1. Approaching The Subject Matter

Calculus is one of the great achievements of the human intellect. It's fundamentals were discovered by Newton and Leibniz in the 1660's through 1680's - long before computers, before calculators, before electricity. It is beautiful and powerful; it has shaped the world we live in and made possible much of our technological advancement. Approach it with the knowledge that it is a very special subject.

2. High School Is Not College

Some of the study methods which worked in high school will not work at Cornell University - and certainly not in your mathematics courses. In particular, you cannot learn everything in class from your teacher. The teachers in Mathematics 111 are specially chosen and are of a very high quality. But the pace of the course is such that the teacher is only a guide on your journey. It is your journey.  Therefore,
 

a) You have to read the text.  The pace is too fast and the material is too deep for your teacher to tell you everything you need to learn. Your time in the classroom is assumed by a college teacher to be only a small part of the time you spend on the course. (Incidentally, "reading the text" does not mean just trying the homework problems and then checking back for examples when you get stuck. This will not give the depth of understanding to earn more than a mediocre grade. It means reading the entire exposition and carefully following the motivation and line of reasoning presented.)

b) Falling behind can be disastrous. Do some work on the course every day.  Consult the course schedule, and read about what will be happening in the next class, so that attending that class will be useful. And work on the week's homework assignment from the start of the week. Do not get into a situation where you have to cram for an exam. The single most helpful thing before an exam is a good night's sleep.

It is extremely common (despite warnings like this) for students who have had some calculus before to coast along (under the pressure of other courses) thinking "yeah, yeah, I know that" and not to do the daily detail work required. Then at some point they find that the ground under them has slipped away. They discover that the level and depth at which they are expected to understand things is different than it was in high school. The course has irretrievably passed them by and they must settle for a grade and a quality of understanding which is lower than they had hoped.

3. Asking For Help

Cornell students are here because they have been very successful in the past. Often they have gotten where they are because they are extremely independent. Such independence is invaluable, but in a new and more competitive environment it must include an awareness of when one is in trouble and the strength to ask for help.

First, try intensely to understand the material or do the homework yourself. Then, if you find you are having trouble, consider using the following sources of help:

a) Your instructor:  Ask questions in class and go to office hours. Don't worry that you might "look stupid."  If you already knew the material you wouldn't have to take the course. What a teacher looks for are students who are alive enough and care enough to ask honest questions.

a) Your teaching assistant:  There will be a TA assigned to Math 111, and he will hold his own office hours. His hours may be at a more convenient time, or he may be able to provide a different perspective on the material.

c) Your fellow students:  Talking about mathematics is a very important step towards understanding it. When students work together they should take turns explaining the material to each other, or, once A explains it, B should explain it back. It doesn't work well if one student talks and the others listen passively. If you find that you're not getting a fair share of the talking time, then the group study is not empowering you effectively.

d) The Mathematics Library:  Located on the fourth floor of Malott Hall, the Mathematics Library has a large number of calculus books. When you need another way of looking at a topic or more examples, you might wish to check this out.

4.  Is Mathematics 111 the Right Course For You?

Although we think Mathematics 111 is great, it is in fact not the best course for everyone to take. Even if you should take it, now might not be the best time.

a) Sometimes students don't understand what else is offered and think that calculus is the only "real" college mathematics. This is false.  Other worthwhile Freshman Courses offered by the Mathematics Department are Mathematics 103, 105, 106, 121, 150 and 171. These are all bona fide college mathematics courses with serious purposes.

b) Sometimes students hope to eventually go to medical school and they think that only Mathematics 111-112 will make this possible. This is false.  The sequence Mathematics 105-106, Finite Mathematics and Calculus for Biologists, is an excellent sequence. All but extremely few medical schools will accept a year of college mathematics which includes a semester of calculus. Math 106 gives a good introduction to calculus (a little bit easier than Math 111, with more biological examples) and Math 105 gives topics outside of calculus which are of great importance to biologists. [Math 105 is taught in the Fall and Math 106 is taught in the Spring semester.]

c) Sometimes students going into science think that they have to take mathematics, biology and chemistry in their first year. Some colleges or majors require this. However,  in our opinion (not everyone agrees), it is usually unwise for a Freshman who has never taken a Cornell science course to take these three courses simultaneously. On the one hand, the pace and depth of all three at the same time can cause great problems to the inexperienced college student. On the other hand, many students who expect to major in science end up doing otherwise, and it is very valuable to have an extra course slot to explore other interests and possible majors. Whether only two of these courses (mathematics, biology, chemistry) should be taken, and which ones, are questions to consider and discuss with your faculty advisor, teachers, parents and friends. Math 111 is also taught in the Spring, and you can wait till then to start calculus.