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When I was in my first semester of college, a professor gave me the best advice I could have ever gotten. I went to him confused about the material for College Algebra. I explained that his lectures were not helping me, nor was the book or online homework. He explained—in a nice way—that to be successful in college, the only person I could rely on to learn from is myself. In other words—If I am in a job and I cannot figure something out, who am I supposed to go to, to help me figure it out when the very reason I was hired was to figure it out?
ii. reading a textbook properly
The above title may sound odd, but there is a correct (subjective) way to read a math-based textbook.
First—most students do not like to open the textbook or read notes the professor has provided. Sure, you got through Algebra, Trigonometry, and Precalculus without opening a book. But now you are in actual Calculus and/or Physics and are wondering why you are doing so terribly in the course?
It should be immediately understood that math beyond Precalculus is only reiterations of what you have already learned or applications of what you have learned. It is like knowing the alphabet and sentence structure—now you must write paragraphs, stories, and so forth.
My point is that Calculus and higher courses are more related to English courses than math. You cannot solve any problem without knowing the words, their definitions, the theorems they are used in, and how to apply them. Everything else just boils down to basic algebraic arithmetic.
When you read the textbook, you should not read it like a novel or a history book, and you do not need to read every word. You must read the bold words and the [boxed] definitions and theorems. If you wish to read around that, it will only help you better understand—but it is not necessary. Then, you must work on every sample problem in your reading section. Let it digest, and then go back through it. This should be done long before the section(s) lecture.
If you do this, you will cut your study time by at least 50%, maybe even more, as you will quickly absorb the lecture.
iii. preparing for the first lecture
Let us assume you are just finishing summer vacation and the furthest thing from your mind is a desire to crack open a textbook covering a foreign subject. It is a dilemma. I know; I am guilty. I am not a saint; I only know the best route, and when I have taken this advice and observed my students take the advice, school becomes so much easier.
For example, assume you are taking Physics 1 or Mechanics in college or perhaps Calculus 1—Differential. The first week may or may not be a review of previous courses covering basic
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