how to teach yourself physics

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  • เผยแพร่เมื่อ 19 พ.ค. 2024
  • Serway/Jewett pdf online: salmanisaleh.files.wordpress....
    Landau/Lifshitz pdf online: actu.epfl.ch/news/all-landau-...
    Feynman lectures online: www.feynmanlectures.caltech.edu/
    Solutions to problems on my second channel:
    • some problems from Ser...
    Physics gre daily problem: grephysics.net/ans/all-soluti...
    Learn a physics-problem of the day:www.learnapphysics.com/proble...
    PHet online physics simulations and labs: phet.colorado.edu/en/simulati...
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    / acollierastro
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  • @Takosaga
    @Takosaga 4 หลายเดือนก่อน +1686

    Directions unclear, taught myself math

    • @Vegedow
      @Vegedow 4 หลายเดือนก่อน +198

      It's ok, its ok, you can get back on track. Just find the relation between reality's behavior and those maths functions over time, and you'll end up connecting those maths to the physics world.
      Just don't overwork yourself or you'll end up learning chemistry.

    • @emilysort
      @emilysort 4 หลายเดือนก่อน +81

      Congrats, that means you already know half of physics.

    • @idontwantahandlethough
      @idontwantahandlethough 4 หลายเดือนก่อน +58

      @@Vegedow Yes, good points. Whatever you do, DO NOT APPLY THE PHYSICS THAT YOU LEARN.
      That would be gross and impure :)

    • @stopkillingmemes7259
      @stopkillingmemes7259 4 หลายเดือนก่อน +3

      That's better

    • @mastershooter64
      @mastershooter64 4 หลายเดือนก่อน +28

      This is how mathematical physicists are born, they wanna do physics, but they're left unguided and start to deviate into the math realm and instead of doing GR and QM they go into differential geometry and functional analysis

  • @angrycharizard
    @angrycharizard 4 หลายเดือนก่อน +616

    I just want to say: To any undergraduate physics or astronomy students watching this video, don't worry if everything listed in this video is difficult for you. I graduated with a bachelors in astrophysics, and frankly I don't think I ever took a physics class that I thought was easy. It's okay if it's literally all hard! Physics is hard, but you can do it regardless!

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน +6

      First semester is definitely too easy.

    • @teckpass-pn2nu
      @teckpass-pn2nu 4 หลายเดือนก่อน +1

      Thanks for that

    • @KitagumaIgen
      @KitagumaIgen 4 หลายเดือนก่อน +6

      If it is easy the teaching doesn't bring you forward at the fastest pace you can handle! If you see it that way the struggle might be more acceptable, if you just manage you know you don't waste your time on repeating stuff that's too easy for you. And there's so so much interesting stuff to study that is on the hard end of our current knowledge, so please hurry up and bring new light to some dark corner...

    • @justinwatson1510
      @justinwatson1510 4 หลายเดือนก่อน +3

      I don't think I genuinely understood most of what I learned until about a year after I finished the class.

    • @madjohnshaft
      @madjohnshaft 4 หลายเดือนก่อน +24

      it's important to approach math like exercise. there is no innate ability. You just need to work very hard at it and you will be able to do it. I think too often a mathematical ability is portrayed as something you are born with. I'm an electrical engineer in my case I got really good at calculus because I worked my ass off on it staying up late, studying and crying and fighting for every little bit of new knowledge until I was a master - since I was a little teeniebopper.

  • @savona35
    @savona35 4 หลายเดือนก่อน +471

    I honestly think that we should teach linear algebra in high school, it's at least as important as calculus, especially in physics

    • @emilejetzer7657
      @emilejetzer7657 4 หลายเดือนก่อน +23

      I think we could go further, weirder and more useful, with applied courses on algebraic geometry and calculus. If the goal is to teach deep, fundamental tools and their practical uses, I think there’s a lot of value in going as general as possible in the theoretical tools, even though it bypasses the traditional build up of the underlying theory. Call it « mathematical tools and techniques »

    • @c4oufi
      @c4oufi 4 หลายเดือนก่อน +39

      Wait, you guys don't learn linear algebra in high school?

    • @siy2740
      @siy2740 4 หลายเดือนก่อน +34

      linear algebra is probably a lot more important than calculus, in general.

    • @warpigs330
      @warpigs330 4 หลายเดือนก่อน

      @@emilejetzer7657 I feel like math education is still in a mode from before computer tools and information were so universal. I feel like people would be so much more motivated if math education was like "What do you want to do? here's what math you need to solve the problems to do that." Whereas it feels like math education is all about teaching you all the tools you need to know to solve any problem, before you get to use it to solve real problems in the world. But google exists now, I don't need to memorize every formula in order to solve my problems.

    • @0sm1um76
      @0sm1um76 4 หลายเดือนก่อน +38

      Linear algebra is also way more important to people who don't end up specializing in math/physics than calculus is.

  • @KarelPletsStriker
    @KarelPletsStriker 4 หลายเดือนก่อน +274

    Quick tip. You can basically find all textbooks in PDF form anywhere. I'm currently a grad student in physics and have basically relied solely on PDF versions of my textbooks this semester. I know a lot of faculty members who just have giant folders full of all the textbook PDFs

    • @sanador2826
      @sanador2826 4 หลายเดือนก่อน

      This, but the one thing I HATE about PDF's is that you're reading chapter 6.3 and then the text is "using equation 2.4 from chapter 2..." and then realizing you have to scroll 300 pages because they didn't re-write it and you don't know what they are talking about; it is a real pain in the ass. It is much easier to flip pages in a physical book. I usually get all mine used on AbeBooks website.

    • @oasntet
      @oasntet 4 หลายเดือนก่อน

      One great resource if you don't have access to faculty with giant folders of textbook PDFs is a site known as Library Genesis. Can't link here, for obvious reasons, but it is the first three letters of those two words, follow by [dot], followed by 'is'. That's actually an index; the files themselves are hosted in a full-encrypted distributed file share called IPFS.

    • @mastershooter64
      @mastershooter64 4 หลายเดือนก่อน +34

      Lmao as an undergrad who has giant folders full of textbook PDFs this makes me feel better

    • @drbeavis4211
      @drbeavis4211 4 หลายเดือนก่อน

      Library Z is still alive and kicking on the dark webs. It's pretty reliable and fast like its now banned clearnet site. Worth a google!

    • @1eV
      @1eV 4 หลายเดือนก่อน +16

      Same. I only read PDFs. Costs nothing

  • @philurbaniak1811
    @philurbaniak1811 4 หลายเดือนก่อน +157

    The idea that a quantum mechanics book simultaneously _will and won't_ help seems oddly appropriate 😆👌

    • @georgelionon9050
      @georgelionon9050 4 หลายเดือนก่อน +6

      Except this quantum joke is just sooo overused.. We dont know if anything is simultaneously anything, only that the result is clear when the example function collapses.

    • @1eV
      @1eV 4 หลายเดือนก่อน +2

      ​@@georgelionon9050It is simultaneously every possibility. Nothing is deterministic

    • @philurbaniak1811
      @philurbaniak1811 4 หลายเดือนก่อน +13

      So is a bad joke potentially funny until it's heard 🤔😃?

    • @georgelionon9050
      @georgelionon9050 4 หลายเดือนก่อน +3

      @@philurbaniak1811 Look, I wont say its bad, but its got quite a beard by now. A joke everyone heard at last a dozen times.. every month.

    • @jasonbender2459
      @jasonbender2459 4 วันที่ผ่านมา

      @@georgelionon9050 this guy gets it. thank god someone does!

  • @Chris-b-2
    @Chris-b-2 4 หลายเดือนก่อน +77

    On practicing without computers: When I was getting my math bachelors, my real second analysis professor didn’t use a textbook, but instead made his course around a list of theorems he’d teach to build up calculus. In the course, we had received a numbered list of unnamed theorems. No one was able to easily look up the theorems to get the proof online, and as a result everyone in the class struggled through the theorems. It was a great class to learn in, and everyone who I knew that received at least a B could fluently push through proofs in other courses and elsewhere.
    People who took the other professors? Not so much, and a common problem was that they had thought they knew the proof but never had to discover the necessary arguments from tools they had up to that point.
    When you (the royal you) find the answers online and ‘cheat on the homework,’ you don’t train yourself to identify and tackle parts of the problem.

    • @ThePrimeMetric
      @ThePrimeMetric หลายเดือนก่อน +1

      I think physicists in general really undervalue how useful and satisfying it is to able to write basic proofs. I only took a basic proof writing course. Not Advanced Calculus or anything crazy but I still think it helped me a lot. I can't prove anything too difficult like a full fledged mathematican would but I use things like proof by induction and proof by contradiction more often than you would think. In the grand scheme of things it probably wasn't strictly necessary but it scratched my itch to be more mathematically rigorous when I want to be. I definitely want to learn Real Analysis, Differential Geometry and other more advanced math topics at some point. Although I don't know when I'll find the time to learn these subjects.

