What Books Should I Read to Prepare for My High School Math and Physics Topics?

[CodeFreakC]

Hey guys,
I'm new to these forums but I've actually used these forums a lot in the past for research, etc. I decided to make an account because I'm just about to go through year 12 exams in an Australian high school doing Specialist Maths (Highest level maths), maths studies(High level), physics(the only level) and english. I've always been interested in IT, I have most of my Adv Diploma of IT in computer networking, but I tend to look at that as a hobby/personal knowledge. I love programming and that's driven a lot of my maths skills throughout high school, for instance writing a program that uses the theorems from cyclic quadrilaterals to solve for theta, etc.
Recently I've taken to just doing maths and physics by itself, without IT and I love it. I've started pushing the boundaries in physics and I'm getting there in maths.
Problem:
I don't really know where I want to go, I'm thinking a double degree of some form of engineering with a degree of science/maths. I'm really struggling with specifics though. I'm not going to ask you "What type of engineer should I be?" because only I can really make that choice for myself, so I was thinking I could get some books for the summer holidays and just read some of them and see what makes me tick. BUT I'm also reading because I want to expand my knowledge in some areas, like physics mainly. So, I was hoping that I could give you guys a run down on the topics I've covered in maths and physics at school, and you guys could give me some good reads I could look at getting? I would like to get my hands dirty in some examples too if there are any other more 'involved' reads available.

In Maths we've done the following this year
Single variable calculus (Integration and deferential equations)
cyclic quadrilaterals
complex numbers
real polynomials
trig preliminaries
3d vectors
trig calculus
exponential/log functions
stats (binomial dists,etc )
matrices

I'd like to get a head start in uni maths so I cruise a bit smoother through first year

And in physics
electromagnetism
classical mechanics
wave mechanics
a lot of physics history (like the different models (plum pudding atom, etc))
fields
the particle model of light
orbital mechanics

I'd ultimately like to be able to look at the maths that is string theory and other GUT's and actually understand what's going on.

Looooooonnnnnnnnggggg thread sorry guys but this is a big thing going through my head at the moment, I wanted to be thorougher haha.

Thanks

 

[CodeFreakC]

Alright, the fact that I have gotten no responses after 340 views leads me to the conclusion that I was not clear in my question in the original post. Allow me to reiterate.

I'm looking for some recommended reading in maths and physics based on what I have said I've covered. Some books I can read in my own time. If anyone has any ideas please put them forward, I don't want to buy a book only to find out that its way too complex for me.

Thanks again

 

[chiro]

Hey CodeFreak and welcome to the forums.

One recommendation is to get the Feynman Lectures on Physics: It's a huge 3 volume set (last time I checked) and it goes through quite a bit of fundamental stuff in a more conversational tone.

There is math in there but learning math is a different skill and you can get good insights both from non-mathematicians (physicists, engineers, etc) and both pure mathematicians and applied mathematicians (like applied mathematicians and statisticians).

These books will keep you busy for a long time and he covers everything in a standard 3 year course (possibly 4) for a physics major at the time he wrote it (which was around the mid 50's).

It's a serious set of books and it is a good way to get introduced to things that is supplementary to other stuff (but not a substitute).

Good luck!

 

[CodeFreakC]

Thanks for the reply Chiro!
They look like a great set of books, I'll definitely find myself a copy. Question though: I've already covered classical mechanics in high school, so do these books cover all the topics I've covered in more detail? (ie. Is high school physics watered down?). Also, would it be worthwhile covering some topics in maths like some more advanced calculus before reading them? Are the derivations tricky?
Thanks again!

 

[chiro]

These are above high school: they were taught by Feynman for university level physics majors and although things have been discovered and new ideas have brought in new understandings, a lot of the basic ideas that the more modern stuff builds off uses these ideas.

I don't really think that high school physics is physics at all: maybe in the way of doing a couple of experiments yes, but the math used (at least when I did it just over ten years ago) was a joke.

The one thing that I think will help you is to understand geometry in detail for 3D space. This means understanding how geometry works with projections, decomposition of vectors as well as how to think about solving different situations where you need solutions for cases when you have all these vector equations (like intersection of two lines, smallest distance between two lines, breaking up arbitrary vectors into orthogonal components and so on).

Once you are able to understand this in enough detail, then you can focus on the physics which is probably your focus other than the math.

As you take more math you will develop an intuition for that, but in terms of the basic physics that you will be doing in your first year, the best recommendation I can give you when you get to that point is to understand intuitively 3D geometry in its different forms since this is where you will get all the vector stuff being introduced and if you don't have this understanding, then you'll get thrown problems that will sink you.

It's not about memorizing a lot of rules: it's more about knowing how to break things down in a general way and understand this from different perspectives.

