Clear mathematics books from A to Z ?

[Kuriza23]

Hi ! I've been reading on here for a long time through google and decided to join !

I started learning physics material mostly through general layman books from Hawking,Greene,Asimov etc and while I do not aim to become a physicist in occupation (luckily for physics), I do want to progress to a more proof-based level of physics rather than just thought-based which is very practical but lacks the PUNCH of mathematics.. I often find myself think after reading something important "this is very nice but how the HELL did he come up with that ? "

I have not touched mathematics since my SAT's ,,
I understand you can't put calculus,geometry,algebra,statistics, probability etc in one book,
so, considering that I have limited budget and these are probably expensive books, what "bundle" can I add to my amazon cart that would allow me to get a great level of the math needed for basics physics ?
Again, my current level is low.

Thank you very much 1

 

[micromass]

There are many books out there which are very cheap or even free! For example, you could look at lecture notes at universities. Free materials are likely to be less good than actual textbooks though.

As for free material, you can always look at:
http://www.khanacademy.org/
http://tutorial.math.lamar.edu/
(warning: do not use the previous two links as your only source but rather as a secondary source! In mathematics it is crucial to make as many exercises as possible. Just watching khan academy videos is not sufficient, but it can be a huge help)
http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/
http://www.matrixanalysis.com/DownloadChapters.html
http://hbpms.blogspot.be/2008/05/stage-1-introductory-calculus.html

Some nice cheap books:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20

 

[Kuriza23]

VERY NICE ! Bookmarked !
So I take it CALCULUS is most important when dealing with the basic level ?

Do I need special Geometry and Algebra books for now ?

 

[micromass]

VERY NICE ! Bookmarked !
So I take it CALCULUS is most important when dealing with the basic level ?

Do I need special Geometry and Algebra books for now ?

Geometry and algebra are very important. They're even more important than calculus (because if you don't know algebra, then it will be impossible to do calculus). However, you probably learned all the relevant stuff in high school. You can always take your old high school books and relearn you stuff. Additionally, there is good free stuff online on algebra, trig and geometry, for example: http://hbpms.blogspot.be/2008/05/stage-1-elementary-stuff.html

A very good book on algebra, trig and geometry is: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20
You can apparently get a used copy for $30 on amazon, and probably cheaper elsewhere. In any case, it is cheaper and better than most or all $200 textbooks out there (like the awful books by Stewart).

 

[rezeew]

Hello and welcome to our community! It's great to hear that you are interested in advancing your knowledge in physics and mathematics. I can definitely understand your frustration with wanting to know the foundations behind the concepts you are learning.

First of all, I would highly recommend starting with a solid foundation in mathematics before diving into more advanced physics concepts. This will not only help you understand the mathematical principles behind physics, but it will also make it easier for you to grasp more complex topics in the future.

To answer your question about finding a "bundle" of books, I would suggest starting with a comprehensive textbook on calculus, such as "Calculus: Early Transcendentals" by James Stewart. This will cover the basics of calculus, which is essential for understanding many physics concepts.

Next, I would recommend a textbook on linear algebra, as it is also an important mathematical tool in physics. "Linear Algebra and Its Applications" by David C. Lay is a good choice for beginners.

If you are interested in learning more about statistics and probability, I would suggest "Introduction to Probability" by Joseph K. Blitzstein and Jessica Hwang. This will give you a solid foundation in these areas, which are also important in physics.

Lastly, you may want to invest in a book specifically on mathematical methods for physicists, such as "Mathematical Methods for Physicists" by George B. Arfken and Hans J. Weber. This book will cover a wide range of mathematical topics that are relevant to physics.

I understand that these books may be expensive, but they are valuable investments in your education. You can also try looking for used copies or e-books to save some money.

Overall, I believe that with these resources, you will have a strong foundation in mathematics that will greatly enhance your understanding of physics. Good luck on your learning journey!