  • @ChrisSham
    @ChrisSham 4 หลายเดือนก่อน +263

    0:00 - Textbooks
    14:55 - Finding textbooks
    21:10 - Convincing you not to buy those books
    28:07 - 6 random problems
    28:50 - Landau/Lifshitz theoretical minimum
    32:00 - A terrible idea
    33:05 - Top five tips
    1. 33:19 - Schedule
    2. 37:07 - Supplies
    3. 38:37 - Lab component
    4. 45:16 - Daily physics brain
    5. 49:03 - Talk to other people about physics

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน +7

      I can’t do the talking part. It puts the physics in episodic memory which is the wrong place to store it. Especially if I don’t completely understand it yet. I’m autistic and talking to other people inflames my amygdala.

    • @Volkbrecht
      @Volkbrecht 4 หลายเดือนก่อน +6

      @@nuclearcatbaby1131 Talking isn't required to understand physics. As a physicist friend of mine often says: you understood it when you can calculate it.

    • @raindawnson9254
      @raindawnson9254 4 หลายเดือนก่อน +6

      @@Volkbrecht that's a poor mindset to have, sure just being able to calculate it gets the job done but that doesn't mean that you truly understand the concepts behind the calculations. Talking is a huge part of exploring and establishing your thoughts, you don't even need to talk with other people just talking aloud to yourself (or a plant or literally anything) is better than not talking at all. Though it should be noted that collaborating with other people to help build your thoughts is an amazing tool because they can provide more perspectives that may shift your way of thinking and even correct some of the concepts you may not have a solid understanding of. If the basis of understanding lies in calculations, then calculators "understand" many topics more than we ever will and that simply isn't true, they can't teach us squat really (computers maybe but that's if you're using them in place of books or articles which come from people so that doesn't really stand).

    • @Volkbrecht
      @Volkbrecht 4 หลายเดือนก่อน

      @@raindawnson9254 If you want to get serious about science it's actually the best mindset to have. I used to try and visualize physics exercises as a chemistry undergrad. Problem is, at some point you run out of fingers, and at the point where physics get "silly", also out of dimensions that your brain can make sense of. So the first step in understanding a problem is to "translate" it into its mathematical form, then derive your insights from there.
      Equations and graphs is also how experts in adjoining fields will "talk" to you professionally. And it's the best for all parties involved if you train yourself to understand that. It's even expected if you want to earn your salary in a multi-disciplinary environment.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      @@raindawnson9254 I talk about it in my head if it counts. I come up with random metaphors for everything that would make no sense for me to talk about.
      Also in my autistic state any talking goes into episodic memory which is a poor place to retrieve math data from. For me it’s a form of... well for an autistic all socialization is trauma on some level. I want to make sure I understand it 100% before I even begin talking about it or I could lock some half-formed egregiously wrong concept - or even just the feeling of confusion regarding the concept akin to repeatedly forgetting right and left - into episodic memory where it will be poison and difficult to unremember and replace with correct semantic memories.

  • @arctic_haze
    @arctic_haze 4 หลายเดือนก่อน +87

    I have a PhD in physics. Before I went to the college, I found that I am able to follow the Feynman lectures (I did some calculus at the high school) but some other physics textbooks as well as the algebra and calculus books for students were above my reach without actually taking the courses. So learning physics on your own is a very hardcore activity.

    • @UnconventionalReasoning
      @UnconventionalReasoning 4 หลายเดือนก่อน

      You must be so dumb, unable to study all of these on your own. Students at TH-cam university will crush it, saving all the time and money you wasted!
      [Complete sarcasm, I agree with you 100%, and also have a PhD in physics. The phrase "self-study" really needs to be taken out of the general discourse of education.]

    • @entelektuel.yolculuk
      @entelektuel.yolculuk 2 หลายเดือนก่อน +4

      what sucks even more when it comes to physics is that finding a great list, that can promise ye all the physics from start to finish... I guess physics does have a lack of books that explains the topics in a well-structured and fully way. I looked up a lot of physics books, they either exaplin stuff too verbally (meaning that they don't maybe add enough mathematical processes to see that side of modern physics) or they fill up the book with too many off-topic jokes and references to music bands and political events etc. I don't know, matey, ...

    • @UnconventionalReasoning
      @UnconventionalReasoning 2 หลายเดือนก่อน

      @@entelektuel.yolculuk Clearly you need to write the perfect physics textbook!

    • @AndrewBlucher
      @AndrewBlucher 2 หลายเดือนก่อน

      Interesting to hear how things are done in different places. In Australia we did Calculus and introductory Physics in High School. I did a couple of years of a Applied Physics degree before dropping out to start an IT career. I still have my textbooks, I'll have to dig them out ... (I recall the HS text: PSSC Physics, and one of the UG texts was Sokolnikof (I think) and Redheffer, another was Apostle).

    • @SivaS-qb2xj
      @SivaS-qb2xj หลายเดือนก่อน

      @@AndrewBlucher In the US we also take calc anb phys in HS...She is exclusively talking about college/uni level courses.

  • @berserker8884
    @berserker8884 4 หลายเดือนก่อน +115

    As a math grad student, I can recommend some good math books:
    1. Linear algebra: Axler's book is the best of the best. But you will need some more computational stuff also, but you'll do that a whole tone through physics anyways, so I wouldn't be too worried. The point is to understand how it actually work and be comfortable with the theory.
    2. ODEs: Arnold's book is the golden standard. While it is a msth book and there is plenty rigor there, it is very accessible for a phydicist too. Not only is this a good ODE book, it is one of the best math books for undergrad topics. Get the MIT edition, not the Springer one.
    3. PDE: now this is difficult to recommend. I will be blunt, PDEs become "accessible" and interesting only through proper rigorous and detailed study. It is kind of how QM requires very serious study through functional analysis to really understand and undergraduate QM is usually pretty bad. This might require more maturity, comfort with geometry and analysis, but I recommend Evans. This is where PDEs become beautiful and interesting.
    4. Functional analysis: this is big boy linear algebra. I actually don't think you need measure theory to understand most of introductory graduate functional analysis. Peter Lax's book is amazing and goes far, while also being very soft on the prerequisites. If you want to be super thorough, you would want to do a semester of functional analysis before PDEs. Functional analysis is also crucial for QM, because pure linear algebra techniques are not sufficient.
    5. Differential geometry: stick to Lee's trilogy of books. These are thorough, transaprent, well written and very self contained. For mathematicians I would recommend other books, but for physics students who want to be strong in math, these books are the best. Also, ODE's make even more sense when you understand basic differential geoemtry. It is all about flows of vector fields on manifolds.

    • @sinclairabraxas3555
      @sinclairabraxas3555 4 หลายเดือนก่อน +1

      would add manfredo as a differential geometry textbook if y'all wanna do general relativity

    • @berserker8884
      @berserker8884 4 หลายเดือนก่อน

      @@user-to2wn9ry7y I can't really speak on difficulty, because it is all subjective and any serious piece of math will be difficult at some point.
      Also, it all depends on your interests. Functional analysis srems like a great setting for a lot of juicy algebra through von Neumann algebras, but also the field of math that helps one with PDEs the most. That is because in PDEs you can study spaces of functions (or distributions) and when we add some regularity, these can become Banach spaces or Hilbert spaces. These are called Sobolev spaces and those are the rich function spaces we care about. Then one can do say spectral analysis on your operator that defines your PDE and you can get good info about your PDE using functional analysis.
      Some people also really want to study functional analysis itself. If linear algebra was your favorite, you might fall into that camp too.

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน +1

      I really like Harley Flanders Differential Forms with Applications to the Physical Sciences. (Cartan was a beast.)

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน

      I liked Churchills book Complex variables with Applications. It seemed difficult to cobble together an understanding of the subject from my physics texts.

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน

      If you like general relativity differential geometry is definitely your friend. Spivaks comprehensive introduction to differential geometry has everything from Gauss and Riemann to fiber bundles. Helgasons Differential Geometry Lie Groups and Symmetric Spaces is nice too I think. (I was reassured by a buddy that if I bought a textbook I didn’t have to read it. :) ) Im sure I don’t read math math books with the depth or understanding of a mathematician.

  • @patrickgreene5028
    @patrickgreene5028 4 หลายเดือนก่อน +97

    I loathe Boas. But I also had an AMAZING math professor. He created his own course called "Linearity", which was diff-eq, linear algebra, and Calc 3, all in one. He made his notes the textbook, and they were excellent. Funny, readable, great examples. We were constantly laughing in his classes. And he was so precise. It made Boas seem sloppy, opaque, and confusing in comparison. I was always confused that so many physics professors loved it so much.

    • @expendedAmmunition
      @expendedAmmunition 4 หลายเดือนก่อน +13

      it's not that Boas is particularly good. it's that she's so much better than A LOT of stuff out there.

    • @mc_va
      @mc_va 4 หลายเดือนก่อน +9

      Ok, now I want your teacher's notes as a book 📚

    • @robertmaltby4113
      @robertmaltby4113 4 หลายเดือนก่อน +3

      @@expendedAmmunitionI totally agree. I still keep Boas on my desk for reference when I need to code up a solution to a problem, but I remember it being super dense and unfun to learn from.

    • @andspenrob
      @andspenrob 4 หลายเดือนก่อน +4

      Gotta share the teacher, in case he's still teaching or is willing to share syllabus/notes!

    • @1eV
      @1eV 4 หลายเดือนก่อน +4

      Share the the notes. For science.

