Course Syllabus

The course syllabus contains the policies and important dates for Math 307 in the fall of 2020. If you are confused about anything in the syllabus, please don't hesitate to let the instructor know.

Course Details

Class format Due to the COVID-19 pandemic, the class is run fully remotely. We will have 3 synchronous meetings per week and 2 asynchronous lectures. A typical week's schedule will look like this:

Login information for the Zoom channel for our course will be sent directly to your email address at the start of the semester.

Professor The professor for this class is Andy Schultz. You can contact the instructor at if you have any questions. Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email about a homework problem, please: follow standard email etiquette (e.g., choose a reasonable subject line, include a greeting and signature, write in complete sentences, avoid abbreviations, etc.); specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help"); and send along whatever ideas you've already tried in solving the problem (just take a shot of whatever work you have and attach the photo to the email).

Office hours Zoom office hours will be held several times throughout the week (all times listed below are relative to Wellesley's time):

Login information for office hours will be sent to your email at the start of the semester. Office hours will not be recorded. If you want to discuss something confidentially during office hours, you can send me a private chat message through Zoom asking to set up a confidential conference, in which case we'll move to a breakout room to talk. These times have been selected to minimize the number of curricular conflicts. If these times don't work for you, please reach out to the instructor directly to either ask your question via email or set up another way to talk.

Text The course is centered around Munkres' Topology, 2nd edition. You can purchase a used copy of this text for between $20 and $30 online (abebooks.com has more than a handful to choose from). The soft-cover international edition should work fine. The ISBN for the text is 978-0131816299. Munkres' text has a well-deserved reputation for being a solid exposition of the foundations of topology, and is one of the more "readable" advanced mathematics textbooks out there. Though homework problems will often be drawn from the text, you do not need a copy of the text in order to access homework problems. If purchasing this text presents a financial burden for you, PLEASE let the instructor know so he can help facilitate.

Online Resources You'll be able to access homework assignments and find links to recorded lectures (together with lecture summaries) through the course webpage at http://palmer.wellesley.edu/~aschultz/f20/math307.

Topics During the course of the term we plan to cover much of chapters 5, 6 and 8 from our text. This includes the basics of integration theory (motivating the integral via the area problem, exploring Riemann sums as a first (approximate) answer to the area problem, using the Fundamental Theorem of Calculus to create a link between antiderivatives and the area problem, developing a handful of integration techniques (like $u$-substitution, integration by parts, partial fractions, and trigonometric substitutions), improper integrals, and numeric integration), delving into the applications of integration (including more sophisticated area problems, volumes, and some physical, economic, and/or biological problems related to integration), and then exploring sequences and series as a gateway to Taylor polynomials (including defining sequences and their convergence, defining series, developing the geometric series theorem, the integral test, the alternating series theorem, the ratio and root tests, defining power series and their convergence, and -- of course -- Taylor polynomials and their intervals of convergence).

Learning Goals While learning the content of the course, you will

Resources

Instructor Your go-to resource for topology this term is the instructor; he literally gets paid to help you learn this material! He is extremely happy to answer any questions you might have, so don't be shy about asking questions. Questions do not need to be deeply penetrating or otherwise earth-shattering in their impressiveness, nor do they need to be strictly about content covered in this course. For example, you might find that you have a hard time recalling some of the material you saw in 302, so that some of the motivation for what we're introducing isn't clicking. You might have a hard time understanding an example from class when you go back to review your notes. Or you might be struggling to organize your time efficiently and productively for the course. All questions are welcomed!

Accountability Buddy For all interested students, the instructor will help coordinate (at least one) accountability buddy for each student in the course. The purpose of this system is to ensure each student has a peer in the course they can "check in" with during the term. Some students use their accountability buddy as a go-to partner for understanding course material, working through homework sets, or preparing for exams. Other students use their accountability buddy to help coordinate logistical details around the class, like mapping out their study schedule.

Math Cafe The department organizes some drop-in tutoring (via Zoom) that requires no appointments. Information about the math cafe is distributed through the department's Google group.

PLTC The Pforzheimer Learning and Teaching Center helps coordinate individual and group tutoring for students. The service is free for all students, but does require you to fill out some paperwork.

Accessibility and Disability Resources If you have a disability or condition, either long-term or temporary, and need reasonable academic adjustments in this course, please contact Accessibility and Disability Resources (ADR) to get a letter outlining your accommodation needs, and submit that letter to me. You should request accommodations as early as possible in the semester, or before the semester begins, since some situations can require significant time for review and accommodation design. If you need immediate accommodations, please arrange to meet with me as soon as possible. If you are unsure but suspect you may have an undocumented need for accommodations, you are encouraged to contact (ADR). They can provide assistance including screening and referral for assessments. Disability Services can be reached at accessibility@wellesley.edu, at 781-283-2434, by scheduling an appointment online at their website, https://www.wellesley.edu/adr.

