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.
Course Description: Real number system, Lebesgue measure, Lebesgue integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus, Lp spaces, Holder and Minkowski inequalities, and bounded linear functionals on the Lp spaces.
Prerequisites: MATH 4523/5223, and graduate standing in mathematics or statistics, or departmental consent.
Text: Measure, Integration & Real Analysis, by Sheldon Axler. An open access electronic copy of the book may be found on the author's website. We will begin the semester with the Supplement for Measure, Integration & Real Analysis from the same website. Other resources include the (out of print) textbook Real Analysis, 4th edition, by H.L. Royden and P.M. Fitzpatrick.
Scheduled meeting times: Monday, Wednesday, and Friday, 9:40–10:30 a.m., August 23–December 8, 2021, SCEN 322.
COVID-19 policies and precautions: If classroom size and enrollment total allows, please practice social distancing in class. Per university policy, face coverings are required. Please remember that some of your classmates may have health conditions or unvaccinated family members, and behave accordingly.
Remote/hybrid delivery: All students are expected to turn in homework electronically via Blackboard. Exams will be take-home exams and may be turned in the same way as the homework.
As the COVID-19 delta variant is increasing in our area, my class attendance policy will allow you to attend class via a Zoom meeting (in real time) instead of attending face-to-face. A link to my Zoom meeting is available in Blackboard. I will under normal conditions be lecturing face-to-face in the classroom if you want to attend the face-to-face class session. If you would like to attend Zoom meetings instead of attending the face-to-face class session, please send an email directly to me at aeb019@uark.edu making this request. Please remember that I reserve the right to stop remote participation and require face-to-face attendance at any time.
Remote participation will be most effective if you can communicate effectively. In particular, you should set up a way to share your writing.
A minimal solution is to share your screen to Zoom and display typed work. You are also strongly encouraged to set up a way to share your handwriting, preferably in real time as you write it. This can be either on a carefully illuminated whiteboard attached to the wall, on an iPad or other tablet whose screen you can share to Zoom, or via Microsoft Whiteboard or other collaborative editing application. Do not try writing on paper with a pencil and holding it up to a laptop camera. Nobody will be able to see it.
Recording of Class Lectures: Students are allowed to record class and office hours. By attending this class, the student understands the course is being recorded and consents to being recorded for official university educational purposes. Be aware that incidental recording may also occur before and after official class times. Recordings may include personally-identifiable comments submitted to the chat stream during class.
Office hours: Office hours will be held over Zoom at the following times:
If the selected times do not work for you, if you want face-to-face office hours, or if you wish to speak to me privately, please email me and we will schedule an appointment at another time.
Inquiry-based learning: Students will be supplied with a list of lecture problems (PDF or HTML). This list of problems constitutes the notes for this course. Written homework assignments will be posted to Blackboard.
Students may choose to either present solutions to lecture problems during class, or to turn in written homework assignments.
Specifically, a student who presents a complete solution at the board during class will be granted 2–24 presentation points (depending on the problem and on originality of their solution). Students may view their remaining presentation points on Blackboard.
If a student does not turn in a written assignment or turns in an assignment with fewer than 3 problems worked, and has remaining presentation points to spend, then 12 presentation points will be deducted per unworked problem and the assignment score will be recorded as though the student had received full credit on the missing problem or problems.
If at least 80% of the students in this class complete the online course evaluations, then a student with an outstanding balance of 36n presentation points at the end of the semester will have their lowest n homework scores raised to full credit. (A student with a balance that is not a multiple of 36 will have their lowest homework score increased, but not to full credit.)
Homework: Homework assignments will be posted to Blackboard. You may work together on the homework assignments, but each student must write up their work in their own words and submit their own work for grading. Graded homework will be returned via email.
Homework formatting: Homework submission is generally required to follow the following rules. If you feel that they place an undue burden on you (for example, if you do not own a computer), talk to me and we will arrange an exception or accommodation.
It should be in PDF format (a compiled PDF, not TeX source code).
My annotation software (the software I use for grading) can deal with PDF files better than almost any other format. Also, it is generally straightforward to convert other formats to PDF and my grading is much smoother if all homework files are in the same format.
It should uploaded to the correct location in Blackboard.
This collects all students' homework in a standardized location (meaning I am less likely to lose your homework) and also gives your homework standardized file names (which makes it much easier to return). If you are unable to upload your homework to Blackboard, instead email it to me. The file name must be HW-N-username.pdf, where N is the homework number and username is your UA username (that is, your university email address without the @uark.edu).
It must be easy to read, and the file size must not be too big. This generally means that you must type your homework using LaTeX.
Do not type your homework using Microsoft Word. Here is a guide to typing your math homework using LaTeX and Overleaf: How to type your homework. LaTeX templates for each assignment will be posted to Overleaf. Learning to type math with LaTeX is a useful skill beyond this course.
Exams: There will be one midterm test and a (comprehensive) final exam. The exams will be open book, open note, take home exams. However, you may not discuss the exams in any way with any person other than Professor Barton between the time when you receive the exam and its due date. I will not give hints, suggestions, or guidance on the exams once you have received the exam questions, except in the event of a mistake made in writing the exam.
We will cancel one class to allow you time to take the midterm exam. The exam will be posted to Blackboard by 5:00 p.m. on the day of the previous class. The final exam will be due at 11:59 p.m. Wednesday of finals week.
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.
Certain accommodations will be granted only at the CEA’s request. Some accommodations must be fulfilled using the CEA's resources. Other accommodations 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).
Course grade: Here is how I plan to weigh your grades:
| Homework | 50% |
| Midterm Exam | 20% |
| Final | 30% |
| Date | Event |
| Monday, Aug. 23 | First day of class |
| Friday, Aug. 27 | Last day to add a course |
| Friday, Sep. 3 | Last day to drop a course |
| Monday, Sep. 6 | Labor Day holiday (all classes canceled) |
| Friday, Oct. 22 | Midterm exam due at the end of the day. Good luck! |
| Monday, Oct. 25–Tuesday, Oct. 26 | Fall break |
| Friday, Nov. 19 | Last day to withdraw from a course |
| Wednesday, Nov. 24–Friday, Nov. 26 | Thanksgiving break |
| Wednesday, Dec. 8 | Last day of class |
| Dec. 10–20 (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, we will allow leftover presentation points at the end of the semester to boost your grade as described above. |
| Wednesday, Dec. 15 | Final exam due at the end of the day. Good luck! |
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. 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 honesty.uark.edu 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 http://provost.uark.edu/. 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.
