Math 440H Fall 2020

Announcements


General Course Info

Overview. This is an advanced undergraduate course in proof based mathematics. The course will be divided into 3 roughly equal parts: (I) the real numbers, basic point-set topology of metric spaces, continuity; (II) integration and differentiation; (III) spaces of functions.

Meeting Time and Location. MWF, 3:30-4:30 pm in UNIV 101.

Textbook. The required textbook for this class is "Real Mathematical Analysis," Second Edition, by Charles Chapman Pugh. See the course Brightspace page under "Content/Textbook Information" for options on accessing the textbook.
Though not required, I highly recommend Richard Hammack's "Book of Proof" as a supplementary guide to the basics of mathematical proof. The author has made the book free to download as a pdf file.

Contact. The best way to contact me is by email. My email address is tsincla(at)purdue.edu. I will usually respond to emails fairly promptly during normal business hours. If you have not received a reply within 48 hours, feel free to follow up.

Office. My office is 744 in the Mathematical Sciences building.

Office Hours. Office hours will be online only via WebEx. See the course Brightspace page for details. Outside of regular office hours, I am also happy to meet by appointment. Please email me to schedule.

Brightspace. The course page on Brightspace will serve as the main point of contact for announcements, assignments, course policy, and virtual content. Students will be expected to check the course page regularly, at least before every class meeting.

Piazza. The course will have a Piazza forum accessible through the course page in Brightspace. Students are expected to enroll in the course forum. I will moderate and reply to discussions daily on weekdays, likely in the evening. Questions of a mathematical nature, and requiring a detailed response, are best posted in Piazza rather than emailed to me.

Gradescope. Assignments must be uploaded to Gradescope via the course page in Brightspace. No hard copies of assignments will be accepted.

Kaltura. Audio and screen captures of each lecture will be available via Kaltura on the course Brightspace page. Please allow up to 24 hours for processing.

Academic Calendar For ease of reference, here is a link to the academic calendar detailing all breaks, add/drop deadlines, etc.


Course Policies and Procedures

Lecture. Lectures are held in-person, but will be recorded and posted to Brightspace. Every precaution to maintain a safe classroom environment will be taken, but please do not come to lecture if you are feeling unwell or are otherwise uncomfortable with attending in person. In case that I am unwell or need to quarantine/isolate, every effort will be given to maintaining the regular lecture schedule via recorded lectures posted to Brightspace. Class cancellations and other changes due to a health-related absence on my part will be communicated via the course page in Brightspace.

Accommodations. In this mathematics course accommodations are managed between the instructor, student, and the DRC Testing Center. You should make a brief appointment with me to discuss your accommodations as soon as possible. Purdue University strives to make learning experiences as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, you are welcome to let me know so that we can discuss options. You are also encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247.

Exams .There will two take-home exams during the semester. These will be open book, open note, with a one-week completion window. (See below for schedule and further details.)

Homework. There will be 8 homework sets. (See below for details and due dates.) Students are encouraged to collaborate on homeworks as long as: 1) all collaborators are listed on the cover sheet of each student's assignment; 2) each student turns in their own, individual work. Rote copying of solutions from peers, internet forums, or plagiarism of any kind will not be tolerated.

Homework Formatting. Homeworks must be typed or neatly written and scanned. There is a strong preference for assignments to be prepared using LaTeX. (See the section on LaTeX below.) There should be no significant cross-outs, rewrites, scratchwork, scribbling, etc. Problems should be clearly indicated and be placed in the correct sequence. Homework should have a cover sheet with your name, the homework set number, and the names of your collaborators, in that order. Homework should be uploaded to Gradescope by 11:59 pm on the due date.

Late Homework. No penalty will be assessed for assignments which are not excessively late (less than one week past due).

Semester Project. Students will be expected to complete a semester project. This may be either an individual or team project. The project must be related to, and make use of, mathematical concepts discussed in class and reflect roughly 15 hours of effort per individual. There are many possible ideas for projects including: researching and writing a short biography of a famous mathematician describing some of their major mathematical contributions; writing an expository paper; developing code; creating an educational youtube video or tutorial; creating an animation/visualization of a proof or concept; etc. I will work with each team or individual to develop a suitable topic. Each person or team must craft a 1 page proposal briefly describing the project along with a concrete plan for meeting the objectives which must meet my approval. The initial draft of the proposal is due by the end of eighth week, 5 pm on Friday, October 16. More details will be made available in the "Semester Project" section in the Brightspace course page.