  • @jaronhuq2067
    @jaronhuq2067 4 หลายเดือนก่อน +79

    There is at least one book that can help you develop a physics brain without a full lab. Hands on Physics Activities with Real-Life Applications by Cunningham and Herr is intended for middle school and high school teachers, but it covers every basic branch of physics. Basically every page describes a demo you can do on basically no budget and it has typical questions a teacher can give students.

    • @twentytwentyeight
      @twentytwentyeight 4 หลายเดือนก่อน +10

      Love referencing AP/IB high school texts for an eli5/beginner friendly reference

    • @UnconventionalReasoning
      @UnconventionalReasoning 4 หลายเดือนก่อน

      A lab is entirely unnecessary to develop a physics brain. A full lab can even be counterproductive.

  • @mehill00
    @mehill00 4 หลายเดือนก่อน +25

    Experimentalist here. I love hearing theorists who believe in the importance of lab work for building understanding. Bravo.

    • @ThePrimeMetric
      @ThePrimeMetric หลายเดือนก่อน +1

      Experiment gets a bad rep I think because I generally think the college curriculum for it is pretty bad and isn't representative of what it's like to be an experimentalist. Their all cookbook labs where all you do is follow a list of instructions from a lab manual. Maybe it's fine for simple labs like ones in physics I and physics II but for more advanced experiments it feels like you don't have time to understand what your doing or how the equipment works. You typically have only a few hours, unless you make an appointment to come back before the lab report due date with the Professor, so it feels like your constantly getting rushed out of the lab. I hate not having full access to the lab and being pressured to move at a certain pace. On top of the time constraints you usually work with lab partners whether you want to or not. This usually ends up in one or two of the lab partners understanding what their doing quicker and doing the whole experiment while the other partners watch on the sidelines in confusion or not knowing what they can do to help. I get that your an undergrad still, so they don't trust you and don't want to spend the money to give every student a solo lab experience, but I feel like this experience doesn't tell me at all if I would enjoy experimental work. The one thing the reports tell me is I like the data and error analysis side to it but not necessarily working in a lab and devising my own experiments.
      To be honest I am also naturally better at theory and not good working with my hands. So that would be a contributing factor as well but typical lab courses make it difficult for me to grow out of that and try to become a more well rounded physicist.

    • @ChristopherSadlowski
      @ChristopherSadlowski 24 วันที่ผ่านมา

      I wish we gave a bajillion dollars a year to experimental physicists, and experimental scientists in general. First, it's just fun to build things and think about them and plan them out. Second, it's totally different to see something and have a thing to poke and prod. Plus, sometimes the math works out but there might be some small thing that was overlooked or deemed unimportant but in reality it's actually really important to consider and that pushes knowledge forward. Like, I watched a video about Bose-Einstein condesents, and I still don't really know what that is, but it was amazing to listen to the scientist talk about this huge apparatus she built with her team. And she showed how it worked and how she figured out if you calibrate the laser system just right the light can actually "steal away" energy to make the little cloud even colder. Like, it's as close to absolute zero as we can get right now. How cool is that! I don't know what will come out of this experiment, but I don't care, it's neat and will lead to more cool stuff. I mean, I don't think we're all going to get little ultra cold clouds of matter to carry around with us or here in the world, but just knowing what happens to matter in that state will impact us somehow, somewhere, and at some time.

  • @definitelynotofficial7350
    @definitelynotofficial7350 4 หลายเดือนก่อน +84

    The Dirac book is not a bunch of compiled papers! It's a legit book, and in fact an amazing book that most graduate QM texts have cribbed a lot from! It's not outdated in the least and very clear. Not necessarily for beginners though.
    He also wrote a great GR book which is ridiculously short (I believe under 80 pages). It just gets straight to the point.

    • @MR-backup
      @MR-backup 4 หลายเดือนก่อน +1

      For beginners?

    • @1eV
      @1eV 4 หลายเดือนก่อน +8

      ​@@MR-backupHell no

    • @definitelynotofficial7350
      @definitelynotofficial7350 4 หลายเดือนก่อน +6

      @@MR-backup Beginners maybe not. But it's a good book.

    • @MR-backup
      @MR-backup 4 หลายเดือนก่อน +2

      😆@@1eV

    • @MR-backup
      @MR-backup 4 หลายเดือนก่อน

      👍

  • @davidb2380
    @davidb2380 4 หลายเดือนก่อน +27

    Fun Fact: Jackson was able to buy a house from the money he made writing " Classical Electrodynamics". It is not a house I would not want to visit as it almost certainly haunted by the ghosts of students who failed their Jackson based EM classes. The second edition is much better than the third.
    A very nice book is "Principles of Electrodynamics" by Melvin Schwartz. It is on a level between Jackson and Griffith. I like his approach where he starts the discussion on magnetism by first showing it must exist using special relativity and electricity, or more generally showing how the two fields are united by special relativity.
    I am reading now "Physics of Binary Star Evolution" by Tauris and van den Heuvel which was published only just a few months ago. Covers everything from how we get stellar masses from binary stars, to how they produce gravitational waves. It is a really nice book.

    • @davidb2380
      @davidb2380 4 หลายเดือนก่อน +1

      Schwartz book is published by Dover so it is cheap

    • @nullor
      @nullor 4 หลายเดือนก่อน +1

      second edition still has Gaussian units doesn't it? what makes is better than 3rd

    • @jasonbender2459
      @jasonbender2459 4 วันที่ผ่านมา

      @@nullor That is what makes the 2nd better than the third. Heaviside-Lorentz units are mostly useful for string theory - a huge, pathetic dead end.

  • @albertqhumperdinck
    @albertqhumperdinck 4 หลายเดือนก่อน +71

    One resource that I, (an obligate novice who flunked high school math) have been really enjoying as an intro is a lecture series that Caltech has available on their youtube channel, called THE MECHANICAL UNIVERSE that was filmed in 1985. I think it was meant to accompany a correspondance course or something, but its 52 parts, half an hour each, and if you are someone who struggles with the motivation or executive function to pick up a book and make yourself do homework every week, these are a great way to dip a toe into the pool. I`ve been watching one every saturday morning for a few months now, taking notes about the physics and identifying the gaps in my math, so I can then go back and figure out which Khan Academy math videos I need to review. And the 80`s aesthetics of the whole thing are just *chefs kiss*. So that`s something that is free and available right now!

    • @hasch5756
      @hasch5756 4 หลายเดือนก่อน +6

      th-cam.com/play/PL8_xPU5epJddRABXqJ5h5G0dk-XGtA5cZ.html

    • @anthonybrennan4416
      @anthonybrennan4416 4 หลายเดือนก่อน +1

      I got you beat I failed Math for Idiots Three times

    • @lallas92
      @lallas92 4 หลายเดือนก่อน +2

      We had Goodstein’s Mechanical Universe series on VHS when I was an undergrad. We would roll the TV cart into the TA office and watch. Great recommendation.

    • @juliavixen176
      @juliavixen176 4 หลายเดือนก่อน +2

      OMG! I used to watch The Mechanical Universe on PBS when I was a little kid and it was my favorite show! I even have the ridiculously expensive DVDs that Annenberg/CPB released.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I can’t do videos. For executive function I just need a distant professor to threaten me with bad grades for not studying.

  • @jarrodangove1921
    @jarrodangove1921 4 หลายเดือนก่อน +13

    I'm really happy I found your channel last year -- I've seen every video you've made since. As a grad student in a slightly different field, I love hearing you share your perspective with the same casual tone that I would discuss stuff with friends in my research group. It's a cool window into another field, and a great way to spend an hour while I work on something easy or commute to school. Just wanted to say I appreciate you and your work. Thanks for taking the time to do this :)

  • @backgroundnoise8013
    @backgroundnoise8013 4 หลายเดือนก่อน +19

    Your line about not knowing enough math hits hard, I've quit my physics degree after actually passing all calculus classes with mediocre grades and having to face stuff like Classical Mechanics and Electrodynamics later without having any solid math foundation, the worst part was that I couldn't go back to the classes which I had performed poorly, so even today I'm still trying to self teach me math, from algebra up.

    • @user-sl6gn1ss8p
      @user-sl6gn1ss8p 4 หลายเดือนก่อน +6

      I did that (passing with mediocre grades) and took a few years off before going back, it really is painful

    • @devinvagt7914
      @devinvagt7914 4 หลายเดือนก่อน +3

      Same-- got a D in electronics lab, mainly because I couldn't remember how to solve differential equations and couldn't re-learn fast enough in a 10 week quarter.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I’ve taught myself a lot and I’m going to bully my college into letting me take the upper division courses.

    • @devinvagt7914
      @devinvagt7914 4 หลายเดือนก่อน

      I don't think I have what it takes to be a physics professor but I might be able to swing high school physics

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน +1

      Hang in there! My experience was Intro physics has such broad scope and my math background was so meager it left lots of dark areas and a few spots of light. But the curriculum circles, and your math tools get better, so the spots of light begin to coalesce as you revisit each of the areas so you gain confidence.

