Earlier quoted context omitted.
Do you write bug free code?
Is publishing a book the same thing as writing code?
Yes. You're programming a person instead of a computer but that's the only difference.
Ask HN: How do I learn math/physics in my thirties?
101–110 of 160 posts
Re: Ask HN: How do I learn math/physics in my thirties?
#102Buy a book and take a course. It won’t be enjoyable but being examined on what you learn will provide focus. Find a small group of people doing the same or similar learning, so you can discuss the different problems each of you will have. Persevere and plan carefully. Otherwise you’ll waste time and energy. Don’t get sidetracked by great presentations and new tech from internet-based resources; remember what the objective is...
Re: Ask HN: How do I learn math/physics in my thirties?
#103Earlier quoted context omitted.
It's not just linear algebra, 3blue1brown also has an entire series on undergraduate calculus, and series on Statistics, Linear Algebra II and Group Theory are in the works. Plus a large number of excellent videos on miscellaneous math topics. I think I understand what you're saying -- one needs more than just cool videos and cool intuition. You need to do exercises. This is a point made multiple times in those very…
Ah, the videos come with pointers to exercises? I'm quite excited about https://www.edukera.com/ and possibilities for interactive learning through automated theorem proving. Thanks!
Actually, there are not many pointers to exercises. I believe they may be planning to add some written materials, so maybe in the future, but not currently.
The videos suggest pausing and trying to figure the next bit out yourself and a couple of the videos do end with a suggestion to prove something yourself.
Re: Ask HN: How do I learn math/physics in my thirties?
#104There 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…
> You sit down in a warm or hot room What is wrong with airconditioning?
In cold parts of the world, warm has connotations of comfort, not cold...
Re: Ask HN: How do I learn math/physics in my thirties?
#105Earlier quoted context omitted.
Do you write bug free code?
Is publishing a book the same thing as writing code?
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".
Re: Ask HN: How do I learn math/physics in my thirties?
#106Earlier quoted context omitted.
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.
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.
Re: Ask HN: How do I learn math/physics in my thirties?
#107get spivaks calculus. Took me months to get though chapter 1 :D, but gave me through understanding of how to think about maths and how to prove stuff and that proof are the real fun of math. If you can't prove it, you don't understand it.
I have no idea why someone would have down-voted you - Spivak is brilliant. It's not really about calculus, it's really about Real Analysis, and it's excellent.
Highly recommended.
Re: Ask HN: How do I learn math/physics in my thirties?
#108To quickly review a broad range of math up until 1st or 2nd year of university, I really recommend Khan Academy https://www.khanacademy.org/math . I am currently using it to brush up my math skills for machine learning.
Before going to Khan Academy, I started reading a rigorous math textbook, but my motivation didn't last long. You really need high motivation to complete a rigorous textbook, but Khan Academy is different and I am finally able to continuously improve my math skills.
The best thing I like about Khan Academy is the large amount and instant feedback of exercises that you don't get from regular textbooks. I really wished that Khan Academy was there when I was a kid.
To get deep knowledge of math, I think that rigorous textbooks are the way to go, but before those and to prepare for them, I really recommend Khan Academy.
Re: Ask HN: How do I learn math/physics in my thirties?
#109Hi,
I'm 30 and trying to relearn the math courses I did in college (Computer Science degree) and more. I am currently using Standford & MIT's open couseware. I feel like I am moving slower than I would if I were in a course but able to grasp the material better at this rate... I made good grades in my math courses but like you, I didn't have to use them in software engineering that much. I would like to get into a field that requires a stronger grasp of mathematics but also has a need for programming and computation (maybe machine learning or computational biology). I feel like I'm getting tired of being a software engineer (defense contractor) at a small company and looking for something higher level
Calculus (with a pdf version of the text book): https://ocw.mit.edu/resources/res-18-001-calculus-online-tex...
Linear Algebra (text book link: https://www.amazon.com/exec/obidos/ASIN/0980232716/ref=as_at...) https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
Optimization course & book link (Stanford) https://web.stanford.edu/~boyd/cvxbook/
Statistics: http://greenteapress.com/wp/think-stats-2e/
Re: Ask HN: How do I learn math/physics in my thirties?
