Seriously, I'm looking for some community feedback on the kinds of things they want to learn about in physics/applied math. I'm bored and want to teach people some stuff. Here's your chance to get detailed knowledge of something fun you can't learn in school!

Possible topics off the top of my head are below. The idea would be that I would pick an aspect of one of these disciplines and do a few nice sets that explain that aspect and give serious practice. So, rank your top five topics in comments on this note, and if there is a large enough feedback I can do a series of sets with notes/problems over the next few weeks that will illuminate the most popular topic. Other topic ideas are also welcome.

*Physics-y topics*:

Relativity

Black holes

Gravitational waves

Dark matter/energy

Cosmology

Pulsars

Entropy

Uncertainty principle

Entanglement

Quantum information theory

Chaos

Extra dimensions

2-d materials like graphene

Particle accelerators

Neutrinos

*More mathy topics*:

Topology and geometry in physics

Principle of least action

Mathematical methods in physics

Group theory in physics

The role of symmetry

Representation theory

Fiber bundles

Why do we care about complex numbers? (life would be harder if we had to use quaternions all the time)

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## Comments

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TopNewestAlright, here is the list with my admittedly unscientific summation of votes. I took every mention of a topic in a list as a vote. I did not take into account rank order within lists, as some people did rank and some listed "in no particular order". Even with a little noise, I think it's pretty clear where people's interests lie.

As a result of the voting, we will start off with the following sequence: a little basic relativity, what is a black hole?, what is information and thermodynamic entropy?, what is the entropy of black hole?, why is that so surprising?, holography.

This makes for a nice story, is something you may have heard about in pop sci books/stories, and hits the first three topics. Then we can run down the list. Expect the first set in a few days. Each set will have expository notes, some basic problems which you should be able to do to move on to the subsequent sets, and some challenge problems for those who want it. And yes, I can make Hawking radiation, black holes, the holographic principle, and relativity accessible to those who may have only taken a minimum of physics, so it'll be fun!

TopicVotesRelativity 19

Entropy 13

Black holes 12

Gravitational waves 11

Uncertainty principle 10

Dark matter 10

Mathematical methods 9

Extra dimensions 8

Cosmology 7

Dark energy 6

Complex numbers 6

Chaos 6

Topology and geometry 4

Symmetry 4

Group theory 4

Quantum mechanics 3

Quantum information theory 3

Pulsars 3

Fiber bundles 3

Entanglement 3

Representation theory 2

Particle accelerators 2

Neutrinos 2

Thermocouples 1

Quantum field theory 1

Nuclear 1

n-d displacement 1

Gravitational force 1

Graphene 1

Gaussian distributions 1

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Awesome response so far. What I'm going to do is to let this note sit for today, so that everyone who wants to has a chance to vote, and then I'll tally up the results and put them here. The first set on the chosen topic should then come a few days after (probably over the weekend).

One thing I'd like is for people to not just submit answers to the problems on the sets, but if you get it right to submit a nice solution too. We all know that there are topics for which there are few resources around. It'd be great to have nice community solutions so that those who come after in the Brilliant community have a resource to learn this stuff too. Giving back and all that :)

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I love physics but I have only few knowledge on those out-of-school topics. So, I hope you can start a set with fundamental notes of that topic and advancing the notes as the problem gets tougher. For example, I'm eager to know what chaos theory is and I can solve the first 3 problems but now I have still no idea on the 4th problem and I don't think I really understands it.

Looking forward to it! I would like

Chaos,Black Holes,CosmologyandRelativity.Log in to reply

If you want to learn Chaos Theory, I would suggest the following books (to be introduced to the subject):

"Chaos" by James Gleick "Does God Play Dice? The New Mathematics of Chaos" by Ian Stewart

You should know differential equations though, before those books and chaos theory in general.

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@Christopher Boo ,Actually The 4th question of the set, doesn't require any knowledge of chaos theory(way to advanced), All that is required is the way things bounce of each other (angle of incidence equal to the angle of reflection), plus since \(Ne \ll 1\), you can reasonably assume \(sin\theta =\theta ,\quad and\quad tan\theta =\theta\). The solution might not seem clear since a lot of small angle approximation is required. I hope that clears things.

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And please make them hard like the good all days:))

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They will start easy and become harder with something devilish at the end. The sets would be meant to be educational as.well as fun. Hence we'd begin with basics, end with sophisticated questions, and people just go as far as they can. Something for everyone!

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Why

dowe care about complex numbers?Log in to reply

All the topics are equally interesting!!Make sets on all of them please!! ^_^

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Ha! I wish I had the time...

