## Main Question or Discussion Point

Hi Guys I am new here...I need a favour from you guys...Here's my background first...I'm seventeen years old and somewhat obsessed with Physics and Math as I am sure most people on this forum are...
As a kid I had a teacher who came to teach me advanced math thought it was a good idea to help me grow my interests blah blah...So for a 17 year old I have a really strong Math background (high end calc, diff geometry, number theory blah blah)...However my Physics background has always been far more self study...Over the last 2 years this is the work that I have done and the subject material I have covered...I'll be going to college next year...and I am curious as to how advanced this is...I know its not high school physics but I would like to know exactly where I stand... I figure there must be some people like me here...SO yeah like the title says...just tell me the level of my work so I know...Cheers. Thanks in advance!

Fluid Dynamics : Consistency Equations (Navier-Stokes, Euler), Linear
Hyperbolic Systems, Convective and Diffusive analysis for systems in 1-D and 2-
D, Finite Difference Operations - Point, Matrix, Pade's formula, Stability and
Consistency of Flow by Fourier stability analysis, Vortex, Turbulence of Flow,

Differential Geometry in Physics: Vectors and Curves, Differential Forms - 1
forms, Tensors, Exterior derivatives, Hodge-* Operator, Connections - Frames,
Curvilinear coordinates, Covariant Derivatives, Theory Of Surfaces - Flux,
Manifolds, Fundamental Theorems

Electromagnetic : Integral and Differential Calculus of Vector Fields,
Electromagnetic Theory - Maxwell, Vector Potentials, Principle of Least Action,
Solutions to Maxwell's equations of Free Space and Currents Charges,
Waveguides - Transmission Lines, Cut Off, Cavity Resonators, Alternating
Currents, Lorentz Transformations for fields, EM Mass, Internal Crystal
Geometry, AC Circuits, Reactance, Susceptance

Semiconductors: Junction Diodes, Transistors, Characteristics, Light based
devices, Amplifiers, Oscillators.

Quantum Theory: Introduction and History of the Quantum Theory, Wave-
Particle Duality, Probability Amplitudes, Spin One and Spin Half Mechanics,
Time-Dependence of Amplitude, Hamiltonian Matrices, Schrödinger Equation in

Quantum and Classical Contexts, Hyperfine Splitting in H-Atom, Heisenberg's
Uncertainty Principle

Relativity: Introduction to theory of Relativity, Special Relativity, Relativistic
Effects on Radiation, Relativistic Effects on Matter - Time Dilation etc.,
Geometry of Space time, Dynamics in 4-D, Unifying Electromagnetism and
relativity

Mechanics: Translational and Rotational Kinematics, 2D and 3D Mechanics,
Forces, Energy, Transients, Resonance, Oscillations, Wave mechanics,
Gravitational Field, Elasticity, Molecular Forces and Solid Materials

Optics: Introduction to Geometrical ray optics, Hygens principle, Freunhofer/Fresnel diffraction, Interference, YDSE, Single slit, Multiple slits, Polarisation, Wave-Particle duality of light

This isnt quite exhaustive but I think is a bulk of what I have done...Tell me if you need any more detail. Thanks!!

Oops! Sorry Here's the Math Part as well...

Number Theory: Computational Number theory, Combinatorial Number theory, Zeta
Functions, Introduction to Riemann Zeta Functions, Diophantine and Pade' Approximants,
Fermat's Last and Little theorems

Discrete Mathematics: Fuzzy Sets, Interference Theory, Duality Laws, Boolean algebra,
Introduction to Game Theory and Decision Theory, Minimax Theorem

Relations and Functions: Cartesian Cross Products, Set theory, Domains, Co-domains and
Definitions, Graphing, Asymptotes, Inverse Functions, Binary Operations, Relations, Properties
of Functions, Composition and Operations

Calculus: Techniques of Integration, Multivariable Calculus, Multiple integrals, Vector Calculus, Advanced differential calculus, Series expansions, indeterminate forms, Fourier Transforms, Laplace Transforms, ZTransforms,
Complex Function Calculus