 

[CodeFreakC]

Oh alright. We covered 3D vectors, once again, in high school. ie Parametric equations for lines, shortest distance to a line, distance from line to plane, etc, etc. But I'm assuming you're talking more advanced than that too? Can this stuff be learned online or can you give me some resources? I don't really know just how deep vectors can go so I can't really look for myself.

Also, I've read about Feynman before, he's considered to be the 'Father of nanotechnology' right? I've read some of his quotes, he seems like an amazing mind.

Lastly, as you said previously, while not being the latest material its all still valid, correct? I sort of got the idea older material would be better because newer stuff would be filled with 'Quantum this, String that' sort of talk, but I just want to make sure.

 

[chiro]

You don't really look at stuff like that until you get enough physics "maturity" for lack of a better word: it's the same as anything where you start off simple build intuition and then when the intuition gets built, you get hammered with harder stuff and it keeps going. Don't start a marathon just yet!

You won't do a proper introductory Quantum course until your final years and a lot the String stuff is mostly done in graduate school, although some do offer advanced undergraduate course in the topic.

The main thing you'll want to focus on is getting the intuition for whatever stage you're on so you move on to the next. There are many ways to do this, but the way that most people who are teaching have structured this in a way that goes along the lines of the standard physics major curriculums.

The first stage involves getting very familiar with geometry and basic physics and mathematics (i.e. calculus). Once you get this intuition, you move on to stuff that builds on this intuition.

I don't know about the nanotech stuff, but he is most famous for his work in Quantum Electro-Dynamics which he shared the Nobel Prize for with other contributors and creators.

In terms of learning this stuff, most of it unforunately like a lot of things comes down to experience: I used to do quite a lot of work with computational geometry in the past but if I had to narrow it down, I would say that you should work on anything that gets you to take a vector based or linear based problem (so vectors, planes, and all those things) and then figure out how to take your information and use the math to break it up to get where you need to.

If you can do that, then you have the math out of the way. If you don't have this kind of thinking in physics, you'll get screwed over really quickly.

Even though physics isn't "math" per se, it pretty much is up to a point so knowing the math makes your life easier for physics.

The focus on math for you should be how to break things up (i.e. how to decompose vectors, matrices, integrals, differential equations and so on) and how to introduce constraints (i.e. you introduce a condition or an approximation and you see how that affects the final result).

Once you do this for a while you get used to it, but the thing is that this will have a physical context which is on top of all the mathematics. The mathematics will have a connection with the physics, but doing the decompositions and introducing constraints is more mathematical but it is still required to do physics.

These decompositions often include these "tricks" that math does when you say do a sneaky substitution or when you introduce new terms to do a nice algebraic technique to get a solution.

Although a lot of the "mathematicians" do this kind of thing (especially for really abstract and general problems), you will at some point have to do a bit of this yourself and this just comes with experience.

But what you can do is to keep this in the back of your mind: if you have a problem then think about all the ways you can do these "tricks" so that you can change it mathematically to something that is closer to the thing that you want.

If you are actually going to do exercises, I'd recommend you wait until you do university and then the professor/lecturers will give you tonnes of exercises. A lot of the homework is done via the internet in introductory physics and the books if you buy them (or borrow them from the library), have tonnes of problems so getting problems isn't really that hard at all.

Feynmann's stuff is a supplement for learning and it's a good thing to read if you want to get some kind of intuition of which you can build off when you first encounter all these problems that your professor will throw at you.

 

[CodeFreakC]

Alright cool! That answers my questions. Thanks

Also, sorry if I came off as wanting to jump straight into Quantum and string stuff, that was not my intention and I'm aware that I've got a long way to go before I'll understand all that stuff. What I was trying to say was that I don't want a book that's going to be too complex for me right now.

The aim of this, really, is to give myself a bit of a head start for uni and to enhance my knowledge in general of Maths and Physics. If I can achieve those goals I'll be happy. I've had a look at the Google Preview of Feynmens Lectures and they look like they're written in such a way that I can understand them. I read through a chapter and it seems as if it's written specifically for someone in my situation honestly, because from that quick skim through he was talking about topics I've recently covered in high school maths and physics.

Once again thanks for that, I'm considering getting a copy of the volumes.

 

[WannabeNewton]

Get the book "An Introduction to Mechanics" by Kleppner and Kolenkow. It is an indispensable book on intro mechanics; I can't stress how awesome it is.

 

[CodeFreakC]

Alright thanks! So I think I've now got my collection, using the books you guys have given me, plus my physics teacher recommended Halliday and Resnick: Fundamentals of Physics and G Holton. So I will probably be at it for a long time. Well into my uni career. Thank for your helps guys :)

 

[cjl]

I'm coming into this a bit late, but I just wanted to say that I fully agree with the Feynman recommendation - I have the full 3 volume set, and it is a wonderful set that basically covers the first 3 semesters of university level physics in a semi-conversational tone (without sacrificing too much rigor in the process). It's probably my single favorite reference for basic university level physics.

(Halliday and Resnick isn't bad either)