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Quantum, relativity and nuclear :)

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It would be really great if you answer me only about one question. To my satisfication nobody has ever answered me this. When physicists tried writing equation for sound wave for first time, whatever function that would describe the sound wave was taken to be real because obviously sound wave is real. But then what happened when they tried to build theory of quantum mechanics? How and why did they start with complex \(\psi\) instead of real? How did they a priori know that it has to be taken to be complex? Why didn't they start with something real and then swithced to complex?

I would be really greatful to you if you answer my question. Thank you

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Since we're not going to get to this this time around, did you ever read Aaron's note mentioned in this Brilliant discussion?

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Think abt it this way..the most fundamental equation in qm the schrodinger in itself is complex in nature. The wavefunction are the possible solutions to the schrodinger equation...so they must be complex obviously. ..

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It's actually more basic than this! You don't need a specific equation, and indeed there can be extensions of qm that use variations on the schrodinger eqn. It boils down to some basic physical requirements and the fact that complex numbers are algebraically complete. But we're getting ahead of ourselves....

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Gravitational waves(quite recently, on March 14, they were experimentally detected)

Relativity

Mathematical methods in physics

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Pulsars and entanglement to be added here too. that completes 5!

I guess symmetry as in Gaussian surfaces and method of images? Well that is taught in school. If any other articles are present related to symmetry then I am willing to learn.

And of course Dark energy.

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Oh there is so much more to symmetry...symmetries dictate the content of our physics, they tell us what is out there in the universe.

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I vote representation theory and fiber bundles!

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Well, I would definitely want the topics related to astrophysics and cosmology to be addressed. :)

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Extra dimensions, Representation theory, complex numbers, Mathematical methods in physics, Uncertainty Principle

Not listed according to degree of interests.

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@David Mattingly I would definitely like to learn about -

Relativity

Black holes

Dark matter/energy

Cosmology

Topology and geometry in physics

I really admire your effort regarding this initiative .... Days are going to be tough for you(There is lot of expectations)All the best!

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My top 5 subjects would be

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I'll go with black holes, dark matter, and gravitational waves \m/

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Gravitational waves, Topology and geometry in physics

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My Top 5:Relativity, Gravitational Waves, Entropy, Mathematical Methods in physics, Group theory in physicsLog in to reply

I wud like to know about entropy in detail

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All my votes go to gravity waves!

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The first set is up!

Link is here

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Electricity genration by thermocouple

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The role of symmetry, Chaos, Why do we care about complex numbers? ,Mathematical methods in physics, Relativity

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For me, it would be Quantum information theory, Entanglement, Black holes, Cosmology and Dark matter/energy. I have this insane fascination for these topics.

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The uncertainty principle made sense to me when I first read about it: obviously, measuring a system affects it, which affects other measurements. That's why we can't measure position and momentum simultaneously, because to determine position, we need to "take a photograph" of the particle, but photographs don't tell us anything about the momentum/direction of motion, unless we take a long-exposure photograph, which in turn makes the position uncertain. I don't remember where I read that analogy but it was very intuitive. But I always wondered, is the UP an inviolable principle of physics? Won't better measuring devices someday make it possible to determine such quantities simultaneously? Apparently not, and I don't know why.

I've studied the basics about entropy in thermodynamics but want to learn more about it (it's pretty interesting).

Quantum information theory is (apparently) the future of computing, so I obviously want to hear about (qub)it. In fact, some basics about information theory would also be welcome, since I don't understand present computing either!

And finally, symmetry has been used to derive conservation laws (I don't know how or why) and that intrigues me, since they're used so commonly everywhere.

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would u teach me all of them??

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A lot of interesting topics indeed! If I were to choose, I'd pick dark matter, uncertainty principle, chaos theory, complex numbers and Gaussian distribution (maybe, I think it's such an important concept :-0 Just my opinion). All of them are great, those were just my choice.

Looking at the comments, I see quite a bit of people going for quantum theory, entropy, relativity and gravitational waves seem quite popular! Those are amazing things too. ^^

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Yep quantum and entropy seem to be popular. What is your major in MIT?@Vishnuram Leonardodavinci

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Next set is up!

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That's awesome I will be interested in studying the following topics : Mathematical methods in physics, Dark Energy/Matter Relativity Extra dimensions (My interest in Extra dimensions arose after I watched the TV show of Stephen Hawking in which he told that the TIME is probably the fourth dimension) Black holes (Order represents my preferential choice)

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It would be relativity, black holes, uncertainty principle

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Topology ans geometry of in physics!

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Well hw abt group theory???

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I have heard that to understand the quantum world we need to understand group theory...

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Thank You :) Relativity Black holes Gravitational waves Dark matter/energy Cosmology

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I would say Uncertainty principle / Entropy / Quantum Information Theory / Fiber Bundles / Topology and Geometry in Physics

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please do teach entropy in a detailed way.. i always wanted it..

