Order

[Lightfuzz]

I hope I'm doing this right. This is my first topic.

Well, as I said in my introduction topic. I'm a really 'wonky' person. I like to learn things miles away from my level. For example, (I'm in Year 7, by the way) I learned calculus before I had any knowledge of trig. And my geometry skill is still... well, let's just say not great. I learned relativity and quantum mechanics before classical physics. So now I hope to get some advice on the order to learn maths and physics and great websites or books on them. (That's the main idea of the topic.)

Maths:
Algebra: I'm familliar with one-degree equations and I think I'm alright with inequalities and quadratics)
Geometry: I have a problem with inductive thinking and I have to memorize some of the formulas.
Trigonometry: I know the six trigonometric functions but I only know a few identities.
Precalculus: I'm familiar with functions, exponents, logarithms. I just have to learn the Binomial Theorem. So I'm pretty good with this one.
Statistic: Ok. Now this one I've almost got no knowledge on.
Calculus: I'm alright with limits and differentiation. But I'm not too good with partial fraction and trig integrals. I don't really remember infinite series.

Well this is my idea of the curriculum for high school mathematics. And I'm not too sure about university but I'm not too urgent with that. I do know there's linear algebra, abstract algebra. But if anyone has one then please post it. I'll do the same with physics.

Forces: I'm still practicing. I know Newton's laws of motion, the law of universal gravitation, friction and mostly circular motion. Do not really understand inclined planes.
Energy: Still practicing. I know my kinetics and potential energy and momentum. Do not understand torque.
Thermodynamics: I just have to practice. But I've heard about statistical mechanics and I don't know a thing about it.
Electrodynamics: Still reading. Do not understand voltages and resistors. Know not a single thing about Maxwell's equations except that they are best shown in vector calculus.
Relativity: Slowly progressing. Know the basic idea and learning the equations.
Quantum Mechanics: Know the basic idea but not the maths.
Quantum Field Theory: I've read about the basic ideas.

I've probably missed some topics but this is long enough. So please help and give recommendation of where to learn it. Thanks.

[maddog]

Originally Posted by Lightfuzz

I'm a really 'wonky' person.

I not sure what you mean by "wonky" ?

Originally Posted by Lightfuzz

I like to learn things miles away from my level. For example, (I'm in Year 7, by the way) ...

Do I understand this to be "grade" as "seventh grade" ? or "seven years old" ? or ??
Either way I am impressed from your post. I read Einsteins book, "Relativity" in 8th
grade before I had formal physics myself.

Originally Posted by Lightfuzz

I learned calculus before I had any knowledge of trig. And my geometry skill is still... well, let's just say not great. I learned relativity and quantum mechanics before classical physics. So now I hope to get some advice on the order to learn maths and physics and great websites or books on them. (That's the main idea of the topic.)

I'm not sure -- depends on your talents and interests. I found a book on Topology in
my school library in 7th grade and found it interesting. Topology is the Mathematical
study of Deformable Geometry.

Originally Posted by Lightfuzz

Maths: Algebra: I'm familliar with one-degree equations and I think I'm alright with inequalities and quadratics)
Geometry: I have a problem with inductive thinking and I have to memorize some of the formulas.
Trigonometry: I know the six trigonometric functions but I only know a few identities.
Precalculus: I'm familiar with functions, exponents, logarithms. I just have to learn the Binomial Theorem. So I'm pretty good with this one.
Statistic: Ok. Now this one I've almost got no knowledge on.
Calculus: I'm alright with limits and differentiation. But I'm not too good with partial fraction and trig integrals. I don't really remember infinite series.

Again, impressive.

I see you could about 6 separate tracks depending on interest (skill already met):
Mathematics, Physics, Chemistry, Astronomy, Biology, Computer Science (could also be
considered part of Math).
High School Level
Mathematics: Algebra, Geometry, Trigonometry, Analytic Geometry, Precalculus, (you have already coverd).
Chemistry, Biology (self identifying).
Astronomy (optional), Physics (you already covered) -- Note did you use Calculus to study Physics (?)
Computer Science: Some simple Languages: C/C++, C#, VB, Perl, Python, others.

University Level
Mathematics: Calculus (be sure to cover Calculus of many variables), Linear Algebra,
Abstract Algebra, Differential Equations, Linear Analysis, Real and Complex Analysis,
Differential Geometry, Fourier Analysis, Probability, Topology, Numerical Methods,
Chaos Theory, Set Theory, Logic, etc
Physics: Mechanics, Electricity and Magnetism, Electronics, Modern Physics, Relativity,
Optics, Quantum Mechanics, Thermodynamics, Solid State Physics, Statistical
Mechanics, etc
Astronomy: Solar System, Stellar Astrophysics, Galactic Astrophysics, Cosmology,
Observational Techniques, etc.
Computer Science: More Languages: Assembly (various processors), Smalltalk, Objective-C, etc,
Engineering: Circuit Analysis, Computer Architecture ... (Couples with Physics).