  • @user-ph3me7wx1k
    @user-ph3me7wx1k หลายเดือนก่อน +9

    I'm 15 and I plan to read every popular science book I see and study mathematics and physics for three years and then major in physics in college. Tell me what you think

  • @pizzaguy552
    @pizzaguy552 4 หลายเดือนก่อน +15

    I'm starting my engineering professor job in a few weeks and needed textbooks for my shelf. Absolutely perfect timing for me! (I promise I will read them)

  • @jazzanarchy1342
    @jazzanarchy1342 4 หลายเดือนก่อน +15

    This is such a good video. I realized that you had already gone through all your book recommendations for undergrad and graduate courses but there was still 40 minutes left in the video. I also noticed you hadn’t left a 20 item long list of books in the description.
    Anyway, thanks for giving us concrete, realistic, actionable steps for “teaching ourselves” physics. The next time someone tells me they want to learn piano or whatever (I’m a musician) I could just point them to this video. Apparently it’s very similar learning physics and music. You have to learn the basics, practice the material (physically when possible, not just theoretically), and become part of a community.

  • @andspenrob
    @andspenrob 4 หลายเดือนก่อน +7

    Loved your Top 5 tips as a way to not just get thru Physics, but more broadly to approach learning... Not every job or lifestyle requires an academic background, but nearly every good one requires the ability to rigorously apply yourself, and you nailed the approach.

  • @robertmaltby4113
    @robertmaltby4113 4 หลายเดือนก่อน +9

    At 36m, I feel like this is the most underrated part of getting an education in anything, though I think physics especially tends to do a good job of teaching intellectual humility. Knowing how to be wrong about stuff and being mentally tough enough to keep going are the two things I brought along from my physics BS that help me the most in my everyday job. So glad you brought this up, as I feel like most education tends to focus much more on the performative aspect of taking tests and proving knowledge (which is important), but it doesn’t insist on learning how to be wrong first.

  • @pablorepetto7804
    @pablorepetto7804 4 หลายเดือนก่อน +7

    In summary:
    - buy one book, spend a year with it (you'll be spending many years with many books, but take it step by step)
    - let physics take over your brain; you won't learn unless you're constantly thinking about it
    - have a test bank, redo problems periodically
    - experience physics physically; a stupid-sounding analogy may be the thing that keeps you from drowning in a sea of abstract equations (and quitting physics)
    - talk with other serious physics students
    - college courses are good actually; steal books or maybe even take one

  • @DataRae-AIEngineer
    @DataRae-AIEngineer 4 หลายเดือนก่อน +31

    Hey there. I've taught DiffEq and my favorite books are Blanchard, Devaney and Hall "Differential Equations" which covers the ODEs. And if you need PDEs, then use Farlow's "Partial Differential Equations for Scientists and Engineers."

    • @highviewbarbell
      @highviewbarbell 4 หลายเดือนก่อน +2

      Have you ever had a look at Strang's combined textbook on DiffEQ and Linear Algebra? I'm curious if it's any good

    • @DataRae-AIEngineer
      @DataRae-AIEngineer 4 หลายเดือนก่อน +1

      @@highviewbarbell No sorry I haven't looked at that one. But I find there are 2 ways that linear algebra books can be written... there's the pure math version that combines it with functional analysis which could be sort of like what your desrcibing. Those are okay but I find most students like the applied math version that doesn't have probability spaces and hilbert spaces and other stuff they might not need. Of course, i teach math to engineers which is different than what a physics student probably needs. :) Hope this helps.

    • @highviewbarbell
      @highviewbarbell 4 หลายเดือนก่อน +1

      @@DataRae-AIEngineer I've actually dual declared for Engineering Physics and Mathematics so I'll have to learn them both from several angles eventually, I suppose!

    • @lallas92
      @lallas92 4 หลายเดือนก่อน +1

      I like BDH, too. Also, Braun is fun to read for diff eq. For PDEs, Gockenbach has a nice book geared toward engineers.

    • @ComputerScienceMadeEasy
      @ComputerScienceMadeEasy หลายเดือนก่อน

      @20:10 very good and practical advice to know which textbooks are worth buying. Thank you.

  • @budsyremo
    @budsyremo 3 หลายเดือนก่อน +4

    Huge respect to people who are making channels that teach . TH-cam can be a gold mine for people who want to learn .

    • @281992pdr
      @281992pdr 3 หลายเดือนก่อน

      You are right. I would add - as I used to say to my students - read everything, and I mean everything, with both a genuinely open mind and critical thinking. Admittedly a hard call, but it can really reap benefits.

    • @krox477
      @krox477 หลายเดือนก่อน

      But it can also trick you into learning

  • @thelittledevil2103
    @thelittledevil2103 2 หลายเดือนก่อน +3

    the analogy of the ball being connected to the earth with a spring undergoing SHM is fascinating. It gives a whole new wonderful prospective to the ball's motion.

  • @NASAistheway
    @NASAistheway 4 หลายเดือนก่อน +11

    This channel & the Math Sorcerer go well together.
    Would be cool to make a series together.

    • @idontwantahandlethough
      @idontwantahandlethough 4 หลายเดือนก่อน +1

      math sorcery?! that sounds right up my alley, thank you:)

  • @timurshahauthor
    @timurshahauthor 4 หลายเดือนก่อน +1

    I love this video! Of course, it's awesome to see such an honest and thorough guide to learning physics for those new to the field, but also because it reminded me that these big complicated concepts are things I can learn, even on my own!

  • @0sm1um76
    @0sm1um76 4 หลายเดือนก่อน +4

    I love your suggestion to use multipule sources/texts while learning something. I actually did exactly what you suggested during my undergrad and I read the Feynman lectures in paralell with my normal courses and I thought it was absolutley excellent for that.
    I heisitate to reccomend the Feynman lectures as one's sole resource (I think they are fine especially if you are doing the practice problems) but they are absolutley fantastic as supplimental material.
    Side note, in my edition of the Feynman lectures in hard copy there is a foreward by the man himself saying that he himself wasn't happy with how the third modern physics section turned out. But I found the second book on electromagnetism very helpful.

  • @lazyman7505
    @lazyman7505 4 หลายเดือนก่อน +47

    Extremely helpful video, thank you. I just want to add something I've learned over decades in my "field" (computer science) - there is SO.MUCH.CRAP out there it's extremely hard to find books worth buying (and I do love having physical books over digital versions). Considering how expensive books are, I usually recommend to people to first go to Library Genesis, "preview" the book and then buy it. .

    • @sp123
      @sp123 4 หลายเดือนก่อน

      People are better off trying free OpenStax books to work on problems then try other content if needed

    • @franciscodanieldiazgonzale2096
      @franciscodanieldiazgonzale2096 4 หลายเดือนก่อน

      Completely agree. CompSci is full of jack of all trades, underdeveloped Math understanding, trend of the month, do it yourself in few hours/minutes, just type anything, methodologies that nobody use ever and some theoretical books that mostly oversimplify the Maths and overstate the problems. oh, and they tell you they know Turing stuff but for some reason not Gödel theorems.
      If you are lucky.
      Because the books I mentioned above are real books.
      Then you have the bigger bunch of books that are basically with the rigor and level of a popular newspaper talking about some scandal by a celebrity.
      That’s CompSci books.

  • @evawilliammusic
    @evawilliammusic 4 หลายเดือนก่อน +2

    This is brilliant I wish more people would do practical subject overviews filled with textbook recommendations

  • @mynt4033
    @mynt4033 4 หลายเดือนก่อน

    Honestly, the best thing to help keep up the science brain is friends. Someone to bring/share you problems to you so that way you don't exhaust all your self motivation. And someone to keep you doing problems, learning, and accountable.

  • @SuperSonic-fk6yq
    @SuperSonic-fk6yq 4 หลายเดือนก่อน +4

    David Tong's lecture notes are a great resource, he has lecture notes on a fairly wide range of topics as well.

  • @michaelkalin2209
    @michaelkalin2209 4 หลายเดือนก่อน +6

    SO glad you brought up the importance of stat mech. most important book i've ever read.
    love to see the simon clark "shoutout," he's awesome!

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน

      I learned soooo much from my undergrad stat mech text:
      Statistical Physics by F. Mandl
      not so much from Landau and Lifschitz.

  • @GuillotinedChemistry
    @GuillotinedChemistry 4 หลายเดือนก่อน +1

    Came here because I was curious about the booklist. Stayed because of the insightful take on the potential roadblocks and workarounds of self-education. Great thoughts on education as always. Thank you and happy new year!

  • @joinkusbelinkiusthethird
    @joinkusbelinkiusthethird 4 หลายเดือนก่อน +2

    Ty for making this. I'm undergrad physics rn, just got done with physics foundation, like right before modern physics. I really enjoyed learning about electric current and inductance and waves and lenses this last semester it was so much more fun than pulleys and throwing balls and weights. Anyways, it's nice to get a better idea of what lies ahead of me and success tips from a source that seems so earnest and knowledgeable. I'm really looking forward to modern physics.

  • @DaneDuPlessis
    @DaneDuPlessis 4 หลายเดือนก่อน +3

    Wow this was a great video. I did a bachelors in physics and mathematics, then studied engineering. I really miss the physics. It takes a huge amount of focus and energy to master multiple topics in physics, but it can be quite satisfying.
    Brolliant advice. I can’t recall many of the equations for SHM or kinematics or the wave function (psi?) but think I might be able to derive them in a few minutes. I still do calculus in my head to help me fall asleep sometimes, or derive trig identities.
    I really want to give my children the influences they need to be confident enough to tackle physics at varsity if they want to.
    This has been quite inspirational. I’ve always wanted to know something about QED. I’ve also forgotten a lot of math after 15 years of LIFE getting in the way. I’ll follow your advice and dig out my old “fundamentals of physics” text by Halliday Resnic and Walker and work the problems again :)
    Many thanks for putting this together. I’ll likely refer back to it. So great to have an overview of the important books (I remember some of the Griffiths ones fondly). Only problem is knowing few people who are in my current circle who know anything about physics. Perhaps it’s time to engage people on the subject!