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1.relativity 2.black holes 3.The role of symmetry 4.Extra dimensions 5.mathematical methods in physics

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Extra dimensions..!!

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Teach me entropy

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A brief introduction to Cosmology.

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By the way, all of these topics are taught at university.

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Relativity Entropy Dark Matter or Dark Energy

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All the topics are very interesting! I love to learn more about these things! Since only 5 should be chosen, My votes go to: 1.Gravitational waves 2.Uncertainty principle 3.Extra Dimensions 4.Complex numbers 5.The role of symmetry

Thank you!

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I want to learn plasma physics

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Sir plz try to put some questions on automotive engineering... Most of the group mates r having keen interest in bikes cars n engines... So pl do this small favour.. Thank you fr this site sir

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I would like to know about the relativity

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if you start something like this, that will b interesting way of learning PHysics for me ...............thanks

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That's a good idea!!!!!!

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This is AWESOME! It will be years before I even TAKE Physics 1, though. I hardly even understand acceleration and/or displacement. Actually... That's a good question. What is \(n\)-dimensional displacement and how can it be practically applied to problems?

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I agree

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I'm a classic example of a theoretical physicist: doesn't know a thing about math or physics equations but just sits around on his butt thinking about the universe. :D

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Also, you can't conduct actual research on the universe or practically any other topic without knowing the appropriate mathematics and physics knowledge.

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Recognize, however, that it is likely that you will not be correct unless you do know all the high end math and physics, as very smart, well trained people have been thinking about deep questions for a long time. If you don't understand what others have done and

whythey've done it, then likely your physical theory will veer off into crackpottery. That's one of the defining characteristics of a crackpot - they ignore what others have done and experimentally tested. But, if you are serious about physics, then sure, dream up new theories, even at a young age, and then go about and try to determine why your theory is wrong in a serious manner. This last point is key. A crackpot dreams up a theory and spends all their time believing it's right. A professional theorist dreams up a theory and spends all their time trying to see how it could be wrong.Log in to reply

I completely agree.

What I meant to say is that he can't be called what we generally refer to as a theoretical physicist (i.e. someone with a doctorate/master's degree in theoretical physics or something related.

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How is the prerequisite knowledge of theoretical physicists related to them "testing" a theory?

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How about Quantum Field Theory, with a touch of mathematics?

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black holes,gravitational waves,particle accelerators,neutrinos,group theory in physics

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It's awesome...I want to know that if it is required that there should be a medium to pass the rays..than how Sunrays comes to earth from sun.

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Nope..a medium is not required for light propogation...

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By medium, we just mean some quantity that changes from location to location. For sound, it's air pressure. For light (and all other electromagnetic radiation), it's the electric and magnetic fields, which are present everywhere. There is no physical medium required for ER to propagate, unlike sound waves.

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Entropy, Uncertainty Principle and 2D materials like Graphene.

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extra dimensions!!!!!!!!!

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Neutrinos and dark matter

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I was having trouble with a problem I was thinking about. Its calculating the amount of force a particle weighing .1kg would impart when moving at close to the speed of light

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Hello David can you please write solution for self-similar circuits problem. Sorry for interrupting in anotheer discussion

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relativity,black holes,dark energy,quantums,entropy......................please upload soon

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Relativity Entropy Uncertainty principle Chaos Extra dimensions

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mathematical methods in physics

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Vote goes for uncertainty principle.

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mines are 1)-relativity 2)-dark matter/energy 3)-pulsar 4)-entropy and the last but not the least 5)- mathematical methods in physics.

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Mathematical methods in physics, entropy, chaos... and yes want to know what is meant by extra dimensions?

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Dark energy. Why complex numbers.

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Bring it on!!!!!

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Here are the five topics i would want to know a lot more about. 1.entropy 2.particle accelerators 3.uncertainity principle 4.gravitational waves 5.the role of symmetry

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Black holes Gravitational waves Dark matter/energy Extra dimensions

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Relativity Group theory in physics Black holes Uncertainty principle Entanglement

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gravitational force, cosmology,Fiber bundles, Chaos and Relativity.

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However black hole is a difficult topic i would like to learn....

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So what if it's difficult? That just makes it more exciting sometimes :D

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My five topics are relativity,gravitational waves,entropy,principle of least action,math methods in physics. The other topics are quantum physics, entropy,cosmology, gravity.

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Can you help me to know more about neutrinos.you can even send me an email at vaibhav1579@hotmail.com.I would even like to know about relativity.

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Entropy

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Quantem mechanics

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group theory in physics, extra dimensions, topology and geomtry in physics, relativity :)

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Sir, first of all, I express my heart-felt gratitude towards your selfless effort. Here are my top five topics: 1. Mathematical methods in physics 2. Topology and geometry in physics 3. Extra dimensions 4. Principle of least action 5. Representation theory

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relativity entropy chaos black holes qantum mechanics

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i want to learn about the concept of resonance in physics and how to solve problems on the topic.