Application Of Calculus: Integral and Differential Geometry, Partial Differential Calculus,
Polar and Cartesian Curves, Curvature, Pedal Equations, rate of change, Maxi/Minimization
using partial differentials, Errors and Approximations

Non-Euclidian Geometry: Hyperbolic Geometry, Poincare' Half-Plane Model, Ultra-parallel
theorem, Riemann Surfaces, Elliptical Geometry - Introduction, theory

Numerical Methods in Engineering: Difference Equations, Matrix Inversion and Eigen Value
Problems, Finite Differences and Interpolation, Algebraic, Transcendental and Simultaneous Equation, Matrix Algebra

2D and 3D Geometry: Vectors, Circle, Line, Plane, Conics, Sphere, Cone, Cylinder, Skew
Lines, Surfaces Of Revolution, Solid Vector Geometry

Probability: Conditional Probability, Baye's Probability, Random Variables, Convergence of
Random Variables, Stochastic Processes, Discrete Probability Distributions - Binomial,
Negative Binomial, Poisson, Geometric and Hyper-geometric

Computer Science: Numerical Methods in Computers, Numerical Techniques in
FORTRAN-77, C, C++

cristo
Staff Emeritus
Wow, that's quite a bit of work you've done there; how did you manage it in two years? Well, I'm not really sure what sort of comments you're after: you probably know that you're going to be way way ahead of anyone else in your class (supposing, of course, you actually have knowledge in the courses you list and haven't just read some books). Do you know which colleges you are applying to? Try looking up their course catalogue and compare it to the work you've done.

How did I manage that in 2 years? Well not really sure how to answer that because I just have. I suppose I dont quite spend my time on anything else (which makes my school grades suffer a tad)...

I think I have a good understanding. I dont just read I make sure my problem solving/conceptual questioning is strong before I move from one topic to another. So yes I believe I have a strong understanding of what I have learnt.

What kind of replies am I looking for? Yes I know I am ahead of my class in Math/Physics. But let me ask it this way. How would I compare to say an undergrad student with a physics major in terms of knowledge? and Where do I go from here?

The reason I am asking is because my learning has become a bit lost in the last few months. I am just learning physics and working out problems. I love doing it but I am not sure why I am doing it.

Some specific questions:

1. Should I pick a speciality of study? Fluid dynamics/Quantum Mechanics really interest me? am I ready to say "yes this is what I want to do"
2. How do I compare do a physics major undergrad? Like freshman/sophomore year ish? Less than that?
3. When I go to college will this help me? WIll I be able to cut down teh time it takes me to graduate? If so how?
4. Am I going about this the right way? I mean its fine learning a million topics in general fundamentals of Physics concepts but at higher levels shouldnt I chaneg my approach from picking a topic in the dark and running with it?
5. ANY ADVICE you guys can give me to better myself? or just in general any advice about physics education career etc etc...

Colleges I am applying to: Well the obvious choices MIT Caltech Stanford but its really hard to get in...SO Columbia Cornell Carnegie Mellon Harvey Mudd...Duke...Hopkins I suppose and a few others...Pretty interested in Cornell's engineering physics programme but will probably stick with pure physics.

1. Should I pick a speciality of study? Fluid dynamics/Quantum Mechanics really interest me? am I ready to say "yes this is what I want to do"
2. How do I compare do a physics major undergrad? Like freshman/sophomore year ish? Less than that? the average sophomore probably knows calculus and diff eq, they have taken 2-3 physics with calculus courses, and classical mechanics or E&M
3. When I go to college will this help me? WIll I be able to cut down teh time it takes me to graduate? If so how? I'm not sure, talk to the physics professor about testing out, if you feel confident in your knowledge in introductory physics
4. Am I going about this the right way? I mean its fine learning a million topics in general fundamentals of Physics concepts but at higher levels shouldnt I change my approach from picking a topic in the dark and running with it? Learn what interests you and what you enjoy. If you don't enjoy it, stop.
5. ANY ADVICE you guys can give me to better myself? or just in general any advice about physics education career etc etc... Don't burn out, or be afraid to take a break. I entered college not knowing what force was.
If you did in fact learn all that, you will probably be reviewing until junior year at some point. I wouldn't be in a rush to finish. Talk to some professors about research though.