  • @Kceam
    @Kceam 4 หลายเดือนก่อน +7

    You can also look at the websites of professors. They often have their own lecture notes for free on there. And some of them are great to learn a specific topic

  • @mehill00
    @mehill00 4 หลายเดือนก่อน +1

    I’m so glad the internet was in it’s infancy when I was in school. It existed, but barely, and not helpfully for solving problems.
    Also, Angela, your advice of just getting used to feeling stupid when you first start a problem is dead on. I’ve been saying that for years. Studying for the qualifier was an exercise in starting every problem completely stumped and then realizing that I eventually usually get there. The training to some extent was becoming accustomed to setting that strong-as-fuck feeling aside and getting to work anyway.
    (PhD ‘01)

  • @bolaronald8555
    @bolaronald8555 3 หลายเดือนก่อน

    I think your advice is genuine n honest .Pls continue doing these videos you will surely inspire many people. You are talking from your life experience, I can feel it.thanks.

  • @lukewatson8848
    @lukewatson8848 4 หลายเดือนก่อน +19

    Had to retake Physics II twice in college (math major). I wish I had this video back then 😭😭
    Maybe I should revisit physics without the pressure, might like it a bit more.

    • @gee8419
      @gee8419 4 หลายเดือนก่อน +2

      I think the main detriment to me actually learning physics in undergrad was the fact that I didn't use it at all for my microbiology major and yet it was imperative that I cram it into my packed schedule and get a good grade in it. If you're not already inclined towards physics I can't conceive of a worse way to learn the material than to make it a required class you have to get a 70% in to graduate when you have no plans to ever do it again afterwards.

    • @lukewatson8848
      @lukewatson8848 4 หลายเดือนก่อน

      @@gee8419 Oh absolutely. I did not give it the time or attention it needed what with all the other classes I had, I ended up taking it with a different prof. during an 8wk in the summer when I could focus on only that. Did just fine 👍

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I would teach myself and insist on skipping straight to upper division electricity and magnetism. Lower division classes are a waste of time.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      @@gee8419I can’t do it if I’m forced to attend class for a grade. I’m autistic and I need to stay at home in order to learn it.

  • @seabecks
    @seabecks 4 หลายเดือนก่อน +3

    My diffEQ textbook in school was made by our professor so I’m guessing he agreed with you on diffEQ textbooks. My best understanding came from the adjunct professor who taught my systems, dynamics, and controls class.

  • @10-AMPM-01
    @10-AMPM-01 4 หลายเดือนก่อน +1

    Your approach and advice is (IMO) wonderful and wise. I am a dunce in math. How humble you need to get is a mystery only you can solve.
    I'm grateful that you've spent time assisting the newbs like me. I've been so curious about the problems facing our greatest scientists and engineers. Alas, I may be unable to assist intellectually for another decade or so.
    Perhaps I should just stick with photography and learning one new language. Although, I'm ever tempted by the allure of field theory.

  • @0786875
    @0786875 4 หลายเดือนก่อน +1

    This is a great video. And is actually a wonderful reference if you're actually studying physics, too - the advice about how to learn, particularly about working on problems with friends is truly excellent. Where was this advice when _I_ was studying physics!

  • @arryaxx263
    @arryaxx263 4 หลายเดือนก่อน +4

    Though to people who want to start running, March 15th is just about the perfect date to start your year in most places. If you're just starting out, don't rush for January. Running in January is awful. You can wait for your custom shoes. Also don't get custom shoes. That would be weird.

  • @angellahoz1985
    @angellahoz1985 4 หลายเดือนก่อน +1

    I love your content so much Angela! Please have a great new year + holidays

  • @stauffap
    @stauffap 4 หลายเดือนก่อน +3

    I also recommend Julius Summner Millers old videos. He has a great energy and talks about a ton of phenomena in a very short amount of time. So it's a great way to find tiny physics problems to think about and describe mathematically.
    Always use interesting things you want to understand as opportunities to learn physics. For years i was very interested in understanding climate science and what really advanced my knowledge was to not be satisfied with qualitative answers. You should only be satiesfied once you know how to actually calculate something yourself. So with regards to climate science you might want to know how you chould approach calculating the amount of warming we get by doubling the CO2 concentration. That will teach you a lot of physics - a lot more physics then just being happy with a qualitative answer. Qualitative answers often just give you the illusion of understanding something. They often don't give you the full picture.
    Climate science also led me to the Navier Stokes Equations and computer simulations via the finite difference method. Also very interesting. That's how they are able to model wind patterns so accurately in climate models. It's really fascinating.

  • @signumscaler
    @signumscaler 4 หลายเดือนก่อน +9

    We'll need the video on how to read research papers cause I know I'm not the only one who's struggling lol.

    • @idontwantahandlethough
      @idontwantahandlethough 4 หลายเดือนก่อน +2

      I think it just comes with practice and familiarity, but yeah that might be a neat video idea! I bet there are a lot of little tricks and shit that people [like me] who don't spend a ton of time reading research papers for work would probably never think of

  • @michaelspinks9822
    @michaelspinks9822 4 หลายเดือนก่อน

    I agree, fully working through an entire calc based introductory physics text, especially with modern, would give most people a solid understanding that could even be useful in day to day life.

  • @jameslai6879
    @jameslai6879 4 หลายเดือนก่อน +2

    1. Thank you for sharing the bouncy ball story, on both personal and theoretical levels.
    2. There is no mention of Zee’s books! This is a noteworthy exclusion.

  • @thiagokimgarcia8705
    @thiagokimgarcia8705 4 หลายเดือนก่อน +52

    Linear algebra on year 3? That's very surprising to me as a math person. If someone how to get into math I'd say to do calculus and linear algebra first - and I'd say that learning linear algebra is more important than learning calculus (MUCH more important depending on what area of math you want to specialize in)

    • @Tome281
      @Tome281 4 หลายเดือนก่อน

      Physics departmant at my uni has only 1 pure physics course first year, the rest is real analysis, linear algebra and some more math courses

    • @user-sl6gn1ss8p
      @user-sl6gn1ss8p 4 หลายเดือนก่อน +1

      the thing which will use it the most is quantum mechanics, so it's okay to leave it for later if the focus is just the physics, but yeah, sounds unusual

    • @apmcx
      @apmcx 4 หลายเดือนก่อน +1

      That's true, but where I live in Colorado, if you do 2 years in community college first, then transfer to complete an undergraduate degree, you can't even take linear algebra until year 3. Or at least you can't use financial aid towards it since they don't require it for the AS.

    • @thepapschmearmd
      @thepapschmearmd 4 หลายเดือนก่อน

      Same. Undergrad degree is in math and I did linear algebra in my third semester. They might not need it until later though and if you take something in year 1-2 that you’ll need in year 3-4 that kind of puts an unnecessary gap between the two.

    • @najawin8348
      @najawin8348 4 หลายเดือนก่อน +3

      Also, what self respecting calc 3 course isn't teaching you div/curl/grad? Is it just me who's utterly perplexed by this? When she mentioned vector analysis I half expected her to hold up Spivak.

  • @naakatube
    @naakatube 4 หลายเดือนก่อน +4

    For ADVANCED ELECTRODYNAMICS i recommend "A Modern Introduction to Classical Electrodynamics" by Michele Maggiore, it's a modern version of Landau, but more accessible!!

  • @douglasstrother6584
    @douglasstrother6584 7 วันที่ผ่านมา +1

    "Modern Electrodynamics" by Andrew Zangwill
    It's on the level of Jackson without the sharp edges.
    The selection of examples and problems are very physics-oriented.

  • @mrm.7328
    @mrm.7328 15 วันที่ผ่านมา +1

    You have textbook strength!
    Tossing around heavy tomes as though they were holiday novels.
    Respect the wrists!

  • @crisoliveira2644
    @crisoliveira2644 4 หลายเดือนก่อน +12

    Saw your video on crackpots the other day. That subject always reminds me of Jair Bolsonaro's late guru. He was a junior-high dropout who wanted to be recognized as a philosopher, but in fact he was an astrologist and a columnist. He was vocally opposed to Einstein's relativity and stated the geocentric claim was as valid as the heliocentric claim (or any other model where the Earth is not in the center) because the only difference was, according to him, the frame of reference. He wanted to roll back science to the Aristotelian model, because he was a TradCath (Earth in the center as proof of man's importance in God's creation, plus Thomas Aquinas' neo-Aristotelianism). He also said there was no fossil fuel because hydrocarbonates were also found in another galaxy [EDIT: where there's never been a dinosaur - yes, he said that]. And he believed Pepsi was made with aborted foetus as sweetener. And then he died because he didn't believe smoking caused cancer and that COVID was real. But while he was alive, he got to influence a president, albeit a very stupid one.

