Math & Physics Books for College Level: Recommendations

[computerperso]

So I have read both of the following books

Teach yourself physics
http://www.amazon.com/dp/1444103091/?tag=pfamazon01-20

complete mathematics
http://www.amazon.com/dp/1444105027/?tag=pfamazon01-20

Now I am not sure where to go from here. My goal is to have a firm understanding of physics and mathematics which is a little bit more than freshmen level. Am I ready to tackle the college physics and math books yet?

Also, is there any other math and physics books which go from GCSE to Foundation Degree Level?

And recommendations would be nice. Thank you for your time. xx

 

[micromass]

Judging from the concepts in the book, I don't think you're quite ready for college math yet. I think you should try out a more serious book.

I always like to recommend "basic mathematics" by Serge Lang. I adore this book because it contains everything one needs to know before starting calculus, and nothing more. I suggest you read this book, and after that you can start college math.

 

[qspeechc]

You can probably start studying physics that doesn't use calculus. I'm sorry but I don't know any good books like this, perhaps try an O- or A-level book. Ask around, or try the library and see what appeals to you. As a last resort try google or amazon.

I know that second book you linked covers geometry, but I suggest you take the time to learn the subject well. Try this book:
http://www.amazon.com/dp/0977985202/?tag=pfamazon01-20
You can read quite a bit of the book here:
http://www.sumizdat.org/
and check out the reviews on amazon.com:
https://www.amazon.com/dp/0977985202/?tag=pfamazon01-20

I guess you're probably not too enthusiastic about doing geometry again, but this book introduces you to the correct type of mathematical thinking, which will be very important later.

Then you can try an O-level or A-level maths book, depending on how much preparation you think you need. In my opinion you should start with an O-level book. Again, I can't really recommend a specific book, but you should follow the suggestions I gave for physics books.

On the other hand, if that feels like too much work, you can work through Schaum's Outline of Precalculus:
http://www.amazon.com/dp/0071508643/?tag=pfamazon01-20
The title exactly describes the contents: all the maths you need to know before you can do calculus.

At this point, after doing A-level mathematics or reading the pre-calculus book, if you want a overview of higher mathematics you can read Courant's What is Mathematics?:
http://www.amazon.com/dp/0195105192/?tag=pfamazon01-20

You've heard us talking a lot about calculus. That's because it's a very important topic to both mathematics and physics. This can be learned at two levels: rigorously and very mathematically, or less rigorous and more intuitively.
Of the former type, the most popular book is definitely Spivak's:
http://www.amazon.com/dp/0521867444/?tag=pfamazon01-20
I haven't read that book, but it comes highly recommended from many mathematicians and even students. The book I learned from and absolutely love is Courant and John, which also covers some nice applications to physics:
http://www.amazon.com/dp/354065058X/?tag=pfamazon01-20
Another well-know and excellent (from what I hear) book is Apostol:
http://www.amazon.com/dp/0471000051/?tag=pfamazon01-20
But I don't recommend it at that price.

Calculus that is not mathematically rigorous is covered in A-level maths books. Other books covering it are Stewart, Thomas, Lang, Strang (available for free online: http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/), and many, many others which are probably as good :
http://www.amazon.com/dp/0495383627/?tag=pfamazon01-20
http://www.amazon.com/dp/0321643631/?tag=pfamazon01-20
http://www.amazon.com/dp/0387962018/?tag=pfamazon01-20
http://www.amazon.com/dp/0980232740/?tag=pfamazon01-20
By no means should you think that because I chose to name these books that therefore they are the best; they are simply the ones I know by name.

It's not necessary to get the latest edition of these books, the cheapest copy you can find will do fine.

Again, I cannot recommend one over another. Have a look at some calculus books in the library, in a new or used bookshop, or ask around.

If you want to study further in mathematics you really must read one of those mathematically rigorous books I listed earlier.

After learning calculus, rigorously or not, you can start doing physics that uses calculus. For this I like Physics by Halliday and Resnick:
http://www.amazon.com/dp/0471024562/?tag=pfamazon01-20
NOT Fundamentals of Physics by Halliday, Resnick and Walker. Shop around for a cheap copy. Other books will probably do just as well, such as Young and Freedman:
http://www.amazon.com/dp/0321762193/?tag=pfamazon01-20
I haven't read it, but I know it is commonly used.

You may want to get a book to help you with the mathematics, such as Boas or Riley:
http://www.amazon.com/dp/0471044091/?tag=pfamazon01-20
http://www.amazon.com/dp/0521679710/?tag=pfamazon01-20
These cover not only the mathematics you need at this level, but for all undergrad physics (but not mathematics). They are not really meant to be studied from cover to cover; you should study the relevant chapters when you need to know the mathematics it covers to understand a physics book. But there is certainly no reason why you shouldn't read it cover to cover if you wish to.

You can look for used books here:
http://www.abebooks.co.uk/?cm_ven=Google&cm_cat=UBT&cm_pla=abebooks.uk&cm_ite=abebooks.uk

Those books should get you started in physics and mathematics, that is, approximately freshman-level (but not higher). After that you can study more topics and go more in-depths, but these books are the necessary beginning.


Good luck.

 

[Monster92]

You can probably start studying physics that doesn't use calculus. I'm sorry but I don't know any good books like this, perhaps try an O- or A-level book. Ask around, or try the library and see what appeals to you. As a last resort try google or amazon.

