College of Liberal Arts and Sciences

Department of Mathematics

Mathematics 120, section B

Calculus and Analytic Geometry, I

9-9:50 AM MWF

314 Altgeld Hall

Professor Daniel R. Grayson

Office: 357 Altgeld Hall

Phone: 3-6209

**Quick links:**

**Introduction:**

For those of you who are new on campus, welcome to the University and to college life! You have a straight A average so far at the University of Illinois, and I will try to help you keep it that way. For the rest of you, welcome back!

You can succeed in calculus, even though it is harder than the math courses you have had in high school. It might be twice as hard! Here is what you have to do.

You should study the book carefully and learn from it outside of class. It is well written and will reward close study. Plan on allotting at least an hour per day for this, starting from the first day. We love to answer questions about the material in the book, so if there is a sentence or paragraph that doesn't make sense to you, let us know (hopefully, using the news group) so we can help you out.The main thing is to start today! At the pace things happen in college, you don't want to procrastinate for even a week.

**Goal of the course:**

The chief difference between calculus and high school geometry is that we take the passage of time into account and use it as a tool. For example, we might try to measure the volume of a sphere by letting its radius shrink to zero and recording the rate at which the volume dissipates.

The fundamental laws of physics that govern the world tend to be expressed as differential equations. These equations encapsulate information about how each little bit of matter interacts with each other little bit. One of the applications of calculus is to pass from the fundamental laws to explicit formulas for the global behavior of particular systems.

In this course we take the first step toward understanding the role mathematics has to play in coordinating the basic laws of nature by learning about differentiation and integration of functions.

**Textbook:**

The textbook is "Calculus: Early Transcendentals", by Stewart, 3rd Edition. It's available in the book stores.

**Lectures:**

Lectures take place on Monday, Wednesday, and Friday at 9AM in 314 Altgeld Hall. In the lectures we will present to you the basic concepts and tools which you will need for learning the material and attacking the problems.

**Discussion leaders:**

Discussion sections take place on Tuesday and Thursday at 9 (the M sections) or 10 AM (the N sections). They have a maximum enrollment of 35, so this is the place where you can get practical help in executing the algorithms explained in lecture, and you can get answers to your questions about the material in the book or homework. Prepare for discussion by reading the material, reviewing your notes from lecture, and doing the homework.

The discussion leaders will have office hours, mark your homework, and spend time looking at the news group to answer questions that appear there.

Click on the links below to view your discussion leader's home page, to send email to your discussion leader, to find out where your discussion leader's office is, or to find out where the discussion room is, respectively.

**Our web page:**

Our web page (the one you are reading now) is located at https://faculty.math.illinois.edu/~dan/120b/.

You may use a web browser such as Netscape or Internet Explorer to take a look at it. Click on my name at the top if you want to learn more about me.

**Our news group:**

I've set up a news group called uiuc.class.math120b. Click on the link in the previous sentence to take a look at it. The professor, teaching assistants, and other students will be able to see it, and we will monitor the news group and try to answer your questions promptly.

If your newsreader needs to know the name of a news server, tell it to use "news.cso.uiuc.edu".

Don't be embarrassed about not knowing the answer to a problem. Just post your question and get the help you need to succeed!

Learn how to post articles to the news group. There are two ways, depending on whether you want to follow up on a topic in a message previously posted, or to initiate a new topic of discussion. If your followups are posted as such, it makes it a lot easier for readers of the news group to follow the various threads of discussion.

Here is a primitive but serviceable way to include mathematical formulas in email messages and articles in the news group. Use a caret (^) to indicate exponentiation, an underscore (_) to indicate a subscript, and an asterisk (*) to indicate multiplication. Thus "x^2" would mean "x squared", "x_3" would mean "x sub 3", and "x*y" would mean "x times y". Never use "x" as a "times" sign. Some formulas can often be rendered in a 2-dimensional form that looks like this:

2 2 (x + 2) = x + 4 x + 4 dy 2 -- = 2x if y = x dxSome of you may also wish to experiment with methods for including graphical images, but keep in mind that perhaps not everyone will be able to view them.

If you can't get netscape to work, you may have to configure some things on your computer. This will depend on your operating system, but your you need to tell it somehow what the IP addresses of the name servers are. Use the following numbers:

**Email:**

My email address is drg@uiuc.edu. Send me some introductory email telling me about yourself, once you get the hang of the email system here. I always reply to email.

If you have a question about a homework problem, I prefer it to be posted to the news group so my teaching assistants can answer it, and so the other students can benefit from the answer.

**Syllabus:**

We will cover chapters 0 through 6, omitting sections 0.3, 1.4, 4.6 and 6.3, and we will also cover sections 8.4 and 8.5.