Grades. There will be 100 total points. Homework will be worth 5 points per assignment (40 points total). Exams will be worth 15 points each (30 points total) and the semester project will be worth 30 points. For marginal cases, there will be some discretionary leeway in final grade assignment to account for course participation/engagement or extraordinary effort. The following is a sample cutoff distribution which is fairly typical for courses I have previously taught. The final grade cut-offs may differ slightly. A >92, A- >88, B+ >84, B >77, B- >73, C+>69, C> 64, C- >60.

LaTeX is the language for mathematical typesetting. If you are a CS, Math, or Stats major, I would strongly recommend becoming proficient in LaTeX. Here is the link to A.J. Hildebrand's excellent collection of beginner LaTeX resources. Another great place to start is Jon Peterson's advice and resources for new researchers. You will probably also frequently need to consult the LaTeX Wiki.

Academic Integrity. See the Academic Integrity webpage from the Office of the Dean of Students. Penalties for academic dishonesty will be, at minimum, a score of zero on the exam or assignment. Egregious cases will be referred to the Dean of Students and may result in failure of the course or expulsion.


General Policies

Attendance. Students should stay home and contact the Protect Purdue Health Center (496-INFO) if they feel ill, have any symptoms associated with COVID-19, or suspect they have been exposed to the virus. In the current context of COVID-19, in-person attendance will not be a factor in the final grades, but the student still needs to inform the instructor of any conflict that can be anticipated and will affect the submission of an assignment or the ability to take an exam. Only the instructor can excuse a student from a course requirement or responsibility. When conflicts can be anticipated, such as for many University-sponsored activities and religious observations, the student should inform the instructor of the situation as far in advance as possible. For unanticipated or emergency conflict, when advance notification to an instructor is not possible, the student should contact the instructor as soon as possible by email. When the student is unable to make direct contact with the instructor and is unable to leave word with the instructor’s department because of circumstances beyond the student’s control, and in cases of bereavement, quarantine, or isolation, the student or the student’s representative should contact the Office of the Dean of Students via email or phone at 765-494-1747. Our course Brightspace includes a link on Attendance and Grief Absence policies under the University Policies menu.

Guidance for Quarantine. If you become quarantined or isolated at any point in time during the semester, in addition to support from the Protect Purdue Health Center, you will also have access to an Academic Case Manager who can provide you academic support during this time. Your Academic Case Manager can be reached at acmq@purdue.edu and will provide you with general guidelines/resources around communicating with your instructors, be available for academic support, and offer suggestions for how to be successful when learning remotely. Importantly, if you find yourself too sick to progress in the course, notify your academic case manager and notify me via email or Brightspace. We will make arrangements based on your particular situation. The Office of the Dean of Students (odos@purdue.edu) is also available to support you should this situation occur.

Mental Health. A link to CAPS (listed as Purdue Counseling and Psychological Services) is on the Brightspace template, under the Student Services and Resources section. If you find yourself beginning to feel some stress, anxiety and/or feeling slightly overwhelmed, try WellTrack. Sign in and find information and tools at your fingertips, available to you at any time.
If you need support and information about options and resources, please contact or see the Office of the Dean of Students. Call 765-494-1747. Hours of operation are M-F, 8 am- 5 pm.
If you find yourself struggling to find a healthy balance between academics, social life, stress, etc. sign up for free one-on-one virtual or in-person sessions with a Purdue Wellness Coach at RecWell. Student coaches can help you navigate through barriers and challenges toward your goals throughout the semester. Sign up is completely free and can be done on BoilerConnect. If you have any questions, please contact Purdue Wellness at evans240@purdue.edu.
If you’re struggling and need mental health services: Purdue University is committed to advancing the mental health and well-being of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of mental health support, services are available. For help, such individuals should contact Counseling and Psychological Services (CAPS) at 765-494-6995 during and after hours, on weekends and holidays, or by going to the CAPS office of the second floor of the Purdue University Student Health Center (PUSH) during business hours.

Emergency Preparedness. In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted to the course page in Brightspace or can be obtained by contacting me via email. You are expected to read your Purdue email on a frequent basis.

