Math Textbooks: Intermediate/Advanced Series for Physicists

[FuturePhysicist]

Hello I was looking for a volume set in intermediate/advanced math and I can't seem to find anything. I already have a book in calculus 2 but I'm looking to self study everything after that through advanced math. I want to be a theoretical physicist, but I'm open to learning interesting math that does not apply if need be. Most books I have studied varied in format and it made it frustrating. I would like everything else to be in a similar format to make things faster and easier. Overall, just a good series that goes through everything.

 

[QuantumCurt]

I don't think there really is a series that goes through everything in math. One must often search around to find books that are to their liking in a given subject. Not all people prefer the same type of textbook. The best thing to do is try to look at several different options before buying a book in a given subject area. Amazon book previews can be very useful for this.

 

[NumericalFEA]

In what exactly area of Physics are you going to specialize ?

 

[FuturePhysicist]

In what exactly area of Physics are you going to specialize ?

Most likely cosmology

 

[NumericalFEA]

Most likely cosmology

Broadly speaking, it's a huge area. Stars, galaxies, exoplanets; space flight (manned and unmanned); inner planets, outer planets (and their satellites). Closely related areas: rocket technology, new types of rocket engines; robotics, electronics for unmanned probes. Some of those specializations have excellent employment opportunities (mostly: technologies); others have very limited funding, mostly areas of pure research, like astrophysics, etc. An important thing to remember is that all of the listed areas are exciting: for example, mechanical behavior of materials used in the aerospace industry is as complex science (including mathematical fundamentals) as quantum mechanics or general relativity. I think that careful choice of the exact area in which you are going to specialize is a matter of extreme importance for future career. Depending on your choice, further recommendations about math textbooks can be made.

 

[Wyn]

I have Arfken's book and I recommend it.

 

[snatchingthepi]

Arfken's book is great but also quite advanced in its application and scope. I would recommend Mary Boas' book any day as a stand-alone, or as a more generous complement to Arfken's.

 

[Wyn]

But the OP is looking for intermediate/advanced? Anyway, I don't think it's that advanced, because even I can understand it and I'm bad at maths

 

[IGU]

Hello I was looking for a volume set in intermediate/advanced math and I can't seem to find anything.

I suggest you take a look at the books from Art of Problem Solving. They are very good, intended for the most capable students. However, at the moment they only go up to introductory calculus. Given where you are now, I think you would find it very valuable to work through them. They will give you the best foundation for your further mathematical studies.

There are associated classes which have pre- and post- quizzes to facilitate placement. You might want to look at those to see where you are. They also have a variety of other things for the math competition people, but I doubt that would interest you. But you might find their free Alcumus learning system interesting.

 

[snatchingthepi]

These seems quite elementary in comparison to the level of preparation one has when studying calculus. What makes you suggest them IGU?

 

[IGU]

These seems quite elementary in comparison to the level of preparation one has when studying calculus. What makes you suggest them IGU?

The OP posted this thread a month ago. It indicates to me that he would be well served to make sure his grounding is sufficient. The AoPS books provide a very solid and well-defined foundation for both calculus and discrete mathematics, well beyond typical high school. If he finds those books easy then it sets a lower bound on how capable he is and can guide other recommendations. If he finds them hard then it says something else. From his postings so far I have no good feel for what he's capable of handling. Suggesting that people tackle something beyond them is just discouraging and therefore doesn't serve them well, so I'd like to avoid that.

 

[FuturePhysicist]

The OP posted this thread a month ago. It indicates to me that he would be well served to make sure his grounding is sufficient. The AoPS books provide a very solid and well-defined foundation for both calculus and discrete mathematics, well beyond typical high school. If he finds those books easy then it sets a lower bound on how capable he is and can guide other recommendations. If he finds them hard then it says something else. From his postings so far I have no good feel for what he's capable of handling. Suggesting that people tackle something beyond them is just discouraging and therefore doesn't serve them well, so I'd like to avoid that.