Graduate Level
Mathematics: Abstract Algebra (Group Theory), Numerical Analysis, Real Analysis,
Complex Analysis, Partial Differential Equations (PDEs), Number Theory, Differential and
Non-Euclidean Geometry, Tensor Analysis, Lie Algebras, Topology, Algebraic Topology,
Functional Analysis, Spectral Theory, Topos Theory, Markov Chains, Stochastic
Statistics, Category Theory, way more other field that I can count.
Physics: Mechanics, EM Theory and Maxwells Equations, Special and General Relativity,
Quantum Mechanics, Quantum Field Theory, Solid State Physics, Quantum Optics,
Superconductivity, High Energy Physics, and many more, including lots of field of ongoing research.

This is really more a tree structure which my list doesn't do justice.

I would recommend three things:

1) From what you have already looked into, I would investigate both Complex Numbers
and Quaternions (by Hamilton). Investigate what they can do and how they are very
different than what you may already be familiar.

2) I would do a Google Search on each of the topics I mentioned. You will probably find
much more.

3) Consider what field I like more (not a big deal as you may end up liking more than one).

Just some things to think about.

maddog

ps: Welcome to Hypography BTW...

[maddog]

Originally Posted by Lightfuzz

I just have to learn the Binomial Theorem.

I had to pick this one up by myself, so you actually doing good.

I thought about this some more and would like to add a few things regarding order of study:

High School
Order taught in High School (US)
Algebra - Geometry - *more* Algebra - Trigonometry - Analytic Geometry - Precalculus.
Biology - Chemistry - Physics
For Physics: Mechanics - Strings/Springs - Electricity & Magnatism - Thermodynamics - Statistical Mechanics - Modern Physics &/or Relativity (Special only).

University (Undergrad)
Mathematics: Calculus (3 courses: Derivatives, Integration, Sequences & Series, Multivariate Calculus, Vector Calculus, Calculus of Variations, etc) - Linear Algebra - Linear Analysis / Fourier Series - Real / Complex Analysis - Probability - Differential Geometry - Topology - Abstract Algebra (Groups / Rings / Fields / Galois Theory) - Tensor Analysis
Physics: Freshman Physics (3 courses: taught with Calculus as prerequesite; Mechanics - E&M - Thermo/SM - Optics - Modern Physics) - Electricity & Magnetism (incl Maxwell's Equations) - Modern Physics - Thermodynamics - Statistical Mechanics - Optics - Quantum Mechanics - (Electives: QCD, High Energy Physics, Solid State Physics, etc)
Astronomy: Freshman Astronomy (Survey), Observational Techniques, Astrophysics (Local - Solar System, Stellar, Galactic), Cosmology

University (Graduate)
Mathematics: Abstract Algebra (Groups, Rings, Fields), Real Analysis, Complex Analysis, Number Theory, Topology, Differential Geometry, etc (many more)...
From there it is mostly research... Lie Algebras, Quantum Groups, ....
Physics: Mechanics, E&M, Quantum Mechanics (QM), Quantum Field Theory (QFT), Solid State Physics, Quantum Electronics, Quantum Optics, Low Temperature Physics,
Superconductivity, High Energy Physics, etc (many more)...

I simplified where I could. Maybe this helps.

maddog

[Lightfuzz]

Note: I don't really get the quoting system here, so I won't quote, sorry.

Thanks, you can't possibly imagine how much I appreciate this. I'm in seventh grade. Can you please expand on the list for graduate university? Are most of the topic in the list? And does high school physics include all the maths and equations? No, I did not study physics with calculus, in what field of physics is it used in? And where's a good source for learning all this?

[maddog]

Originally Posted by Lightfuzz

Note: I don't really get the quoting system here, so I won't quote, sorry.

This is realy quite simple. To respond to a post in a thread, there is a button which is label "Quote" (blue button) in lower right of each post. You push that and you are post in
response to that post. You can also type the pair "

....text...

" where your
quote is between the header "["quote"]" and trailer "[/"quote"]". This is XML based.

Originally Posted by Lightfuzz

Thanks, you can't possibly imagine how much I appreciate this. I'm in seventh grade. Can you please expand on the list for graduate university? Are most of the topic in the list? And does high school physics include all the maths and equations? No, I did not study physics with calculus, in what field of physics is it used in? And where's a good source for learning all this?

I will have to expand on the Grad a bit later. I probably missed a few fields. There are a lot more.

At the university level - freshman physics uses Calculus as a prerequisite for Physics Majors.
I should know I were one (are in the past). My BS degree was in Physics (though I
originally studied Astrophysics more than half of it). This make me with all three heavily
studied (Math, Physics, Astrophysics). I also minored in Computer Science and ended
up in a career in Aerospace/SW Engineering.

