Quote:
Originally Posted by Lightfuzz
I'm a really 'wonky' person.
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I not sure what you mean by "wonky" ?
Quote:
Originally Posted by Lightfuzz
I like to learn things miles away from my level. For example, (I'm in Year 7, by the way) ...
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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.
Quote:
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.)
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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.
Quote:
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.
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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...
