What are some affordable textbooks for learning math concepts for physics?

[AdvaitDhingra]

Hey guys,

so I was on this thread on tips for self studding physics as a high schooler with the aim to become a theoretical (quantum) physicist in the future. I myself am a 15 year old who wants to become a theoretical physicist in the future. A lot of people in the thread were saying that learning calculus and linear algebra, vectors etc. was a good way to prepare and self-study. A lot of people also recommended textbooks.

Now, my question is, what is a good textbook for learning the mathematical concepts helpful for physics that also won't set me back a couple hundred euros ? (yes, I'm from Europe)

Most of the recommendations in the linked thread were over a hundred euros, which is hard to convince my parents to buy.

Thank you in advance!

 

[fresh_42]

There is only one good recommendation for your age: learn all the mathematics, physics and chemistry you can get at school. As you said, you will need a good foundation in mathematics to start physics. It is taught in parallel at university, which is hard to do at home. To learn the calculus tools before you learn the basic steps at school could be problematic. The risks of learning it wrong, or doing it right and get bored at school are high. However, you have a fair chance to learn linear algebra, since it is not or only very basically taught at school.

It will be easy to find a good book about linear algebra. Prices vary from $€\,0$ for lecture notes or free books on the internet, to a few Euros for secondhand books or older editions, which is no problem since the subject hasn't changed in the last 200 years, or $€\,40-70$ for standard and new textbooks, e.g. Greub (Linear Algebra). But I would start with pdf from the internet before I'd buy a book. See first how it works. Plus I would look for books in your native language, such that you don't have to learn two things at once. The English necessary for reading scientific books comes along and automatically with your studies.

If you get stuck: come on over and check on our forums how to carry on, and to check whether you understood it correctly.

 

[AdvaitDhingra]

There is only one good recommendation for your age: learn all the mathematics, physics and chemistry you can get at school. As you said, you will need a good foundation in mathematics to start physics. It is taught in parallel at university, which is hard to do at home. To learn the calculus tools before you learn the basic steps at school could be problematic. The risks of learning it wrong, or doing it right and get bored at school are high. However, you have a fair chance to learn linear algebra, since it is not or only very basically taught at school.

It will be easy to find a good book about linear algebra. Prices vary from $€\,0$ for lecture notes or free books on the internet, to a few Euros for secondhand books or older editions, which is no problem since the subject hasn't changed in the last 200 years, or $€\,40-70$ for standard and new textbooks, e.g. Greub (Linear Algebra). But I would start with pdf from the internet before I'd buy a book. See first how it works. Plus I would look for books in your native language, such that you don't have to learn two things at once. The English necessary for reading scientific books come along and automatically with your studies.

If you get stuck: come on over and check on our forums how to carry on, and to check whether you understood it correctly.

Thank you for you advice!

 

[PeroK]

Hey guys,

so I was on this thread on tips for self studding physics as a high schooler with the aim to become a theoretical (quantum) physicist in the future. I myself am a 15 year old who wants to become a theoretical physicist in the future. A lot of people in the thread were saying that learning calculus and linear algebra, vectors etc. was a good way to prepare and self-study. A lot of people also recommended textbooks.

Now, my question is, what is a good textbook for learning the mathematical concepts helpful for physics that also won't set me back a couple hundred euros ? (yes, I'm from Europe)

Most of the recommendations in the linked thread were over a hundred euros, which is hard to convince my parents to buy.

Thank you in advance!

There are good free online resources these days. For example:

The UK A-Level mathematics syllabus is here:

https://www.examsolutions.net/

There's a comprehensive set of notes for all things calculus here:

https://tutorial.math.lamar.edu/

There's a good treatment of linear algebra here:

https://math.byu.edu/~klkuttle/Linearalgebra.pdf

If you don't get on with any of these, just look for something else.

 

[AdvaitDhingra]

There are good free online resources these days. For example:

The UK A-Level mathematics syllabus is here:

https://www.examsolutions.net/

There's a comprehensive set of notes for all things calculus here:

https://tutorial.math.lamar.edu/

There's a good treatment of linear algebra here:

https://math.byu.edu/~klkuttle/Linearalgebra.pdf

If you don't get on with any of these, just look for something else.

Thank you!

 

[Frabjous]

Are you on path to learn differential and integral class (or higher) in high school? If the answer is yes, then you are on the correct path. After this, in no particular order, generally come vector calculus, differential equations and linear algebra. The first two require calculus, so linear algebra is the choice if you want a head start.

(Edit: @fresh_42 makes a good point below)

If the answer is no, you will want to try and learn differential and integral calculus on your own so that you can take the calculus based physics your freshman year. Other than making sure that your reference is for scientists and engineers, the choice of book is not critical; i.e. find a cheap used textbook.

If you want a serious book that will expose you to the beauty of mathematics, try “What is Mathematics” by Courant and Robbins. This is not an easy book.

 

[fresh_42]

Are you on path to learn differential and integral class (or higher) in high school? If the answer is yes, then you are on the correct path. After this, in no particular order, generally come vector calculus, differential equations and linear algebra. The first two require calculus, so linear algebra is the choice if you want a head start.

This will do more harm than good in my opinion. If someone jumps into higher mathematics at age 15, then he will get frustrated, unless he is a genius. There is a reason university starts with calculus, linear algebra, and classical mechanics, namely to make the step from school to university as smooth as possible. Studying STEM fields isn't a sprint, it's a marathon. There are no shortcuts. And starting in the middle of that all is no good advice.

 

[AdvaitDhingra]

Are you on path to learn differential and integral class (or higher) in high school? If the answer is yes, then you are on the correct path. After this, in no particular order, generally come vector calculus, differential equations and linear algebra. The first two require calculus, so linear algebra is the choice if you want a head start.

(Edit: @fresh_42 makes a good point below)

If the answer is no, you will want to try and learn differential and integral calculus on your own so that you can take the calculus based physics your freshman year. Other than making sure that your reference is for scientists and engineers, the choice of book is not critical; i.e. find a cheap used textbook.

If you want a serious book that will expose you to the beauty of mathematics, try “What is Mathematics” by Courant and Robbins. This is not an easy book.

Yes, I have taken Maths as one of my main subjects. Thank you for your advice

 

[BvU]

https://www.physicsforums.com/threads/free-math-books.796225/
https://www.physicsforums.com/threads/free-physics-books.796223/

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