Highly Technical books

[DyslexicHobo]

After I'm finished with Brian Greene, it looks like I will start reading Feynman, as that seems to look like a popular selection.

Most of you say that I will need an in-depth understanding of advanced (well, more advanced than I know now) to realize what these physicists are trying to get across. Do you think it's a bad idea that I'm reading without the underlying foundation of strong calculus, etc.? Sure, I don't know why or how E=mc^2, or exactly how to measure how fast a galaxy is moving away by monitoring the red shift; I would love it if I could truly understand how these concepts were formulated, but I have the feeling that I wouldn't be able to grasp the math without a good teacher (which aren't very readily available in my school district... ). Which would benefit me more in the long run? Trying to get the basic gist of the physics concepts now, or trying to learn the math so I can understand where the theories of the universe come from?

Again, thanks for the list of reading material. I'll definitely be set for a while.

 

[f95toli]

It is always good to read books. My point in the post above was simply that it is important to understand that some concepts in physics are more or less impossible to understand properly without math. However, that does not mean that you should not read about said concept, you will at least get some idea about the basic ideas etc whcih is always a good start.

 

[cougar1]

Like f95toli, I agree that it is good for you to read these books to get some of the general ideas. The problem is that because the results of QM are strongly linked to the mathematics rather than intuition, with these books you will only learn about the "what" (the conclusions of QM), but not the "why" (how these conclusions arise or why they are so). As a result you will have no ability to evaluate one possible interpretation versus another or to extrapolate what you learn to another situation that isn't identical to what is described in the book. Only by understanding the underlying mathematics can you make these deeper connections, which are necessary to really "get" QM.

In fact, during the early development of QM, it was often these counter-intuitive, mathematical results which caused many to doubt its validity. "Quirky" results were interpreted as a byproduct of the complex mathematics, rather than a reflection of reality. Only after experimental methods were developed to test these results, was it confirmed that QM did in fact effectively represent reality as we know it.

Finally, you might be interested in http://www.nanohub.org and in particular http://www.nanohub.org/resources/833/ , which gives an overview of the capabilities available through nanohub, including a lot of QM educational and simulation tools. The project is based primarily at Purdue and has a lot of info about nanotechnology, even some stuff for the K-12 crowd!

 

[cougar1]

As for advanced mathematics, you need to understand that in many ways mathematics is really about abstraction and short cuts.

For instance, when learning to add, you probably first learned 2+2 = 4 by lifting two fingers on one hand and two fingers on the other and counting the total number of fingers, 2+2 being an abstraction of your fingers. Soon thereafter, you simply learned the shortcut that 2+2=4 and a few other short-cut rules and stopped bothering with your fingers. Later you learned that 3*2=(2+2+2)=6, with 3*2 being an abstraction of (2+2+2). Once again you learned a series of short-cut rules and stopped bothering with (2+2+2) and simply did multiplication.

In calculus, you probably learned that the derivative is defined such that:

df/dx = lim[h->0] (f(x+h)-f(x))/h (1)

But then you learned (or are learning), a series of short-cut rules, and instead of having to resort to equation (1), you simply differentiate:

d(x^2)/dx = 2x , d(sin x)/dx = cos x, d(xsinx)/dx = xcosx + sinx, etc...

For integration, you simply do the reverse (find the antiderivative).

In advanced mathematics you will do the same. You will generalize addition, subtraction, multiplication and division to vectors and matrices (ordered groups of numbers) and learn a new set of short-cut rules (Linear Algebra). You will generalize derivatives and integrals to vectors and again learn a new set of short-cut rules (Calculus of Multiple Variables). You will learn to solve equations involving derivatives of a single variable (Ordinary Differential Equations) and of multiple variables (Partial differential equations) and again learn a set of short-cut rules for solving them. Then you will learn how to solve systems of such equations. Finally, you will recognize that for some problems the short-cut rules for the partial differential equations are basically the same as those you learned previously in linear algebra and that the two are simply different faces of the same puzzle!

Now the key is to recognize that purpose of the short-cuts is to allow you to focus on the big picture of what the mathematics are telling, with out getting caught up in the details of the solution. Therefore, as you continue to learn mathematics, don't get bogged down with the short-cuts. It is critical to learn them, but more importantly, make sure you understand the big picture. What does an equation mean? What does it say about how a function changes in time and space? Where does the equation apply? and What happens at the boundaries where the equation no longer applies? Once you know that, the shortcuts will help you learn how to transform the equations into a form you can solve.

 

[Rastus]

Subscribe to Scientific American and join their book club. You will get plenty of opportunities to see what's out there at all levels, with reviews.

 

[RossGr]

I'll second Lintman's suggestion of John Gribbin. Exellecent writer.

OP,
Good to hear that you are taking Physics and Math, stick with it though the first year (at least) of University and you will find most of the Pop sci stuff pretty easy to read.