Thony's math and astronomy posts are great. Very careful with the details (a real scholar) yet readable as Asimov. Quite brave of Strogatz!
(Notice the tag cloud on that page? ... he's been at it for a while!)
Calculus for the Curious
11–20 of 42 posts
Re: Calculus for the Curious
#12I 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…
Dr Jim Fowler, from Ohio State Uni, explains Calculus concepts with simple examples, https://www.youtube.com/user/kisonecat/videos
Re: Calculus for the Curious
#13Earlier quoted context omitted.
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?
Depends on the process and the exact form of the discreteness.
Discreteness introduces discontinuities and errors, and it's usually possible to describe the errors analytically. But there are situations where discrete systems become numerically unstable and blow up while the smooth analytic equivalent has no problems.
Re: Calculus for the Curious
#14Holy, commas, Batman
Re: Calculus for the Curious
#15"See for example Euler, who made great strides in the development of calculus without any really defined concepts of convergence, divergence or limits, but who doesn’t appear here at all."
Can anyone say more about this? I always suspected this was so, because the end of high school / start of uni is roughly that sort of time period, and I always thought there was something about convergence/limits that was missing, it seemed very ad hoc.
Re: Calculus for the Curious
#16"See for example Euler, who made great strides in the development of calculus without any really defined concepts of convergence, divergence or limits, but who doesn’t appear here at all." Can anyone say more about this? I always suspected this was so, because the end of high school / start of uni is roughly that sort of time period, and I always thought there was something about convergence/limits that was missing,…
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?
Re: Calculus for the Curious
#17I used to always associate 'math smarts' with 'code smarts'. Spent most of my life telling myself that since I was bad at math I had no hope learning how to code. Now I'm 2 weeks into a coding bootcamp after losing my job and am realizing they are complete different parts of the brain.
I believe in myself more with every push to heroku. maybe I will do a Calculus class next and prove to myself I can learn anything. Anyone have recommendation on an online calc course for the math-insecure?
Re: Calculus for the Curious
#18I used to always associate 'math smarts' with 'code smarts'. Spent most of my life telling myself that since I was bad at math I had no hope learning how to code. Now I'm 2 weeks into a coding bootcamp after losing my job and am realizing they are complete different parts of the brain. I believe in myself more with every push to heroku. maybe I will do a Calculus class next and prove to myself I can learn anything. A…
> 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.
Re: Calculus for the Curious
#19"See for example Euler, who made great strides in the development of calculus without any really defined concepts of convergence, divergence or limits, but who doesn’t appear here at all." Can anyone say more about this? I always suspected this was so, because the end of high school / start of uni is roughly that sort of time period, and I always thought there was something about convergence/limits that was missing,…
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?
In high school mathematics, you're not really given the definition of a limit. Consider the definition of the derivative
limit as h -> 0 of (f(x+h) - f(x)) / h.
That's well-defined on (0, inf) but not on [0, inf). So you can't just evaluate at h=0 and be done with it.
The intuition is 'as h gets smaller and smaller, the ratio gets closer and closer to a new function of x'. But many high-school students aren't given a clear definition of what it means for one function to be 'close' to another, or what it means for x to 'get smaller and smaller'.
To see the confusion more clearly, try having the debate about whether 0.999... = 1 with someone who doesn't understand what a limit is.
Re: Calculus for the Curious
#20I 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…
>... calculus isn't really necessary; the world is completely discrete
Erwin Schrodinger would like a word with you.