Schaum's outlines

What Hacker News says

1. JachMar 2022
   Yes, all tracks of math involve people using math. Proof writing is a part of use for a lot of it. There are also very many tools within the use of proof writing where a lot of education is around learning a bunch of tools so that you can better "recognize which tool to apply, then apply tool", in a future real-world use where you want or need to prove something.

   I'm a little snarky, but you have a broken idea of what math is. It's not even your fault. I don't even claim an unbroken idea for myself, I went through public education too, though I do think it's less broken. Somehow compulsory education has managed to get near universal basic literacy, but seems to have failed on whatever equivalent some sibling comments have hinted at exists for math or at least mathematical reasoning. A lot of algebra work taught for junior high can be understood as just a foundation to be able to understand later things (though you can of course use some of it directly as taught without having to learn more for every-day things like some boy scouting activities, or helping with putting together a garden or a fence, or programming -- and some of course is entirely useless). But instead of pushing algebra even earlier, states are instead moving to push it even later. (Let alone trying to spread awareness of even a hint of the subtle divide between more general algebra and analysis that a lot of STEM undergrads don't even really get a whiff of except maybe knowing it's often said to be a thing.)

   To try and be more helpful, I'll suggest you don't actually want to learn math at all. So don't! At least, not directly. Instead, find something you want to learn more about in science, engineering, or technology/programming, and dig into it until you start hitting the math being used. For many things, especially at the introductory level, it's fundamentally no more complicated than being able to read a junior-high-school level equation. Occasionally you'll need to know about some functions like square root, or sine, or exponentiation, or some other new functions that will be explained (like a dot product) in terms of those things. When you don't understand something, you may need to find an outside reference (or a few) for it, if the book itself doesn't cover it enough or to your liking. Even then, you can often find outside presentations of that thing which are still motivated by the general field and are thus not proof-heavy.

   However sometimes the best explanation may still be found in a "pure" book just about the thing, and if you can get over whatever problem you have with proofs you can learn to see how they can be used to build your understanding of the thing in smaller pieces, not just as tools to say whether this or that is true or false. In other words, proofs can serve the same function as repetitive problem-solving exercises, and are often given as exercises for that reason.

   I'm a fan of the Schaum's Outlines series of books just for the sheer amount of exercises available in them, I just wish I had better self-discipline to actually do more exercises. Though they maybe aren't the best resources for a brand-new introduction to something.

   To give a small example, maybe you're interested in game programming, and eventually want to dive into studying 2D collision detection more specifically so you can implement it yourself instead of using someone else's library, so you might stumble on a copy of "2D Game Collision Detection: An introduction to clashing geometry in games". Its explanation of the dot product comes early (its whole first chapter is on basic 2D vectors), consisting of 2 diagrams and two code examples (the first mostly defining dot_product(), the second using it as part of a new enclosed_angle() function) and some text all over 2.5 pages. It gives things in programming notation instead of mathematical notation, apart from some ² squared symbols occasionally. It gives a few equivalences like a vector's dot product with itself is its length squared, shown as dot_product(v, v) = v.x² + v.y² = length², without proving them, and points you to wikipedia of all places if you want to know more about how that or another detail are true. Why learn it? It's used immediately after in explaining projection, and then later in collision detection functions. Generally that book is structured as: learn the bare minimum of vectors, use them to implement collision detection for lines, circles, and rectangles.

   I'm not saying this is a great book but it's representative of what you'll find that I think you're really after, which is motivated use of some bits of math. If you don't like that book's treatment of vectors, there are a billion other game programming books that cover the same thing as a sub-detail of their main topic, and maybe even better for you because it'd be grounded in e.g. a graphical application you've already got setup and running to see results rather than a standalone library. Or there's special dedicated math books like "Essential Mathematics for Games and Interactive Applications". Or you can go find dedicated "pure math" books on linear algebra if you want. Or maybe your junior high / high school math education was good enough you can more or less skip most of this and move on to something more interesting, like physically based rendering (https://www.pbr-book.org/) which also of course has vectors and dot products with brief explanations. Or maybe you don't care at all about game programming, and want to learn about chemical engineering, or economics, or the mechanics of strength and why things don't fall down, or...

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2. mindcrimeFeb 2022
   I left with the certainty that I would never take a math class again, and a lack of desire to explore other scientific fields for fear that I would have a similar experience.

   That is one of the most tragic things I can imagine reading. A student who really, genuinely wants to study Maths, just for its own sake... and is dissuaded from doing so by myopic, short-sighted, inane policies. It makes you wonder "could you fuck up education any worse, if you were intentionally trying?"

   On the other hand though... I believe a student with enough self motivation can overcome those inane department policies and learn the Maths by pulling in outside resources. Yes, it's more work, and yes maybe it's not "fair" that you have to do that in addition to attending (and paying for!) a class. But it's possible.

