FAQ
This page collects together some questions that come up on a regular basis. You need to read it at the start of the semester, and it's not a bad idea to re-read it once we're 3 or 4 weeks into the semester and you've established a rhythm for the class.
Logistical Questions
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My preference is for you to call me by my first name: Andy. My feeling is that in college you're learning how to work in the world of adults, and often (but not always) in that world you'll address people by their first name even if they are a few years older than you.
Disclaimer: many professors do NOT want you to address them by their first name. In general, if you're not sure how to address your professor, you can use ``Professor " without creating any offense.
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If you've taken Math 205, you should be ready to tackle this material.
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Probably not. Though we do teach some introductory ideas about vectors in our multivariable class here at Wellesley, picking up that concept shouldn't be difficult for students who haven't yet taken multivariable calculus. What's more important is that you have the mathematical maturity to think abstractly and reason precisely.
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Some students like to have the text on hand so they have a resource to lean on when they are trying to digest content from the lectures. I can't stress how valuable it can be to have another mathematical presentation of content to make sense of things, and this is another asset the book has going for it. Finally, I might occasionally draw homework problems directly from the text. The only downside to owning the text is the cost, and since we're using a pretty cheap textbook, I think the pros outweigh the cons. Go buy the book.
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I'm very happy to meet outside of office hours, but it will take a little work to coordinate a time that is amenable to both of our schedules. Contact me via email and let me know the dates and times that work well for your schedule. You optimize your chances of getting to chat with me outside office hours if you contact me two or three days before the day you want to meet.
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The syllabus gives you the breakdown I use for each component of the course, together with information about any grades that might get dropped. The challenge in computing your current course average is that you'll have lots of data: we'll likely complete about 20 homework sets, 10 quizzes, 3 midterms and a final. If you want to know how you're doing in the course, I advise you to create a spreadsheet with those grades. Your current scores in each of the four components of the course (homework, quizzes, etc.) can then be calculated pretty easily. Of course I'm also happy to do this for you if you want to set up a meeting.
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Unless you hear from me otherwise: no. Sometimes I'll try to hold office hours on a holiday, but this depends on many factors; if I am able to hold an office hour on such a day, you'll hear from me by email.
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Get in touch with one of your classmates to get a copy of the notes. After you've reviewed the notes and read through the relevant section of the book, feel free to ask me questions about anything that doesn't make sense.
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Most students who complete 206 would consider the course to be pretty intense. This course has two things that require diligent work. The first is the mathematical content itself. The hurdle in understanding this material is that we'll be discussing it through a mathematical lens that's probably more abstract than you're accustomed to, and as such you'll have to invest time in becoming fluent in the language/art of mathematical thought and proof. The course is really designed to be both an introduction to linear algebra AND mathematical proof, so you don't need to be worried if you've never seen a proof in your life. What you do need to do is come into the class with an open mind about how we're approaching mathematics, and then do your best to internalize this new perspective.
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I'm under no illusion that everyone who takes this class is in love with mathematical abstraction, and there's no doubt that there's a place in this class for discussing specific examples. Indeed, a substantial portion of our classtime is spent on working through specific examples! However, there are good reasons for approaching this course material abstractly (even if you hate the idea of mathematical proof). On the most broad level, the careful analytical thought process that underlies mathematics is a wildly applicable skill across all disciplines. More specific to this course, however, a solid understanding of mathematics is what allows us to take our geometric knowledge from lower dimensional settings and rigorously carry it through to higher dimensional settings as well
Questions about homework
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All homework problems should be worked by hand. You can use a computer algebra system (like a calculator or WolframAlpha) to verify that you're performing your calculation correctly (especially if you have reason to believe that your answer seems fishy). You will do yourself a serious disservice if you regularly use a calculator to complete your assignments, because you cannot use a calculator during quizzes or exams.
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Working collaboratively on a problem set has huge pedagogical benefits for everyone involved; you're highly encouraged to do this. Issues of academic integrity come into play only when one student is siphoning off answers from other students without meaningfully engaging in the process.
