Reddit mentions: The best mathematics reference books

If you're genuinely interested in learning quantum physics, the first thing I would start off with is learning multivariable calculus and differential equations. You can find lots of resources online, and it is absolutely crucial to have a solid background in math before you begin studying physics.

So following that, I would just learn basic physics using the calculus that you've learned. You can also find these resources online-- a detailed high school physics text using calculus will be more than enough to give you a background on kinetics and electricity and magnetism. This is to provide you with a solid background in physics, which will benefit you moving forwards. Along that vein, I would then read a textbook about "math methods for science and engineering," something like this. It will teach you several advanced math methods, but will avoid the sort of theoretical math that you will not need for an understanding of quantum physics.

After that, I would go through and gain a good foundation in modern physics. This will give you an introduction to the special theory of relativity, wave-particle duality, a very basic overview of quantum mechanics, and things like Schrodinger's equation and atomic models.

After that, I would take a deep dive into classical mechanics, which means you'll need to pick up an advanced text. Taylor's Classical Mechanics is a solid choice.

After that, I think you will be well equipped to tackle advanced quantum mechanics, and you can find excellent texts for that as well. I'd recommend Intro to Quantum Mechanics by Griffiths.

tl;dr-- I know this might be a bit overwhelming, but the basics of it is

1. Learn multivariable calculus
   
   
2. Learn differential equations.

I agree that authentic materials are essential. The blue book is the way to go for that.

In the interest of using everything available...there are some really good "guides" on collegeconfidential. It's obvious that a lot of the kids (adults? whatevers?) on that site have put a LOT of time and thought into their preparation and are altruistically choosing to share it with others. No reason others shouldn't benefit from it.

Students who are scoring below 700 can greatly benefit from these sorts of courses. After suffering a lot of anxiety about how to organize such a course myself a few years ago, I ended up finding, using, and really liking this book: The New Math SAT Game Plan

I'd love to hear what sort of thoughts you have on running the prep course. Do you have a good location? Administration is the main thing that has prevented me from getting something like this up and running on a consistent basis...

I'm 2 years into a part time physics degree, I'm in my 40s, dropped out of schooling earlier in life.

As I'm doing this for fun whilst I also have a full time job, I thought I would list what I'm did to supplement my study preparation.

I started working through these videos - Essence of Calculus as a start over the summer study whilst I had some down time. https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

Ive bought the following books in preparation for my journey and to start working through some of these during the summer prior to start

Elements of Style - A nice small cheap reference to improve my writing skills
https://www.amazon.co.uk/gp/product/020530902X/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1

The Humongous Book of Trigonometry Problems https://www.amazon.co.uk/gp/product/1615641823/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus: An Intuitive and Physical Approach
https://www.amazon.co.uk/gp/product/0486404536/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

Trigonometry Essentials Practice Workbook
https://www.amazon.co.uk/gp/product/1477497781/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Systems of Equations: Substitution, Simultaneous, Cramer's Rule
https://www.amazon.co.uk/gp/product/1941691048/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Feynman's Tips on Physics
https://www.amazon.co.uk/gp/product/0465027970/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1

Exercises for the Feynman Lectures on Physics
https://www.amazon.co.uk/gp/product/0465060714/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus for the Practical Man
https://www.amazon.co.uk/gp/product/1406756725/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

The Feynman Lectures on Physics (all volumes)
https://www.amazon.co.uk/gp/product/0465024939/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

I found PatrickJMT helpful, more so than Khan academy, not saying is better, just that you have to find the person and resource that best suits the way your brain works.

Now I'm deep in calculus and quantum mechanics, I would say the important things are:

Algebra - practice practice practice, get good, make it smooth.

Trig - again, practice practice practice.

Try not to learn by rote, try understand the why, play with things, draw triangles and get to know the unit circle well.

Good luck, it's going to cause frustrating moments, times of doubt, long nights and early mornings, confusion, sweat and tears, but power through, keep on trucking, and you will start to see that calculus and trig are some of the most beautiful things in the world.

The BEST way to study history of math is to read classic math texts from history such as the Elements, the Conics, the Principia, etc.

Original texts aside, I recommend The World of Mathematics by James Newman.

I also recommend Newton's Principia: The Central Argument by Densmore.

Mathematical Notation: A Guide for Engineers and Scientists has helped me out a lot. It isn't really a "math book", in that it doesn't really teach you concepts. But it tells you what things are and what they do in general. So if you don't know what Σ means, it will tell you, and at least give you a place to start.

