Excellent course. Very well explained and in detail.

It’s working for me. I would prefer the question choices to be fractions rather than decimal (eg 6/13 rather than 0.46) but that is only my preference.

Awesome

works for me

I generally prefer to know where did the formula come from before I start using it. Understanding comes before calculation. But I can cope with it …

This approach works for me.

I think this is a good approach. All my life I have experienced the opposite method of derivation first and I am comfortable with that, but I can see the benefit of your approach.

I personally prefer to see derivations of the formula first, I am coping though.

This work for me.

I found that just using the formula, and choosing to just believe it is true for now is less confusing than deriving the formula before really understanding all the information needed to logically think through where the formula comes from. I was able to look at the answers to the example problems and estimate what the answer should be by just understanding HOW the formula works, not where the formula comes from. Also, realized that I am very rusty on my algebra skills, so the detailed walk through of the answers is much needed. Really enjoying the brain training.

It is perfect the way it is now. Enjoying it!

it is a good way to make realize the difference with galilean relativity, although not explaining yet the new formula.

I’m comfortable either way

Either way is good

Excelent!

u r the best sir!!!!!!!

Excellent course!

This work for me.

I think this is a good way.

It’s better to see the demonstration first.

I need to see derivations before

For me there is no need to see the derivations first as long as the formulas are derived at a later point in the course.
I am enjoying the course very much: thanks!

All good so far. Beats hanging out a Senor Cerveza’s and getting sick. Itching to derive the formula.

Good session

Works for me either way!

As it depends on the combination of the age of the student and teaching experience, seems appropriate for entry level, and somehow less for older dogs dealing with new tricks.

Great Course, Professor Green! I started browsing through the animation pictures of your Light Clock, then watching the Characters George and Gracie and every time I was feeling more enthusiast while jumping from Modules at the middle to Modules at the end.
Now, revisiting the Course in a quieter mood I found myself deeply impressed with your way of teaching. Yes, dropping and practising with the addition velocity formula is the best way of awake our feelings accustomed to Newtonian Mechanics.

Thank you so much for making World Science U Proffesor Greene. I am really enjoying this course and I am ok with you deriving the formula later Sir.

So far so good. I am hoping to see Lagrangian/Hamiltonian formulations soon

If it is not too complex for the level of the course, I would like to know where the formula comes from before I use it. In this case, I will wait for Module 25 to satisfy my curiosity.

I think derivation is also important for understanding the situation before applying the formula.

thank you very much

well explained content . Keeping going.

i usually prefer to know how the formula is derived first but i am fine the way it goes. I like very much your teaching style, speed and the choice if words and examples

Absolutely loved it! Looking forward to the derivation.

very interesting way.

Using the formula first works for me, it allows me to explore how it behaves with different parameters. It’s similar how you might try to understand functions written by someone else in software development. Exploring a more complex formula might take too much time to achieve the same level of familiarity, though.

Personally I like it when I know how the formula has come up before just using it but the approach currently used is fine for me

wsu please make courses for quantum mechanics also with ‘”brain greene”

It works for me .

I have to refresh my basic algebra…but I’m fascinated nonetheless…I think this formula works given my learning style…you are a remarkable teacher and I hope you will eventually give us another master class, this time on the theory of general relativity…thank you so much for your intellectual generosity…we are privileged to live in a time where knowledge is not reserved for an exclusive elite…

I am used to deriving the formula first, but this way works too.

Thank you for this approach. It’s very good first to have an intuition and feeling about some phenomena. The logic explanation should come when in your mind the idea already exists and already works with your subconscious and conscious. From my experience it’s the best way of learning. Thanks once more.

This works for me. It’s helpful to get used to using formulae in different situations before seeing the derivation later in order to cement the understanding before getting bogged down in those details. Thank you for providing this course – your teaching method and style are excellent and you put across concepts in a way that are easy to grasp.

Yes, it’s fine thank you. You are very clear and I can fill in what my own gaps are.

I am comfortable .By doing the problems first I can wonder how such a type of combination comes .And by studying the derivation I can the the way the genius scientists think

So far, this course, although challenging given it’s been 40 years since I was in college, has worked for me.

I’m loving it. Relative velocity was a very hard concept for me since my college but after taking this course all the gaps are clear.

No, I seem to struggle with this way of learning. I am the kind of person who first wants to get an intuitive sense of the topic, and then work over it.
I find it hard to directly apply things without knowing how they have arrived.
But above all, the course designer knows more than me and would have definitely planned such a structure for better understanding of students.
So I have no problems from my side

So it then looks like in general the formula is

(v+w)/(1+v•w)

with v•w the (normalized) dot product of the velocities (implying the factor of cosine of the angle between directions)…

Derivation would be great sir

I find this approach very helpful. It enhances understanding of the way the formula works out, and enhances my curiosity to learn the basis / the derivation of it.

excellent

Both work for me but I prefer derivation first. Then calculation internalises the insight.

