Fall 2013 Math 20200: Calculus II

Course Meeting: MW 12:00-1:40 PM, in room 4115 of North Academic Center
Section: CD
Instructor: Alice Medvedev
Office: 6278 NAC
Office Hours: Special: Wednesday, September 4th 12pm-2pm; Regular: probably Monday 4:30-5:30, or by appointment.
E-mail: amedvedev at ccny

Useful links

Coursepage for all 20200 courses, including textbooks and content.
Drop-in tutoring is available for all levels at the Math Help Desk, MR418S.
Appropriate academic accommodations are offered to students with disabilities.
The university's policy on academic integrity.

Basic structure of the week

About half of each class will be devoted to lecture: me talking at you about new material. This is not enough time to cover everything, so you must read the textbook! You will also get much more out of the lecture if you read ahead in the textbook. If you don't understand something in the lecture, raise your hand and ask!! If you don't ask questions, I cannot answer them.

A largish homework will be assigned each Wednesday, to be done before the beginning of class on Monday. Some of Monday's class will be devoted to discussing the solutions of some of the problems on this homework. There will be a quiz almost every Monday, very closely related to this homework. The quiz will be graded; the homework will not be collected.

A smallish homework will be assigned each Monday, to be completed by the following Wednesday. You will spend some of the class each Wednesday working in groups at the board. This way you get hands-on understanding of new material, and get immediate feedback from me on conceptual errors.

Grading etc

The course grade will consist of: the final exam 40%, each of the other exams 15%, and classwork 15%.

The 15% of your grade that comes from classwork will come from quizzes, groupwork, homework problems presentations, and general class participation.

Exam dates: midterms in class on September 25th, October 28th, and December 9th; and final exam on December 19th.

Homework

You may work together on homework problems (and I encourage you to do so), but make sure you understand the solution well enough to solve similar problems on your own: your friends cannot help you on quizzes and exams! Similarly, if you use a calculator for the homework problems, mae sure you can do the problems without it!

High-school calculus

Most of you have taken calculus in high school, perhaps even covering some of the topics in this course. Beware that college courses usually require a deeper conceptual understanding of the material. Do not tune out because the topics seem familiar: by the time you realize you are lost, you will be two weeks behind!

Etiquette and Attitude

These are things that most professors take for granted; some are more obvious than others; some are more important than others; many are equally standard outside academia.


Communication. Written communication, such as emails, begins with a greeting, probably addressing the recipient, and ends with a signature, probably including the full name of the writer. You have no idea how much some professors are offended by informalities such as "Hey," and "See ya."

It is reasonable to expect emails to be answered within a day or two; it is unreasonable to expect an answer within an hour. The truly urgent questions (where's the final exam - i'm already late?) are better answered by google or a phone call to the relevant university office. Some questions that feel urgent (did I pass the class?) simply require patience.

Email is great for logistics: finding a time to talk outside regular office hours, making special arrangements for missed work, telling me about a problem with the web page or a homework, etc. Email does not work well for discussing mathematics - come to my office hours instead.

If a professor (or, really anyone else!) agrees to meet with you personally, outside of lecture and standard office hours, and then you find out that you will not make it to the meeting, you should inform the professor of this at least several hours in advance. I have had enough problems with this issue that I will take 1 percentage point off your grade for each missed appointment.


Lectures Attendance is not mandatory but strongly recommended. Most of the material covered in lecture is in the textbook, and most of the announcements will eventually be posted on this course webpage. However, you are responsible for the exceptions, so if you miss a class, talk to someone who didn't. You will also find the class much much harder if you do not come to lecture; in my experience on both sides of the game, missing more than half of the lectures will cost you about two letter grades.

The best use of lecture is to focus all of your attention on it, for the entire duration. If you are not doing this, please do not disturb the people who do. If you come late or leave early, sit near the door and don't let the door slam. If you're eating, please don't be loud or smelly (if you bring hot pizza, bring enough for everyone!). Whether or not you're playing with your cell phone, make sure it's silent. Basically, if it's distracting, don't do it. Common sense, right?

