Hey nerds, I’m planning on going back to school in a few years and want to smash the math proficiency test so I don’t have to spend years relearning things that will probably only take me a few months at most. What books do you all recommend to get me from college algebra to Calc II or III?

Bonus points for stats and physics recs, as well.

  • PorkrollPosadist [he/him, they/them]@hexbear.netM
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    11 days ago

    I don’t know if it will help your test scores, but I found the 3Blue1Brown Youtube channel to be incredibly helpful in learning fundamental linear algebra and calculus. My interest in learning this was for 3D game development in Godot, but math is math I suppose. Around the same time I hit up my local library and checked out an “outdated” college textbook on calculus (which was also great, but I had to return it too soon).

    I generally prefer literature over video content, but these video series have absolutely fantastic visual representations of the concepts being explained. I think they are a great place to start before dipping into more rigorous literature. You must consider that the traditional way of teaching mathematics is on a chalk board, which is ultimately a visual medium.

  • radio_free_asgarthr [he/him, comrade/them]@hexbear.net
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    11 days ago

    For the advanced calculus (depending on your university, usually either linear equations and ordinary differential equations or multivariate calculus is calc III) I learned multivariate calculus from Marsden and Tromba Vector Calculus. I don’t remember the other textbooks I used for calc in undergrad, but I found trying to search for what the textbook I used that UC Berkley has one of their ODE textbooks free online. Can’t verify the quality, but since it is free, you could just look and see if you find it useful.

    EDIT: I found that I used Stewart Calculus books for my Calc I and II classes. They were alright. Also, Kline’s calculus book is one I heard of other universities using and that is now a Dover book. I never used it, but it is a common introductory book and would be cheaper than others for a physical copy.

    For stats and physics I have a bit better recommendations. (I don’t recommend using the provided Amazon links to buy them, but just so that you have the relevant info)

    Eisberg and Resnick is the entry level lower division optics and quantum mechanics text book (https://www.amazon.com/Quantum-Physics-Molecules-Solids-Particles/dp/047187373X)

    And there is the entry level (freshman science major) mechanics and electromagnetics books with Resnick as the first author. The other authors change with editions, but my Dad used those books when he was in college, so you should be able to find very cheap old editions. I did actually use the Eisberg and Resnick book, so I assume the other Resnick books should be good.

    Griffiths Quantum mechanics and electrodynamics would be the next step, but that is getting into ~3rd year (junior year) levels (https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/1107189632 and https://www.amazon.com/Introduction-Electrodynamics-David-J-Griffiths/dp/1009397753/140-6128986-2705400?psc=1)

    Edit: If you are interested, Kittel and Kroemer’s Thermodynamics is a common ~2nd year introduction to thermodynamics and statistical mechanics. I used it and thought that it was decent (https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp/0716710889)

    Also, broadly, I would say that if you are looking for a book on a particular subject, a good place to start is Dover books (https://store.doverpublications.com/pages/math-science). They buy a lot of books from other publishers and print them very cheaply. And so they sell very highly regarded books on their topics for very cheap. Many grad school classes used their textbooks and also I still use several of their books as references currently in my job.

    For statistics, I have briefly used Mandel’s The Statistical Analysis of Experimental Data, which I remember being very introductory. And I see Kolmogorov https://store.doverpublications.com/collections/math-probability-and-statistics/products/9780486821597 being cited and used as an introductory text book. But I have never read that one myself.

    And of course, most of the books I mentioned, including the Dover catalog, will likely be found on libgen or annas-archive.

    • quarrk [he/him]@hexbear.net
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      10 days ago

      Griffiths QM is kinda meh. It’s the one I used in my courses, but later while trying to relearn, I found Shankar’s Principles of Quantum Mechanics to be pedagogically superior. From the intro,

      “Since the math introduced has to be taught sooner or later, I prefer sooner to later, for this way the students, when they get to it, can give quantum theory their fullest attention without having to battle with the mathematical theorems at the same time. Also, by segregating the mathematical theorems from the physical postulates, any possible confusion as to which is which is nipped in the bud.”

      Shankar’s lectures are on YouTube as well.

      A QM book is probably beyond the immediate need of the OP, but this might be useful to someone.

      • It is better, but because of going more fully into the mathematics immediately, it is a bit more advanced. My undergrad university used Griffiths for upper division QM and Shankar for Graduate level. Which is why I recommended it earlier for self training. But there is value in just immediately diving into the full mathematical framework right away.

  • grouchy [she/her]@hexbear.net
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    11 days ago

    Since I don’t think anyone else mentioned it yet, Paul’s Notes is a really good old school resource for math if you don’t like videos. (Old school as in the site is more than two decades old and the interface can be a bit annoying to navigate haha): https://tutorial.math.lamar.edu/

    Very clear and thoroughly worked out examples.

  • TraschcanOfIdeology [they/them, comrade/them]@hexbear.net
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    11 days ago

    Try a precalculus module from either Khan Academy as someone else suggested, or from the ones some universities make available to the public. If anything it’ll let you know which parts you struggle the most and which ones you have more ease remembering. Then focus on those.

    Math is largely about practice, and once you’ve done enough peoblems, you’ll catch the little details that make things click, or that point you towards a certain kind of solution rather than another.

    I would focus on making math feel natural (at least until Calc 1) before moving onto physics or stats, since having a solid grasp of math will make learning the actual concepts much easier, rather than spending time and energy figuring out how the math bit of those two work before actually learning.

    As for books, Stewart’s calculus (I think he also wrote a pre-calculus book, too) is kind of the default for most non-math major college calculus classes. It’s very thorough, has lots of problems and examples, but it will not replace a lecturer. It’s not the best book, but you could certainly do a lot worse.

  • LisaTrevor [she/her, they/them]@hexbear.net
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    11 days ago

    https://mathispower4u.com/

    this is what my calc 1 professor gave us to brush up with when i took it a couple years back. they’re just videos though, if you want everything to stick you’ll have to spend some time grinding problems.

    there are free textbooks here https://openstax.org/subjects/math
    the instruction isn’t very thorough, worth skimming when you need a quick refresh. use it for the exercises. I’d go through the Algebra + Trig book and Precalc, you’ll need to understand trig pretty well to get through calc 2 hell

  • SocialistVibes01@lemmy.ml
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    8 days ago

    For a deep understanding of Calculus, either Apostol or Spivak.

    For exercises, since we’re on hexbear, N. Piskunov.

  • Sabbo [it/its]@hexbear.net
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    8 days ago

    After getting covid I forgot math… like, all of it… which as someone in engineering is a serious problem. Luckily I had been laid off at the time and had about a year to relearn everything. To my surprise, I now have a much greater understanding of math, and no longer rely on memorization. So here’s how – much like puberty – I learned math the second time as an adult.

    Start with the video The “Game” of Mathematics, by Prof. Herbert Gross. He explains arithmetic in a way that makes things a lot easier to understand.

    From there I began learning about logic formulas. By doing this math became a language rather than something independent and isolated. Each symbol was nothing more than a word. Numbers are shorthand for something else (see “game” of mathematics).

    With that I went to Khan academy, started at elementary algebra (it doesn’t take long and it’s better safe than wrong) and worked my way up. If I ran into an issue I would try to describe it using logic words instead of algebra.