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As someone who's taking a university entrance course in Calculus I find these kind of "calculus made easy" pamphlets irritatingly trite. The hard part isn't th

• getcrunk 2y ago
  Most of your first point is … algebra? Yes if your algebra is weak you will not be able to cope with solving calc equations. The solution to that problem is not to be found in a calculus made easy. It would be found in algebra made easy.
  • sieabahlpark 2y ago
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  • conwy 2y ago
    Yes, it's algebra. Math isn't like programming. In programming you can often solve a problem using a library, framework, language facility, etc. without entirely understanding why it works all the way down to the binary level. In math you can't often solve a more advanced problem such as Calculus problem without understanding the more foundational math such as algebra, fractions, etc. If "information hiding" / layers of abstraction was possible in math, I would have completed my university entrance course months ago, but here I am still struggling. Sure, we could have Algebra made easy and also Trigonometry made easy, Fractions made easy, Functions made easy, etc. etc. I just find it personally irritating that all this foundational knowledge is brushed aside when it's really core to someone's actual competence dealing with actual math problems. Maybe it's just assumed that people went to a good high school or had a private math tutor and already learned the foundations very well, but I think at least that assumption would be coming from a place of privilege. It's similar to telling someone to take a Bootcamp in React and that will be enough for them to succeed as a software engineer. But to solve the kind of problems they are going to face in reality they will eventually have to learn at least some foundational Javascript and maybe a little about algorithms and data structures.
    • goosejuice 2y ago
      Do you find it surprising though? Certainly not everyone is in the same place in their learning journey as you. Material on calc, at a university level, is typically going to focus on calc. Yes it is assumed that you have learned the fundamentals before taking that course. I was in a similar situation as you. If you really want to learn it there's no substitute for skipping over the fundamentals. I did that and did fairly well but it's all long forgotten. Never use the stuff :)
      • conwy 2y ago
        > Never use the stuff :) So many people tell me this that it's become cliche at this point. I find it demotivating, but unfortunately I have to press through, as there is literally no other way I'm going to gain entry to my university's bachelors program. A part of me wonders if this kind of fundamental knowledge could be actually useful, similar to being able to cook your own food instead of takeaway. Kind of like how "first principles" thinking can apparently lead to new discoveries because you're not just mimicking / re-using the same structures that were already built.
        • RF_Savage 2y ago
          Being able to check the numbers software and manufacturers provide is a good use.
        • vnce 2y ago
          I’m a product manager and I use the concepts to read and understand new algos, research papers, etc. you’re right that you won’t be calculating (that builds problem solving) but grasping the principles will help you proceed to more advanced concepts in other fields Good luck you’ll get there.
        • goosejuice 2y ago
          My experience certainly isn't representative! I just happen to build things where university level maths rarely comes up. Stats comes up more than anything and sadly only had to take one course in that area. Since you bring up food. As a former professional baker it would also take me some time to make croissants professionally at the level I used to. At least for me personally, if I don't use it I lose it. But I can certainly pick up faster than someone seeing it for the first time if I needed to. Along the way you'll pick up some intuition that you can use elsewhere that's hard to quantify. Outside of the loans I don't regret taking any of the maths required for my CS degree. Personally, I found the calculus lifesaver by Adrian Baker to be helpful in my studies as someone that was missing some fundamentals
  • hintymad 2y ago
    Algebra is the simple part. I’d say it’s more about math maturity. At least 1/3rd of my classmates had a hard time grasping the epsilon-delta definition of limit, let alone the deeper definitions like Cauchy sequence or those used in the proof that R is dense(and we were in an elite university’s competitive program). Among the survivors of single-variable calculus, at least 1/3 could barely get by the multi-variable calculus. I saw too many of my friends struggle with different integrals, and got massacred by Green’s equation. My guess is that most people hit a wall of abstraction at certain point.
    • conwy 2y ago
      > My guess is that most people hit a wall of abstraction at certain point. I don't think it's a limit to their abstraction, I think it's that they didn't work properly on the fundamentals, so they had a superficial understanding of the abstractions. To give a fitness analogy it's like trying to do heavy barbell presses before you can even do 10 pushups in a row. My experience with programming is that once you get really really good with fundamentals you suddenly leap ahead and pick up new languages, paradigms, etc. incredibly fast. Maybe this partly explains the 10x phenomenon - it's because they worked very hard on the fundamentals.
      • globalnode 2y ago
        my view is software by comparison is like a single surface of knowledge; once you know the basics, thats it, nothings too hard to learn. maths on the other hand is more like a volume of knowledge.