Expectations

Prerequisites Students are expected to have completed Math 302 (or the equivalent), and there is an additional co-requisite of Math 305. In particular, the instructor assumes that students are comfortable with the basics of reading and writing rigorous mathematical proofs. On the other hand, the instructor knows that learning math is a continual process of improvement, and that we're all constantly honing our ability to read proofs, solve problems creatively, and embrace abstraction.

In-class expectations A student's engaged presence is expected in classroom lectures. While the professor is in charge of determining what content is covered during a class period, students share the responsibility of directing lectures and discussion sections so each is as clear as possible. In particular, students should feel comfortable stopping the instructor to ask him to repeat a particular exposition, to present a concrete example of an abstract concept, or to explain a confusing concept in a new way; this can be done in a variety of ways, though the two easiest are probably raising your hand or sending the instructor a message via the chat function of Zoom. Classroom time is there for the benefit of students, so should be treated as an interactive resource. During group-based problem breakout sessions, you should have yourself "on mic", and it is often great to have your camera on if that's possible. You're highly encouraged to keep your camera and mic on during lectures, but this is not required.

Attendance Mathematics requires that a student understand one concept before moving on to the next, and since our course moves at a fast pace it is critical that you attend each and every class. You should make every effort to attend every class period! On the other hand, I know that the pandemic presents everyone with unique challenges when it comes to attending lectures, and those challenges can include being in a timezone or home situation that makes attending class extremely difficult. If you are running across problems that prevent you from doing the work you need to do for this class, please let the instructor know as soon as these obstacles arise. The semester runs very quickly, and a delay in reporting a problem can exacerbate any underlying issue.

Effort Many students have the impression that "understanding the material'' means instantly knowing how to do problems assigned in the class. On the contrary, most students find they don't truly understand the course material until they have struggled through several attempts at solving problems or understanding concepts. You are expected to exert a good amount of effort in working through the course material, and you shouldn't be discouraged if a certain topic remains elusive when you first encounter it: try some suggested problems, review your notes on the topic, and ask your instructor or friends for help when you need it. Because this course is being run during a 7-week term, you should be spending LOTS of time outside of class trying to work through problems, and not just the problems that are assigned for a homework grade. If you find that the time you're devoting to the class is unproductive or spiraling out of control, please let the instructor know so he can help.

Academic Integrity Students are expected to read and understand the college's Honor Code. Incidents where academic integrity have been compromised will be dealt with severely. Although most students have a good feel for what constitutes a violation of the Honor Code, for this class you will also need to be familiar with the instructor's policy on homework collaboration. Please be sure to thoroughly read and understand the section on homework below to avoid an inadvertent violation of the Honor Code.

Assessment

Homework Homework problems be due once per week, and they play a considerable role in determining your overall grade in the course. Homework will be assigned in 2 parts, and students will submit their work for each part as a PDF. If you don't have access to a scanner for converting written work into a PDF, you can take advantage of any number of free camera-to-PDF conversion tools (e.g., GeniusScan).

Because homework plays such a significant role both in your understanding of the material and your assessment in the course, It's critically important that you complete all homework assignments and submit them on time. While it's important to stay "on schedule" in order to stay apace in this quick term, the realities of our current life mean that some students might run across obstacles that prevent them from doing their work on time. If you find yourself in this situation, please reach out to the instructor so that suitable accommodations can be arranged.

An important note about collaboration and the Honor Code. Students are more than welcome to work with the instructor or their friends when solving homework problems. In the event that you have taken notes while working with someone else, you must put these notes away and recreate the solutions on your own when you submit your solutions for the homework assignment. If you have any confusion about this policy, please talk to the instructor.

Participation/Diagnostics You will occasionally be asked to complete short "diagnostic tests" to make sure you understand the basic concepts, definitions, or objectives from a video or class discussion. These are not timed, nor are they closed-book or closed-notes. Given the collaborative nature of mathematics (and the increased need to be conscious about community building in a remote learning setting), you're participation in class is also an essential ingredient for both your personal success in the class, and the success of the course as a whole. Participation can manifest in many ways, including: asking questions when you have them (either verbally or through the chat (including private messages on the chat)); answering questions during class; participating in group activities; sending topology memes to the class.

Tests There will be 2 exam in the course: one over the weekend of November 20, and one during the final exam period. The exams are not cumulative. If the dates for the exams present a conflict for you, please let the instructor know as soon as you possibly can.

Computing your grade Your grade is computed by weighting your homework score at 50% homework, your participation and diagnostics at 10%, and each of your exams at 20%. Students who score at or above a 90 are guaranteed to receive some sort of `A' in the course. A score of 80 or better guarantees some sort of `B,' 70 or better some sort of `C,' and 60 or better some sort of `D.'

If you're taking the course credit/non, remember that you have to have an overall grade of C or better in the course; a C- results in no credit for the class.