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MATH 4331/6312:

 Introduction to Real Analysis

Fall 2020

Class Place/Time  

This course is being offered in the Synchronous Online format. Synchronous online class meetings will take place according to the class schedule: Monday, Wednesday, Friday 11:00-11:50am. There is no face-to-face component to this course. In between synchronous class meetings, there may also be asynchronous activities to complete (e.g., discussion forums and assignments, see below).

Online class will meet online in Microsoft Teams. You must login in Microsoft Teams using your UH credentials. Go to the Live Meetings channel for the link to the live class meeting.

When signing in to live meeting, turn off your camera and your mic, and keep them turned off during the meeting. This will improve connectivity and will help keep distractions to a minimum. If you would like to ask a question during a class, use the chat feature, which I will review periodically during the class. Do not use "Raise a Hand" feature during a lecture, but you are free to use it during discussions. I will let you know when it is appropriate to use the feature.

If an unforeseen technical difficulty or emergency makes live meeting impossible, we will disconnect, and slides from the lecture will be posted under "Files" tab. You will be responsible to review the slides and read the textbook.

Every class will be recorded. By participating in live meetings you give your consent that some of your information and image might be displayed during the event, and possibly recorded and accessed by others. This might also be due to you forgetting to turn off or turning on your video/mic. By participating in this class, you also give your consent to be recorded during exams, when your audio and video will be turned on.

Aug 24 - Sep 14: Class recordings will not be openly shared with all students in class. Only if you have missed a class for a reason described in the UH Excused Absence Policy, you may send me an email with a request to access the recording. You should treat live meetings as you would in-person classes, and miss them only for a valid reason. It is understandable that you might have internet or technology disruption that are out of your control. If that happens, let me know and I will share the video with you. But if you expect to have frequent disruptions, you should consider enrolling in an asynchronous class, as its material is better suited for off-line study.

Sep 16 - onward: Class recordings will be available for all students in the class right after the class.

Slides will be posted after every lecture to be openly access by all students. The materials provided by the instructor in this course are for the use of the students enrolled in the course only. Copyrighted course materials may not be further disseminated without instructor permission. Students are also prohibited from sharing/posting/sending/... materials derived from the instructor's content (for example, slides, video, problems/solutions/comments in homework, tests and practice problems and tests).

Chat

You are welcome to use chat before and during the class, but you can post only information related to the class, no personal information or communication is allowed in this team. I will review chat before the end of the class, and will answer all relevant questions. I will also review the chat periodically during the lecture, so please be patient if your question is not answered right away.

Please do not post stand alone well intended but meaningless messages such as "Hello", "Bye", and others. I appreciate such communication during in-person meetings, but in online environment it will clog the chat and will make it harder to find relevant information and questions.

When using chat, it is polite to use a proper etiquette. For example, do not use ALL CAPS, it often comes through as shouting and makes you look angry. It's also best to avoid sarcasm, as it can be very difficult to understand in online environment. Check you grammar every time, and do not use any shorthand and slang. While it's tempting to use chat as you would use it with your friends, keep communication professional and respectful for in-class messages.

Keep chat communication to a minimum, and post questions or comments only relevant to the covered material. Any general questions can be emailed me directly, or asked at the end of the class during discussion period.

Attendance/Presence

Presence for the online class meetings is not mandatory, but strongly advised. If you decide to treat a synchronous class as if it were asynchronous in terms of "live" attendance, you might be at a real disadvantage, and it would be advisable to consider taking an asynchronous class instead.

If you miss class, for whatever reason, you are responsible for all material covered, any assignments missed, and any announcements made in class. If you have to miss classes for a prolonged period due to a serious illness or an event, you should contact me as soon as possible.

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Technology requirements

Students should be aware of the minimal technology requirements for this synchronous class, which can be found here. These requirements may change at any point during the semester, and the change will be communicated in class.

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. You must be able to scan and upload your work in under 5 min (certainly no more than 10).

Recording 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 that such that you need to record class-related activities, please contact the Center for Students with DisABILITIES. If you have an accommodation to record class-related activities, those recordings may not be shared with any other student, whether in this course or 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 and notetaking. Instructor's recordings are not authorized to be shared with anyone without prior 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

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 using Teams chat. 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.

I will not respond to Teams chat messages or video calls outside of scheduled class times, and I do not check Blackboard communications.

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.

