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Four Tips on How to Study and Learn This Course
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Here are four important suggestions I have on how you should approach learning this course. (1) Set yourself clear goals each week. For example, decide what lesson in my book you are going to study and attempt to master each week (I will also direct you each week in my tips as to what lesson you should study in order to prepare for a current assignment). If you have a goal, then you can devote the time to achieve the goal. Maybe you end up thoroughly learning the lesson in one day of study, and
you can reward yourself with a few days off from math. If the lesson is proving difficult to learn, you can parcel it out over a few days of study. It is better to take a break if the information is evaporating the minute you read it because you just can't think straight, than wasting another hour or two getting nowhere. Often, after a rest or diversion, something makes a lot more sense than it did initially. (2) Do not treat your hand-in assignments as "open book", and do not start working on them too soon. That is a ticket to disaster in this course. I suggest you don't even start working on your assignment until about three days before it is due. Prior to that, focus on
studying the appropriate lesson in my book. You can then supplement my lessons by studying the appropriate material from your class notes and textbook if you wish, trying to achieve a full understanding of the concepts. Treat your assignments as a test of your knowledge. Your goal is to be able to do 80% or more of an assignment without any assistance whatsoever. If you achieve this goal, you will build confidence. In addition, you will find you
often need no more than an hour or two to do the assignment. Students who, instead, decide to "learn" how to do the questions while working on the assignment will frequently spend 10 to 15 hours doing the assignments, and will actually learn very little. Instead, they have temporarily learned it just to get the assignment over with. A constant refrain I hear in this course is, "I don't get it. I was getting such good marks on my assignments, but I bombed the
exam." That is because students have never treated the assignments as tests of their knowledge and have papered over the cracks in their understanding.
Of course, if you are taking this course by classroom lecture rather than distance, you probably won't have hand-in assignments. That demands even more focus and commitment from you. Treat the homework I assign at the end of each lesson like a hand-in assignment. At first, you may need to look at my
solutions to help you understand how to solve the problems. Don't be satisfied with that. Once you think you understand a problem, come back to it the next day, and see if you are now capable of doing it without assistance. Again, your goal is to be able to do at least 80% of my homework problems without assistance in any given lesson.
(3) Make those index cards, I suggest on page 6 of my book! Make sure you follow my advice, putting every single integral you do in this course on an index card. Have the cards ready to go when you first do your homework, so that it takes just a moment to write the integral on the front of the card. On the back, make a short note telling you where to find
the answer if you get stuck. Do not put any information besides the integral on the front of the card! Don't even number the question. Leave that kind of stuff for the back. The key is to gradually amass hundreds of cards, ready to be shuffled. That way, you can test your ability to recognize what technique of integration is necessary to solve any randomly selected card. Students are frequently unaware how weak they are at that because, when they did their
homework originally, they knew what technique was necessary merely by the section the homework came from at the time. (4) Pick a day in the week that will be your Review Day and stick to it. On that day, go through all of your old assignments
(starting with the most recent and working backwards) and test yourself. Do you still know how to do the questions? Maybe even redo some of the questions if you think they will be a good workout. Obviously, if you don't remember how to do a question, go back and learn how. Also, go through my Practise Problems again, picking some questions to test yourself with. A good idea might be to circle particular questions (let's say at least 10) in each of my
Lessons that you found particularly interesting or challenging when you first studied that lesson. Then, each week when you do your review, test yourself on those questions again. If you review on a weekly basis, you will not have to cram in a bunch of info a couple of days before your exam. |
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