- #1
sahilmm15
- 100
- 27
What are good books for learning about math? Not textbooks, but books that provide insight into mathematical phenomena.
Yeah, well ...sahilmm15 said:Not textbooks
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 said:Yeah, well ...
It's like wanting to read russian litterature without learning russian.
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 said:
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.mathwonk said: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=pfamazon01-20the same book with a new title: Undergraduate analysis:
https://www.amazon.com/dp/0387948414/?tag=pfamazon01-20In 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.
An introductory math textbook is designed to provide a foundational understanding of mathematical concepts and principles. It serves as a guide for students to gain insight into the subject and develop their problem-solving skills.
Introductory math textbooks typically cover topics such as basic arithmetic, algebra, geometry, and statistics. They may also include some advanced topics, depending on the level of the textbook.
Yes, there are different levels of introductory math textbooks. Some are designed for elementary or middle school students, while others are geared towards high school or college students. The level of difficulty and topics covered may vary depending on the intended audience.
Yes, an introductory math textbook can be used as a standalone resource. However, it is often recommended to supplement the textbook with practice problems, online resources, and teacher instruction to fully grasp the concepts and improve problem-solving skills.
When choosing an introductory math textbook, consider your level of understanding, the topics covered, and the style of the textbook. It is also helpful to read reviews and ask for recommendations from teachers or peers. Additionally, some publishers offer sample chapters or online resources to help you make an informed decision.