Personally, I prefer to apply formulas after seeing them derived, however using a standard formula without the derivation may be simpler to not complicate things.

I was a bit surprised at first but indeed, I realize that it is nice to get a feeling for the principle and its consequences first, to develop an intuitive understanding of the theory (particularly its differences with the “everyday” Galilean model) before delving into the mathematical derivation of it. And thanks again for this great course; the content, the pace, the exercices and simulation tools are absolutely top-notch. I can’t believe we have access to it for free. Thanks a million!

I am very excited to have the opportunity to dig into this stuff, and my fantasy quest is to find out what’s behind the black holes in our universe. I”ve just dusted off my 40+ year-old calculus book, and don’t remember a thing from my Frershman 101 Physics course from 1959. In the in-between time, I was a fashion designer, mother, and wrote text books on how to use microsoft office apps. Completed my math degree somewhere in-between and have since regretted that I didn’t take my math further, or get some more physics in my head. My skills are a bit rusty, but I’m slowly regaining them. I wouldn’t like things to get much more complicated just yet (yes a little later), or I would not be able to find the time to mow the lawn.

As this is the formula, it simply needs learning. Thank you for asking. New knowledge often lags on comprehension.

Best way of teaching

Working with the formula and going through problem sets is an excellent way to get acquainted with the function before we go into a derivation of it later on in the course. I think that understanding how it functions and then learning the inner workings of the formula is an excellent way to learn.

the formula deals about one of the most mindboggling concepts ever, so holding nerve without trying to know how is it possible is a bit difficult but as we have so many other works, we tend to go on with the process and wait until you derive

Works well for me.

either way works for me, as long as I end up with knowledge of both, eventually.

Work for me.. I appreciate the thorough and detailed presentation of the course you provided.

Ladies and Gentlemen,

Prof. Greene`s book To the End of Time is well worth a read.

Topics that have clarity are Entropy, black holes being hotter when smaller, and kid explosions frm too much gas in the oven.

It is a thorough book.

I am a Monroe Institute distributor. We may be answering some questions Prof. Greene has asked in his book.

http://www.monroeinstitute.org

I appreciate your consideration in introducing the new velocity combination formula without deriving it initially. While I understand the value of gaining familiarity with key ideas before diving into technical details, personally, I am more comfortable and find it easier to grasp a new formula when I have seen its derivation first. Understanding the underlying principles and how the formula is derived helps me connect the dots and solidify my understanding of the concept. So, I would prefer to see the derivation before fully embracing the new formula. Thank you for understanding my learning style.

Actually I have gone through derivation in my university course, but I like the idea of introducing students a formula before derivation and then show them where it came from.

I think deriving the relativistic velocity correction formula (“formula”) sooner, or providing some additional background, might help with some confusion I have as described below.

My confusion is in regard to 2 moving objects approaching a “stationary” object from opposite directions, their associated frames of reference, and the “types of” velocities being observed. I am assuming that by “stationary” we mean an object has zero velocity relative to the velocity of light.

In module 3.8 exercise 1, we have 2 taxis approaching a “stationary” person from opposite directions, and the “stationary” person is observing the velocity (or rate) at which the gap between the taxis is closing. In this case we just add the 2 taxis velocities together even if the total is greater than the velocity of light. No confusion here (I hope!).

In module 5.4 exercise 2 and module 5.6 exercise 1, we again have two objects (taxis and spaceships respectively) approaching a “stationary” person from opposite directions. In this case, if we are observing the velocities of the moving objects relative to each other (not the velocity of the change in the gap between the moving objects), then the formula would be applied; the formula is applied with v and w being the velocities of the two moving objects relative to the velocity of light. If the velocity being observed is of one of the moving objects relative to the “stationary” person, then the formula can still applied but the velocity of the “stationary” person (v or w) would be zero.

I know it’s tough to be clear about this topic, but if any one has comments that would further clarify or confirm the above, that would be appreciated.

Rather formula deduction first, but it works perfectly fine

Examples would help

I’m used to get good grab on conceptual principles on the 1st step. On the 2nd step the formula “as is” without derivation, in order to strengthen the alredy learnt concepts. On the 3rd step, after I’ve tried and succeeded or failed myself, I’d like to check the derivation done by the professional scientists.

This works for me. The physics course I took forced us to derivate our own formulas from scratch for everything. There were no formulas provided or derivation done for us.