Course Syllabus

The course syllabus contains the policies and important dates for Math 305 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 at the following times

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 Gallian's Contemporary Abstract Algebra, 5th edition. Students will be expected to read from the book in preparation for class each day, and they should treat the book as a helpful reference when attempting to digest lectures. It is not essential that you get the fifth edition of this text for the class; any edition which is reasonably close to the fifth should suffice. If you get a copy of the text which differs from the fifth edition, it will be your responsibility to ensure that you complete the correct problems when homework assignments are drawn from the text.

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

Online resources You'll be able to access homework assignments, lecture summaries and copies of quizzes online through the course webpage at http://palmer.wellesley.edu/~aschultz/f23/math305.

Mask policy We will practice a mask optional policy this semester. Masks are not required but respected.

Expectations

Prerequisites Students are expected to have completed linear algebra before taking this class. In particular, students should already been familiar with the basic concept and execution of mathematical proof. Students who are interested in brushing up on this skill can see the professor for additional help. If you find that you are struggling to remember how to write certain kinds of proof, or if your proof writing isn't as sharp as you'd like at the start of the semester, that's completely fine and not at all unusual. Simply contact the instructor as soon as you can so he can help you get caught up to speed.

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.

With that said, it's silly to pretend we aren't in the midst of a perpetual 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, they should solicit notes from someone who was in attendance. (If needed, the instructor can help facilitate this process; if this is the case, it is the student's responsibility to notify the instructor that they will need help securing a copy of the notes.)

Effort Sometimes 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 between 8 and 12 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.

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 approximately 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 part of one homework set late during the term; if you intend to submit a late part, you should email the instructor to let him know that you are using your late pass, and then you should submit your homework set by the start of class on the following Monday. In addition to this late homework part submission, there is also one dropped homework grade per term. For most students, these two contingencies should absorb most issues that come up during the term that interfere with the completion of homework assignments. If a student has further issues that require more than these two measures, they should contact the instructor as soon as possible (but not later than the day before the next homework assignment they can't complete on time) so that a meeting can be set up to discuss the issue.

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 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. Please read the prompt on the homework page which describes the expectations for how your work is written up! The work you submit should be the final, edited draft of the work you have done. 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.

An important note about collaboration and the Honor Code. Students are more than welcome to work with the instructor or 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. You should always write your solutions up in isolation of others or notes about discussions taken with others; give yourself time (at least 20 minutes) after talking with someone about a solution (or reviewing notes you took during such a discussion) before writing up your own answers. 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 short quizzes given in this course each week. With the exception of exam weeks and the first week of classes, we will have a quiz every Wednesday that we have class. The quiz will be administered electronically, and you'll submit it in person the next class day (Thursday). 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 include recitation of definitions or theorems learned in class and calculations which should be familiar to students who are up-to-date on the homework.

Tests There will be 2 midterm examinations and 1 final. Both midterms will consist of two parts, one out of class and one in class. The out of class portion will consist of a few proof problems which are to be completed without the aid of books or notes; it will be timed, with students given somewhere between 2 or 3 hours to read the problems, produce solutions, and write up their results. The out of class portion of an exam is due on the day of the scheduled in-class portion of the exam. The in-class portion of an exam is given during the regularly scheduled lecture period in the regularly scheduled classroom, so there should be no conflicts which prevent you from taking a midterm as scheduled. The in-class portion of the first exam will be held on Thursday, October 19, the second will be held on Thursday, November 30. Your final will be self-scheduled.

Computing your grade Your grade is computed as follows: Quizzes (10%), Homework average (30%), Final (20%), Midterm 1 (20%), Midterm 2 (20% each).

Advice

Start working on your homework as early as possible. Homework is where you get a chance to sit behind the wheel and see if you can operate the machine. For many people, it will take some time to tackle the problems that have been assigned. If you don't start the problem set until 48 (or 24!) hours before it is due, it's far more likely that you'll not have time to really grapple with the problems sufficiently. Problem sets will generally be posted late on Friday or by Saturday at noon, so you should get in the habit of at least reading over the problems as soon as they are assigned, and trying to tackle a few problems a day.

Come to office hours. Office hours are your chance to spend time with the instructor and some subset of your classmates outside of lecture. If you have issues that are confusing you, it's a great place to ask those questions. Even if you don't have questions you want to ask, sometimes it's useful to come hear what other people are thinking about.

Be fully engaged in classtime discussions. Lectures will likely move quickly, and the process of taking notes is significantly taxing and requires a lot of attention and focus. To the degree you're able, also try to find time during class to ask yourself whether you have a general sense of what we're doing and how we're approaching issues. If you're confused during class, ask questions!

Work collaboratively. Spend some time meeting people in the class. If it works for your schedule, see if you can set up a time to work on problem sets together. It's truly amazing how beneficial it is to have people working together as they are digesting new material.

Think both "big picture" and "fine details". As you study for exams, you'll want to think about what we've covered that is relevant for each exam. In doing so, you should be able to see our topics broader perspective: what are the basic questions we're interested in asking, and what are the general techniques we bring to bear? At the same time, you should have a strong enough understanding of the particulars that you don't have to reinvent the wheel when the exam itself comes: do you know relevant theorems? have you practiced executing --- from start to finish --- the strategies we've developed?

Give yourself permission to struggle. Don't be discouraged if this course is challenging. You are learning new mathematics, including even a new way of thinking about what mathematics is and how one "does mathematics." If you embrace the challenge and are bold enough to talk to someone when you are confused, there is opportunity for significant growth...and even enjoyment along the way.