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There is one sure way, and it’s a test of your fortitude. You find a a college textbook with the answers to the even-numbered problems in the back. You sit down in a warm or hot room, and solve them. If the textbook is in its 4th printing or so, the answers are correct. On a few, you’ll have to work for hours. Now here is a very, very, important point. All the learning occurs on the problems you struggle with. In the blind alleys. A lot of learning in physics comprises paring down your misconceptions until the correct methodology, often surprisingly simple, appears. Then, you understand how to apply the basic laws to the problem at hand, which is what physics is. I’ll emphasize the point by stating it’s converse. A problem you can solve easily and quickly yields zero knowledge.

I would recommend two outstanding textbooks. Halliday and Resnick, early editions , printed in the late 60s and 70s. If you can do all the odd problems in this two volume set, you are an educated person, regardless of your greater aspirations. Edward Purcell’s Berkeley Physics Series Second Volume on Electricity and Magnetism. Might be the best undergraduate physics textbook ever written. Did you know that magnetism arises from electrostatics and relativistic length contraction? It’s right there. You should also get yourself a copy of Feynman’s Lectures on Physics. Warning. Read it for intuition, motivation, the story of Mr. Bader, and entertainment. It’s at much too advanced a point of view to help you solve nuts and bolts physics exercises, which is what you must do. One final warning. Every one of us sits at a desk with a powerful internet-connected computer. Don’t do this. Even get a calculator to avoid this. Of course, when you are stumped you’ll want to see how a topic has been treated by others. Do it in another room.

I agree with this suggestion. It took me a year to slowly absorb the entire book of Statistics [0] including solving all exercises. It's just like walking to school but there is no external supervision. I made a rule to complete one chapter every evening including exercises and sticked to it.

[0]: https://www.amazon.com/Statistics-4th-David-Freedman/dp/0393...

Your story implies there are 365 chapters.

It implies he completed 365 chapters but says nothing about repetition of the chapters.

> sit down in a warm or hot room

While I agree with everything else, I'd have to vehemently disagree with this. Studies [1] have shown that warm temperatures severely diminish our performance on complex mental tasks.

As some examples [2]:

> Sales for scratch tickets, which require buyers to choose between many different options, fell by $594 with every 1° Fahrenheit increase in temperature. Sales for lotto tickets, which require fewer decisions on the part of the buyer, were not affected.

> participants were asked to proofread an article while they were in either a warm (77°) or a cool (67°) room. Participants in warm rooms performed significantly worse than those in cool rooms, failing to identify almost half of the spelling and grammatical errors (those in cool rooms, on the hand, only missed a quarter of the mistakes).

[1] https://www.bauer.uh.edu/vpatrick/docs/Influence%20of%20Warm... [2] https://www.scientificamerican.com/article/warm-weather-make...

> You sit down in a warm or hot room

What is wrong with airconditioning?

I am not sure about OP's reasoning, but I personally find it a bit 'motivating' to study in a slightly not-so-comfortable environment. I mean, it gives me sense that I am actually determined and am working hard. It also reminds me of my college days when even finding an air-conditioned room anywhere was just not possible.

Could also give you the feeling of being uncomfortable. Then when you are struggling working through a problem you get so frustrated. And think "If only it weren't so damn hot in here." Then all you can think about is the heat, and you are so lost it cannot be returned. So then you give up for the day, and really haven't accomplished anything.

Exactly, your mileage may vary, but my mindset has to be completely free from distractions to be productive.

The library on my uni when I was in Math undergrad did not have AC at the beggining but was the only place where I could do any work, it was extremely difficult and I am sure impacted my progress.

I find it impossible to think or stay focused in a hot or even warm environment. People are different I guess.

I'm the same. During winter months, when I needed to cram a lot, I would open the windows wide, and sit with my jacket on. The cold would help me not fall asleep.

A hot room sounds horrible, but the memories of college days does make sense to me. My college was freezing cold, and my search would be for a room where you didn't need to wear 2 sweaters to be comfortable.

