What are some good math books for beginners?

[Ryoukomaru]

Well I ll have some free time soon, like 2 months and i won't to learn some math.
I want to books on Calculus, 2D & 3D Vectors + Tensors. I also want to learn about Conic Sections but i don't know in which filed it is. 2D geometry ?
Anyway if you know some good books, I would welcome any advice !

 

[Ryoukomaru]

ahh wait, there is a section for books

 

[Chrono]

But he wants math books.

 

[hypermorphism]

Well I ll have some free time soon, like 2 months and i won't to learn some math.
I want to books on Calculus, 2D & 3D Vectors + Tensors. I also want to learn about Conic Sections but i don't know in which filed it is. 2D geometry ?
Anyway if you know some good books, I would welcome any advice !

How much calculus do you know ? If you're new to calculus, I recommend Courant. If you've been exposed to multivariable calculus, I recommend Spivak's Calculus on Manifolds.
Edit: A broad introduction to multivariable calculus can be found in the very readable textbook "Vector Calculus, Linear Algebra, and Differential Forms (A Unified Approach)" by Hubbard and Hubbard. It has a lot of practical problems and applications to avoid the the lull of increasing abstraction with little computation.
Before going to multivariable calculus or anything to do with general tensors, I recommend a solid grounding in linear algebra. Try "Linear Algebra Done Right" by Sheldon Axler.
Tensors are best studied as part of differential geometry. Only after having mastered linear algebra should you proceed to multivariable calculus and differential geometry. A good start for DG is Spivak's Calculus on Manifolds followed by his "Comprehensive Introduction to Differential Geometry". You will want to know ODEs and PDEs (ordinary and partial differential equations) as well. Get some Dover books on those (very inexpensive).
Darling's "Differential Forms and Connections" is a good companion for a course in DG, but should not be used by itself. A short intro to mechanical manipulation of tensors can be had by using Schaum's Outline of tensor calculus.
There are a myriad of topics associated with the above, such as group theory, topology, modern algebra, and such, but you'll probably find those on your own. :)

 

[da_willem]

Well I ll have some free time soon, like 2 months and i won't to learn some math.
I want to books on Calculus, 2D & 3D Vectors + Tensors. I also want to learn about Conic Sections but i don't know in which filed it is. 2D geometry ?
Anyway if you know some good books, I would welcome any advice !

For calculus vector fields and multivariable caculus the standard introductory studybook is (at least here in Delft) Calculus by Stewart.

 

[fourier jr]

how about the one by edwards & penney
http://cwx.prenhall.com/bookbind/pubbooks/edwards/

 

[mathwonk]

stewart and edwards penney are cookbook, courant and spivak are for people who want to understand something.

 

[JasonRox]

stewart and edwards penney are cookbook, courant and spivak are for people who want to understand something.

True.

It's sad to say that math majors at my school aren't interested in learning something, so we are stuck with Stewart.

I own Spivak, but I'm reading through a text on Analysis and Number Theory for now.

Spivak actually makes you think where Stewart makes you annoyed of the same damn problems over and over again.

 

[Gecko]

i've been using Anton's Calculus and Analytic Geometry text, and its been working great for me, even though I am not quite at the proper requirements for calc (i only took trig for a month through self study, so i didnt learn it in its entirety, plus, i wouldn't half trust the book i was using) I've managed to make it up to definite integrals with no teachers aid. I am pretty sure its a fairly basic text however, but it's been working great for me.

 

[Eratosthenes]

Ebay usually has plenty of cheap books. I'd get a book on trigonometry, algebra, geometry, and pre-calculus. The one on algebra or pre-calculus will most likely have the conic sections. Do all the problems and keep them organized. They should keep you busy for a while. It's more than what you need, and very inexpensive. If you get stuck, there are tons of good websites that can help, the forums, and even IRC if you use that.

As for calculus, stewarts is really popular, and it's the one most universities use. The downside is that it's very expensive, but you can get an older version for very cheap on ebay.

Spivak is good, but you will get stuck, and you might lose interest because of it, so it's probably better to learn all that other stuff really good first. Also spivaks is expensive, you can get a dozen books on ebay for what it will cost you to get spivaks. It's definitely worth buying, I bought it, but not at this stage of the game. Goodluck.

 

[Chrono]

Ebay usually has plenty of cheap books. I'd get a book on trigonometry, algebra, geometry, and pre-calculus. The one on algebra or pre-calculus will most likely have the conic sections. Do all the problems and keep them organized. They should keep you busy for a while. It's more than what you need, and very inexpensive. If you get stuck, there are tons of good websites that can help, the forums, and even IRC if you use that

I agree. It's probably best to get a good foundation in algebra, geometry, and all that fun stuff because you're going to use it quite a bit in calculus.

 

[Ryoukomaru]

Thank you for all your advices. I will have to read a lot of reviews and find out what i really need before buying a book.

Btw, anyone heard of Tom Apostol ? Is his books any good ?

 

[daster]

I use Apostol, and I like it very much.

 

[mathwonk]

the top books are apostol, spivak, and courant. they are also expensive. but i used courant and john, a second version of courant last fall and found a lot of reasonable priced used copies for my class.


Anton is another cookbook. If you want a cookbook, and better than most, the classic is thomas, and it has gone through so many editions that surely some old ones are out there cheaply.

i still like calculus made easy, by silvanus p. thompson, also pretty cheap.

 

[mathwonk]

here is a copy of apostol for 40 bucks that someone is bragging was "never read".