So what part of Physics uses Calculus ??? ALL of IT !!!
Mechanics heavily uses Differentiation (Velocity, Acceleration), Integration (Force, Power), Differential Equations.
Electicity & Magnetism -- Maxwell's Equations (use Vector Calculus, Div, Grad, Curl)
Quantum Mechanics (uses Complex Analysis, Linear Algebra, some Group Theory)
General Relativity (use Tensor Analysis, Differential Geometry, Topology)
Statistical Mechanics (uses Statistics)
Thermodynamics (uses Fourier Analysis)
Optics (uses Calculus, Sequences/Series, DiffEq)

Even now I forgetting some... Good Luck!

maddog

[Lightfuzz]

Again, thanks. So is QFT about the Theory of Everything? And mechanics is the study of motion? Is there like an order of study for biology, chemistry, earth science and astronomy?

Electicity & Magnetism -- Maxwell's Equations (use Vector Calculus, Div, Grad, Curl)

What's curl?

[maddog]

Originally Posted by Lightfuzz

Again, thanks.

You are welcom.

Originally Posted by Lightfuzz

So is QFT about the Theory of Everything?

Not exactly. "QFT" stands for Quantum Field Theory (QFT). This is typically a second level graduate course in Quantum Physics (after a solid year of graduate Quantum Mechanics [QM]).

Originally Posted by Lightfuzz

And mechanics is the study of motion?

Yes, though as I was thinking over the weekend, Mechanics is actually a potpourri of subjects
served up ale carte, one at a time. This is so whether it be High School Physics, Undergradute
College Physics (Freshman/Upper division), or Graduate Level Physics.
With each iteration, you get more rigor.
High School is typically done without Calculus or Differential Equations.
Freshman College Physics (majors) typically use Calculus though don't use Differential
Equations.
Upper Division Physics will use Calculus and DiffEq yet won't use PDEs (Partial DiffEq).

Mechanics:
1. Force and Motion of single particle.
2. Gravitation
3. Springs, Strings and Harmonic Oscillation
4. Fluid Statics
5. Thermodynamics
6. Gases (Statistical Mechanics, Systems of motion)
7. Electricity
8. Magnetism
9. Electro Magnetism and Maxwell's Equations
10. Special Relativity
11. Fluid Dynamics (Optional)
12. Modern Physics

[quote=Lightfuzz;267932]Is there like an order of study for biology, chemistry, earth science and astronomy?
I have seen a lot of variation in High School. In College I don't there is any real order to study.

High School (my Curriculae) is/was:
Earth Science (Freshman/9th grade)
Biology (Sophmore/10th grade)
Chemistry (Junior/11th grade)
Physics(Senior/12th grade)

Originally Posted by Lightfuzz

What's curl?

This definition is taken from the Wolfram Website

The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at each point and to be oriented perpendicularly to this plane of circulation for each point. More precisely, the magnitude of del xF is the limiting value of circulation per unit area.

The definition written in math notation (I hope this displays):



where is the Grad or Gradient which a 3D Partial Derivative and are vectors under a vector "cross product"

For more info goto this link at Wolfram

Curl -- from Wolfram MathWorld

maddog

[sanctus]

Or more intuitively curl is how a vector field turns :-). Imagine you are at a point A in a given vector field (= a "map" where ate every point you associate a vector, in 2D you can imagine the cartesian plane with arrows at every point). Examples of a vector field with no curl are a map where all the arrows point in the same direction or one where all the arrows point to the center. An example of a vector field with curl would be a map where all the arrows are tangent to circles around the center.

Physically, the first example could show the electrical field between a negatively and positively charged (infinite) "planes" (i.e imagine a vertical line at x=-1 charged positively and one at x=1 charged positively then the field would be horizontal arrows, they have to be of inifinite length otherwise curly stuff happens at the borders);
the second example could be the electrical field of a charge situated at the center;
the third example, could be the velocity vector field of particles of water going down a sink

[maddog]

Yesterday after my post, I got to thinking of a visual way to think of it (Curl). Like Sanctus, I
was thinking of the first two vectors forming a plane (The Gradient Vector and the F vector).
So the Curl is then the "cross" or Vector product (also known as the "outer product"), is then
the Vector "Normal" to the other two (this means it points out of the plane of the first two
vectors).
In Electricity & Magnetism, the Field flux or field strength is a vector
pointing in circle in the plane (like putting the fingers in your right hand and curling then in
a circle). When you stick your thunb out it points in the direction of the Curl of the two
vectors. This often called the Right Hand Rule.
You see this often in E&M, Rotational Kinematics (Rotation Mechanics of rigid bodies) and
other places.

maddog