Learning Curriculum : self-study

[watters1989]

This is for all those that have the will/motivation to learn outside of the classroom. I am a "prospective" student to the field of mathematics/physics/electrical engineering. I am curious as to what the curriculum you guys are taken is like? Like, what subjects are you learning from the day you start your degree to the day you graduate? The books you are assigned/recommended? And ultimately what institution do you go and/or best recommend?

Due to unfornunate circumstances, I'm not currently qualified for the majority of student aid, so I am saving up for college. I plan to double major in physics and mathematics. Possibly get masters in both (baby steps first right ... ) I would simply like to learn these subjects to the best of my ability before stepping into a university.

 

[Ackbach]

For math, I always recommend Morris Kline. His Mathematics for the Nonmathematician is excellent, as is his Calculus: An Intuitive and Physical Approach. If you're wanting to do Differential Equations, I'd recommend Tenenbaum and Pollard. All those books are quite inexpensive.

For physics, just about any of the general intro books are good. I like Young and Freedman. Once you've done that, try out Marion and Thornton's Classical Dynamics of Particles and Systems, as well as Griffiths' Introduction to Electrodynamics.

I've found all these books to be good for self-study.

Have fun!

 

[watters1989]

For math, I always recommend Morris Kline. His Mathematics for the Nonmathematician is excellent, as is his Calculus: An Intuitive and Physical Approach. If you're wanting to do Differential Equations, I'd recommend Tenenbaum and Pollard. All those books are quite inexpensive.

For physics, just about any of the general intro books are good. I like Young and Freedman. Once you've done that, try out Marion and Thornton's Classical Dynamics of Particles and Systems, as well as Griffiths' Introduction to Electrodynamics.

I've found all these books to be good for self-study.

Have fun!

Thanks! I greatly appreciate this. I have heard good things about the Young and Freedman texts, so that'll probably be top of the list. @Ackbeet, for my future reference, what are some of the texts related to the more advanced topics from what you listed? Or, better yet, what would you recommend after these texts listed?

 

[Ackbach]

Well, let me see. For math, you'll want the following:

Linear Algebra: Nicholson is quite good.

Real Analysis: Rudin's Principles of Mathematical Analysis is the standard, but I also like Kirkwood quite a bit as well.

Complex Analysis: I'd go with Gamelin.

Abstract Algebra: Herstein.

Functional Analysis: Kreyszig.

Topology: Crossley

Numerical Analysis: Burden and Faires.

Summary: once you've done calc, DE's, and linear algebra, the big courses that are really important are Real Analysis, Abstract Algebra, and Topology. I would still hit the others on this list, especially Numerical Analysis, but those three are the ones all math graduate students, at least, are expected to have taken.

For physics, try this:

Quantum Mechanics: I like Griffiths for this, though others may differ.

At this point, you're talking about more specific courses like astrophysics, solid state physics, relativity, etc. I don't have terrific recommendations for those except that the Mermin book is excellent for solid state. Indeed, one of the very best books I've ever read is Mermin's book Boojums All the Way Through. It's about how to write science, and I can't recommend it too highly. This guy can actually write well!

That'll keep you busy for a while.