Yeah I am in no rush...I mean its not a race to finish college right...I'm still seventeen...plus I would like to "enjoy" my college life...At the same time I dont want to waste too much time like you said "reviewing" courses for a good 2 2&1/2 years...

I mean if you say I am currently equivalent to a sophomore year student it does open up possibilities like double majoring right? I could keep going with Math...Do a Math/Physics double maybe?

I am not exactly burning out...I only learn this stuff because I enjoy it more than a lot of other things...@Ekrim you said research? Would I be able to do research as an undergrad?

and anyone has an answer for me on picking a speciality within Physics this early? I mean I know topics that interest me more than others...Should I pursue them or do you think a wider knowledge base is better than a deeper one?

You guys are really really helpful by the way! Wish I found this place earlier..! Anyone who has been in a position like mine or known of someone: what did you do? How did it turn out for you?

*would I be able to do research as a freshman was my question sorry...

As an undergrad you can assist professors with their research. It's a good experience, and helps you get into grad school, especially if you get your name on a published paper. People usually start research later in their undergrad career, but since you have the knowledge, why not? When you get settled in a college, find a professor in your department who is doing interesting research and talk to them about it.

You don't have to pick a specialty until graduate school, but you can specialize in something during undergrad by taking your physics electives in a particular area. Remember that your freshman peers will be learning vector addition and Newton's Laws.

Ok...Wow...That clears some stuff up...Thanks a lot guys...Anything else you have to say is invaluable...

Cheers!
~ElNino

Staff Emeritus
First, I'm afraid that your understanding of these topics is not very deep. I can tell that just from the list of topics - for example, you list the principle of least action as an electromagnetic topic, not a mechanics topic. While there is an action for electromagnetism, historically this has been taught as part of mechanics (where there are many more applications). It relies on something called "the calculus of variations", which is not listed in the math that you say you know. So while I don't doubt that you've learned something about these topics, and while you are to be commended for learning on your own, you shouldn't think you've mastered them.

Second, can you do research as a freshman? That depends on your school and the professor you want to work for. Some professors have no room for new undergrads, or not funding for them, and some want to wait until you've learned a little more. So you may not get to work with your first choice. I can tell you two things you can do that will help you:

(2) Recognize that "look at how smart I am" is not a particularly endearing or useful quality in an undergraduate researcher.

I was afriad of that...Look I am not trying to show off or brag that "ooh I am a seventeen year old who knows physics", I am truly in love with the subject and have been for a long time, just like you...I dont think I have mastered anything, I dont think that I am as good as you though I have no idea how good you are, I think I have put in work which you should not write off because I am a high-school student...Look Vanadium 50... you dont know jack all about me...Do you want me to list professors who are qualified who have reviewed my work?
I have done a lot of work on my own but not blindly. Been advised by a professor who is a downright genius in Physics who doesnt quite give me the perspective that I am looking for.Old timer who I cant really talk to. Hence I came here. Do you want me to give you a list of EVERY SINGLE topic that I have covered? I wrote what I wrote in a hurry...this is a forum not an admissions room I didnt think I needed to be that specific and I actually got a bit bored towards the end which is why optics and mechanics are dry...I thought I gave you what would give you a rough idea of what I think I have done...

I am sure you are a great scientist but please, I am not an idiot. You can't judge me based on "where I listed principle of least action"...If you must know one of my advisor professor wrote a paper on its applications in Electromagnetism. I spent a long time and a great deal of effort into understanding what he taught me. I also happen to know about its focus in Morse Theory as well as Maupertuis and Hamiltonian principles and am very aware of the fact that it is a topic that has a focus in mechanics and the fact that it's largest application was in the formulation of Lagrangian classical mechanics. What are you going to do next quiz me?! do me a few favours over here:

1. Just because I said I am a 17 year old kid doesnt mean you have the right to underestimate what I have done. If you arent conviced ask me for more information I dont appreciate disrespect however good you may be.
2. Please oh please find better things to do with your time than judge my writing on a forum for god's sake!! Thats pitiful
3. For the record: I learnt Functionals and Calculus of variations when I was fifteen. I worked out over five hundred problems. I used books by Robert Weinstock, Forsyth as well as in Indian author named Dr. Grewal. If you still want more proof I can give you my professor's phone number and you can call him.

