Calculus for the Curious
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Calculus for the Curious
1–10 of 42 posts
Re: Calculus for the Curious
#2I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented.
My plan is to get through it to get some background on the main ideas of calculus, then work through khan academy and/or read through Aleksandrov’s Mathematics Contents/Meaning.
If anyone knows of active forums/q&a/online practice for self-learning calculus, it’d be a huge help if you could share.
Re: Calculus for the Curious
#3I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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.
Re: Calculus for the Curious
#4I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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.
Re: Calculus for the Curious
#5I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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.
Re: Calculus for the Curious
#6I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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.
The point of Spivak’s book is to be rigorous and offer hard problems, not teach the basics of how calculus is used.
Doing epsilon–delta proofs can be fun, but it’s mostly useful for aspiring pure mathematicians, and not really relevant per se for the grandparent poster.
Re: Calculus for the Curious
#7I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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...
Re: Calculus for the Curious
#8I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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…
Am I wrong to say that even if the universe of your concern is discrete, calculus can at least describe the behavior of recursive discrete processes, among other things?
Re: Calculus for the Curious
#9I just stumbled upon Infinite Powers in B&N, and after reading a bit, decided to buy it. Loving it so far. I’ve been curious about calculus for a long time now, since I’ve never taken a formal class on it and am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented. My plan is to get through it to get some background on the main ideas of calculus, th…
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…
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Re: Calculus for the Curious
#10I just finished reading this, and thoroughly enjoyed it. It provides a clear description of the fundamental intuition at the heart of calculus (chop stuff up infinitely, then put it back together again), and a mix of the historical background of its development and its ancient and modern applications.
All books of this nature are somewhat idiosyncratic – it's not a history, not a textbook, nor an applied maths book; it's a packet of passion sent by someone who's clearly excited and enthralled with his topic: "Here's a story about something really cool! Maybe you'll think it's cool too!"
I've been investigating recent books with different approaches to calculus (trying to build a free online course that empowers people in maths). Here are some other books I can recommend/mention:
[0] "Burn Math Class: And Reinvent Mathematics for Yourself" Goes from 1+1 all the way to derivatives and integrals. My favorite work of math demystification and pedagogy.
[1] "Calculus Reordered: A History of the Big Ideas" Released this year, exactly as the title says. An accessible history, explaining each idea as it enters the world stage. I've only just started this, but it's a definitely more historically thorough, albeit less engaging, book than Infinite Powers. (Since historical accuracy seems to be TFA's main focus, I wonder what they would think of this book.)
[2] "Change Is the Only Constant: The Wisdom of Calculus in a Madcap World" Another just-published book – this is the year for Calculus! Amazon has lost/delayed my preordered copy, but from the author's other work I expect this to be a LOT of fun.
[3] "Magnificent Principia: Exploring Isaac Newton's Masterpiece" Sort of "the annotated Newton". Outlines Sir Isaac's history, social environment, and development of the Principia Mathematica. The bulk of this book is going through each section of the Principia, translating the language into modern speech/formulations (where needed), and explaining what Newton was getting at. Also not as gripping as Infinite Powers, but a great way of reading and understanding one of the most foundational scientific/mathematical texts of all time.
[4] "Introductory Calculus For Infants" I'm about to have my first child, so am naturally collecting suitable reading material for the budding babe (suggestions welcome!).
[0] https://amzn.to/2pVXJwj [1] https://amzn.to/2pMCZr5 [2] https://amzn.to/31Ny32e [3] https://amzn.to/2BIimyM [4] https://amzn.to/33ZxbJj