It would probably help if I told you my percentile for a standardized test my county requires 3 times each year. Last time I took it I scored in about the 98th-99th percentile. It might also help to say that I have helpful tools in my house that make it much easier. I have many whiteboards around that I use.

 

[IGU]

It would probably help if I told you my percentile for a standardized test my county requires 3 times each year. Last time I took it I scored in about the 98th-99th percentile.

No, it doesn't help much. The AoPS stuff is designed to be good for about the top 2% of math students (that's my vague estimate; I don't think they say), so you are probably right in the middle of the pack. But maybe not. If you find all of your high school math courses trivial, then you are the sort of person who should be using AoPS instead. If you find the AoPS books trivial, then that's another thing entirely.

 

[FuturePhysicist]

No, it doesn't help much. The AoPS stuff is designed to be good for about the top 2% of math students (that's my vague estimate; I don't think they say), so you are probably right in the middle of the pack. But maybe not. If you find all of your high school math courses trivial, then you are the sort of person who should be using AoPS instead. If you find the AoPS books trivial, then that's another thing entirely.

Well given that I scored a 98% in my last class without studying once while about 90% of students in it did not even pass, I guess I can say that classes are trivial for me. But I will have to purchase those books and see how that goes.

 

[IGU]

Well given that I scored a 98% in my last class without studying once while about 90% of students in it did not even pass, I guess I can say that classes are trivial for me. But I will have to purchase those books and see how that goes.

There's a truism that if the classes you are in are easy, then you are in the wrong classes. Do you do that well in all your classes, or just some? Why didn't you achieve a 100% score (just curious) if it's so trivial? It doesn't help much to compare yourself to others in your classes, you have to compare yourself to others who are actually good. First you have to find them. I've suggested one way.

Another good way is to see what you can get from your local universities. But first you have to get yourself knowledgeable up to their expected level. If you want to make use of university classes, you have to be prepared for them.

But also, you should be aware that doing well in classes is not what makes an outstanding scientist. And doing well in easy classes isn't even on the radar. Classes are just one aspect, and not the most important.

 

[FuturePhysicist]

There's a truism that if the classes you are in are easy, then you are in the wrong classes. Do you do that well in all your classes, or just some? Why didn't you achieve a 100% score (just curious) if it's so trivial? It doesn't help much to compare yourself to others in your classes, you have to compare yourself to others who are actually good. First you have to find them. I've suggested one way.

Another good way is to see what you can get from your local universities. But first you have to get yourself knowledgeable up to their expected level. If you want to make use of university classes, you have to be prepared for them.

But also, you should be aware that doing well in classes is not what makes an outstanding scientist. And doing well in easy classes isn't even on the radar. Classes are just one aspect, and not the most important.

I am aware of that. The reason I brought up classes is because of your mention of classes being trivial and that being related to studying the books.
P.S. I looked up those books and found nothing past high school level besides statistics and number theory. Are those competition prep books more advanced, or did I miss something?

 

[IGU]

I looked up those books and found nothing past high school level besides statistics and number theory. Are those competition prep books more advanced, or did I miss something?

The books are intended for kids who love math and are good at it. Elementary school, middle school, high school. Mostly high school and "not on the calculus track" math (like number theory), all done fairly rigorously and in a way that isn't boring. My homeschooled math kid did some of them in middle school but then moved on to more serious stuff. They do classes too, which are useful for those who learn best that way. My kid didn't much like them and used the books straight at his own pace.

The competition type books are mostly intended for kids who enjoy competitions. Many top competition kids nowadays are using AoPS. So are those who are finding school math too simple and dull. The company is pretty much a bunch of math guys who made a pile of money on Wall St. and then decided to put together the learning materials they wished they had when they were in school. And you get to benefit. I suggest you get one for a subject you think you know (maybe geometry?) and see if you can work all the problems correctly without looking at the answers.