For the people who don't think I am trying to show off to a bunch of people who dont know me...I welcome any input you have. But I think I have heard what I need to hear.

Look guys I came here because I thought people would understand the position I am in, please dont go offensive on me like this. If I had never mentioned my age you wouldnt have reacted that way. I know enough Physics to know what I put on the list was bits and pieces but it's purpose was for you to know what I have worked on not a resume!

RonL
Gold Member
(2) Recognize that "look at how smart I am" is not a particularly endearing or useful quality in an undergraduate researcher.
In addition to these two points.
I would say don't get in the habit of comparing yourself to others so much, and above all learn how to do some self evaluation, of what makes you happy and fulfilled.
Learn how to be content working with, and around others, that might not be as advanced as you become, the world will be full of this type situations.
Don't be afraid to change goals if you find you really don't like, what you thought you would.

@RonL...
I know changing goals is something that is hard to admit but I am not really afriad of it. And I dont really compare myself to others that much I have confidence in my own abilitiy. It's just unless you compare yourself to others around you it's difficult to judge exactly where you stand and I think that is important. I know myself well enough to know that Physics is the one thing that makes me happier than anything else. Honestly...and that doesnt come without self evaluation...But I will keep in mind what you said...

cristo
Staff Emeritus
ElNino,

Please don't take offence by the things people say. Yes, if you hadn't said you age, then people won't think twice, but then that would defeat the point of your post, wouldn't it, since you are seeking advice on what to do next.

The reason I haven't replied to your reply above was that I'm not from the US and thus have no idea on what the level of knowledge of a physics undergrad is, nor on what it's like to be an undergrad at an American unversity. I agree that one shouldn't immediately judge your writing here and, if you want my opinion, I don't think you were coming here to try and show off.

I'm afraid, due to the reasons above, I don't really have any more advice for you. However, I strongly encourage you to apply for the top schools in the US. I would also advise enclosing a letter of recommendation from your professor to back up all the information you have learnt on your own. Saying that you've studied x,y and z doesn't mean nearly as much as having a professor prove you have.

Finally, I hope you stick around on PF; it's a great place to be and has a mix of people; be they current professors, researchers, teachers, grad students, undergrad students, high school students, along with many professionals in other fields and in industry, from whom you can learn a lot (I know I certainly have!)

Good luck with the applications!

I'll be going to college next year...and I am curious as to how advanced this is...
I think probably your best bet is to talk to an adviser at the college you will be attending (or potentially will be). If your background is so advanced, you might be able to test out of many courses. Certainly, it would depend on the school policies. I think it is obvious you are a special case, so why not talk to someone that would be able to give you some real answers?

Thanks Cristo...It's just that I have faced a lot for being who I am ...you know sometimes its not easy with the classmates and the professors even, I just don't like disrespect, I don't dish it out so why should I get it back, you know? I will definitely get a professor reccomendation I actually hadn't thought of HOW i'd get this across to a university will keep that in mind. Hopefully I can become like one of you Physicist guys if I play my cards right. Looking forward to it...

I will definitely stick around here. Will be gone for a while have my exams soon but will be back later. I was reading some of the other threads and looks like the kind of place that I want to hang around in...

Thanks again!

@Bravernix...Yeah I think I will talk to an adviser for sure. Just thought the more information I could get the clearer it would be for me. I've just started thinking about my future and stuff so this was the first place I landed up! But definitely will talk to a college adviser as you said...

Staff Emeritus
I see. So by "rate my work", you really meant, "tell me only positive things about it".

What are you going to do next quiz me?! do me a few favours over here:

1. Just because I said I am a 17 year old kid doesnt mean you have the right to underestimate what I have done. If you arent conviced ask me for more information I dont appreciate disrespect however good you may be.
2. Please oh please find better things to do with your time than judge my writing on a forum for god's sake!! Thats pitiful

...