• gofreddygo 2y ago
  So you want to do calculus ? You need algebra. What parts of algebra ? Go figure ! this is one big hurdle in learning math backwards. You discover new missing pieces at every corner. Each missing piece leading to another missing piece. Learning math from the basics to advanced (as recommended by most) is very frustrating at how slowly you actually develop the math muscle. At a deeper level, conceptual grasp does not make you good at math, its not enough. You may fool yourself into thinking you "get it" till you try to solve a few exercises. You need to repeat the lower levels enough to make it into muscle memory (which some people refer to as math intuition or groundwork) before embarking onto higher levels that build on it. So working your way bottom up is slow and frustrating, top down is slow and frustrating. What do you do? Just keep at it. One key observation for me was that at some point the misery and rabbit hole nature diminishes, quite rapidly. The groundwork of solving all those exercises repeatedly pays off and the next set becomes a little easier. Getting to calculus after spending ridiculous amount of time on algebra is the only way I have known to work. And this is true for learning progamming too. knowing the concept of loops is essential but, you still can't write efficient code to sort an array. You need to get the syntax and write enough loops and then progress to exercising writing specific sorting algorithms repeatedly to get them into muscle memory. But there is an inflection point beyond which the same concepts repeat but in different variations and they take progressively lesser time to get a grasp on. thats just how I've learned math and programming. Also why a large percentage of people just give up hope and accept they just don't have the math gene. Meh.
  • conwy 2y ago
    > this is one big hurdle in learning math backwards. You discover new missing pieces at every corner. Each missing piece leading to another missing piece. Yes this is exactly what happening to me. E.g. I got up to Week 2 of the course and suddenly made the big (to me) discovery that sqrt(a/b) = sqrt(a)/sqrt(b). It seems trivial I know when you see it written like that, but the problem is to recognise and apply that principle in the context of a broader problem such as factoring. > Just keep at it. Thanks, this gives me confidence that I'm not wasting my time haha I am beginning to get better at it, to the point that I can often work out why I got a question wrong on my own without referring to the answer.
• svat 2y ago
  > these kind of "calculus made easy" pamphlets The link is not a pamphlet (unless you read only the linked HTML page). It is an entire book, published in 1910 by Silvanus P. Thompson, and sufficiently well-regarded that it was re-edited in 1998 by Martin Gardner, and (independently) lovingly re-typeset in TeX by volunteers (and also turned into this website). Clearly it serves a need, and is not merely a “trite” pamphlet. (The edition by Gardner is actually recommended against by some, who see in it a clash of two strong personalities, individually delightful.)
  • conwy 2y ago
    It serves a need just not my need! (As someone who's surprisingly bad at math and trying to undertake a Calculus pre-req to get into university!)
    • radicalbyte 2y ago
      I read Calculus Made Easy about 15 years after my last math lesson, and had forgotten a lot of the mechanics of algebra. I went through Algebra and Algebra II for Dummies before reading it. They're really concise, very easy to read and absolutely did the job for me. Calculus Made Easy is an amazing book btw, by far the best introduction and much better than the way I was taught at school as it actually builds your intuition.
      • conwy 2y ago
        Ok well thanks for the Algebra book recommendations, will see about working through those first.
    • latexr 2y ago
      > It serves a need just not my need! Which is fair, but if you believe that you shouldn’t have insulted the work itself by dismissing the value of its content and calling it a trite pamphlet.
  • weebull 2y ago
    It's a great book, and one my father recommended to me to get me through the concepts when I was having trouble with the standardised teaching of the day. It comes down to Leibnitz Vs Newton, and the world has standardised on the notation of one (I forget which). However the notation is a destination when learning it all, and the foundational ideas behind calculus were best explained taking ideas from both of them. That's what this book does. It takes you through with every simple jumps in logic allowing you to discover calculus yourself and you therefore have the foundations to reason about it yourself. You don't just have to learn the final answers by rote.
• beltsazar 2y ago
  I feel the opposite. In high school I was pretty good at solving calculus problems but had little understanding what "limit" actually is. When in college I finally understood the definition of limit and all the foundational theorems arised from it, I was blown away. For most people—who won't solve complex math problems daily at work—the takeaway from learning math is not their mechanical ability at solving math problems. The takeaway is their understanding of math concepts and ideas, which will shape their thinking skills in general.
  • jasomill 2y ago
    For me, the biggest stumbling block in understanding the usual ε/δ limit definition in high school was teachers reading |x - a| as "the absolute value of x minus a" rather than "the distance between x and a". The later reading suggests a more intuitive (to me) definition: a limit f(x)→q as x→p exists if, for every open interval Y containing q, an open interval X containing p exists such that f(x)∊Y for all x≠p in X (and then if f(p)=q, f is also continuous at p). Another nice property of the above definition: replace "interval" with "ball" or "neighborhood" for analogous definitions for functions between metric and topological spaces, respectively.
  • conwy 2y ago
    > For most people—who won't solve complex math problems daily at work—the takeaway from learning math is not their mechanical ability at solving math problems. The takeaway is their understanding of math concepts and ideas, which will shape their thinking skills in general. Agree, but for some others, there are real world consequences, e.g. whether they get accepted into a university or whether they can read and properly understand an academic paper.
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• ecshafer 2y ago
  Your issues seem to be algebra. I recommend Khan academy personally and just working through all of the highschool math that he goes over. I found his stuff when he was still just a guy on youtube back when I was in the same position as you. Studying calculus, did fine in high school, but my school was not good and totally unprepared me for actually studying math, skipping over a lot of those fundamentals. So often I would have a professor or TA take a complex equation, show an "obvious trick" that we "knew from algebra" and it would be the first time I ever saw that in my life. There is really no other solution than to study and relearn algebra, geometry and trig yourself as you learn calculus.
  • Yhippa 2y ago
    I remember taking a graduate level cryptography course several years ago and relying on Khan Academy to grok the fundamental concepts.