Course Syllabus
The course syllabus contains the policies and important dates for Math 310 this term. If you are confused about anything in the syllabus, please don't hesitate to let the instructor know.
Course Details
Professor My name is Andy Schultz, and my preference is that you address me by my first name (no title necessary). My office is on the fourth floor of the Science Center, room W408. Office hours will be held in (or near) my office at the following times
- Mondays from 2-3;
- Wednesdays from 10:30-11:20;
- Thursdays from 8:30-9:45;
- Fridays from 11:30-1:00.
You can contact me at . Though I'm always happy to receive emails from you with questions or concerns about the course, I can't guarantee that I'll be able to promptly reply to emails late at night or over the weekend. If you do contact me by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting me to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").
Text The course is centered around Complex Variables and Applications by James Ward Brown and Ruel V. Churchill (6th edition); the ISBN for this text is 0-07-912146-2 or 0-07-912147-0. It isn't critical that you get precisely the 6th edition; I've selected it because it's older (and therefore cheaper) and readily available. If it's more convenient to purchase a different edition, you should feel free. Since students will be presenting lectures based on the content of the text, it will be an invaluable asset to student understanding.
When going through the text on your own, remember that mathematical reading is an active process; it's a good idea to keep some scrap paper on hand so you can perform calculations that the text leaves out, and you shouldn't be discouraged if it takes a few attempts at a passage to understand precisely what the text is saying. This can't be stressed enough: to make sense of the content in the book, you will need to read (and reread, and reread,...) this text while actively working through any computations it discusses.
Online resources You'll be able to access homework assignments and presentation plans through the course webpage at http://palmer.wellesley.edu/~aschultz/f22/math310.
Pedagogical structure The traditional pedagogy model in mathematics has the instructor lecturing content to students that are taking notes (and, ideally, asking questions). This classroom will be structured differently, with students delivering lectures to their classmates. The course text will be split into small chunks and assigned to individual students who are then responsible for learning the content from their section, determining how to package it for a lecture, and then delivering that lecture to their classmates. This structure has been chosen in favor of the standard model because I find that it not only leaves students with a very solid understanding of the mathematical content of a class, but it also gives them a chance to develop a whole suite of skills that are useful in a variety of settings (not just in a mathematics classroom).
Learning objectives It is perhaps obvious that the objective of this course is to give students a rigorous treatment of functions of a complex variable. Outside of this content, however, there are a handful of skills that this course will help students sharpen. As in many courses, pattern recognition is a skill which is exercised a lot in this course; in this particular class, this manifests itself by connecting ideas across disparate contexts, particularly by asking which phenomena we observe for the real numbers (or perhaps for $\mathbb{R}^n$) extend to other ”similar” collections. In the same way, we’ll build on our intuition to determine what results still hold true in this new complex setting, and which results need to be rewritten. Finally, we’ll have a LOT of practice writing and presenting logical arguments in a clear and concise way; this includes not only the formal write-ups you’ll do when writing up problems for homework and exams, but also student presentations on the content itself (not to mention the informal conversations you’ll hold with the instructor and your peers as you work through the particulars of a variety of problems during the semester).
Mask policy We will practice a mask optional policy this semester. Masks are not required but respected. The instructor will not be wearing a mask to begin, but may later choose to mask at various times for personal reasons. As a class, we will practice grace and understanding of people's individual choices in our classroom space.
Expectations
Prerequisites You are expected to have completed Math 302 before taking this class. In particular, you should already be well-versed with the basic art of mathematical abstraction and proof writing. If you feel you need some practice in brushing up on these skills, let the professor know.
Out-of-class expectations for students Students are responsible for reading relevant sections of the text prior to any given class. This optimizes each person's chance of understanding the material as its being presented, since it not only gives students some exposure to what will be discussed, but gives them a chance to know which parts of the text are unclear to them. The nature of the class means that it is difficult to know precisely what we will cover on any given day. As a guide for what could possibly be covered in a given class, our policy will be that we will not complete more than 2 "new" presentations on a given day. This means on a given day a presenter from last class can finish her lecture, and at most two new students will be giving presentations.
Out-of-class expectations for the instructor The instructor is expected to post lesson plans in a timely fashion so that students have the opportunity to do the necessary prep work. He is also expected to be available as a resource for students as they work through their own understanding of the material (either from the text or another student's presentation). He will provide feedback on each presentation to help students identify their strengths and weaknesses in preparation for the next presentation. He is happy to help students think through lesson planning.