    • @AlexanderPetersonml
      @AlexanderPetersonml 4 หลายเดือนก่อน +1

      The frame of reference thing is technically true. I interned under an old physics PhD who said Newton could have saved himself a lot of trouble by saying "hey these calculations are a lot easier if we just *pretend* the sun is at 0,0,0 in this wacky temporary coordinate system"

    • @crisoliveira2644
      @crisoliveira2644 4 หลายเดือนก่อน +3

      @@AlexanderPetersonml
      But in this case, it's geocentrism. How would you explain the motion of other bodies in the solar system through geocentrism? You'd have to say the sun goes around Earth and everything else goes around the sun that goes around the Earth. For a TradCath, that undermines Earth's importance, as everybody else in the sky is cuckolding her with the sun. It's not geocentrism anymore, but outsourced heliocentrism.

    • @idontwantahandlethough
      @idontwantahandlethough 4 หลายเดือนก่อน +2

      @@crisoliveira2644
      The Earth... _likes to watch._

    • @AlexanderPetersonml
      @AlexanderPetersonml 4 หลายเดือนก่อน

      @@crisoliveira2644 yes I suppose you can't get around the idea that the conceptual center is fake. Bolsonaro's guy seems to have admitted that, but If I wanted to mollify the Church in the old days I would say that if the Earth and Sun were connected by a bar, and the Sun to the remaining planets, you're free to declare Earth the "mover" of the bar just as an athlete is the "mover" of a pull-up bar. They won't understand the details anyway, and you can say that this is better than accusing God of making the purest Heavens engage in tempestuous behavior

    • @jeanpablo3995
      @jeanpablo3995 4 หลายเดือนก่อน

      o cara veio militar num video bicho... vaitomanoseucu imundo some daqui

  • @theveloper3678
    @theveloper3678 4 หลายเดือนก่อน +3

    Awesome Video!
    Computer Science Student here(Graduated 2 years ago), Sometimes I get the urge to just start over in probably physics or core maths.. I've done Calculus, Linear Algebra etc And this doesn't just happen for physics, it happens for Biology & Chemistry(Probably because high school was shiit). I also currently work as a software engineer. Might get a 5 year study plan to go through these. Cheers.. Happy New year

    • @timeslices7923
      @timeslices7923 4 หลายเดือนก่อน +1

      Good luck to you. I'm also a software engineer and learning a bunch of math for fun now. It's definitely enriching!

  • @kenmcguire5837
    @kenmcguire5837 6 วันที่ผ่านมา

    Some background. I have a BA in Chemistry with a Physics minor, so my qualifications are way less than our good doctor who gave us this video. When this video came out, I saw all the textbook recommendations and while I agree that there are very good reasons these are standard texts to teach, it is overwhelming.
    Now in watching the whole thing I see how I should have watched more.
    Back when I was in school we used Serway for Sophomore Modern Physics, and I liked how he explained things enough that I grabbed a review copy of the Freshman book you recommended. I have used it enough that I definitely would recommend it over the Freshman book I used as a Freshman. That said, it is Halliday, Resnick and Walker that I used basically being a TA for a summer class that sits on my bookshelf.
    Everything that you recommended in this video is good. Do problems. Talk with others doing problems. Talk with a someone who has the patience to direct you through this.
    My first Physics professor hammered into us that in so many ways Physics is simple but not easy. One of the hardest parts is to remember or recognize that simplicity when things get, uh, interesting.

  • @ermiasawoke192
    @ermiasawoke192 4 หลายเดือนก่อน

    You tube?? I thought i have covered all physicist youtuber....but here she is doing what i was looking for.
    Thank you for your vital information. Im undergrad student of physics. Want to be a theoretical physicist.

  • @post-modernneo-marxist8102
    @post-modernneo-marxist8102 4 หลายเดือนก่อน +7

    I think differential equations as a subject has a way that its been taught that hasn’t changed for centuries. There’s a good article by Gian-Carlo Rota wherein he states that when he was assigned to teach an undergrad differential equations class he went back and found that the order and presentation of the material in the current textbooks were exactly the same as they were in textbooks by Cauchy and George Boole. But for my money, ‘Differential Equations with Applications and Historical Notes’ by George Simmons is the textbook i found most helpful.

    • @post-modernneo-marxist8102
      @post-modernneo-marxist8102 4 หลายเดือนก่อน +1

      Also, that was indeed a book by Dirac. A great book too. I don’t feel i know the subject well enough to know but I learned a lot from it.

  • @annasofienordstrand3235
    @annasofienordstrand3235 4 หลายเดือนก่อน +6

    I would recommend "Vector Calculus, Linear Algebra and Differential Forms" by Hubbard and Hubbard instead of the usual vector analysis approach.

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน +1

      Differential forms are definitely the modern way to go…surprising that they haven’t caught on more.
      Bernard Schutz has a book called Geometric methods for mathematical physics that is nice.
      Flanders is my favorite introduction to differential forms.

  • @davemcdonald2150
    @davemcdonald2150 3 หลายเดือนก่อน

    Brilliant! I have to agree with all you said, especially about thoroughly understanding a comprehensive first year text and your discussion on labs. I have an engineering degree from the early 70's and until retirment used my university texts, (most written in the 40's and 50's), to solve real life problems. My only add would be to buy books with hard covers especially if you can find them with "library specification" binding.

  • @waggawaggaful
    @waggawaggaful หลายเดือนก่อน

    I feel like studying something casually in one's free time takes all the stress and expectation out of it. Thanks for the tips 👍

  • @YTEdy
    @YTEdy 4 หลายเดือนก่อน +8

    Oh . . . the thoughts about picking up studies again at my age. Quite the challenge, but tempting. I took physics in college and may have even gotten an A the first semester, but that was 40 years ago. Struggled bigly with the more advanced courses though.

    • @xglosis
      @xglosis 4 หลายเดือนก่อน +1

      You’re never too old to learn something new. It’s good for the ole noggin.

  • @padremochismusical
    @padremochismusical 4 หลายเดือนก่อน +5

    21:18 I think this is a very specifically american thing (to get a bunch of stuff and then return it or sell it back in a garage sale) because my 3rd world country brain can't get around getting a bunch of preparatory hardware before doing a thing... I typically had to start with bad - usually detrimental - equipment and if I did well or felt I was getting better I could get better equipment (some examples: Guitars, swimming goggles). For something as broad as physics a guideline of your favorites makes absolute sense. Thanks for the lagrangian/hamiltonian recs!

  • @paulalmquist5683
    @paulalmquist5683 หลายเดือนก่อน

    It is cool seeing the oscilloscope sitting on the shelf behind you. I hope you actually put it to use occasionally. I don't use mine often enough that I remember what all the controls actually do. I enjoyed physics and math in high school and college. I ended up teaching IT stuff. Now retired. Still enjoy sciencey things and dabble in electronics. Your videos are fun to watch. Thanks for sharing your enthusiasm.

  • @Jacob-nz8ok
    @Jacob-nz8ok 4 หลายเดือนก่อน +1

    >She is linking free PDFs.
    We STAN this QUEEN. Thank you!

  • @jsdutky
    @jsdutky 4 หลายเดือนก่อน +5

    This book may be a little before your time, as it was a little before my time 30 years ago, but I really liked Elementary Differential Equations by Boyce & DiPrima. I used my father's copy (from 60 years ago) as a backup to the textbook assigned by my prof, and felt that the explanations were actually better than the more modern text.

    • @carpediemyes
      @carpediemyes 4 หลายเดือนก่อน

      I can highly recommend Boyce and DiPrima. It is the textbook I used 60 years ago at Rensselaer Polytechnic Institute. I can also recommend as a basic physics book Resnick and Halliday. Robert Resnick was my physics teacher back in the late sixties. I think the book is now in its 10th edition.

  • @saturdaysequalsyouth
    @saturdaysequalsyouth 4 หลายเดือนก่อน +4

    My differential equations class used “Fundamentals of Differential Equations” by Nagle, Saff and Snider. I didn’t think it was that bad. It was 15 years ago though.

  • @samratnagarjuna1754
    @samratnagarjuna1754 4 หลายเดือนก่อน

    Hi, I’m very glad I found this video. Thank you so much all your inputs. I’ve been studying a lot before but had to give a break. Somehow your video makes me go back to my schedule and start enjoying math and physics again. Thank you so much ❤

  • @almostinfamous42
    @almostinfamous42 4 หลายเดือนก่อน

    Happy new year and thanks for all of your hard work.

  • @pieterkok7486
    @pieterkok7486 4 หลายเดือนก่อน +4

    The Dirac book is actually by Paul Dirac. He kept updating it until late in his life. Contrary to most other older textbooks on quantum mechanics, Dirac's book is still very accessible, and it feels modern because he uses his "Dirac" notation (BTW, John Von Neuman, in the preface of his book, totally has a hissy fit over the Dirac delta function; worth a read!).

    • @1eV
      @1eV 4 หลายเดือนก่อน

      Which book by Neumann?

    • @sfitzsi
      @sfitzsi 4 หลายเดือนก่อน

      I loved Shankar…the penny rely dropped for me when he explained how Poisson brackets in the classical theory get replaced by commutators in the quantum theory. Then I came upon Dirac’s classic…he actually created that method of quantization. Dirac assumes a lot from his audience though…he makes Messiah seem verbose.

