Math 4523 and 5223, Spring 2021

Information on this syllabus is subject to change. Any updates will be posted to this site. In particular, any required changes in course delivery, such as transition to remote delivery only, may necessitate significant modifications to this syllabus.

Office hours

I will hold virtual office hours Tuesdays starting at 12:30, and on Thursdays starting at 2:00. If you want to attend office hours but expect to be late, please let me know; otherwise, if no one attends in the first 15 minutes I will assume that no one intends to attend that day. These office hours are on a drop in basis; you do not need an appointment to attend these office hours. Zoom links will be made available via Blackboard.

If the above times do not work for you or if you wish to speak to me privately, please email me and we will schedule a private one-on-one Zoom meeting just for you.

Exams and accommodations

There will be three midterms tests (covering material learned since the previous midterm) and a (comprehensive) final exam. I plan to hold midterm exams during class time on the dates indicated in the calendar below. The final exam will occur at the time indicated on the registrar's website.

Accommodations: All accommodations requested by the Center for Educational Access will be fulfilled to the best of the instructor's ability. It is the student's responsibility to discuss the implementation of the accommodations with the instructor, either in person or via email. In particular, accommodations to testing must be discussed at least one week before the date of the exam (two weeks before the final).

Certain accommodations (such as extra time on exams) will be granted only at the CEA's request. Other accommodations (such as large print exams or permission to write answers on lined paper) are available to any student who makes the request in a timely fashion. Please consult with your instructor in all such cases.

Make-up exams: Make-up exam requests also require written documentation as to your conflict. Except in the case of medical or other unforeseen emergencies, make-up exam requests must be made at least one week before the exam is to be held (two weeks before the final). Make-up exams are at the instructor's discretion; if you do not provide a documented reason why you cannot take the exam at the usual time, if your reason is considered inadequate, or if your request for a make-up exam is not made in a timely fashion, I reserve the right to refuse a make-up exam or to assess a late penalty (deduction from your score).

If you have three or more final exams scheduled for the same day, then under University policy you are entitled to reschedule one of your finals. If you wish to reschedule the final for our class, please notify me by email at least two weeks before the final, and I will arrange for you to take a make-up final on another day.

Illness during in person exams: If you experience potential COVID symptoms the day of an in-person exam and feel the need to self-isolate, please let me know by email as soon as possible. If you are self-isolating but still well enough to take an exam on the scheduled day, you will be expected to take the exam remotely on the same date. As noted above, if you need to schedule a make-up exam for a later date, you will need written documentation (that is, a doctor's note).

In the event that some students take exams in person and some students take exams remotely (because of illness or other factors), I reserve the right to put different questions on the two forms of the exams.

Video lectures, text, homework

Text: A First Course in Analysis, John B. Conway, ISBN 978-1107173149. This was the text used in MATH 4513 during both semesters of 2020, and so all students should already have copies.

Homework assignments will be posted to Blackboard. Assignments have the following components:

Students are to do the following: Students are strongly encouraged to ask as many questions as possible during the class time regularly scheduled sessions; however, students are also allowed to ask questions during office hours.

Course meetings

We will hold a course meeting for discussion of video lectures and homework problems 11:50–12:40 MWF. This is the time assigned by UAConnect.

Course meetings will be either in person or remote. In person meetings will be in BELL 2286 or the classroom indicated on UAConnect. Remote meetings will be via Zoom. The first day of class will be in person; on that day we will discuss whether students prefer in person or remote instruction going forward.

COVID-19 policies and precautions: University policy requires the wearing of face coverings in all campus buildings unless you have a health exemption. Please do not come to class without a face covering. This also means you cannot consume food and drink in the classroom. Do not congregate outside the door before class. Do not share pencils, paper, or other items. Attend virtually if you have any COVID symptoms or have been exposed.

If at any time you feel you need to self-isolate, please inform me by email and I will try to arrange for you to participate remotely. If you are diagnosed with COVID-19, please inform the instructor, as in this event the course will switch to remote delivery for two weeks.

Conditions for remote instruction: I currently plan to switch to remote instruction on a temporary basis if any of the following things happen:

I plan to switch to permanent remote instruction if any of the following things happen:

Attendance: Attendance will be taken in person only for contact tracing purposes only. Attendance will not affect your grade directly. (You will do better on the exams and homework if you attend regularly, and that will certainly affect your grade!)