Calculus : One-Variable Calculus with an Introduction to Linear Algebra (Vol. 1) (Calculus Ser., Vol. 1) (ISBN:0471000051)
Apostol, Tom M.
Price: US$ 40.00 [Convert Currency]
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Book Description: Hoboken, NJ, U.S.A.: John Wiley & Sons, Incorporated, 1967. SOFTCOVER-Like New, International Softcover Version-Printed Overseas for Asia in English-Word for Word the Same, Printed in Black and White, 2nd Edition No Highlights, No Marks, Never Read, Never Used. Bookseller Inventory #893876326583876

Bookseller: Word Nerd Inc. (Plainview, NY, U.S.A.)


and here is a 40 dollar spivak:


Calculus 3ed (ISBN:0914098896)
Spivak, Michael
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Book Description: PUBLISH OR PERISH INC. 3 HARDCOVER ISBN: 0914098896 Textbooks. SALE, Standard. Bookseller Inventory #17091409889611

Bookseller: Powell's Books (Portland, OR, U.S.A.)


sylnauvs p thompson for under 5 bucks:

Calculus Made Easy 3ed (ISBN:0312114109)
Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus
Thompson, Silvanus P
Price: US$ 4.50 [Convert Currency]
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Book Description: ST MARTINS PRESS @. 1987 MASS MARKET ISBN: 0312114109 Mathematics-Calculus. USED, Standard. Bookseller Inventory #04031211410901

Bookseller: Powell's Books (Portland, OR, U.S.A.)

and the find of all: courant for 10 bucks!


Introduction to Calculus and Analysis
Courant, Richard
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Book Description: New York: Interscience Publishers, 1965. Hard Cover. Good. 23.5 cm. Showing wear to cover; writing on inside cover; pages slightly warped. Bookseller Inventory #004364

Bookseller: Mount Angel Abbey Library (St. Benedict, OR, U.S.A.)

need i say more?

another great deal: Thomas for 2 dollars!


ELEMENTS OF CALCULUS AND ANALYTICAL GEOMETRY.
Thomas, George B.:
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Book Description: Menlo Park: Addison-Wesley: 1967 - revised edition. 8vo (8.25" x 5.5"); pict. cloth; pp. xii, 692; pencilled note on eps. Good. Bookseller Inventory #1574

Bookseller: Ronald Hanko Books (Lynden, WA, U.S.A.)


here is anothere xcellent book, offereed used for up to 100 dollars, but available new for 38 dollars:

Calculus: The Elements
Michael Comenetz

Format: Paperback
Pub. Date: November 2002


FROM THE CRITICS

"Unlike any other calculus book I have seen...A scholarly, meticulously written explanation of calculus for the intelligent person who wants to understand the subject...Not only more intuitive in its approach to calculus, but also more logically rigorous in its discussion of the theoretical side than is usual...The style of exposition is well chosen to guide the serious beginner...A course based on it would in my opinion definitely have a much greater chance of producing students who understand the structure, uses, and arguments of calculus, than is usually the case...Many recent and popular works on the topic will appear intellectually sterile after exposure to this one."


at these prices no one need go without an adequate calc book.

these books are not written by people trying to make a million bucks, but by people who actually understand calculus and are trying to teach you to do so as well. thompson and thomas were engineers and the others are or were research mathematicians of some accomplishment.


here is a lovely book, hard to find. i do not know who the authors are, but the book is well thought out, well motivated, and well written. I was one of the original reviewers back when I did not understand the game of "i'll scratch your back if you scratch mine", and i stupidly criticized it for some minor mathematical errors. the publisher never changed them because they really only wanted praise from me, not criticism. they offered me two free books for my review and just assumed i would only say nice things. i thought they actually wanted to improve the book. but it is a good book because the authors care about making it interesting to the student.

i still recall the beautiful example of buffon's needle problem they use to motivate integration. i.e. if you throw a stick on the sidewalk, what is the likelihood it hits a crack in the sidewalk?

 

[Ryoukomaru]

Well, I recently learned that my cousin who graduated several years ago has Tom Apostols books ( Vol 1+2). Do you think it is wise to start with them ? Should I first start with so called "cookbooks" ? I am in 12th grade right now and I am thinking Aposol might be a little hard without a teacher. But time is no prob for me. I am willing to devote lots of time to this and if it is going to pay off at the end, I can even start this weekend coz I have a week break. You see, I don't want to start a book which is too hard for me to understand yet.

Any feedback is most welcome and appreciated.

Sorry for reviving a long dead thread but I didnt want to pollute forum by starting a new one. :)

 

[mathwonk]

you are wasting time "dancing around the fire". Go get a book and try to read it. If it is too hard, your face won't break out or anything. Just get an easier one. It takes courage to learn math.

 

[Ryoukomaru]

Excuse me but i m not wasting any time here because I don't have "time" to waste. I have been busy having exams for the last few weeks and even if I wanted I wouldn't be able to start a book. I would appreciate it if you didnt jump to conclusions without having sufficient knowledge about the topic.

It is not like I am afraid to start a book, I just want to use the little time I have before the end of years exams efficiently, that's all.

 

[JasonRox]

I would go and borrow your cousin's books.

 

[mathwonk]

the following two sentences of yours seem not to be true.

"You see, I don't want to start a book which is too hard for me to understand yet.

Any feedback is most welcome and appreciated."

I am not busting your chops, I am speaking from 40 years teaching experience. but ignore it if you wish, that is your prerogative.


But to be honest, you are right, I do not know you that well, so i am being rude. My apologies.