Calculus for the Curious

Try http://www.math.smith.edu/~callahan/intromine.html which is a very conceptual and simulation-focused calculus curriculum, without so much symbol twiddling.

The concepts of calculus (the mathematics of motion and change) are absolutely fundamental across science, but being able to get closed-form solutions to tricky indefinite integrals (while an enjoyable puzzle) is only marginally useful per se.

> work through khan academy

YMMV, but I don’t find KA to be especially pedagogically enlightened. I think of it as roughly an average-quality high school lecture videotaped, plus a big pile of mindless exercises. It’s still nice that it exists: it makes a quality floor for students with below-average teachers, and is free for everyone in the world, without any forced schedule.

You’ll get roughly the same result from just reading a standard introductory textbook and working the problems.

For better results, if you can afford the time, hire / find a private tutor to meet with regularly face to face.

Spivak has a pretty decent calculus textbook that you might find interesting. I used a different textbook, but I believe that Spivak is more popular.

If you have the chance, try to go through a formal proof and analysis based course that requires convergence proofs and all that (mathematical "analysis" isn't what you might think; it's a specific subject). For calculus, it is what drove home the point and the magic for me.

We used this book (https://smile.amazon.com/Introduction-Calculus-Analysis-Clas...) but I expect it may be a bad fit for self study. Try to find something with similar subject matter.

Oh, hey. Are you me? I am wrapping my time in CS grad program, and I also, never took calculus as a formal class.

Now, I will say, save machine learning/AI, calculus isn't really necessary; the world is completely discrete.

That being said, that doesn't mean that knowing calculus wouldn't _enhance_ your ability to understand and digest some of the more difficult reductions and proofs in, say, a theory of computation course.

I relied on "The Calculus Tutoring Handbook"[0]. I wanted a book that had answers to _all_ the exercises for confidence building purposes. The book goes slow and provides a great amount of detail -- the authors are pretty good at not hand-waving.

I also found \r\learnmath useful as a "I have a problem and can't ask anyone" site. They are really friendly.

[0] https://www.amazon.com/Calculus-Tutoring-Book-Carol-Ash/dp/0...

Dr Jim Fowler, from Ohio State Uni, explains Calculus concepts with simple examples, https://www.youtube.com/user/kisonecat/videos

This is a fantastic thread https://twitter.com/nntaleb/status/1163192701472428032?lang=... from Taleb. As always, a little bit over the top, but mostly on point. I've seen the exact phenomenon he describes play out so many times now its not even funny. I'm doing a PhD in mathematical statistics, which is sort of like "calculus on steroids". I basically do calculus day in day out. Many of the problems we attack are simply not of much interest to mathematicians. I used to run my problems by math profs & they would say something like yeah it can be done, have you tried mathematica etc. instead of buckling down to do it. For instance, yesterday I had to prove that Fisher information of Cauchy is half. Now that's entirely calculus. You take a function f(x,t) = (pi*(1+(x-t)^2))^-1. You then take the log of that. Then you differentiate that w.r.t t. What you get is called the Fisher score function S(t). So you take the score function and differentiate that again. Lets call that g(x,t). Stick a negative sign in front of that. So now you have a complicated looking new function -g(x,t). You multiply the -g(x,t) with your original f(x,t) and integrate that product over the reals. The result is half. Most mathematicians usually get stuck on that last step. But for (mathematical) statisticians, this os sort of our bread and butter integral. So we know a bunch of tricks. Here's one such trick - https://stats.stackexchange.com/questions/145017/cauchy-dist...

Its like riding a bicycle. Those who ride the most know how to ride. But there are some who want to know how do bikes actually work...which is not going to help you much with riding the bike.

I recommend "The Mechanical Universe" TV program, produced by Caltech with the Annenberg foundation.

Although it's not about calculus per se, it shows how it is used with physics. Newton having invented calculus in order to describe physics. However, they use the more standard Leibniz's notation on the program.

You probably won't be able to sit down and solve integrals after the show, but the program helps to take a practical and beautiful mathematics branch and gives viewers an intuition to its application that I didn't find in an actual math course.

https://www.youtube.com/playlist?list=PL8_xPU5epJddRABXqJ5h5...

> Anyone have recommendation on an online calc course for the math-insecure?

Honestly I'd say do one thing at a time, and do it well. It takes a year to stop being bad at anything worth doing, and a lifetime to get good. You're only two weeks into learning to code. Maybe you should go full-bore into that for the next year and pick up calculus some other time.

What did you do before if you don't mind me asking ? Would you have done an investment banking bootcamp if it guaranteed higher pay ?

I have bury-the-needle good spatial reasoning and somewhat above average general intelligence. Gifted programs, all that stuff. Ought to be anywhere from somewhat good to very good at mathematics. But... I feel the way I figure dyslexics feel reading human language, when I read math.

Code? Natural and easy, even “hard” concepts. There, my measured natural abilities come out just as you’d think they would. My best guess is I find algorithmic thinking easy, but proof/equational thinking unnatural. All I can figure. I’ve had some limited success approaching math with a “what does this term _do_?” attitude, but it’s slow going.

IOW don’t worry, there are others out there. Sometimes we even get a reputation for being the ones to go with for the tricky stuff. Go figure.

> Spent most of my life telling myself that since I was bad at math

Note that very few people are actually “bad at math” in any kind of inherent way. The problem is usually a combination of psychologically damaging (and technically poor) teaching, parental/peer pressure, etc. leading to a phobia/mental block, which eventually leads people to construct an identity as “not a math person” (which has been tragically normalized in our society – in some places this doesn’t happen).

Plenty of the folks who say they are “bad at math” try again later under more relaxed and encouraging circumstances and are plenty successful.

So good luck!

If you are serious about it, my recommendation is to try to find a private tutor to meet with face to face.

I used to suck at algebra, then I wrote c++ code for 30 years... now I can see how they differ and how they are similar.

sometimes when you are programming in a big body of code you are dealing with lots of types (types in the programming sense)... and you are dealing with functions that have type signatures that must be satisfied to avoid compile errors... so you wrap this type in that one so you can call that function.. or you convert the return value from one type to another so you can call something else...

anyway, that is all similar to what you are doing when you manipulate an equation. you follow the rules and change it into a form that is more useful.

Euler lived in the 1700s. Not sure how that would have affected your training unless you’re much older than average.

Cauchy and Taylor both formalized many concepts, again in the 18th and 19th century.

What are you thinking is ad box?

As I understand it our modern notion of what rigorous mathematics is didn’t exist back then. The justification for analysis was basically physical intuition and simply that it worked.

Euler and company just worked directly with the intuition of infinitesimal quantities. To be fair though, infinitesimals are the essential intuition for how calculus works anyway.

Personally I don’t really care about constructions of the real numbers or technical details of calculus. It’s enough for rigorous mathematics to know that models exist of the theories which produce calculus; that is models of complete ordered fields and even plain old ordered fields with infinitesimals.