For the people who don't think I am trying to show off to a bunch of people who dont know me...I welcome any input you have. But I think I have heard what I need to hear.

...

Look guys I came here because I thought people would understand the position I am in, please dont go offensive on me like this. If I had never mentioned my age you wouldnt have reacted that way. I know enough Physics to know what I put on the list was bits and pieces but it's purpose was for you to know what I have worked on not a resume!
You shouldn't be so hostile toward people giving you advice. I don't think he was being offensive at all, but you are sounding really arrogant now. You're "dishing out" quite a lot of disrespect for the people here.

edit: I predict you're going to receive a lot of criticism on this thread, and you need to learn how to take it in.

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I find it very difficult to believe that you learned all of that material in 2 years. If you're being honest in "presenting your work," then you're claiming to have learned more on your own in 2 years than what I will have learned at the end of my undergraduate career (and I'm a math phys major/pure math minor).

What kind of comments are you looking for, exactly? It really just seems to me like you're trying to show off and fishing for some compliments.

To be honest, it looks like he just copied most of those topics from somewhere. I can't imagine anyone who is truly studying within the field to list what they know in a fashion such as this:

Semiconductors: Junction Diodes, Transistors, Characteristics, Light based
devices, Amplifiers, Oscillators.
Also

Electromagnetic : Integral and Differential Calculus of Vector Fields,
Electromagnetic Theory - Maxwell, Vector Potentials, Principle of Least Action,
Solutions to Maxwell's equations of Free Space and Currents Charges,
Waveguides - Transmission Lines, Cut Off, Cavity Resonators, Alternating
Currents, Lorentz Transformations for fields, EM Mass, Internal Crystal
Geometry, AC Circuits, Reactance, Susceptance
I don't believe you've learned these topics beyond reading a table of contents. In fact, I don't really believe you've learned 99% of what you've listed in your original post.

However, please don't give me your professor's phone number or anything like that - I don't really care. I'm just replying to a post on a message board and have no desire to do a fact/background check.

Moonbear
Staff Emeritus
Gold Member
ElNino, I think the above responses demonstrate a key problem with us being able to evaluate you. We have no idea how WELL you have learned those topics just by reading that list, and it seems you really don't either since you have no objective test of your knowledge. You may have a very superficial understanding of them all, you may be great at solving problems in a very formulaic way without really understanding the concepts behind it (or you may be developing some misconceptions without having a way to identify this).

The other difficulty is that while you may understand some of those topics very well, have you done all the topics that would be included in a single course in university, and done them well enough to have mastered the course? Even someone transferring from one university to another with great grades can find themselves struggling if they missed a topic or two that were taught in a different order or different courses in the school they transferred from than the one they transferred to.

You also say your grades in school are suffering because you're spending too much time on these other subjects you're learning independently rather than focusing on the subjects you need to take in school. Why are you short-changing yourself on those subjects?

Perhaps you should spend some time in our HW and coursework forums discussing your understanding of the concepts in some of these topics to get some feedback on how well you're really understanding them. If folks start pointing out a lot of errors and misunderstandings in what you present, you'll know you do need to review these subjects further. If your work checks out, maybe you do have a sufficient understanding.

-If you think you can help me or have anything useful to say thanks for that.
-If you find it hard to believe I have covered this then again, you are completely entitled to your opinion again, I can understand where you are coming from
-I have no reason to prove myself to anyone here, nor am I fishing for compliments I have better things to do with my time
-If you think I have come here to get compliments, show off or don't believe what I have done I suggest you don't reply because its a waste of your time writing it and waste of mine reading. If you think I have come here to hear compliments don't give me any.

What books have you been reading?

@Moonbear yes I believe it is impossible for you to evaluate me without more information, it was a bad idea.

As for what comments I am looking for not really anything more. Among all that I got, I got a few answers as well. I would try and clarify for you the level of my understanding but I don't believe that its possible unless I give you a huge amount of information about my work which is hard in little text boxes. Due to that I understand it will be difficult for you to evaluate me and I will look for another means of evaluation (i.e find another professor to look at it)