**Homework:**

It is important to do the homework so you can learn the material and do well on the exams, which will draw material substantially from the homework. Since students often make mistakes on homework, we will assign homework, but we will not score it, and your performance on the homework will not enter directly into the computation of your grade.

Homework is collected every Tuesday and Thursday at the beginning of the discussion period, and is marked by your discussion leader. It may happen that more solutions are submitted than can be marked in the time allotted, in which case we will mark just some of them.

If you are confident that you have the right answer to a homework problem, then there is no particular reason to turn it in for marking.

One thing I especially like about the book is the sections called "Applications Plus" and "Problems Plus". The problems in these sections demand extra creativity and extra time spent thinking about it. Please don't get discouraged when you encounter a problem like this and you don't know the method for solving it immediately. We'll discuss problem solving techniques in class that ought to apply to this type of problem.

**Tricky problems:**

Some students complain that math courses contain tricky problems put there just to weed out the weaker students, and not for any useful pedagogical purpose.

This is not true. Doing homework problems is a lot like lifting weights - you have to do it a lot to get strong. We want you to be strong at solving problems and thinking about mathematics. You will enjoy it!

**Mathematical theory:**

Some students complain that there is too much emphasis on theory in math courses, and that math professors spend too much time explaining the ideas and not enough time teaching how to execute the algorithms.

If it were possible for you to live in this world and be successful at your chosen career by following a simple algorithm we would teach you that algorithm. Life today demands a broad set of adaptible skills, and a solid intellectual understanding of science and mathematics is one of them.

Think about those algorithms - do you want to spend all of your time studying to do something that computers can already do so well? Will that skill be valuable to your future employer? In real life, the problems aren't like homework problems. For example, suppose the problem you confront is to design a way of encoding sound on a CD to render it more resistant to scratches. Are you going to find the answer to that in a textbook? Or will you have developed ways of thinking about problems that will allow you to invent something new and better than what came before?

**Independent learning:**

Some students complain that they learned all the material from the course without help from the professor.

If you don't attend the lectures, I will assume that you are a good student who doesn't need my help to perform well on the exams.

We're here to help you if you need it, but if you don't need help, then that's great! You are an excellent student! I want to teach all of my students how to learn things by themselves.

**Multiple choice questions:**

Most, if not all, of the questions on the quizzes and exams will be multiple choice. There will typically be eight answers offered, only one of which is right. You will get 25%-33% of the credit for the problem if you leave your answer blank. (That might be 3 points out of 10, or 2 points out of 8, for example.) This will help those students who can't get the answer, as well as those who get the wrong answer and know it.

In the unlikely event that none of the answers offered on a multiple choice question turns out to be right, then full credit will be awarded for leaving the answer blank. Be prepared!

Some students complain that with multiple choice questions you don't get credit for effort. Our goal in this course is different - we want to train you for success, not for failure! Do you think your future employer will give you partial credit when you manage to give the astronauts on the space station 80% of the oxygen they need?

You should bring #2 pencils to the quizzes and exams for entering your answers on the answer sheet.

**Quizzes:**

Pop quizzes will be given approximately once a week, on material covered previously in the homework.

New [9/17/97]: If you miss a quiz, we'll count the next quiz double.

**Exams:**

There will be 5 hour exams and a 3 hour final exam, on the following dates. We intend the exams to be mostly multiple choice and perhaps graded by machine.

**Grading policy:**

We will use a scoring scheme where 90% or better is an A, 80-90% is a B, 70-80% is a C, 60-70% is a D, and 0-60% is an F. We will average your scores so that

If some calamity that may affect your performance befalls you or your family during the semester, let me know about it right away.

**Appeals about scoring:**

You are welcome to appeal a score which you think was assigned incorrectly. We try our best to score correctly.

**Scores:**

We intend to use the Campus Grade Book to record the grades. You will be able to use your network ID and password with a web browser to view your scores, once it's all set up. We'll post the details on the web page.

**My schedule:**

You may come to my office at 11 on Mondays, 12 on Wednesdays, or 1 on Fridays for help, except for the days I'll be out of town (see below).

On October 24 I'll be organizing a session on K-theory and Motives at a mathematics conference in Milwaukee. The last week of class and the first part of exam week I will be in Japan attending a Computational Commutative Algebra Conference in Kyoto, and a Workshop on Mathematical Software in Kobe. I will provide a suitable replacement for me on those occasions.

**Free Tutoring:**

Free Tutoring by Tau Beta Pi Engineering Honor Society starts on Monday the 29th of September!

Tutoring times: Monday: 1-5pm; Tuesday: 1-5 & 7-9 pm; Wednesday: 1-5 pm; Thursday: 1-5 & 7-9 pm; Friday: 1-3 pm.

Place: 306H Engineering Hall