In-class expectations for students A student's engaged presence is expected in classroom lectures. While the instructor is in charge of setting guidelines for what content is covered in a given presentation, students will be responsible for giving a large portion of the lectures in the class. Student presenters are expected to have worked on their presentations prior to class, and should set their standards high for delivering interesting, mathematically correct and engaging lectures. Students who are not presenting are expected to stop the lecturer to ask them to repeat a particular exposition, to present a concrete example of an abstract concept, or to re-explain a confusing concept. Classroom time should be treated as an interactive resource, and the best class periods will feel more like discussions than lectures. If a presenter is unclear or is presenting material that seems mathematically incorrect, it is the responsibility of the class --- not the instructor --- to work towards resolving these issues.
In-class expectations for the instructor For the most part, the instructor does not actively participate in a given presentation.
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. If you are going to miss any classes this term, please let the instructor know as soon as possible. More than 1 absence could negatively impact your final grade, in the sense that absence from class will likely result in you getting behind on material. I do not tabulate absences and use them in determining your grade in the course.
With that said, it's silly to pretend we aren't still in the midst of a serious public health crisis. This means that there will inevitably be some students who have to miss class because they are covid-positive. If a student misses a lecture for which they are not the main presenter, they should solicit notes from that class from someone who was in attendance (the speaker might be a good person to ask, but other students in the course should also have good notes to draw from). If a student is scheduled to present but cannot because they are covid-positive, they should let the instructor know as soon as possible so that appropriate arrangements can be made.
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, go to office hours, and ask your instructor or friends for help when you need it.
Academic Integrity You 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.
Late submissions Students are expected to submit their work according to the deadlines posted with assessments. It is the instructor's responsibility to ensure that assessments are made available to students in a timely fashion so that they have an opportunity to engage with those assessments under an appropriate time frame. In general, this means the instructor should post homeworks 7 days before they are due so that students have an extended period of time to work on problems. (As a corollary: students should begin their homework problem sets well in advance of the deadline.)
Students can submit one homework set late during the term; that late problem set should be turned in without 72 hours of the original deadline. If a student cannot complete their homework because of an illness, they should let the instructor know as soon as possible so that appropriate accommodations can be made.
Accommodations If you have a disability or condition, either long-term or temporary, and need reasonable academic adjustments in this course, please contact Disability Services to get a letter outlining your accommodation needs, and submit that letter to the instructor. 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 the instructor as soon as possible. If you are unsure but suspect you may have an undocumented need for accommodations, you are encouraged to contact Disability Services. They can provide assistance including screening and referral for assessments.
Disability Services can be reached at disabilityservices@wellesley.edu, at 781-283-2434, by scheduling an appointment online at their website www.Wellesley.edu/disability, or by visiting their offices on the 3rd floor of Clapp Library, rooms 316 and 315.
Grading
Homework Homework problems will be assigned throughout the semester. Students are to write their solutions neatly and submit them according to the instructor's instructions. Be sure to start your assignment early so you have enough time to work through problems which require some creative energy. When computing your homework average, each part of each homework is graded with equal weight. We will not have a dropped homework grade unless we submit 10 or more assignments during the semester.
An important note about collaboration and the Honor Code. Students are more than welcome to work with the instructor and classmates when solving homework problems. If you have consulted with someone in preparing your homework, please include a reference to your collaborators when you submit your assignment. 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. Using notes from a collaboration while writing your homework assignment will be considered a violation of the Honor Code. In addition, you may NOT consult a written solution to a problem you're working on (whether it be online or in a book). If you have any confusion about this policy, please talk to the instructor.
Quizzes You will have short, weekly quizzes to ensure that you are staying in touch with the basic terminology and results from class. Quizzes will be available to download each Wednesday from this page, and due (as a hardcopy submission) by the start of class on Thursday. Solutions will be posted after quizzes are submitted.
Tests There will be 1 take-home midterm examination and 1 final. The first exam will be handed out on November 3, and due by November 10; during the exam that the week is out, you will have the chance to choose the best 24 hour period to do your work on the exam. The final exam will also be take-home.
Computing your grade Your grade is computed as follows: Quizzes (5%), Homework average (25%), Final (20%), Midterm (20%), Presentations and Participation (30%).