Pure Math Talent

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[franklsuarez]

The true meaning of Greek life: learning math, having a beard, and getting ripped.

[anniesizemore]

That's great the person is learning calculus by 16. I hope they have people around them to encourage them. I regret I fell in love with math so late in life

[wgap]

Excellent video man. Self study is something that is so very helpful and we should nurture and grow that mentality in our young people. Like you I didn't start getting into math until I was 25 yrs old or thereabouts and it was actually thru learning electronics and having to use and learn the applicable formulas. Learning math is something worthwhile and will make learning and understanding other fields of study much easier IMHO.

[yohannesg.medhin]

you are my inspiration. I live in Africa. I collected the books after your videos. Thank you for your kind guidance to know the books and examine them.

[VivanRangra]

Thomas Calcus is by far the best book for calculus, it starts from basics and its exercises help in building intuition, especially Multivaraite Calculus

[vinceocratic]

I was horrible at math and terrified of it into my mid thirties because I got turned off as a kid; primarily due to the terrible public school system. One thing I couldn’t understand was how I could reason extremely fast, but sucked a*** at math.

So, I went on a mission, bought a subscription to IXL and started at 1st grade math at 35-years old. Breezed through that, and when I got to third grade curriculum I found my weak point - fractions. This might sound stupid, but conceptually, I had never grasped and understood the idea that fractions are pieces of things (wholes) and as such, are simply division problems.

I have a horrendously low opinion of the indoctrination system posing as an educational system, but if I’m being honest, the will to learn is something that’s instilled in a properly structured family and household starting with the parents.

IXL will give you the necessary tools, diagnostics and repetition that you need.

[ansonpang]

My two favorite youtubers uploading right within a minute from each other. This vid and Veritasium's 'Rainist place on earth'. What are the odds. 😁😁😁

[entanglednerves]

I've gone back to Math at 38. The last time I picked a Math book was back when I was 17 in High school. I'm learning Linear Alg, Probability, and Stats. I'm in the Reinsurance industry and I want to pivot to Tech in Financial services. I'd eventually do Data Science or Quant Dev. Both these call for Math skills.

For those who want to explore a career in the Insurance sector using their Math skills, pursuing Actuarial science or Catastrophe Modeling are really cool options. Just saying coz I know folks doing this and are enjoying the work they do.

[blakegundry]

Calculus at 16 is incredible. I finished calc 1 and 2 during highschool but i was 18 when i graduated. Impressive. Keep up the good work and dont stop.

[rjfontenotiii]

Here is the thing about that tricky substitution rule. Once you do enough derivatives, you just start to see what should be substituted. I think it comes down to one's ability to solve simple derivatives by sight alone. Once you can do this, identifying the composite function becomes easy. You can just see what the derivative of the composite function is. And, by then, you will be able to remember when something is a composite function that needs to use the chain rule. Once you solve a ton of integrals, you pretty much master the technique. You can just see what the derivative is of some part of an integral. Then you can see how it causes the whole integral to simplify to something solvable.

[thomaspeck]

The main key to getting good at integration is practice. Diferentiating can be done by following a process, but integration is done more by trying things and seeing what works.
So, keep practicing and you will get better at seeing substitutions.

[forthehomies]

Calc at 16 years old is awesome, man. The substitution rule is fun. Just remember that you'll almost always want to substitute the function that when you take the derivative of it, will turn into the other function in the integral, or close enough to where you can cancel some of the other function out, if not all of it. For example if you have the integral of 2x(x^2), you'll want u = x^2 because the derivative of x^2 is 2x and you'll be able to cancel out the 2x, therefore simplifying the integral down to a formula that is solvable, like 1/u du which is lnu, replace the u with x^2 and the answer is ln|x^2| + C for an indefinite integral.

[alphafound]

Graduate level Economics is mostly applied mathematics. Everyone I know who has a Ph.d in Finance or Economics has an underdraduate degree in Mathematics, Physics, or Computer Science. Some of them also had a second major in Economics. So if you have goals of graduate work, keep this in mind while working on your undergraduate degree.

[JacobKuchkov]

This guy is making math human to me again

[misshannahjo]

As a math major, I am feeling like I seriously am not capable of success. These videos help so much to keep me motivated to learn more! Currently I struggle with financial mathematics and actuarial math/statistics. :(

[FiveTrackTape]

Hey Nick! @0:39 MS reads: "I don't know when to use things, like the substitution rule, without being told when to use it." I had the same issue, knowing the parts but not knowing how/when to put them into use. You'll probably find that as you do more and more problems the processes and what to do when will start to become automatic. Your mind will develop the patterns and pathways. It can't come to you by knowing the parts but only by doing the problems. Anyway, welcome to the wonderful world of being an autodidactic! P.S. Don't overlook linear algebra, you'll need it in Econ.

[guidofeliz]

I am 58 soon to be 59. I am a math enthusiast. It's too late for me to be a math teacher but I love the subject nonetheless. I am currently doing a self-study of college algebra.

[VisionScientist]

I think that one of the most challenging aspects of integration by means of u substitution is the process of figuring out which differential in terms of u is equivalent to dx. After you figure out which part of the integrand will be represented by u, you need to differentiate it with respect to x. Then you need to isolate du and dx on opposite sides of the equation by means of algebraic operations

[mj_dreamer]

Wow!!! I was just practicing Calc., I am 17 (we actually have it in the curriculum in India) got bored and started watching this video..also felt kinda depressed being a nerd been a while now ...but this gives me the hope that there are people like me out there!! So I must keep doing what I am doing, Thanks Nick Thank You Math Sorcerer!
BTW the League of Legends ahhhh OP-

[benheideveld]

When to use u-substitution is not always clear, so you should try one or two substitutions. Sometimes it is clear. When you see two functions being nested like square root sin(x), or sin square root(x), try u-sub.