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How about some Fluid dynamics; Euler equation, Navier- Stokes, Bernoulli equations, things to that effect?

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I want to learn quantum physics,relativity,role of symmetry,gravitational waves,dark energy.

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Dark matter/energy Gravitational waves Cosmology Mathematical methods in physics geometry in physics

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Quantum theory

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No idea if we are taking votes anymore, but I'd love to learn about group theory and lie algebra!

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Mr David sir, i have a question. using special relativity i imagined two lines of charges running with velocity v in anti parallel directions and by considering the situation from different frames i derived that magnetism is a result or side effect of special relativity (about which i had a qualitative idea frpm internet before hand) but in the derivation i used the fact that the distance between adjacent charges in the line is decreased when moving causing a stronger electric field in that frame to compensate for the magnetic field in other frame.but then magnetism is also conveyed for moving point charges... but what contracts for a point charge. where can i apply lorenfz contraction for a point charge moving. or am i righy to assume that electric field weakns along the direction of motion for a point charge ? sorry for long post

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Black holes Gravitational wave Quantum theory of information principle of least action Dark matter

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1.Black holes 2.Gravitational wave 3.Quantum theory of information 4.principle of least action 5.Dark matter

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Applied maths.

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I agree

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Black holes Cosmology

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Entropy!!

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I would like cosmology, black hole, dark matter. .

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Sir I would be happy to learn everything you can teach me :)

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astronomy, cosmology, mathematical method and relativity,

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mathematical methods in physics

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1 Relativity,2.gravitational waves 3.particle accelerators 4.group theory in physics 5. Entanglement...

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cosmology, dark matter, relativity, pulsars

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Black hole

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i do seriously want to learn about spin(Quantum Spin)!! I really hope you could help!!!

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gravitational waves

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What is dark energy ?

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space time dimensions

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hello david sir can u help me with trigonometry...

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hello sir david,can u teach me trigonometry....??

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Dark matter, black holes, graphene, cosmology.....

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The role of symmetry

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relativity,black holes,cosmology,gravitational waves and dark matters !!!

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CAN U INCLUDE QUANTUM COUNTING

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Topology ang Geometry in Physics

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Thank you, sir. My top is .Gravitational waves, Black holes, Dark matter, Quantum information theory, fiber bundle.

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Relitivity,Neutrinos,Black holes bt from basic concept.

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Quantum information theory , Relativity and Black holes

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Gravitational waves

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thanks if you start this . I want to know about ENTROPY..... AND

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Cosmology

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Black hole is having very high density. But temperature s about 6 nK for stars of solar mass! Why and how?

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1..Relativity 2..black holes 3..entanglement 4..uncertainity 5..representation theory Relativity and black holes is my fav. Entanglement and reprentation theory is less known by me. And uncertainity does not seems convincing to me.(maybe because i might not be knowing it well. So i want to learn about that too.)

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Relativistic Mechanics, Relativistic Electrodynamics

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BLACK HOLESS

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Sir I would love to learn more about BLack Holes. I found this very interesting.

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relativity and extra dimensions

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How schodinger darived wave equation

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Hi Sir, Here is the list of topic I would like to learn. Most of them are Applied Mathematics.

Mathematical method Complex numbers Group theory (Abstract Algebra) Gaussian distributions

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I'm studying relativity right now (general) along with the math for it (diff geom), want to probably move to advanced quantum from there, train my relativity and quantum, then move to QFT, train that and maybe some math methods? So I can actually start plaint with the theories independently. So the list might look like:

1.Relativity (with implied topology and geometry)

2.Quantum (advanced with lots of problems)

QFT

Math methods (enough to build on current knowledge so I can start playing with the theories)

Current topics (String/Loop quantum Gravity / Cosmology)

How does that look? I can help on other topics like Hamiltonians and Lagrangians and Principle of least action if you're up for it! Why not just do all of them? ^^ I'm ready

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Sir , it would be Brilliant if you would create a new set on the concepts of work, energy and power.Thanks.

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@Abhijeet Verma Is there anything in particular you're confused about or wished you had a better explanation for regarding work, energy, and power? I'd love to hear back from you and then make some sets this weekend.

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Sir, shall I write my queries here in this set? BTW, my first query is in calculating the effective mass of a spring.I can't understand why the velocity of a point is a linear function of length. Thanks.

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dark matter interests me the most

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Mathematical methods in Phy & uncertainty principle

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I want to learn abt relativity

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Uncertainty principle..mathematical methods in physics

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1.Black holes 2.Dark matter 3.Mathematical method in physics 4.Cosmology 5.Uncertainty principle

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About particle physics

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