Questions

You are welcome to write a question related to the course material in the chat during live meetings. Outside the meetings, you may also write me an email with a specific question, and I will reply to it within two business days. If necessary we will set up live meeting. Answers to most questions related to the material can be found in a textbook. Try working it out yourself first, only if unsuccessful for a serious period of time, you may contact me for directions. Most of the time I will point to where the answer can be found, so you can work it out yourself. The only way to learn any new material is to work with it yourself, so I will not deprive you of that opportunity.

We will be using the following book:

• Kenneth Davidson, Allan Donsig, "Real Analysis with Application: Theory in Practice", Springer 2010
  

Homework will not be assigned from this book. Topics we cover each class are indicated in the calendar below. Here are some tips on how to read your textbook efficiently, and some more here.

• MATH 3333 or 3334
• MATH 3325
  

Course Overview    

During the course we aim to cover the following topics:

• The topology of R^n
• Cauchy sequences, limits, compactness
• Continuity, monotonicity, intermediate value theorem
• Differentiation and the Riemann Integral
• Fundamental Theorem of Calculus
• Normed and inner product vector spaces
• Convergence and sequences of functions
• Compactness in function spaces
  

• Homework: 25%
  
• Two Midterms:  40%
• Final: 35%

Nov 6 update: You may choose to keep your Midterm scores or replace one of it with the score you'll get from several in-class quizzes. There will be 9 short in-class quizzes on previous homework, midterm 1, or in-class material. You can make a choice at the end of the class, once you see your quiz score.

Interim Undergraduate Grading Policy for 4331

Due to the unique and unprecedented challenges associated with the COVID-19 pandemic, the University of Houston has implemented an Interim Undergraduate Grade Policy for undergraduate grades which applies to all undergraduate students in courses offered in all sessions during fall 2020. Under this policy, students have the option of converting final assigned letter grades to S (Satisfactory, applicable to any letter grade from A to D-) or NCR (No Credit Reported COVID-19, applicable to grades of F) on their transcripts.Please visit FAQs for additional information.

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. Since every homework will be active for more than a week, no excuses will be granted for a missed deadline because of a failed equipment.

When uploading your paper to Gradescope, make sure your copy is of high quality (contrast, resolution,...). If I can't see your work properly, I won't grade it, and you will receive a zero mark on that test. To avoid it, please scan your work in high quality. Your handwriting must be clear and easy to read. Solution must be written neatly from top to bottom in a logical way. If I can't read your work, I can't grade it.

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: 972NV7. For security reasons, when entering your name and student id, you will enter aliases created using rules I told you during our first class. If you missed the first class, please contact me by email for these rules.

To make sure that there are no problems, you are required to add yourself before the midnight of Friday August 28. Otherwise, I will contact you to set it up directly.

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.

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Two midterms will be held online during regular class time. Each midterm will consists of two parts: problem set and oral. Each portion will take place during one of the class times indicated in the calendar below.

You are not allowed to use any resources during exam (both portions)

Written portion will consists of a few problems, solutions to which you will upload to Gradescope during the last 5 min of exam time. You will login in CASA Monitor first, then you will open Gradescope and download the exam. Once you downloaded it, you will have 60 min to solve and upload your solutions.

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 rubrics will be ignored.

During a group oral exam in Microsoft Teams during a regular class time, I will ask each student in turn a quick question related to the covered material. Questions for the exam will be given before each exam. For each student a question and answer will take 3 min in total.

If you miss exam for a reason described in the UH Excused Absence Policy, and you are able to provide satisfactory documentations in a timely manner, an arrangement will be made on a case by case basis. The makeup exam might be different and have a larger oral portion.

You are required to adhere to the UH Academic Honesty policy.

CASA Monitor

During problem set portions of both midterms and the final you will use CASA Monitor to proctor your exam. Here are the steps you need to take to set it up.

1) You need to reserve a time slot for the proctored exam on CASA CourseWare website as soon as it is available (I will let you know by email) and at least a few days before your exam.

1. Log in to CASA, choose this course: MATH 4331: 15571 or MATH 6312: 15672 - make sure the section number is correct!
   
2. go to the tab on the top titled "Schedule exams",
   
3. read all information on this page,
   
4. scroll down, click the red button,
5. on the next page choose "Make Schedule",
   
6. choose a time during which you would like to start your exam at. Make reservation ASAP, as the number of seats at each time slot is limited and the seating is on the first come first serve basis.
   

2) Read the instructions on how to set up CASA Monitor and what you need for it.

