These suggestions are based on observations made while teaching Calculus I, II and III for many years.  They are very general suggestions and apply to most math and science courses.  

  • You'll probably find that the material in most university courses, including this one, is covered much faster than it would be in high school.  You'll probably also be asked to have a greater command of the material, especially in understanding the ideas (not just the computational techniques) and applying them in new situations. This may take some adjustment in your style of learning.

    • The instructor and TAs are here to help you understand and learn the material, but actually learning it is your responsibility. The lectures are designed to try to highlight the important ideas and to give you some perspective on the material. From there, you can digest the material as you read the text, think, discuss the material with other students, and practice on problems. You should expect that more learning will happen outside the classroom than inside. On the practical side, a typical WU student should expect to spend at least a couple of hours on calculus, reading and working problems, for every hour in the classroom.  If you do this for all your courses, then being a student is easily the equivalent of a full-time job.

  • Read the text. An instructor can't possibly say everything that's there. A 50-minute lecture would hardly be enough time just to read the day's assignment aloud, let alone try to highlight or clarify. Your instructor's job is to highlight and complement the text so that you can learn from it.  Simply relying on your lecture notes will (and should) only give you part of the picture. Ignoring the text is the path to minimal understanding of the material. 

  • Reading a math text takes time, focus, and active involvement.  You can't do it effectively if you're distracted every few minutes with text messages, etc.  Consider that you might spend a few hours reading a 100-page assignment in a literature or history course.  A 10-page reading assignment in mathematics might take just as much time.  Read it once quickly just for an overview.  Then read carefully with scratch paper at hand and fill in missing steps. If the author says  "...this simplifies to...", then take time to simplify it for yourself!  When he writes "you should check that...", then check it yourself!  Try to work some of the examples given in the text before you read the author's presentation of the solution.  Play with the material: ask yourself  "what if I changed the problem to...?" or "was there any information given in the problem that I really didn't need?".  Write down questions that come to mind.  If you can't answer them, ask your friends. Try to understand why statements in the text are true.  

    One of the marvelous features of mathematics is that you need not (perhaps should not!) trust the author.  If a physics book refers to an experimental result, it might be difficult or prohibitively expensive for you to do the experiment yourself.  If a history book describes some events, it might be highly impractical to find the original sources (which may be in a language you do not understand). But with mathematics, all is before you to verify.  Have a reasonable attitude of doubt as you read; demand of yourself to verify the material presented.  Mathematics is not so much about the truths it espouses but about how those truths are established. Be an active participant in the process. 

    E.R. Scheinerman, Mathematics, A Discrete Introduction, Brooks/Cole, Pacific Grove, CA, 2000, p. xviii-xix.                                       
  • Try the following:  if you get stuck during a reading assignment, go back to the beginning of the assignment and read again carefully.  Find the very first sentence in that reading that you don't understand.  Ask someone about it. Then continue in the same way.

  • Ideally, you should read ahead. The lectures will be much more valuable if you try to digest some of the material in advance.  Also, you'll know that some thing written on the board needn't be copied down.  For example, you'll know that those formulas the instructor is writing on the board are just the ones listed in the text. That frees you to think about what's being said and not be frantically transcribing material into a notebook.

  • If you choose to ignore the advice about reading ahead, then at least read the material in the text before you try  the assigned problems.  Some students start out with the problems and when they get stuck, they page back through the text looking for a formula or an example to help.  This puts the focus in the wrong place.  Simply being able to "do the problems" is at best a minimal strategy for the course. You do have to do problems, and you do want to have certain technical skills that the problems sets can help develop, but you also want to understand the material.  Carefully reading the text is essential for that.

  • You can't learn to speak French by merely sitting and listening, and you can't learn mathematics by watching someone else do problems. You need to be involved. Do as many problems as you can realistically find time to do: the more, the better. It's useful to spend part of your study time with other people as long as eveyone is an active player. Compare solutions to problems; ask each other questions; make up quizzes for each other; agree on some extra problems to try together--such as the review problems at the end of each chapter. Do whatever helps!  But all of this is to improve your understanding: your study group won't be there at quizzes, tests, or when you need your math in another course. 
  • There are some facts and formulas that you need to have at your fingertips: that is, there are some things you simply have to memorize. But that's only the beginning. Formulas are just tools and, admittedly, some assigned problems are nothing but "drill," designed to be sure you really can handle the tools.  But when attacking a non-routine problem, don't just hunt around for a formula. To quote an old but accurate text,

"(the) time wasters are the formula worshipers ... who spend more time hunting a magic formula than they would need to analyze the problem piece by piece using simple familiar methods and calculations ... it cannot be said too often that the ability to understand and solve problems does not come by memorizing formulas ... formulas are not substitutes for thought."   (F.C. Dana and L.R. Hillyard,  Engineering Problems Manual, 4th edition, New York: McGraw-Hill, 1947.)

  • Many problems on tests will be like problems you've seen before.  Others will be connected to problems you've seen but will be a bit different. This isn't grounds to complain that "we never saw a problem like that before."   If you can only do problems exactly like ones you've seen before, what's the point?  The purpose of problems is to help you understand the ideas and techniques, not merely to repeat solutions of more problems of exactly the same type.

  • Stay on top of things. I admit that it's hard to keep up with all the stuff you need to do, but it's important not to fall behind in the course.  A lot of the material we cover is interdependent, and if you're not comfortable with the material from two days ago, today's lecture might be totally incomprehensible.  It's better to be working a bit ahead -- then the lectures will be more helpful and you'll have a buffer when an emergency strikes.  Also, there's a limit to how fast you can digest material and learn to use it in your thinking.  Avoid cramming just before tests by staying on top of things.  It makes life much more pleasant.
  • Make use of your instructor and the TA in your discussion session. Office hours are set aside specifically to see students; those times are for you!  Most instructors are also willing to set up special meetings with students as time permits. Your responsibility is not to waste these times.  Try to solve your own problems first, together with your friends. What you learn that way will be more valuable than the same answer "given" by your instructor or TA.  

  • Bring up questions quickly, as soon as you realize there's some difficulty you can't resolve.  It's hard for any instructor to cope with  "I haven't understood anything for three weeks"-- we aren't magicians.

  • Use the Calculus Help Room, the residential peer mentors (RPM's) and other resources available at Cornerstone: The Learning Center.   Consider the opportunity (at the start of the semester) to join a Peer Led Team Learning (PLTL) group.

  • Use any supplementary material or examples that are linked with the daily syllabus. 
                 These words to the wise should be sufficient.  Best wishes as you enter the world of calculus!