4	September 24 Topology of R^n: Heine-Borel theorem 4.4 Homework 4 Due
September 27 Midterm prep	September 29 Midterm 1	October 1 Surprise class
October 4 Functions: Limits and Continuity 5.1	October 6 Functions: Limits and Continuity 5.1	October 8 Functions: Limits and Continuity Discontinuity 5.1 -5.2
October 11 Functions: Discontinuity 5.2	October 13 Functions: Discontinuity 5.2	October 13 Properties of Continuous functions 5.3 Homework 5 Due
October 18 Functions: Compactness and Extreme Values 5.4	October 20 Functions: Uniform Continuity 5.5	October 22 Functions: Uniform Continuity 5.5 Homework 6 Due
October 25 Midterm prep	October 27 Midterm 2	October 29 Grade Improvement Day
November 1 Intermediate Value Theorem in R Connected Sets 5.6	November 3 Connected Sets	November 5   Connected, Path-connected Sets
November 8 Connected, Path-connected Sets	November 10 Connected, Path-connected Sets Intermediate Value Theorem in R^n 5.6	November 12 Intermediate Value Theorem in R^n 5.6  Homework 7 Due
November 15   Monotone Functions 5.7	November 17 Monotone Functions 5.7	November 19 Differentiable Functions   6.1 Homework 8 Due
November 22 Differentiable Functions   6.1	November 24	November 26 Thanksgiving
November 29 Mean Value Theorem 6.2	December 1 Mean Value Theorem 6.2	December 3 Review Homework 9 Due
December 13 Final 8:00-11:00am

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 Undergraduate Excused Absence Policy and 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

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