3) Do a practice run at least a few days before the exam, the link to the practice website is located in the instructions.

4) Read a list of rules you need to adhere to while taking the exam. If you violate these rules, the exam might be invalidated and you will receive a zero grade. If something unexpected happens beyond your control, write me an email after the test.

On the day of the exam, at the time that you have chosen, you need to:

1) make sure your testing environment is in line with the rules listed in the instructions;

2) set up CASA Monitor just as you previously practiced; if you will be using black scratch paper, show those pages to the camera;

3) open and log in to Gradescope website and download your exam;

4) work on your midterm and NEATLY write down your solutions;

5) scan your work and upload it to Gradescope; you have 60 min to work on your test and upload your solutions once you have downloaded the exam;

5) go back to CASA Monitor website and click "I finished the test" to stop the proctoring services.

I will be available on Microsoft Teams during the exam time period, so please use chat to communicate with me if you have any problems during the exam.

Final will consists of a written portion only. You will use CASA Monitor during the final. You are not allowed to use any resources during exam.

Written portion will consists of a few problems, solutions to which you will upload to Gradescope. You have until the end of December 18th 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 rubrics will be ignored.

Final will be held on December 14th, 11:00am-2:00pm.

Webcams

Access to a webcam is required for all students. Webcams must be turned on during exams to ensure the academic integrity of exam administration.

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 24 Technology check; Introduction;  Proofs	August 26 Proofs (cont.)	August 28 Topology of R^n 4.1 Gradescope enrollment deadline
August 31 Topology of R^n: convergence and completeness 4.2	September 2 Topology of R^n: open and closed sets 4.3	September 4 Topology of R^n: open and closed sets 4.3 Homework 1 Due
September 7 Labor Day	September 9 Topology of R^n: compact sets 4.4	September 11 Topology of R^n: compact sets 4.4 Homework 2 Due
September 14 Functions: limits and continuity 5.1	September 16 Functions: continuity and discontinuity 5.1-5.2	September18 Functions: discontinuity 5.2 Homework 3 Due
September 21 Homework 1 review	September 23 Homework 2 review	September 25 Homework 3 review
September 28 Review	September 30 Midterm 1 problem set	October 2 Midterm 1 oral
October 5 Functions: properties of continuous functions compactness 5.3-5.4	October 7 Functions: uniform continuity 5.5 asynchronous	October 9 Midterm 1 review - asynchronous
October 12 Functions: Intermediate Value Theorem in R 5.6	October 14 Functions: Intermediate Value Theorem in R^n 5.6	October 16 Connected vs path-connected sets RAA supp file (in Teams) Functions: monotone functions 5.7 Homework 4 Due
October 19 Functions: monotone functions 5.7    Homework 4 review	October 21 Differentiable functions 6.1	October 23 Mean Value Theorem 6.2 Homework 5 Due
October 26 Homework 5 review Mean Value Theorem in higher dimensions	October 28      asynchronous learning	October 30 asynchronous learning Homework 6 Due
November 2 Review	November 4 Midterm 2 problem set	November 6 Midterm 2 oral
November 9 Midterm review Homework 7 Due	November 11 In class quiz: midterm Review: sets, topology of R^n, HW 1	November 13 In class quiz: HW 1+sets/R^n Review: convergence, completeness, open and closed sets, HW 2 Homework 8 Due
November 16 In class quiz: HW 2+ convergence, completeness, open/closed sets Review: compact sets, HW 3	November 18 In class quiz: HW3+compact sets Review: functions: limits and (dis)continuity	November 20 In class quiz: limits and (dis)continuity Review: Midterm 1 Homework 9 Due
November 23 In class quiz: Midterm 1 Review: continuity	November 25	November 27 Thanksgiving
November 30 In class quiz: HW4+EVT Review: uniform cont., connected, path-connected sets	December 2 In class quiz: uniform cont, connected, path-connected sets Review: IVT, HW 5	December 4 In class quiz: HW 5+IVT Review: differentiable f., MVT   Homework 10 Due
	December 14 Final 11:00am-2:00pm

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. 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

Resources for Online Learning

The University of Houston is committed to student success, and provides information to optimize the online learning experience through our Power-On website. Please visit this website for a comprehensive set of resources,tools, and tips including: obtaining access to the internet, Access UH, and Blackboard; requesting a laptop through the Laptop Loaner Program; using your smartphone as a webcam; and downloading Microsoft Office 365 at no cost. For questions or assistance contactUHOnline@uh.edu.

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