But yeah, the idea of studying in a really cold room "makes sense" to me, and this might be why.

I think that's just building the idea that it's going to be a painful and uncomfortable process

In cold parts of the world, warm has connotations of comfort, not cold...

Is this part of the process? Visit a cold part of the world, set yourself up with a physics textbook in front of a fireplace...

Actually, that sounds quite nice.

my deduction: if you done it in a warm or hot room, you surely have enough will to do it.

Seconded. I really believe there are no shortcuts to doing lots of problems. If you can afford it, getting a physics grad student to discuss problems that stumped you every now and then might also have quite good ROI, talking to physicists might also help convey some of the physics mindset(?).

Reading this made me nostalgic for my days as a physics undergrad.

I'll second this idea having survived a Physics BS doing just this. I'd also strongly recommend a series of books called Schaum's Outlines, they vary in quality but cover many advanced topics and have hundreds of solved problems in them.

Schaum's Calculus was invaluable to refresh my memory of some of the details of "Calc 2" so I could be sure of passing a waiver exam (most schools would have waived it automatically on account of my AP credits but my school limited me to how many I could waive that way...) and get on with Calc 3. The book covered some Calc 3 too so continued being useful. I have a few others in the series, very handy.

"The reader who has read the book but cannot do the exercises has learned nothing." -- J.J. Sakurai

(Incidentally, I tried reading Sakurai's Modern Quantum Mechanics on my own once and was immediately curb stomped. Lots of prep work required for that one...)

Defs agree with op. I learned the more advanced maths I use daily in my thirties. It took about 3 years of exactly ops method. In my case, I found it motivating to take exams because it gives you a bit of skin in the game; forces you to prioritise your study at some point.

A final thing: it's really worth doing. If you long for maths; it's likely it'll conceptually take you places you won't go without it. Do it!

This is also what I did, going straight to the exercises except I used Calculus I by Apostol which covers some Linear Algebra. Perfect book if you need to redo math skills you've forgotten though plenty of times I had to Wikipedia, Khan Academy, and math.stackexchange in the beginning.

There's also this free book, no answers though you could stackexchange if really stuck. I finished most of Apostol before starting it https://infinitedescent.xyz/


Is it that the text you’re referring to? We used the 5th edition in my physics course this year. It was a tough textbook to learn from but I feel like I learned a ton.

I almost never went to class in university (Waterloo Engineering) and this is how I did it. The best is not letting them explain the concept to you first. Try to invent the math as you go along by covering the explanatory pages with pieces of paper and reading only one line at a time.

It will stick with you forever.

I second this, but, you will need some help initially. Follow the examples a few times - first with help, then without. Once you build your intuition, you will then be in a position to "invent" the maths as you go along.

> Halliday and Resnick, early editions , printed in the late 60s and 70s

Any particular reason to recommend the old editions over the latter ones?

I actually had to look into this recently.

The recent ones are less "textbook." The older ones are FILLED with information with graphics here and there but it's mostly text. The recent ones are very graphical so I would assume it has less total information. With that said, it's possible that there are techniques for learning that were not considered in the older texts.

It is possible to look at samples online for you to compare if you want to see the difference. I do recommend getting the book if you decide to use it but that's just a personal preference.

Textbooks have generally gotten less information dense over time.

> If the textbook is in its 4th printing or so, the answers are correct

It's terrifying that it takes 4 printings before the answers should be considered trustworthy...

Do you write bug free code?

Is publishing a book the same thing as writing code?

No, writing a math textbook involves (perhaps) thousands of things that might be wrong, none of which will have any impact on one another.

Publishing a perfect book is difficult on par with writing code. Hell, Knuth is incredibly popular and crowdsources his error-checking, and TAOCP is still in its third edition.

Very similar in some ways. There are a vast number of interconnected details that have the potential to be wrong and far fewer automated ways to catch any errors. Your "users" inevitably catch a lot of them at "runtime".

Yes. You're programming a person instead of a computer but that's the only difference.

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