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May 26th, 2012, 01:52 PM   #1
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Book Suggestions

Hi,

I was pretty good at maths in school. I then did an ungrad diploma in engineering (where I had subjects in applied mathematics), and then I went on to get a graduation in telecom engineering (where there was some more applied maths)... but then I dropped out before the final year to become a writer.

Been working as a writer for the past five years now, but recently I've been getting these hunger pangs for knowledge. And I realise how much I miss doing maths. I was pretty good at it before and I would like to get back to it.

I still remember how to solve certain algebraic equations, and I remember a few formulae like [d/dx (x^n) = n x^(n-1)], and sin 30 = 0.5 and so on and so forth. As an engineering student I learned Laplace transforms and Z transforms, but now I don't remember their relation to calculus.

Could I please get a book suggestion or a list of books and the order in which to attack them? I would like to start from the basics, as I have nearly forgotten most of the terms, like the other day I was scratching my head to remember what a 'factorial' meant, then a friend refreshed my memory and told me that n! = 1 x 2 x 3... x n.

This very forum is so vast that I don't know where to start. I wouldn't mind online lessons or e-Books, but I'd prefer to purchase books that are structured well, so that reading and solving the problems from first chapter to last is like sitting in the lecture hall of a great teacher. I would like to refresh my school maths in a week, and in the next three months refresh my high school maths, and then move on to something more complex. My other area of interest is physics, so I'd like to do maths in that direction.

Kindly help. Thanks.
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June 1st, 2012, 09:11 AM   #2
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Re: Book Suggestions

What you should do really depends on your end goal. Are you hoping to return to your old level computation as quickly as possible, or are you hoping to spend some real time on learning the underlying mathematical ideas which tend to be ignored unless one is trying to become a student of mathematics itself? Or are you just looking for a trip down memory lane where you would like to regain some familiarity with all those years of math you used to do? Perhaps your goal is something else entirely?

Perhaps the best way to get reacquainted with mathematics as you knew it before would be to pick up and peruse a calculus book (I would suggest the book by James Stewart, but just about any book would do). Remember that the more problems you work out for yourself, the more comfortable you will get with the material and the better your sense of what you know and what you have trouble with will be. As you come up to algebra concepts you don't remember, you should look them up. Sometimes calculus books have extensive and useful appendices which will explain much of the pre-calculus that you need; for other things I would recommend picking up an algebra review guide from a local bookstore (there are innumerable choices and any of them should be fine).
Calculus is a good place to start because it is central to a lot of mathematics so you need to know it well and it will get you practicing the basic algebra skills you need mastered. Starting your study at precalc will leave you bored out of your mind very quickly and starting beyond calculus will likely get very confusing quickly since the fundamental ideas underlying much of what you studied after calculus are found in calc.
Once you are reasonably comfortable with calculus (or getting bored), you should jump ahead to whatever else you want to relearn, returning to your calc book for clarification (or more work) when you get stuck. Without a better idea of where you want to end up, I can't really give recommendations for textbooks.

On the other hand, now that you have more time and a bit of perspective, you could opt to relearn this material from the ground up and try to learn the underlying ideas from a truly mathematical perspective. This is the more challenging route, but also the more rewarding for its own sake. If this were your goal, I would recommend starting with Lang's Basic Mathematics and progressing to an advanced calculus books, the standards being Apostol's Calculus (2 Volumes, start with the first) and Spivak's Calculus. These are challenging books and can keep you busy for a long time. Spivak's book is quite a bit cheaper but Apostol covers a lot of ground (especially across both volumes) including all of the standard material in single and multivariate calculus, linear algebra, (basic ordinary) differential equations, and probability. As with any math book written for math's sake, these texts are proof based and require thinking about the material far more carefully than "standard" introductory books.

Perhaps you would like to think about something completely new and different. Ian Stewart (not to be confused with the James Stewart I mentioned before) has written several books (mostly about pure mathematics) which may be worth reading. I recommend Concepts of Modern Mathematics.

Hopefully that at least gives you some ideas for places to start. You can always post questions that arise to this forum and someone will (probably) get back to you. If you clarify your goals, I may be able to give you some more directed advice. Best of luck.
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July 14th, 2012, 11:56 AM   #3
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Re: Book Suggestions

there is a really good resource of math information at http://mymathmanual.com/ this might help you.
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