Further remarks

Monday, Jan. 11First day of class
Friday, Jan. 15Last day to add a course
Monday, Jan. 18Martin Luther King holiday (all classes canceled)
Monday, Jan. 25Last day to drop a course
Friday, Feb. 12 First midterm exam--good luck!
Monday, Feb. 22Spring break
Friday, Mar. 12 Second midterm exam—good luck!
Friday, Mar. 26Spring break
Friday, Apr. 2Spring break
Friday, Apr. 9 Third midterm exam—good luck!
Friday, Apr. 16 Last day to withdraw from a course. If you would like to estimate your likely course grade, here is a grade estimation worksheet.

If you have three final exams scheduled on the same day, then under university policy you are entitled to an alternative exam date; please inform me by email ( that you need a make-up exam on or before April 16.
Wednesday, Apr. 28Last day of class
Apr. 20–30 (or dates set by university policy) Complete the online course evaluation. If at least 80% of the class completes the course evaluation before the deadline, I will drop your 4 lowest homework scores; otherwise, I will drop your 2 lowest homework scores.
Wednesday, May 5 Final exam, 12:45–2:45 p.m. or time indicated on the registrar's website.

Good luck!

Course Description: The Riemann-Stieltjes integral, uniform convergence of functions, Fourier series, implicit function theorem, Jacobians, and derivatives of higher order.

Prerequisites: MATH 4513, familiarity with proofs, and the rigorous construction of the derivative.

Course grade: Here is how I plan to weigh your grades:

Homework 50%
Midterm Exam 1 10%
Midterm Exam 2 10%
Midterm Exam 3 10%
Final 20%

Grade Disputes: All grade disputes must be brought to the attention of the instructor and resolved within one week of the day that the graded test paper is returned. The instructor is committed to keeping students informed of their standing in the class. Scores on all graded items will be posted in a timely manner. Students are expected to bring any possible errors to the attention of the instructor within one week of posting. This maintains an accurate grade record throughout the semester. All scores posted before Dead Day will be deemed accurate unless a possible error is brought to the attention of the instructor before Wednesday of finals week.

Cell phones: Cell phones, tablets, laptops, and other electronic devices may be used in class even when attending in person. The expectation is that these devices will be used for taking notes, routine calculations (i.e., calculator apps), accessing course materials, and other course-related uses only. Please do not text or play games in class!

Incompletes: Only given in extreme circumstances, and only when the student has satisfactorily completed all but a small portion of the work in the course. Students must make prior arrangements with the professor well before the end of the semester.

Academic Integrity: Academic dishonesty on any exam, quiz, or other graded item will result in a score of zero that cannot be dropped or replaced. Suspected cases of academic dishonesty are referred to the All-University Academic Integrity Board. The following passage is quoted from and is the policy in this course:

As a core part of its mission, the University of Arkansas provides students with the opportunity to further their educational goals through programs of study and research in an environment that promotes freedom of inquiry and academic responsibility. Accomplishing this mission is only possible when intellectual honesty and individual integrity prevail.

Each University of Arkansas student is required to be familiar with and abide by the University’s ‘Academic Integrity Policy’ which may be found at Students with questions about how these policies apply to a particular course or assignment should immediately contact their instructor.

Unauthorized Websites or Internet Resources: There are many websites claiming to offer study aids to students, but in using such websites, students could find themselves in violation of our University’s Academic Integrity and Code of Student Life policies. The U of A does not endorse the use of these products in an unethical manner. These websites may encourage students to upload course materials, such as test questions, individual assignments, and examples of graded material. Such materials are the intellectual property of instructors, the university, or publishers and may not be distributed without prior authorization. Furthermore, paying for academic work to be completed on your behalf and submitting it for academic credit is considered ‘contract cheating’ per the Academic Integrity Policy. Students found responsible for this type of violation face a grading penalty of ‘XF’ and a minimum one-semester academic suspension per the University of Arkansas Sanction Rubric. Please let us know if you are uncertain about the use of a website.

Classroom Etiquette: Students and instructors each have an important role in maintaining a classroom environment optimal for learning, and are expected to treat each other with respect during class, using thoughtful dialogue, and keeping disruptive behaviors to a minimum. Both students and faculty perceive abusive language directed towards others as the most disruptive behavior. Other behaviors that can be disruptive of in person classes are chatting and whispering during class, the use of smartphones or laptops for texting or in other ways unrelated to the course, preparing to leave before class is over, and consistently arriving late to class. Inappropriate behavior in the classroom may result in a request to leave the class and/or a referral to the Office of Academic Integrity and Student Conduct.

Commercial Note Vendors: Some commercial vendors may reach out to you to sell the notes you take in this class. Notes derived from class lectures are the intellectual property of the instructor. Selling or otherwise sharing these notes outside the class is a violation of the instructor's intellectual property rights and constitute a violation of the University's academic integrity policies. Your continued enrollment in this class signifies your understanding of and your intent to abide by this policy.