How to consolidate one's knowledge of pre-calculus

In summary, Mépris is looking for advice on how to proceed with pre-calculus. She is unsure of where to start, has little time, and is unsure if structured learning is the best approach. She recommends going through college exams with explanations, getting books from the college, and self-study. Additionally, she recommends picking up a few calculus books and referencing Lang, Burnside, Crystal, and Allendoerfer.
  • #1
Mépris
850
11
Over the holidays (very long ones), I intend on going through the two Calculus volumes of Apostol. However, I feel my pre-calc knowledge of math is very shaky. There's lots of little tricks I just can't see. I'm not saying I can't do harder problems, just that they're not very obvious to me.

Take this problem for instance: http://www.khanacademy.org/video/iit-jee-hairy-trig-and-algebra--part-1?playlist=IIT+JEE+Questions
At first look, I have no clue what's going. After poking around for a few minutes, I could have gotten a little further but I would have taken a longer route to square that polynomial. With a little push, I would have gotten somewhere. That's just *one* example of an exercise that I have trouble with.

Like a recent poster in the "who wants to be a mathematician?" thread, I feel like I am very, very late and I want to sort this out asap. I don't know where to begin though. I also don't have *that* much time, so my learning will have to be somewhat structured. Initially, I thought a fun way to go about this would be going through every Math Olympiad problem I come across, then moving on to the JEE questions but that seems a tad haphazard and I'm not certain if that is the most appropriate way to proceed.

Any suggestions?
 
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  • #2
Hi Mépris! :smile:

My recommendation (it's a little "out there"):
Visit college, pick up a couple of books that they're using, get a couple of exams with explanations (you can get those from any senior student, who's usually willing to help), and get to it!
 
  • #3
I'm wondering the same thing. I'm about to enter calculus and I want to have a very strong background in the topics before calculus (I was very lazy in high school). Someone recommended Lang's Basic Mathematics book so I'm hoping that covers all the bases, but other recommendations would be great.


Edit: I just found this post in the books subforum that may be useful...


sponsoredwalk said:
Since you asked the WHY question.

Woods: Analytic Geometry & Calculus,
The first 130 pages have plenty of early 20th century style pre-calculus to shake you up.

Burnside: Theory of Equations,
Will (most likely) explain a lot of the things from your algebra classes & way more.

Chrystal: Algebra,
Will (most likely) explain a lot of the things from your algebra classes & way more.

Allendoerfer: Principles of Mathematics,
The ultimate pre-calculus book, including some calculus, more on this book http://myrtlehocklemeier.blogspot.com/2008/02/tater-says-that-cletus-knows-him-some.html.

Serge Lang: Basic Mathematics,
offers a slightly different perspective, often times better.

These books, either all of them (recommended) or some combination (at least 3) will
more than prepare you for the best calculus books I know of: Courant, Apostol & Spivak.
A bit of self-study with this discrete math book before reading those tough
calculus books would be immensely helpful as well.

All this said, you could just pick up Kline's calculus book read as far as you can if all you
want to do is read calculus stuff, from personal experience I can tell you that every time
you're going to get stuck or not be able to predict ahead of time where things are going
is only because you're missing some knowledge contained in one of the above books, so
you could also just use the above as references for when you get stuck.
 
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Related to How to consolidate one's knowledge of pre-calculus

1. How do I review and consolidate my knowledge of pre-calculus?

To consolidate your knowledge of pre-calculus, it is recommended to start by reviewing the key concepts and formulas. Then, practice solving different types of problems and exercises to reinforce your understanding. You can also use study guides, online resources, and practice tests to supplement your review.

2. What are some effective study techniques for consolidating pre-calculus knowledge?

Some effective study techniques for consolidating pre-calculus knowledge include creating flashcards, making study notes, teaching the concepts to someone else, and solving practice problems. It is also helpful to break down the material into smaller chunks and review them regularly rather than trying to cram everything in one sitting.

3. How can I improve my understanding of pre-calculus topics that I struggle with?

If you are struggling with certain pre-calculus topics, try seeking help from a tutor or teacher. They can provide one-on-one guidance and explain the concepts in a way that makes sense to you. You can also join study groups or online forums to discuss difficult topics with peers and learn from each other.

4. Is it important to review previous material before moving on to new pre-calculus topics?

Yes, it is important to review previous material before moving on to new pre-calculus topics. Pre-calculus builds upon previously learned concepts, so it is crucial to have a solid understanding of the foundation before moving on. Not reviewing previous material can lead to confusion and difficulties in understanding new topics.

5. How can I apply my pre-calculus knowledge to real-life situations?

Pre-calculus concepts are used in various fields such as engineering, physics, economics, and statistics. To apply your pre-calculus knowledge to real-life situations, look for examples and scenarios where these concepts are used. You can also try solving real-world problems and applications to see how pre-calculus can be applied in practical situations.

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