Course Syllabus

The course syllabus contains the policies and important dates for Math 302 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 third floor of the Science Center, room S352. Office hours are

Locations for office hours are currently TBD. Office hours on Mondays, Thursdays, and Fridays will be held in the study area on the far east side of the main floor of Clapp Library (this is right outside my office at Clapp 255). Office hours on Wednesdays will be held in Room 201 209 of the modulars. I will try to remember to bring my laptop to campus so that you can also Zoom into office hours if you like.

You are highly encouraged to attend office hours, and you never need an appointment to do so. If these office hours don't fit with your schedule, let me know so that I can either adjust when ``official" office hours are held or set up an appointment to help you outside of office hours. Please come to my office or send me an email if you ever want to discuss material from the class or ask about homework problems!

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 Introduction to Analysis by Rosenlict (2nd edition); the ISBN for this text is 978-0-486-65038-8. Students should treat the book as a helpful reference when attempting to digest lectures. 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 rereread,...) this text while actively working through any computations it discusses.

Another useful resource to have is Hammack's Book of Proof; you can find a (free!) edition online, or you can order a print copy through Amazon. This book will be particularly useful as we cover material during the first few weeks related to the basics of sets, functions and cardinality.

Online resources You'll be able to access homework assignments, lecture summaries, and copies of completed quizzes and tests (with solutions!) online through the course webpage at http://palmer.wellesley.edu/~aschultz/f21/math302.

As an experiment this term, I'm also going to set up a slack workspace for this course. You'll be able to access it at after I send our invitations during the first week of class. No one is obliged to engage with the slack workspace, but my hope is that it will be a useful resource for folks who want to seek clarification about the course content, ask questions about problem sets, or share stupid memes related to analysis. If you are using chrome to access slack, you might consider installing the "Latex in slack" chrome extension. This should allow you to see fancy mathematical typesetting that the instructor uses to communicate on the workspace. (If you have the desktop app for slack there are also ways to get mathematics rendered beautifully; contact the instructor for details if you're interested.)

Learning Goals It is perhaps obvious that the objective of this course is to guide students through a rigorous treatment of analysis. 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 use the intuition we build in familiar places (particularly $\mathbb{R}^2$, which has the benefit that it can be drawn nicely on a board) to solve novel problems in new contexts. 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 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.

Expectations

Prerequisites You are expected to have completed linear algebra before taking this class. In particular, you should already be familiar 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. If you have not taken the prerequisite for the course, please let the instructor know immediately.

In-class expectations Your 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. Classroom time is there for the benefit of students, so should be treated as an interactive resource.

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.

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. The typical student will need to put in at least 10 hours per week on the assigned problem sets. If you find you are consistently spending more than 12 hours on problem sets, please discuss this with the professor so he can help you manage the time you spend on this class more effectively.

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.

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 due once per week, with most assignments consisting of two distinct parts. 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, and your lowest score is dropped. So, for example, if we had only Assignments 1A,1B,2A and 2B over the course of the term, and you received grades of 27/30, 22/30, 30/30 and 25/30 on them (respectively), then your average would be computed as $$\frac{27/30+30/30+25/30}{3} \approx 91.1\%.$$

An important note about collaboration and the Honor Code. Students are more than welcome to work with the instructor, classmates, or a tutor from the Help Room 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 There will be weekly quizzes in this course. With the exception of weeks following an exam and the first week of class, we will have a quiz every Wednesday. Quizzes will be distributed electronically; you will write your solutions on a blank piece of paper, a printed copy of the quiz, or on a tablet, and afterwards you will submit your quiz via a Google form (specific links for each quiz will be provided upon receipt of the quiz itself). Your quiz average will be computed after dropping your lowest quiz score. Barring extreme circumstances, make-up quizzes will not be given. In general, the material covered on quizzes will be the content covered in-class from the preceding Wednesday, Thursday, and Monday.

Tests There will be 2 midterm examinations and 1 final. Midterms will be distributed electronically, and you will submit your answers in much the same way that you do for quizzes. The first exam will be available to take between October 21--24; the second will available to take betweenDecember 2--5. Your final will be self-scheduled. All exams are closed book, closed notes.

Computing your grade Your grade is computed as follows: Quizzes (10%), Homework average (25%), Final (25%), Midterms (20% each).