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: Rigorous construction of the real numbers, basic set theory and topology, sequences and series, continuity, differentiation, Taylor’s theorem, and the Riemann integral. Emphasis is placed on careful mathematical reasoning.
Prerequisites: MATH 2574, MATH 2803, and either MATH 3083 or MATH 3093. When substituting courses from other institutions, some familiarity with proof-based mathematics is the most crucial requirement.
Text: A First Course in Analysis, John B. Conway, ISBN 978-1107173149. You may use either a paper copy or an electronic copy.
Scheduled meeting times: Monday, Wednesday, and Friday, 2:00–2:50 p.m., August 23–December 8, 2021, Gearhart Hall Classroom 108.
COVID-19 policies and precautions: Our classroom (GEAR 108) has a COVID capacity of 15 students and 21 students are enrolled; please practice social distancing in class if possible. Per university policy, face coverings are required for in person attendance. Please remember that some of your classmates may have health conditions or unvaccinated family members, and behave accordingly.
Remote/hybrid delivery: All students are encouraged 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.
Recording of Class Lectures: Students are allowed to record lectures 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.
Remote office hours will work more smoothly if we can communicate effectively. In particular, I would like to be able to see what you write.
At a minimum, if you type your homework, you can share your screen so that I can see what you typed. You are also strongly encouraged to set up a way to write by hand and to allow me to see your writing, 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. I will not be able to see it.
Flipped classroom: This is a hard course, and most students will need extra guidance beyond lectures in order to succeed. Thus, we will use a flipped classroom setup.
The first lecture for the course will be delivered during the first class, that is, 2:00–2:50 p.m. on Monday, August 23. On subsequent days, we will begin with a discussion session. Discussion sessions will be formatted like traditional office hours; that is, it is the students' responsibility to come in with questions and some idea as to what they would like to discuss. Students may ask about upcoming or past homework assignments, points of clarification on the lectures, or other topics. I anticipate that discussion sessions will be longer later in the semester as the material grows more complicated.
Once all student questions are addressed, if time remains in our scheduled class sessions, the instructor will deliver a full or partial lecture. However, if the students have any significant number of questions, the instructor will not have time to deliver a complete lecture. Thus, in this case, students will need to watch all or part of a video containing the displaced lecture. These videos may be found on the course Blackboard site and YouTube. Students must view each lecture (in one format or another) by the listed due date.
You can find the files I use to make these videos at Box. There you will find .zip files (containing PDFs of my writing and audio recordings) and .note files (the original source; they can be viewed if you have the iPad or Mac app Notability).
Homework: Homework assignments will be posted to Blackboard. Students are strongly encouraged to upload their answers to Blackboard. Homework submitted electronically will be returned via email.
One class meeting (one question-and-answer session) per exam will be reserved for exam review questions. All remaining question-and-answer sessions will have an associated homework assignment of one or two questions. These homework assignments are subject to revision until 5:00 p.m. the day of the previous class, and are due at midnight the day before the next class. I expect to have a total of 35 homework assignments over the course of the semester. If at least 80% of the enrolled students complete the course evaluations, I will drop your 4 lowest homework assignments; otherwise, I will drop your 2 lowest homework assignments.
Rewrites: I will grade each homework assignment twice. The first time will be within a day or two of the due date mentioned above. The second will be one week later. You may turn in your homework at either due date. If you submit your homework electronically (see below), you are allowed to turn in your homework for both due dates. In this case you are expected to correct your homework based on the comments I write on the first version and only the second grade will be used in calculating your course grade. In my experience, student homework scores are often significantly higher on the second try and I encourage all of you to turn in your homework twice.
Homework formatting: Homework must always be neat and easy to read. Electronic submission of homework is strongly encouraged for all students and usually required of all students who want the opportunity to rewrite their homework. (Hint: You want the opportunity to rewrite your homework.) If you feel that this places 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.
Homework that is turned in electronically must follow the following conditions:
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 or Rewrite-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). (An assignment turned it on the second due date should be named Rewrite-N-username.pdf even if you did not turn in that homework on the first due date.)
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 may be found at Overleaf. Learning to type math with LaTeX is a useful skill beyond this course. Furthermore, typed homework is easier to rewrite, as you can easily copy and paste any sections that do not need rewriting.
Exams: There will be three midterms tests (covering material learned since the previous midterm) 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.
For each midterm exam, we will spend one day reviewing in class, and will cancel one class to allow you time to take the exam. The exam will be posted to Blackboard by 5:00 p.m. on the day of exam review and will be due at 11:59 p.m. the day of the cancelled class. We will spend Wednesday, December 8 reviewing for the final exam and 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 (two weeks before the final).
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 1 | 10% |
| Midterm Exam 2 | 10% |
| Midterm Exam 3 | 10% |
| Final | 20% |
| 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) |
| Wednesday, Sep. 22 | Review for the first midterm exam. |
| Friday, Sep. 24 | No course meeting or office hours; students are taking the first midterm exam. Good luck! |
| Wednesday, Oct. 20 | Review for the second midterm exam. |
| Friday, Oct. 22 | No course meeting or office hours; students are taking the second midterm exam. Good luck! |
| Monday, Oct. 25–Tuesday, Oct. 26 | Fall break |
| Friday, Nov. 19 | Last day to withdraw from a course. If you would like to estimate your likely course grade, here is a grade estimation worksheet. |
| Friday, Nov. 19 | Review for the third midterm exam. |
| Monday, Nov. 22 | No course meeting or office hours; students are taking the third midterm exam. Good luck! |
| 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, I will drop your 4 lowest homework scores; otherwise, I will drop your 2 lowest homework scores. |
| Wednesday, Dec. 15 | Final exam due. 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.