For crypto you probably also want a book on number theory.

Also, Understanding Cryptography: A Textbook for Students and Practitioners is the best intro to cryptography book I've come across. I found it easy to understand (relative to other books).

>tens of pages

You're missing out if you've never held a copy of Gradshteyn & Ryzhik. Side note: The top rated Amazon.com review for this book is one of the best reviews I've read.

It was a lifesaver in physics grad school. Some of those integrals you have to do just don't play nice in Mathematica or Maple.

I own a copy of "Mathematical Notation: A Guide for Engineers and Scientists." It is a slim and handy book that is cheap on Amazon.com (http://www.amazon.com/Mathematical-Notation-Guide-Engineers-Scientists/dp/1466230525).

It covers the topics you mentioned and gives very readable definitions for the notation/terminology. As a math student I have found the latex references quite useful as well!

I really believe that Michael Kelly's "Humongous Book of" series are the best resources for getting through all math classes up to Calculus II. These books contain every single type of problem you will ever encounter in Algebra I & II, Geometry, Trig, and Calc I & II, all solved in great detail. They are like Schaums Outlines but much more reliable.

https://www.amazon.com/Humongous-Basic-Pre-Algebra-Problems-Books/dp/1615640835

https://www.amazon.com/Humongous-Book-Algebra-Problems-Books/dp/1592577229

https://www.amazon.com/Humongous-Book-Geometry-Problems-Books/dp/1592578640

https://www.amazon.com/Humongous-Book-Trigonometry-Problems-Comprehensive/dp/1615641823

https://www.amazon.com/Humongous-Book-Calculus-Problems-Books/dp/1592575129

Found a similar book!

We're looking for a book that starts with something as basic as telling you where the position in a number determines its value. (Basically in 304, the position of the letter "3" means hundred!) and I think this book should cover that and what comes after.

And their edition of Newman's World of Mathematics is very nice.

Yes! This is the book I always had with me (though it was the pocket version, IIRC) and I used Gradshteyn's book for my desk reference.

Also check out this book. Good tips for calculating stuff in your head.

Fortunately, mental arithmetic isn't a necessary skill for programming by any means.

I read a book called "Count Down" that was an entertaining story about some more advanced students, but also talked about problem-solving techniques and math as a system rather than memorization. Here.

I'd recommend Mathematical Notation: A Guide for Engineers and Scientists - it's only $10

Mathematics for the Nonmathematician, disgustingly eurocentric but still good, Concepts of Modern Mathematics gives an overview of some higher maths, and I have the set The World of Mathematics which I occasionally read a random chapter, it covers lots of ground.

It has most likely already been said but Cracking Mathematics by Colin Bevridge - I personally have found this interesting and casual to read and would highly reccomend it

Working your way through a beginning discrete math class is kind of an overview of the history of math. But here are some stand-alone books on it. Writing quality varies.

The World of Mathematics

A History of Mathematical Notation. Warning: his style is painful.

Journey Through Genius

The Princeton Companion to Mathematics. A reference book, but useful.

The classical textbook on linear feedback shift registers (used to make large-period pseudo random number generators) is this one by Solomon Golomb. Goresky and Klapper provide a more modern treatment, slanted towards communication applications: (ref)

Is it "Mathematical Notation: A Guide for Engineers and Scientists" - https://www.amazon.com/gp/product/1466230525/ ? It's only 84 pages so maybe not.

I googled "medication calculation workbook"

https://www.amazon.com/Dosage-Calculation-Workbook-Review-Practice/dp/1506208029

Of course you are.

Also, the book you're reading, is it this one?

Table of Integrals, Series and Products [Hardcover]
I.S. Gradshteyn (Author), I.M. Ryzhik (Author)
http://www.amazon.com/Table-Integrals-Series-Products-Gradshteyn/dp/0122947606

this is one of the best for self teaching. the examples are very clear so you don't get tripped up on them jumping steps. You will need to get more problems from somewhere like a more formal textbook, but this will help you get the idea of what to do instead of fuming at an impasse.

http://www.amazon.com/The-Humongous-Book-Calculus-Problems/dp/1592575129

there's also trig and precalc versions if he needs the review.

http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229/ref=pd_bxgy_b_text_z

http://www.amazon.com/The-Humongous-Book-Trigonometry-Problems/dp/1615641823/ref=pd_bxgy_b_text_y