Introductory Math Textbooks for gaining insight into the subject

[sahilmm15]

What are good books for learning about math? Not textbooks, but books that provide insight into mathematical phenomena.

 

[BvU]

Not textbooks

Yeah, well ...
It's like wanting to read russian litterature without learning russian.

 

[sahilmm15]

Yeah, well ...
It's like wanting to read russian litterature without learning russian.

I got you! You can recommend some introductory textbooks which would just build my base for mathmatical concepts and thinking in algebra, geometry, number theory, calculus. Also to mention I am in high school.So you can recommend accordingly.Thanks!

 

[BvU]

I sympathize ! Long, long ago, I was bored with the simple math and exercises elementary school gave us. So I was given extra exercises that were more challenging. They required either a lot of elbow grease OR a spark of brightness to 'look through' them. I'm still grateful for them.
Later I had a similar problem with high school (grammar school) math. The teacher gave a me a book on boolean logic, also with lots of exercises. That way I learned a lot of stuff that was very useful later on at university.

You could ask a teacher too. Or browse through the books forum. Math is so broad that you really need to look around for something to your liking.

PS I find the

button in the books forum is clickable and filters the subject. Cool !
(But everyone under 60 would have found that already, I suppose )

 

[mpresic3]

These days, there are very few textbook selling brick and mortar bookstores. I used to spend my weekends on shopping sprees and have quite a library of textbooks and have been reading them throughout the years and they have made a physicist out of me.

On the other hand, Barnes and Noble, Half-price Books, Waldens, etc sell a number of books (not textbooks) in physics and math. If you want to learn about physics and math, any of these bookstores can provide good material. I like Ian Stewart's books and Nahin's books (are more mathematical, and even at the textbook level). You can almost always find a good science book there

 

[MidgetDwarf]

Edwin E.Moise : Geomery ( do not get elementary geometry from an advance standpoint, that's a college level book), Calculus.

The problem with Moise Geometry is that it lacks constructions. So maybe Kisselev: Planemetry would be a good supplement.

For logic/proof writing: Hammock: Book of Proofs

For Pre-Calculus: Serge Lang: Basic Mathematics.

Theres also a nice number theory book. Although a bit basic, its neat for what it is: Pommersheim: Number Theory. A lively Introduction. (I think this is the correct name). A bit pricey tho. But its very easy to read, problems not to difficult, and proofs are detailed. I like his approach. It has the student in mind.

but it all depends at what level math you are at. in the future, try to be a bit more specific, so that you get more replies, and quality of replies will increase.

 

[mathwonk]

I suggest this little number theory book.

https://www.amazon.com/dp/048646931X/?tag=pfamazon01-20

 

[MidgetDwarf]

I suggest this little number theory book.

https://www.amazon.com/dp/048646931X/?tag=pfamazon01-20

A bit off topic. But do you have a recommendation for multi-variable analysis? I took a class recently using Spivak: Calculus On Manifolds. It was a bit too dense for me, and I don't think I learned anything from that book. I was able to scrape a B- minus in the course ( I got lucky, since I studied a bit a bit of point set topology, so the initial chapter was review). However, after the Inverse function theorem, I was a bit lost.It is a good book, but not for me at this current time. I am reading Hubbard: Vector Calculus, Linear Algebra, and Differential Forms. Very readable for me, but was hoping for something with a bit more rigor, but less than Spivak. So that I may be able to master Spivak.

 

[mathwonk]

In the old days people liked Williamson Crowell and Trotter, and I liked the very rigorous Calc of several variables by Wendell Fleming. Lang's Analysis I is also good for many things. that was the title in about 1970, maybe has a new title now.

a used copy:
https://www.amazon.com/dp/0201041723/?tag=pfamazon01-20


the same book with a new title: Undergraduate analysis:
https://www.amazon.com/dp/0387948414/?tag=pfamazon01-20


In particular, I thought spivak's treatment of stokes theorem was useless, to me at least, in being very abstract and unenlightening. Lang's treatment for a rectangle on the other hand, at the end of his book, made it seem so obvious that I never worried about it again.

of course they are the same, just don't look it. I.e. on a rectangle, stokes theorem is just fubini (the spell checker wants this word to be "tubing") to reduce to the fundamental theorem of calculus in one variable. Then the more abstract version is just done by parametrizing a more abstract set by a map from a rectangle, and pulling the statement back to the rectangle. on a manifold one can arrange this setup by using a partition of unity, so just understanding it on a rectangle is the main idea.

 

[MidgetDwarf]

In the old days people liked Williamson Crowell and Trotter, and I liked the very rigorous Calc of several variables by Wendell Fleming. Lang's Analysis I is also good for many things. that was the title in about 1970, maybe has a new title now.

a used copy:
https://www.amazon.com/dp/0201041723/?tag=pfamazon01-20


the same book with a new title: Undergraduate analysis:
https://www.amazon.com/dp/0387948414/?tag=pfamazon01-20


In particular, I thought spivak's treatment of stokes theorem was useless, to me at least, in being very abstract and unenlightening. Lang's treatment for a rectangle on the other hand, at the end of his book, made it seem so obvious that I never worried about it again.

of course they are the same, just don't look it. I.e. on a rectangle, stokes theorem is just fubini (the spell checker wants this word to be "tubing") to reduce to the fundamental theorem of calculus in one variable. Then the more abstract version is just done by parametrizing a more abstract set by a map from a rectangle, and pulling the statement back to the rectangle. on a manifold one can arrange this setup by using a partition of unity, so just understanding it on a rectangle is the main idea.

Thank you once again. I received my copy three days ago. It is very illuminating. I wish my course would have been based on this book, instead of Spivak. To me, Spivak appears to be a Tour De Force to get Stokes Theorem with the minimum amount of things needed.