The best way to stay focused in class is to get involved. If something doesn't quite make sense, ask about it! I like questions! I like stupid questions, too - for every brave soul willing to ask one, there's ten shy confused students thinking the same thing.

If you think there's a typo on the board, you may well be right - ask about it! Sometimes, I'll make them on purpose, to keep you on your toes. Other times, I'll make honest mistakes - I'm not perfect. And if it's not a typo, your confusion will not get cleared up if you don't ask. Clearing up confusions is what this is all about.

Responsibility. On the most basic level, it is your responsibility to know about all assignments and deadlines and to show up for exams, and to make any special arrangements necessary, from arranging time to meet outside office hours to knowing when your drop deadline is. You are also responsible for your learning, from knowing what material has been covered to making sure you understand that material. The lectures will not cover everything; the problem sets will not cover everything; the textbook is the closest to covering everything. You will certainly have to learn some things on your own, either from the textbook or really on your own. Some of the material this course covers is genuinely difficult: you will probably not get it on the first try; that's ok. To maximize the number of tries, read the textbook before the lecture, noting the parts you don't understand; then come to lecture and pay special attention to those parts and ask lots of questions; then read through the book again and you will discover new subtleties you don't quite get. Come to office hours to clear up those, work on the homework, come to more office hours, present your homework solutions in class and listen other students presenting theirs, read comments on graded quizzes, and read through the text one more time. By this point, two or three weeks after meeting the concept for the first time, you should be comfortable with it. The bottom line is, your job is to acquire knowledge, not simply to follow my instructions. This course is graded on accomplishment, not effort.

Scholarship. Whatever you do with the rest of your life, in this course you are acting as a mathematics scholar, grappling with ideas that are new and confusing to you. Thus, your natural state is confusion: the moment you understand something, you move on to the next topic. Progress is measured by being confused about different ideas over time. So, what do you do with a confusing definition or theorem or proof? First, you make sure you understand each word and symbol that appears in it. Then you try to think of explicit examples. For a definition, look for things that satisfy it, as well as for things that don't. For a theorem, look for an example that satisfies the hypothesis and see that it satisfies the conclusion, and then for some examples that don't satisfy the conclusion and see which hypotheses they fail. Similarly, to understand a proof, it is often helpful to go through it with a specific example in hand; a non-example that fails some of the hypotheses will make it easier to see where the proof needs those hypotheses, i.e. breaks without them. The best way to understand a proof is to completely forget it and then try to prove the result yourself; this is also the slowest way. The next step is to ask why this particular definition was chosen, or why the theorem was stated in this particular way. Varying a definition, you may find equivalent definitions, stupid definitions, or new interesting concepts. Varying a theorem, you will find many false statements, some true generalizations, and occasionally an entirely new result. This is what us mathematicians do when we aren't teaching.

Writing. Ideally, your solutions to homework problems should closely resemble the worked examples in our textbook. That means that they should consist of a few formulas and a lot of complete sentences! There are several reasons for this. Maybe so far, you have always been able to look at a math problem, think a little, and write down the correct answer. This will eventually stop working, and you will need to write down intermediate steps. Also, you will eventually have to work on problems you initially don't know how to solve, and writing down your initial ideas in a way you can understand in a day or two will become very important. Furthermore, on graded assignments, the grader who understands your reasoning and the source of your error will give you more credit than the grader who sees random symbols on a page (graders cannot read minds). Beyond the classroom, you will often need to communicate your computations to collaborators in writing, so learning to write about mathematics is as important as learning to do mathematics.

Cheating. Please don't. If you are writing down ideas somebody else told you and not mentioning this fact, you are cheating. If you are writing down words somebody told you, and you could not rewrite the solution in different words or explain it to another student in the class, you are cheating. Rules around exams are not arbitrary hurdles I place in your way. They are something like arms-control deals among the students in the course: you really don't want infinite-time open-everything take-home exams, because those require, well, infinite time and access to everything.

Letters. If you need a letter of reference of some sort, make sure to ask for it long long in advance: at least a month before any deadlines, and in any case no later than mid-November.