    • @pieterkok7486
      @pieterkok7486 4 หลายเดือนก่อน

      Mathematical Foundations of Quantum Mechanics @@1eV

  • @Bamdd5
    @Bamdd5 4 หลายเดือนก่อน +4

    6:25 lmao I also took two DiffEq classes and they just boiled down to “just guess, but make sure you guess right”

  • @eddieromanov
    @eddieromanov 9 วันที่ผ่านมา

    I'm 49. I never got the chance to do physics for reasons. I'm doing it now. Thanks for this.

  • @theloganator13
    @theloganator13 4 หลายเดือนก่อน +2

    I'm surprised I haven't seen a recommendation for Chabay and Sherwood's Matter and Interactions in your video or in the comments. It's a much more modern approach to teaching physics which integrates a good deal of 20th century understanding into its discussion of classical mechanics and electrodynamics. It also teaches some basic computational modelling, which is essential to every branch of physics today.

  • @archilkitiashvili1227
    @archilkitiashvili1227 4 หลายเดือนก่อน +7

    Just google pdf versions, don't buy textbooks. Even better, you can find lecture note pdfs by famous lecturers/courses from famous universities, which are sometimes at least as good as actual textbooks.

    • @raven-zi4os
      @raven-zi4os 4 หลายเดือนก่อน +4

      but then how will i fill my bookshelves with physics books so when people come over they’ll think im smart

    • @netoskin
      @netoskin 4 หลายเดือนก่อน

      MIT opencourseware Is Amazing I learned so much with their algorithms material

  • @chrisdolan9515
    @chrisdolan9515 4 หลายเดือนก่อน +4

    LOVE the Dover books!!! Yeah, they’re dry and dated, but maybe it’s because my favorite math prof was a big fan and used them as textbooks way back in the day. Also, big shout out to Shankar. LOVE his books (his sense of humor totally resonates, adding an element of entertainment to what can be an otherwise stale discussion). His big, red QM book is an absolute favorite. Regarding GR, Wald’s book has long been a favorite. Bonus…it can be downloaded as a PDF, no cost.

    • @chrisdolan9515
      @chrisdolan9515 4 หลายเดือนก่อน

      BTW, here in Minnesota, Half Price Books can be a gold mine. It’s weird, but a lot of these obscure texts are often on the shelf. I’ve come across some AMAZING finds at used book stores, especially when in a college town.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I bought their mathematics for physics book and I taught myself nearly all of it (I think it later got water damaged)

  • @thecaribbeanbookworm5066
    @thecaribbeanbookworm5066 4 หลายเดือนก่อน +2

    Thank you for the phenomenal video! I was about to make a video quite recently on the subject and saw that you just uploaded one. I am definitely going to refer to this video, as it is so comprehensive and packed with amazing advice (loved the Serway recommendation, the appreciation for labs, and the Landau mention). Regarding the Jackson Mathematics for Quantum Mechanics book, I have it (a friend lent it to me). It is a quite interesting exposure to special functions, PDE solving techniques and linear algebra concepts. It is also very thin, and much more approachable than his electrodynamics book (the bits I read about that at least). But I would still not recommend it in its entirety. It feels a bit dry and the font is not necessarily the best. Though it’s probably very person-dependent and maybe you may enjoy it. All in all, great video! And I will definitely point this video of yours out in my own video. All the best and happy new year’s soon!

  • @rsjisoktoday2892
    @rsjisoktoday2892 4 หลายเดือนก่อน +1

    What great advise! Learning physics well is on my bucket list, and has been for a long time. I'm 56 now, but I still have so many things I want to do. I really feel like I've wasted a lot of my life and I constantly feel like I'm running out of time. Right now I'm learning how to be a draftsman, and I'm retaking Precalculus and will take Calculus I and II before I'm done getting an associates degree in drafting. Then I'm probably going to get a mechanical engineering degree and maybe an electrical engineering one too. I've had two semesters in undergrad college Physics a long time ago and the Calculus is a retake also. I think I'll probably be watching this video again in a few years, with more usage of the material, hopefully. I've actually got a bachelor's degree that I've never done anything with. Hard to explain why. Mental illness is the short answer. God I just keep wishing a was 20 again. Or even 40! I have a good friend who is a Physics professor at Stonybrook University on Long Island. We talk about the current crisis in cosmology all the time, and it really makes me wish I could contribute to the answer. Of course I don't really know anything, but I keep thinking that the Cosmic Background Radiation might not be what we think it is at all, but something different, like some kind of reflection from some kind of gravitational reflection point due to some kind of general relativity thing due to the universe actually being finite. Real clear, right. Takes what it's like to be smart an know a little, but not be able to think fully formed knowledgeable thoughts. I think that's what actually knowing what you are talking about is all about. Maybe I still have time. See you in 10 years, if I'm still around. Well my mother is still around and she is 94 now, but then again I had a brother who died at 61, so who knows. Maybe we'll go to war with China and joke is YOU don't have 10 more years. We'll see. I guess pessimism doesn't ever accomplish anything, so see you in 10 years for real!

  • @iphobley
    @iphobley 4 หลายเดือนก่อน +5

    Not sure about the US but in the UK as a member of the public you can get access to university libraries so if you live somewhere with a university join up and see which books suit you before buying.

    • @drewwilliamforbush2927
      @drewwilliamforbush2927 3 หลายเดือนก่อน

      Absolutely, in the US I went to my universities libraries to start reading way before I enrolled in any classes

  • @xricardox109
    @xricardox109 4 หลายเดือนก่อน +5

    You're awesome I love your videos

  • @benthayermath
    @benthayermath 4 หลายเดือนก่อน +1

    Thank you! This is the sign I needed to stop playing Starfield and work some exercises from Taylor and Goldstein. Happy new years 🎉

  • @lerualnaej5917
    @lerualnaej5917 4 หลายเดือนก่อน

    The freshman physics course that I took had extremely strict homework format requirements and we were literally graded down for not drawing some kind of picture for every single problem. Honestly, forming the habits of drawing SOME kind of picture every time and having to explain, in words, why I was doing the math I was doing did so much for my learning. Later on, when I worked grading for that same class, forcing the students to do that made it so much easier for me, as a grader, to figure out what the students had done wrong and write down "You thought X, but X is incorrect and here's why Y instead." It really was a wonderful system for students who really wanted to make sure that they were learning the material completely.
    I never did anything with physics, and I've lost most of it over the years, but I genuinely cannot recommend enough the rigor of drawing a picture every time and explaining in words why you did the math you did. Made studying for exams a BREEZE as well, because my homework functioned as a complete study guide, annotated in MY OWN WORDS after being forced to spend a couple hours thinking about it, rather than studying from the wording the professor used that I scribbled down while half paying attention because it was an hour before lunch.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I never drew the pictures correctly but I somehow got one of the few A’s in the class. I’m autistic and my math comprehension is very nonverbal. That honestly sounds like some common core BS. The fact that you forgot most of your physics speaks for itself.

    • @lerualnaej5917
      @lerualnaej5917 4 หลายเดือนก่อน

      @@nuclearcatbaby1131 Well, considering that I haven't done any math let alone physics in over a decade, it's not surprising that I'm rusty. If you have a disability which needs accommodating for a particular class style, that's why accessibility offices exist. That doesn't change the value of setting up a class to incentivize students to actually think through the problems and be able to communicate their thought process, both of which are skills that are very useful if they are ever going to, say, write a thesis.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      @@lerualnaej5917 When you’re autistic you don’t forget stuff so easily. I can describe my thought process but it would sound schizophrenic because of all the metaphors I use internally as mnemonics or whatever. Also explaining a theory for a doctoral dissertation is different from explaining why I used this or that value in this or that equation. I might even end up confusing myself and brainwashing myself with the wrong words.
      Also the disability offices aren’t sufficiently accommodating. I need to be allowed to skip as many classes as I want (attending class and the excess socialization that entails stupefies me with anxiety and if I have to attend class every day for a couple of weeks I start behaving like a bipolar person) and turn in homework as late as I want (focusing on deadlines makes it not consolidate into long term memory properly) or better yet just grade me on the test but they have to dumb classes down in every way that makes it more accommodating to neurotypicals and less accommodating to autistics and there is only so far they will allow you to go if the class has mandatory attendance for a grade or homework for a grade. I have had to sacrifice my attendance grade to save my essay grade, or my homework grade to save my test grade (I did the homework I just refused to turn it in because I cannot do homework with the intention of turning it in without stressing my amygdala out so much it fails to form enough long-term memory of the math material, I have to do the homework just to learn it with no intention of turning it in and hopefully get it done before the deadline on accident and then suddenly change my mind about turning it in last-minute but I don’t think that will usually happen unless I set a timer and somehow completely forget that the timer exists)

  • @ariadne4720
    @ariadne4720 4 หลายเดือนก่อน +43

    If you're interested in quantum physics I, I highly recommend the MIT lectures (free on MITs open courseware or on youtube) by Allan Adams (and sometimes Barton Zwiebach): Really well done and easy to follow with excellent lecture notes.

    • @1eV
      @1eV 4 หลายเดือนก่อน

      How does it compare to the playlist only by Barton Zwiebach?

    • @ariadne4720
      @ariadne4720 4 หลายเดือนก่อน +1

      @@1eV Barton's lectures are also very good, but have a more mathematical bent. I find Adams's lectures more approachable if this is your first quantum physics class. In all, they are both very good. Personally I watched Zwiebach's lectures after Adams'; Had I started with Zwiebach I think I would have been a little more confused. All in all, they are both excellent.

