Math 4513 and 5213, Fall 2020

Professor Cashen will substitute for the first half of the semester; please see his web page during this period.

Important dates

Monday, Aug. 24First day of class
Friday, Aug. 28Last day to add a course
Monday, Sep. 4Last day to drop a course
Monday, Sep. 7Labor Day holiday (all classes canceled)
Friday, Sep. 18First midterm exam (take-home; no class meeting)
Friday, Oct. 16Second midterm exam (take-home; no class meeting)
Wednesday, Oct. 14Last class taught by Professor Cashen
Monday, Oct. 19First class taught by Professor Barton
Friday, Nov. 13Third midterm exam (take-home; no class meeting)
Nov. 25–27Thanksgiving holiday
Friday, Dec. 11 Complete the online course evaluation on or before this date.
Monday, Dec. 14, 3:00–5:00 p.m. Final exam. Good luck!

Course Information

Scheduled meeting times: Monday, Wednesday, and Friday, 2:00–2:50 p.m., August 24–December 9, SCEN 407.

Course Description: The real and complex number systems, basic set theory and topology, sequences and series, continuity, differentiation, and Taylor's theorem. Emphasis is placed on careful mathematical reasoning.

Prerequisites: MATH 2574 (Calculus III), MATH 2803 (Transitions to Advanced Mathematics), and MATH 3083/3093 (Linear Algebra). Transitions to Advanced Mathematics or other experience with proof is probably the most important of the prerequisites.

Text: A First Course in Analysis, John B. Conway, ISBN 978-1107173149. A paper copy may be bought from the bookstore; electronic copies may be purchased from several online retailers, including and Barnes and Noble.

Grades: Here is how I plan to weigh your grades:

Homework 50%
Attendance 2%
Each of 3 midterm exams 9.6%
Final exam 19.2%

Homework and exam scores will be posted to Blackboard. All scores posted on or before Dead Day will be deemed accurate unless a possible error is brought to the attention of the instructor before the scheduled final exam.

Class format: Students may attend class remotely at their discretion. If the University is open, the instructor will make every effort to hold class and students may attend in person if they choose. The chancellor may decide to close the university due to COVID-19, in which case remote participation will be mandatory. Online instruction may begin at any time with minimal notice. We apologize for the inconvenience.

Remote participation: For students needing to participate remotely, (and for all students if the university again closes), this course will use Zoom for synchronous (“real time”) class meetings during our regularly scheduled class days/times. Please take the time to familiarize yourself with Zoom. You may choose to use Zoom on your mobile device (phone or tablet).

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.

Face coverings: Face coverings are required inside campus buildings. Wear a mask or face covering while you are in this building and in our classroom. If you require accommodations due to physical of other restrictive conditions, please contact the Center for Educational Access.

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 the referenced website 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 here. There are harsh penalties for violations as prescribed by the Sanction Rubric. Students with questions about how these policies apply to a particular course or assignment should immediately contact their instructor.

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 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.


Professor Barton will be on maternity leave for the first half of the semester. During this time the course will be taught by Professor Cashen, who may use a different course format from Professor Barton. Please consult with Professor Cashen for all questions related to the course August 24–October 16.

August 24–October 16October 19–December 14
Instructor Chris Cashen Ariel Barton
Office TBA SCEN 222

Course format, October 19–December 9

Homework: Assigned homework problems and their due dates will be listed above. You may ask anyone for help on your homework, but you must write up solutions on your own in your own words. All homework problems are to be uploaded to Blackboard. Each homework problem will be graded on a 12-point scale. Any student who types their homework will receive a 1-point bonus. A quick guide to typing your homework may be found here. Acceptance of late homework is at the instructor's discretion.

Each homework problem may be rewritten and resubmitted (once) for correction. The regrade due dates are indicated above.

Video lectures: Whether we have online, in-person, or hybrid courses, video lectures will be posted to Blackboard and YouTube. Students are to watch these video lectures by 2:00 p.m. on the indicated dates.

Scheduled class time: During scheduled class time (MWF 2:00–2:50 p.m.), students are to work on homework problems. Professor Barton will answer student questions. The format is roughly that of traditional office hours. Students will be expected to participate actively, for example by writing on the whiteboard and speaking to their classmates.

Office hours: The in-class discussions replace regularly scheduled office hours, as I do not think we can social distance adequately in my office. One-on-one office hours are available by appointment.


Tests: There will be one midterm examination in November, and one final exam in December at the time indicated on the registrar's web page (currently Monday, December 14, 3:00–5:00 p.m.) Please consult with Professor Cashen for exam scheduling August 24–October 16.

If you require accommodations on an exam, notify your instructor as soon as possible, but in all cases at least one week before the exam is to be held. Documentation from the CEA may be required, depending on the nature of the accommodation.

The third midterm exam will follow the same format as the first two exams, that is, will be a take-home exam available for two days administered through Blackboard. A PDF containing the exam questions will appear on Blackboard at 3:00 p.m. on the Wednesday before the scheduled date (the midterm) or 3:00 p.m. on Friday, December 11 (the final). Students are to write their answers to the exam by hand, either on paper, on a tablet, or on a whiteboard. Students are to scan, export, or photograph their answers and upload them to Blackboard. Exams are to be uploaded by 11:59 p.m. on the scheduled dates.

Online exams are open book, open note, open recorded lecture, and open calculator. However, you may not discuss the exam in any way, either in person or through electronic means, with any person other than Professor Barton while taking it.

Make-up exams: Make-up exam requests 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. 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 date, 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 as soon as possible, and I will arrange for you to take a make-up final later in the week.