   Consider the availability of free resources like Khan Academy, Paul's Online Math Notes, hours and hours of Youtube videos from people like Professor Leonard, Gibert Strang, etc. One can also often find problem sets with solutions by just Googling around and finding previous years course websites for various courses that have been taught at universities all around the world.

   There are also online forums where you can go to get your answers validated, or get additional explanations about Maths problems. They vary in the extent to which they accept "do my homework for me" style questions, but almost any site will acknowledge somebody who has put in some work, come up with an (possibly incorrect) answer and says "Can somebody help me understand what's going on here?"

   Examples:

   * https://www.reddit.com/r/learnmath/

   * https://www.reddit.com/r/cheatatmathhomework/

   * https://www.reddit.com/r/MathHelp/

   * https://www.physicsforums.com/

   * https://math.stackexchange.com (note: but not so much Mathoverflow, which is more for research level Maths and is not a good place for straight up "do my homework" style questions at all)

   And if one is willing to pay a bit, the Schaum's Outlines books and similar books provide a huge catalog of worked problems, along with problems and solutions. There's also Brilliant.org and other paid educational resources for Maths that can supplement ones university course(s). One can also look into hiring a personal tutor as an option.

   Many (most? all?) universities also have something like a "math lab" or "learning center" or something where students can go for individual tutoring and additional support. My experience (albeit dated now) leads me to believe that these are probably drastically under-utilized.

   Should universities do a better job with introductory Maths courses? Almost certainly. But I'd encourage anybody dealing with this to dig in and try to overcomes such shortcomings by using other available resources as well.

   EDIT: inspired by @skywardavocado's answer, I also wanted to add that old-fashioned "study groups" are another valuable arrow in the ole quiver. If you join up with 2, 3, 5, whatever, of your peers to study together, chances are that somebody in the group will understand the thing that the others are struggling with, and can explain it. I didn't do a lot of this in college myself, probably to my detriment. But to the extent that I did occasionally join a study group, I'd say they can be wildly helpful.

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3. KyeJan 2022
   https://www.amazon.com/Schaums-Outline-Elementary-Mathematic...

   Schaum's Outlines are like that "Learn X in Y Minutes" site for school subjects. They give the clearest, most bare bones explanation so you can quickly identify gaps. I had the college algebra book for the required math class in technical school. Between that and YouTube, I was able to pass the class.

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4. glialJul 2021
   For calculus, I like this book [1] for self-study. Also the Schaum's Outlines are great no-nonsense introductions. They're both gentle introductions, while still being useful.

   For probability, I really like Morin's book [2]. It starts really basic (like, super basic), but builds up a coherent understanding of lots of useful distributions, where their density functions come from.

   [1] https://press.princeton.edu/books/paperback/9780691130880/th...

   [2] https://scholar.harvard.edu/david-morin/probability

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5. zw123456May 2019
   Reminds me of the old Schaum's Outlines, I still have a couple of them on the book shelf from college days, saved my bacon many times.
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6. todd8Apr 2019
   I was a math major there. Each math professor had his own style for the smaller classes. There wasn't really a consistent teaching style for my classes except that they were challenging. Every student had to take a year of Calculus and a year of Physics and a semester of Chemistry among other general Institute requirements so the classes were very large, the teaching was top notch, and the problem sets were the first time most of the students had really been challenged at that level. Quizes and Exams were very hard.

   However, first year Calculus is totally doable as long as you have a solid high school math background (polynomials, trig identities, etc). I recommend (and I'm not joking) buying the physical textbook and doing every problem--not every problem assigned--every problem in the book. This will take a few extra 8 hour days of work, but practice, practice, and more practice will make you faster and more able to do the test problems. You may not have a physical text book or you may not like the text in which case look for additional books to use. Schaum's Outlines for Calculus at various levels are good sources of problems to practice on and they have the answers to all problems in the back. Do every problem you can and get help to understand the one's that stump you. Do a few hundred more problems than your classmates and you can expect an A. Like golf, extensive practice will improve your test scores.

   If you are unsure of your preparation for the course get Schaum's Outlines for the prerequisite course and do hundreds of review problems so you're ready for Calculus.

   One other piece of trivial advice is to buy a ream or two of plain copier paper; loose paper always worked better than pads for me because it was less expensive and I could spread out my work. Write on only one side of each sheet, otherwise the flipping back and forth looking for some work you've already done is too distracting. Pages containing final answers to turn in for homework problems can be creased/folded along a vertical axis so they are easy to distinguish from the pages laid out for work on subsequent problems.

   A 0.7mm mechanical pencil with a good sized eraser works well for lots of math (although some like yellow wood pencils). I learned to use ballpoint pens for math and engineering at MIT because crossing out is faster than erasing, but I believe that this is a minority opinion.

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