    • @ariadne4720
      @ariadne4720 4 หลายเดือนก่อน

      @@nickelchlorine2753 thanks for the recommendations, I will check those out, too :)

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      Some of their lecture notes are hand written! Can’t read! I study the material from the classes that are way harder than I am credentially qualified to take.

  • @ChaosKnight7000
    @ChaosKnight7000 4 หลายเดือนก่อน +5

    Good advice all around here. For anyone that wants a calculus-based rather than an algebra-based approach to that broad introductory-level text, "Fundamentals of Physics" by Halliday, Resnick, and Walker is a standard text universities use to teach their calculus-based freshmen-level physics courses.

    • @1eV
      @1eV 4 หลายเดือนก่อน +3

      I was actually surprised that book wasn't mentioned. It's really good.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน +2

      There is no such thing as a calculus based freshmen level math course. I took one and I literally remembered everything from high school and I didn’t even get to take AP in high school. The calculus involved is so superficial you don’t need to understand it at all. Honestly they should just wait until you know enough math to understand calculus of variations before giving you any physics courses.

    • @ChaosKnight7000
      @ChaosKnight7000 4 หลายเดือนก่อน +1

      @@nuclearcatbaby1131 I agree that the calculus is fairly superficial at that level. I've seen many introductory physics students struggle more with the algebra than the calculus.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      @@ChaosKnight7000 Seriously if you get the hand of that you should just skip straight to upper division classical mechanics.

  • @NikolajKuntner
    @NikolajKuntner 4 หลายเดือนก่อน +2

    Back in 2015 I did Landau-Lifshitz classical mechanics, writing down all exercises as Wildberger would.
    Admittedly, I only did this for 2 chapters before I gave up on the idea. But at least I can now reflect on it ten years later in a youtube comment.

  • @ranrubin2833
    @ranrubin2833 4 หลายเดือนก่อน +1

    The Dirac book is really really good! You should read it!
    I once found a very old abandoned copy of it (during grad school) and it was really exciting to read.
    It also teaches linear algebra very nicely (by inventing the Dirac notation). When he wrote it, physicists didn't know linear algebra so he had to give them the tools they needed.

  • @fmdj
    @fmdj 4 หลายเดือนก่อน +34

    6:40 differential equations cannot be taught, it is pure sorcery

    • @juancamarena5775
      @juancamarena5775 3 หลายเดือนก่อน

      I had an excellent teacher. it helps if you already know calculus. because that's what it is. applied calculus.

  • @Szanth
    @Szanth 4 หลายเดือนก่อน +5

    I am in no way going to teach myself physics but I gave the video 7 minutes just in case

  • @trixonic6934
    @trixonic6934 6 วันที่ผ่านมา

    This has helped me further my theories and contribute to the scientific world without a college degree. I’ve gathered great attention from the too in the field after 3 years of study and hope for many more

  • @Mezog001
    @Mezog001 4 หลายเดือนก่อน +2

    I don't have a ODEs textbook to recommend but I do have a PDE textbook to recommend.
    Introduction to Partial Differential Equations by Peter J. Olver published by Spring is a really nice book. I really learned how to think about math working through this book. I used this book to teach myself PDEs before going into work everyday for like 4 months in 2018. It is an undergraduate text.
    I would add that if you're interesting is a specific topic in physical go to the relevant engineering field and start working through those books. They will fill out the space of the topic with application. They are also a little slower at the undergrad level. An Example would be the Sophomore Mechanical Engineering sequence: Statics, Dynamics, and Strength and Material. This will also dump you at the door of Taylor's Classical Mechanics.

  • @EastWindCommunity1973
    @EastWindCommunity1973 4 หลายเดือนก่อน +3

    Bruh, I'm coming here to learn physics from you. I can't do it myself, it isn't as entertaining!

  • @josiahslack8720
    @josiahslack8720 4 หลายเดือนก่อน +6

    Dirac definitely wrote a book called "The Principles of Quantum Mechanics", but it was in the 1930s. Probably not a good choice if you're just trying to learn quantum mechanics.

    • @KingdomHearts1626
      @KingdomHearts1626 4 หลายเดือนก่อน +1

      And it's a DENSE read as well, didn't age really well notation-wise (not necessarily a bad book tho)...

    • @RubALamp
      @RubALamp 4 หลายเดือนก่อน

      This book aided me in understanding the Hamiltonian formulation further, and what quantization "means". But yeah, it's not an introductory book.

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      I think philosophy of quantum mechanics is a good place to start.

    • @josiahslack8720
      @josiahslack8720 4 หลายเดือนก่อน

      @@nuclearcatbaby1131 In that vein, I'm fond of Albert's "Quantum Mechanics and Experience"

    • @nuclearcatbaby1131
      @nuclearcatbaby1131 4 หลายเดือนก่อน

      @@josiahslack8720 I read that and another book for my philosophy of physics class.

  • @brettgoldsmith9971
    @brettgoldsmith9971 4 หลายเดือนก่อน

    I adore David Griffiths Introduction to Electrodynamics. Not only is the subject matter interesting, but it is so well written that it's almost as engaging as a novel.

  • @IsomorphicPhi
    @IsomorphicPhi 4 หลายเดือนก่อน

    Your words on stat mech an on Jackson feel so validating. Dirac's both Principles and Lectures on QM are highly worth the read once (and only once) you know the subject (in my opinion)

  • @bits_for_bytes
    @bits_for_bytes 4 หลายเดือนก่อน +3

    Could you please make a video on the various symbols used in physics equations, there’s Greek symbols and then there’s others like the limit and sum symbols, etc.
    This would be immensely valuable, having an introductory explanation of each symbol that I can refer back to.

    • @bits_for_bytes
      @bits_for_bytes 4 หลายเดือนก่อน +2

      My issue is I don’t know how to read them, like how to say the symbol mentally while I’m reading the equations

    • @petevenuti7355
      @petevenuti7355 4 หลายเดือนก่อน +2

      I think part of the reason why I was turned off from a lot of physics and maths was because of the symbols even when they tell you what they mean, I ended up in computer science but using an analogy from computer science, sometimes they seem more like entire objects than variables.
      Some of these symbols and variables are not just representing a number or unit system, but often are a lot more complex (and I don't just mean literally like i ), they could be entire arrays of vectors and matrix's ! Many simple symbols can be entire concepts wrapped in a function!

  • @jadegecko
    @jadegecko 4 หลายเดือนก่อน +3

    Learning physics isn't hard
    When you've got a library card

    • @1eV
      @1eV 4 หลายเดือนก่อน

      what?

    • @jadegecko
      @jadegecko 4 หลายเดือนก่อน

      @@1eV It's from Arthur (the little stuffed guy on the shelf behind her)

  • @monkerud2108
    @monkerud2108 4 หลายเดือนก่อน +1

    Sorey for a lot of text but you mentioned monopoles and i couldnt resist. Also as a funny curiosity when you turn this thing around it is changed in its orientations of the contituent structure, it all fits together in such a way that you get the double cover rotations and all that as well, hopefully you get to see it in detail some day, because it is pretty amazing and pretty, especially the i finite regress braiding of handedness part.

  • @sanador2826
    @sanador2826 4 หลายเดือนก่อน +1

    I love your videos please never stop making them

  • @paigemcloughlin4905
    @paigemcloughlin4905 4 หลายเดือนก่อน +5

    Looks a lot like my course of study in the mid to late 1990s.

    • @paigemcloughlin4905
      @paigemcloughlin4905 4 หลายเดือนก่อน +1

      but classical mechanics and thermodynamics were required and nuclear physics as well. I only did undergrad physics though.

    • @BlueGiant69202
      @BlueGiant69202 4 หลายเดือนก่อน

      I would agree, although, in 1983-1984 my first year Physics text was "The Fundamentals of Physics" by Halliday and Resnick. In the 1990's there were a lot of calls for textbook reform that fell on deaf ears. It seems to happen about every twenty years or so. Eugen Merzbacher gave a speech on it that appeared in the American Journal of Physics while at the same time another professor stated that students were not properly trained for advanced work in Physics in the same AJP issue. Joseph Agassi noted in "Einstein vs Bohr" by Mendel Sachs that what made a good academic student was not what made a good research physicist. Over the years and decades, I've come to agree with David Hestenes regarding "Physics as Modeling." I now regard the disputes about textbooks as a less important sub issue because many professors and physicists have pointed out that students have been playing the wrong game all along and have not been trained to be physicists nor taught physics in high school that was directly applicable to their lives. Dr. Roger Schank, PhD is an education reformer that majored in math but was a major influencer and professor in A.I. that tells high school students straight out that physics as it's been taught for a long time is useless. And then it's interesting to note that another advocate of education reform, Sugata Mitra, that was teaching computer science was a physics graduate.
      Now, IBM Watson and chatGPT can play Physics Trivial Pursuit better than most students. One has to be an expert to detect chatGPT's hallucinations. It looks like the arguing over letting calculators into physics classes over slide rules. My grade 11 Physics teacher actually made us use slide rules in the early 1980's. We used no programmable calculators in first year University so I liked seeing the calculator come out in this video with a comment on how old it was.

  • @lunasophia9002
    @lunasophia9002 4 หลายเดือนก่อน +3

    Honestly surprised a string theory book is in this video.