Learning on my own - recommendation?

[caharris]

I'm in 12th grade, getting ready to go into college to get my major in physics, getting ready to take the placement exams for my classes, and I'm sitting here thinking: Man my school gives really crappy math education. (The physics teacher is awesome, though.)

 

So this is the predicament I find myself in. I really don't want to take college algebra. For me, that's just unacceptable. While I have a really good understanding of algebra, my knowledge in trig suffered tremendously because of the terrible work ethic of my teacher. (We talked about polar coordinates for about three weeks longer than needed.)

 

So I'm looking for a good trig (and algebra, if you don't mind) review book. Nothing too detailed, because I kept all of my notes and understood it the first time. I just need something to keep on my bookshelf for refreshers.

But I would also like a good pre-calculus book, and most importantly a self-teaching calculus book. I have "Calculus Made Easy" by Silvanus P. Thompson on my Kindle (math books are terrible on the Kindle, by the way) which is good, and "Calculus for Dummies" which isn't bad. But I'm looking for something rigorous and comprehensive. I looked at the 'Master Math' series of books, but I don't know how good they are. I also thought about "Calculus: An Intuitive and Physical Approach" by Morris Kline to teach myself.

 

Are these books any good, and what books would you recommend?

 

Thank you for you time and help,

Chris

[ajb]

For learning basic mathematics required for physics and engineering I hear that Jenny Olive's book "Maths: A Student's Survival Guide" is good. It has full solutions and is designed for self-study. Also, it is meant to fill the gap between school and first year collage or university.

 

You can find Jenny Olive's website here.

 

Other books with a title like "mathematical methods for scientist and engineers" could also be useful to you.

[imatfaal]

Jenny Olives book is great for self-study as it includes a serious amount of self test questions with quite a lot of worked answers - once the test is mastered you can be fairly sure you have understood the lesson. I recently ran through it to stop my mind atrophying totally and to remind me of the maths I had forgotten since A levels. I would have thought any science degree would quickly go beyond the level in her book - but for prep before university it would be about right.

[caharris]

Sounds about right, then. Thank you guys for the help! If anything else comes to mind let me know, if you would please.

 

Edit: I looked at the book as a PDF, and it's exactly what I'm looking for. I will most certainly buy it. Thanks again!

Edited January 14, 2011 by caharris

[Blauwefox]

A lot of my students swear by

 

Engineering Mathematics by KA stroud

 

Don't let the "engineer" in the title throw you off, it is a good text book, with worked examples and practical application, as is the sequel

 

Advanced Engineering Mathematics also by KA stroud

 

The later editions of Stroud text books also include Foundation Math section which revisits school calculus and algebra.

 

 

I'm a bit more old skool, in which I prefer:

 

Mathematical methods for physical sciences -- Mary Boas

 

and

 

Advanced Engineering Mathematics -- Erwin Kreyszig

 

Yes, I'm a physicist

[DrRocket]

I'm in 12th grade, getting ready to go into college to get my major in physics, getting ready to take the placement exams for my classes, and I'm sitting here thinking: Man my school gives really crappy math education. (The physics teacher is awesome, though.)

 

So this is the predicament I find myself in. I really don't want to take college algebra. For me, that's just unacceptable. While I have a really good understanding of algebra, my knowledge in trig suffered tremendously because of the terrible work ethic of my teacher. (We talked about polar coordinates for about three weeks longer than needed.)

 

So I'm looking for a good trig (and algebra, if you don't mind) review book. Nothing too detailed, because I kept all of my notes and understood it the first time. I just need something to keep on my bookshelf for refreshers.

But I would also like a good pre-calculus book, and most importantly a self-teaching calculus book. I have "Calculus Made Easy" by Silvanus P. Thompson on my Kindle (math books are terrible on the Kindle, by the way) which is good, and "Calculus for Dummies" which isn't bad. But I'm looking for something rigorous and comprehensive. I looked at the 'Master Math' series of books, but I don't know how good they are. I also thought about "Calculus: An Intuitive and Physical Approach" by Morris Kline to teach myself.

 

Are these books any good, and what books would you recommend?

 

Thank you for you time and help,

Chris

 

Most calculus texts are awful. One exception is Michael Spivak's book. Believe it or not, you will have an advantage later on by learning your calculus at a university rather than in high school. I had a conversation on this very subject with a very senior engineering professor at MIT, and he was of the same opinion.

 

Teaching yourself calculus and learning it in high school exposes you to the risk of learning to bevfacile in manipulating symbols, but not understanding what they really mean. That is because they don't really tell you why calculus works in a calculus class. That comes in a class on real analysis. Your university instructor will understand real analysis. It is important that the instructor understands why calculus works even though you may not be exposed to proofs in the introductory classes. Any decent university mathematician can prove all of the basic theorems of calculus off the top of his head.

 

Despite recommendations for books like "Advanced Engineering Mathematics" or "Mathematical Methods for Physicists", I would avoid them until you have a solid understanding of calculus. Arfken's book is as good as any when you reach that stage, but you will likely use whatever text is required by your instructor at that time.

 

Kreyzig's "Advanced Engineering Mathematics" IMO is bloody awful -- and I taught from it. I also know one of the guys acknowledged in the autrhor's introduction -- he reviewed the draft for the publisher and recommended that the book not be published.

 

Once you get past calculus, find a copy of Spivak's Calculus on Manifolds. It is the best and most readable introduction to calculus of several variables available. It is quite thin as well, an altogether wonderful little book.

 

As far as trigonometry goes, any college algebra and trigonometry test should be fine. Do a search at Amazon or Alibris and find a good buy. They are pretty much interchangeable. If you have been exposed to the basic trigonometry functions and identities you will do fine. You may find that you understand trig better after having taken calculus.