#110First up, I am no expert, but I have traveled this road for a while so I'll share a bit.
I see Susskind's theoretical minimum is plugged here. Good. That is a fantastic place to start. Start at the beginning. Skip nothing.
Leverage what you know against what you don't. You remember how to find an extremum of a function from Cal 1? The first order necessary condition for an extreme point is that the derivative of the function be zero. Remember that when you get to (deterministic) optimization and a gradient needs to be zero. Next with a constrained optimization you will see the reformulation of an objective function and constraints into one functional by using new variables (Lagrange "multipliers") so that when the gradient of this new functional is zero, not only are you somewhere in the intersection of the constraints and the objective, but you also meet the first order conditions necessary for an extremum to be found. (Second order sufficiency conditions (SOSC) are needed to show that you aren't instead at an inflection point but we are moving fast and breaking things)
Hmm, I didn't say that very well, but there is much intuition to be found in optimization problems. This will serve you well in physics.
Calculus of variations: Nail down cold how to derive the Euler Lagrange Equations for a functional. Hint, Apply the FONC (first order necessary conditions for an extremum) to the functional (now the Action) in question. See Lanczos "Calculus of Variations" (Dover Books) to sort out your initial questions and learn the smooth little trick with integration by parts. Susskind's first book comes in here.
Learn cold the integral of the Gaussian distribution and how to play around with it to find more complicated integrals. Orthogonality. Dot products and Fourier transforms have a lot in common! Fourier's trick is crucial. Oh man... have you got some fun in store here. Do not proceed to Quantum mechanics without having these tools at your disposal. Otherwise QM is just linear algebra over complex numbers together with complex amplitudes from circuits/naval architecture/ spring mass dampers in the frequency domain. (I mention all of these to raise awareness that complex amplitudes are not unique to QM) Supplement Susskind's second book with Griffiths intro QM book. Also see Griffeths E&M book for a great explanation of Fourier's trick and separation of variables in the chapter on special techniques... At least in the 1999 Third edition. (beware, it falls apart under little abuse!) Oh, and pick up the power series methods for solving tricky differential equations - don't learn it from the physicists. Learn it from "advanced differential equations materials". It's not bad in isolation - soon you will be computing recusion relations and bessel functions.
Soon it will be time to start thinking about field theory. A side quest is available if you want to get into fluid dynamics. Incidentally this is a great way to learn about uses for Green's functions... And if you dive deep, your first look at singular integral equations in field theory. But we will proceed dead ahead... to the book reviews (you will need more than one book):
https://fliptomato.wordpress.com/2006/12/30/from-griffiths-t...
https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l...
Somebody else plugged 't Hooft here http://www.goodtheorist.science/ But there it is again. Now is a good time to speak of renormalization: There is an intro book out there: https://www.amazon.com/Renormalization-Methods-William-David...
It's okay but I have yet to derive more utility from it than from various field theory books. Oh and studying complex singular integrals in isolation is good too. Generally have some experience with contour integration around singularities.
See Sydney Coleman on symmetry breaking. (Man in the magnet, flip the sign of a term in your potential to get a mexican hat, see that the ground state is now different etc.)
There are tons of free resources out there for learning QFT. Use many sources. Expect to get stuck with any one of them. Bounce between them to un-stick.
Next up, differential geometry, tensors, and GR.... Google is your friend. I like Schutz's "a first course in general relativity" and really like Zee's Einstein Gravity book but I am working into this now and so my recommendations are running out. Check out this video as an intro to GR: https://www.youtube.com/watch?v=foRPKAKZWx8
To be inspired/get prepared for things to come get John Baez's Gauge-Knots_Gravity book: https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything... and maybe Penrose's Road to Reality - which is like cosmology if the universe consisted of all the math and physics needed to understand all this math and physics. Baez's book probably has more exercises and is more focused in general. Stuff like this will help you see where more advanced mathematics comes in. By now you will be seeing manifolds and fibre bundles. Think of parameterizing a surface instead of a curve and see how a tangent bundle describes a whole new vector space - one vector space for every point in the manifold. Yang Mills... internal symmetry... ok I'd love to talk about how these are new expressions of ideas we've seen before but at some point up there we've passed my pay grade, I have to beg off until I can learn some more!