Protect Purdue. The Protect Purdue Plan, which includes the Protect Purdue Pledge, is campus policy and as such all members of the Purdue community must comply with the required health and safety guidelines. Required behaviors in this class include: staying home and contacting the Protect Purdue Health Center (496-INFO) if you feel ill or know you have been exposed to the virus, properly wearing a mask in classrooms and campus building, at all times (e.g., mask covers nose and mouth, no eating/drinking in the classroom), disinfecting desk/workspace prior to and after use, maintaining appropriate social distancing with peers and instructors (including when entering/exiting classrooms), refraining from moving furniture, avoiding shared use of personal items, maintaining robust hygiene (e.g., handwashing, disposal of tissues) prior to, during and after class, and following all safety directions from the instructor.
Students who are not engaging in these behaviors (e.g., wearing a mask) will be offered the opportunity to comply. If non-compliance continues, possible results include instructors asking the student to leave class and instructors dismissing the whole class. Students who do not comply with the required health behaviors are violating the University Code of Conduct and will be reported to the Dean of Students Office with sanctions ranging from educational requirements to dismissal from the university.
Any student who has substantial reason to believe that another person in a campus room (e.g., classroom) is threatening the safety of others by not complying (e.g., not wearing a mask) may leave the room without consequence. The student is encouraged to report the behavior to and discuss next steps with their instructor. Students also have the option of reporting the behavior to the Office of the Student Rights and Responsibilities. See also Purdue University Bill of Student Rights.

Nondiscrimination Statement. Purdue University is committed to maintaining a community which recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her own potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life. More details are available on our course Brightspace table of contents, under University Policies.



Agenda

The following is a tentative outline of topics covered and is subject to change. If you are absent from class it is your responsibility to find out what material was covered and to obtain notes from classmates. Section numbers corresponding to each topic are written parenthetically.

Week 1, 8/29 Basic Set Theory, Logic, and Proof Techniques (1.1) (see also, Book of Proof, chapters 1, 2, and 4-6.)

Week 2, 8/31 The Real numbers (1.2), Euclidean space (1.3), Cardinality (1.3)

Week 3, 9/7 Metric spaces (2.1), Continuity (2.2) Completeness (2.3)

Week 4, 9/14 Compactness and Uniform Continuity (2.4)

Week 5, 9/21 Connectedness (2.5), Coverings (2.7), Cantor Sets (2.8)

Week 6, 9/28 Differentiation and Taylor's Theorem (3.1)

Week 7, 10/5 The Riemann Integral (3.2)

Week 8, 10/12 The Darboux Integral and Riemann integrability (3.2)

Week 9, 10/19 Series and Series of Functions (3.3). LEEWAY

Week 10, 10/26 Functions Spaces and Uniform Convergence (4.1)

Week 11, 11/2 Power Series (4.2), Analytic Functions (4.6)

Week 12, 11/9 Stone--Weierstrass Theorem (4.4), Banach Contraction Principle (4.5)

Week 13, 11/16 Equicontinuity (4.3)

Week 14, 11/23 LEEWAY. THANKSGIVING BREAK.

Week 15, 11/30 REVIEW/LEEWAY.

Week 16, 12/7 SEMESTER PROJECTS DUE.


Tasks and Deadlines

Week 1, 8/29 HW 1 Assigned.

Week 2, 8/31 HW 1 Due. HW 2 Assigned.

Week 3, 9/7 HW 2 Due. HW 3 Assigned

Week 4, 9/14 HW 3 Due. Schedule a Preliminary Consultation on Semester Project.

Week 5, 9/21 HW 4 Assigned.

Week 6, 9/28 HW 4 Due.

Week 7, 10/5 EXAM 1 Assigned, 10/5.

Week 8, 10/12 EXAM 1 Due, 10/12. DRAFT OF SEMESTER PROJECT PROPOSAL DUE.

Week 9, 10/19 HW 5 Assigned.

Week 10, 10/26 HW 5 Due. HW 6 Assigned.

Week 11, 11/2 HW 6 Due. HW 7 Assigned.

Week 12, 11/9 HW 7 Assigned. Schedule a Consultation on Semester Project.

Week 13, 11/16 HW 7 Due. EXAM 2 Assigned, 11/16.

Week 14, 11/23 EXAM 2 Due, 11/23. HW8 Assigned. THANKSGIVING BREAK.

Week 15, 11/30 HW 8 Due, 12/4. LAST DATE TO SUBMIT HOMEWORK, 12/4.

Week 16, 12/7 SEMESTER PROJECTS DUE, 12/9.