If there is true collaboration between students on a problem, there's little risk of cheating. If, instead, one student asks another student how to solve a certain problem, there is the potential for a violation of academic integrity. To avoid this, follow this simple guideline. If you're a student asking another student how to solve a problem, have a discussion with that student so that you learn how the problem works. Take notes if you like. Once you feel you understand what's happening, take a 20 minute break and then return to the problem without the use of your notes. If you can complete the problem from start to finish on your own, then you truly understand the problem and can write up your solution formally. If you find that you have to reference your notes from the discussion with your helper, carry through to the end and make yourself comfortable with the problem. Take another 20 minute break and return to the problem, again without notes. If you can complete the problem without referring to your notes, formally write it up and submit it. Otherwise, repeat the process above until you can work the problem entirely on your own.
The process above is intended for those students who genuinely do not know how to approach a problem and are guided from start to finish by a helper (peer, tutor, or professor). Of course if you worked on a problem and got almost everything right, but found a small computational error with the help of a friend, you don't have to go through the whole process again. For situations between these two extremes, err on the side of caution when it comes to exercising your ability to complete problems independently after coaching from someone else.
Questions about quizzes and/or tests
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The answer depends on the type of question. For problems that involve computations, relevant material is whatever was covered in the problem set(s) submitted since the last quiz. For problems that are theorem or definition restatements, or problems that involve giving simple examples of some mathematical object or phenomenon, relevant material is whatever was covered in lectures since the last quiz.
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Absolutely not. I consider this a serious breach of academic integrity. If I find out that a student has viewed copies of old tests, or has otherwise solicited information about tests from former students, I will bring up a formal honor code case.
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No. See the above.
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The easiest way to make sure everyone is on a level playing field is for students to wait to talk about the quiz/test until they've heard from me that everyone has taken the quiz/test. If you must talk about the quiz/test with someone before you've been told everyone has taken an exam, only speak about the quiz/test with people that you know have taken the quiz/test already. Do no speak about the quiz/test in the company of others who have no taken the quiz/test. It's obvious that you shouldn't divulge specific information (like particular questions), but you also shouldn't give qualitative information (you felt the quiz/test was ``easy" or ``hard" or ``fair", etc.) or even logistical information (the test was 12 pages long, or printed on white copy paper, or stapled in the top left corner). In short: don't say anything about a quiz/test to a person who has not taken the quiz/test until after you've been told by the professor that it's ok.
It would impossible for me to administer exams and quizzes in this way at an institution that didn't have a robust honor code. It is a privilege --- for you and for me --- that we're at a school where integrity counts. It is your responsibility to ensure that you live up to this standard so that everyone gets the chance to take quizzes and exams under the same conditions, and therefore so that these instruments can reflect each individuals understanding of the course material.
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No. Experience has shown me that practice tests are not effective in getting students to prepare for exams, and they typically do more to hurt than facilitate student learning. Students are better served reviewing the relevant notes, creating their own study sheet, determining their strengths and weaknesses, and then allotting study time accordingly.
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Possibly. Please let me know as soon as you can so I can determine if an accommodation is warranted.
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Our exams will involve several different components. Some requires just rote memory (say, definition or theorem statements); these are best tackled by periodically (i.e., daily or every other day) rehearsing statements until you know them perfectly. Some portions of the text require you to understand the "edges" of the content we learned; for instance, if you take a given theorem and relax a certain hypothesis, the theorem might wind up failing. In these cases, can you give a specific example that exhibits the failure of the original theorem in this "relaxed" case? To get good at these problems, you need to be thinking carefully about how the topics we cover in class interrelate to each other. These kinds of questions require a pretty deep understanding, the kind gained simply by working problems and attempting to synthesize the content we present in this course. Other problems are computational, and these are best prepared for by doing lots of computational practice problems; there are a wealth of such problems at the end of each section of your text, and of course you'll have done computational problems on homeworks and quizzes. Midterms will also include a "rehearsed proof," which means sometime before the test I'll provide a list of possible problems for the exam, and one of these will show up on the exam itself. For these problems, of course it's best if you can think about all possible problems early. For the take home portion of the exam you'll be asked to write proofs for two or three problems you haven't seen before. The best preparation for these problems is the amalgamation of all the other work you do in homeworks, quizzes and tests. In many ways these problems will be just homework problems in a new guise; the difference is that they will have a more stringent timing component, and have to be worked without access to notes or collaborators.
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Why does anyone do anything?