I know that second book you linked covers geometry, but I suggest you take the time to learn the subject well. Try this book:
http://www.amazon.com/dp/0977985202/?tag=pfamazon01-20
You can read quite a bit of the book here:
http://www.sumizdat.org/
and check out the reviews on amazon.com:
https://www.amazon.com/dp/0977985202/?tag=pfamazon01-20

I guess you're probably not too enthusiastic about doing geometry again, but this book introduces you to the correct type of mathematical thinking, which will be very important later.

Then you can try an O-level or A-level maths book, depending on how much preparation you think you need. In my opinion you should start with an O-level book. Again, I can't really recommend a specific book, but you should follow the suggestions I gave for physics books.

On the other hand, if that feels like too much work, you can work through Schaum's Outline of Precalculus:
http://www.amazon.com/dp/0071508643/?tag=pfamazon01-20
The title exactly describes the contents: all the maths you need to know before you can do calculus.

At this point, after doing A-level mathematics or reading the pre-calculus book, if you want a overview of higher mathematics you can read Courant's What is Mathematics?:
http://www.amazon.com/dp/0195105192/?tag=pfamazon01-20

You've heard us talking a lot about calculus. That's because it's a very important topic to both mathematics and physics. This can be learned at two levels: rigorously and very mathematically, or less rigorous and more intuitively.
Of the former type, the most popular book is definitely Spivak's:
http://www.amazon.com/dp/0521867444/?tag=pfamazon01-20
I haven't read that book, but it comes highly recommended from many mathematicians and even students. The book I learned from and absolutely love is Courant and John, which also covers some nice applications to physics:
http://www.amazon.com/dp/354065058X/?tag=pfamazon01-20
Another well-know and excellent (from what I hear) book is Apostol:
http://www.amazon.com/dp/0471000051/?tag=pfamazon01-20
But I don't recommend it at that price.

Calculus that is not mathematically rigorous is covered in A-level maths books. Other books covering it are Stewart, Thomas, Lang, Strang (available for free online: http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/), and many, many others which are probably as good :
http://www.amazon.com/dp/0495383627/?tag=pfamazon01-20
http://www.amazon.com/dp/0321643631/?tag=pfamazon01-20
http://www.amazon.com/dp/0387962018/?tag=pfamazon01-20
http://www.amazon.com/dp/0980232740/?tag=pfamazon01-20
By no means should you think that because I chose to name these books that therefore they are the best; they are simply the ones I know by name.

It's not necessary to get the latest edition of these books, the cheapest copy you can find will do fine.

Again, I cannot recommend one over another. Have a look at some calculus books in the library, in a new or used bookshop, or ask around.

If you want to study further in mathematics you really must read one of those mathematically rigorous books I listed earlier.

After learning calculus, rigorously or not, you can start doing physics that uses calculus. For this I like Physics by Halliday and Resnick:
http://www.amazon.com/dp/0471024562/?tag=pfamazon01-20
NOT Fundamentals of Physics by Halliday, Resnick and Walker. Shop around for a cheap copy. Other books will probably do just as well, such as Young and Freedman:
http://www.amazon.com/dp/0321762193/?tag=pfamazon01-20
I haven't read it, but I know it is commonly used.

You may want to get a book to help you with the mathematics, such as Boas or Riley:
http://www.amazon.com/dp/0471044091/?tag=pfamazon01-20
http://www.amazon.com/dp/0521679710/?tag=pfamazon01-20
These cover not only the mathematics you need at this level, but for all undergrad physics (but not mathematics). They are not really meant to be studied from cover to cover; you should study the relevant chapters when you need to know the mathematics it covers to understand a physics book. But there is certainly no reason why you shouldn't read it cover to cover if you wish to.

You can look for used books here:
http://www.abebooks.co.uk/?cm_ven=Google&cm_cat=UBT&cm_pla=abebooks.uk&cm_ite=abebooks.uk

Those books should get you started in physics and mathematics, that is, approximately freshman-level (but not higher). After that you can study more topics and go more in-depths, but these books are the necessary beginning.


Good luck.

Wow! Thank you so much for your recommendations this list should keep me occupied for quite some time :D. I'm going to continue to read basic physics books which are more algebra related and once I have advanced my maths skills accordingly buy the more advanced physics books, again I can't thank you enough.

 

[rezeew]

I highly recommend that you continue to explore and expand your knowledge in both physics and mathematics. Both subjects are crucial for understanding and explaining the world around us and are integral to many fields of science.

Based on the books you have mentioned, it seems that you have a strong foundation in both subjects. However, college-level courses can be more challenging and may require a deeper understanding of the concepts. I would suggest starting with introductory college-level textbooks in both physics and mathematics, and supplementing with additional resources such as online lectures, practice problems, and study guides.

Some recommended college-level textbooks for physics include "University Physics" by Young and Freedman and "Fundamentals of Physics" by Halliday, Resnick, and Walker. For mathematics, "Calculus: Early Transcendentals" by James Stewart and "Linear Algebra and Its Applications" by David Lay are popular choices.

In terms of transitioning from GCSE to Foundation Degree Level, I would recommend checking with your college or university for specific course requirements and recommended textbooks. Additionally, there are many online resources and study guides available for bridging the gap between these levels.

Overall, my recommendation would be to continue challenging yourself and seeking out additional resources to deepen your understanding of physics and mathematics. Good luck on your academic journey!