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Any resources which introduce mathematical concepts without much emphasis on calculations and computations?

I'm interested in learning more about mathematics to get into AI, but previously I had been turned off from mathematics because of tedious calculations and computations I had to work out. I have forgotten everything I learned about mathematics in school.

noviceFedora
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  • You're not gonna be able to get into AI without grinding through some tedious computations. But if you're looking for pop math where you can enjoy the concepts without doing the work, try looking at some of the more popular YouTube people. Numberphile, 3blue1brown – Alexander Gruber May 04 '20 at 17:57
  • @AlexanderGruber Thanks for the suggestion. Wouldn't the computations in AI be done by the computer? I was thinking I just had to come up with an algorithm and let the computer do the heavy lifting. And a bird's eye understanding of math might be helpful in doing it. Assisting me to come up with algorithm and what area of math might make the algorithm efficient. – noviceFedora May 04 '20 at 18:30
  • The computer does the computation but you need to be able to understand how the systems work internally or you won't be able to make it work. You'll have to work through some examples on paper by hand first, which is grindy. Also, there is a lot of grind even in practice just preparing the data for the system, there is a lot of math in that part. (I work in AI.) – Alexander Gruber May 04 '20 at 19:55
  • You could try to start reading about neural networks but I don't know how far you'll get if you don't remember any school math. You need to know about vector algebra and stuff like that. – Alexander Gruber May 04 '20 at 19:56
  • @AlexanderGruber Wouldn't a conceptual understanding of math be insufficient? Can you give me examples which I would be required to work out by hand and for preparing data for the system? – noviceFedora May 05 '20 at 05:15
  • @AlexanderGruber For example, by watching videos on NN, I learned about sigmoid function, I have a conceptual understanding of it, that it produces a value using the formula 1 by 1 + e raised to the power of a negative number, this produces a value between 0 and 1. I don't know how to raise a number to a negative number, what negative number it should be and why. I don't know the value of e and how it is obtained. The value produced by sigmoid functions is used statistically to determine features in the data set, and millions of such iterations provide learning. Is this correct? – noviceFedora May 05 '20 at 05:33
  • Yeah, it's enough to know what the graph of the sigmoid looks like. The formula is not important. In fact in practice you will likely be using relu instead. But in order to know which one to use, you'll have to think about how the value produced by each of those functions affects the NN's operations. For example, relu may lead to dead nodes in the network--why? The only way to answer that is through the math. – Alexander Gruber May 05 '20 at 05:47
  • To be clear, though, what I meant about working out an example by hand is more about understanding the structure of a neural network. There are a lot of different types of layers out there and you have to know how the layers fit together in order to hook them up to each other. It really is best to construct a couple examples by hand when you're learning that because the notation is super confusing. I'm not saying you'll need to do a bunch of calculating by hand or anything, btw, just like, set up a couple examples with easy numbers, then work out how they move through the network so you can – Alexander Gruber May 05 '20 at 05:55
  • get an understanding of how the layers work. This is especially true once you get into things like convolutional / deconvolutional NNs, with layer masking and stuff like that, or recurrent networks, or systems of several NNs feeding into one another. – Alexander Gruber May 05 '20 at 05:55
  • Regarding preparing data for the system: ok this is where sometimes the math needs to be used directly. Often the data you use to train your network is given to you in some form that needs to be rewritten. An easy example would be, maybe your data gives you a person's birthday, but you think their age is the important variable. Then you have to calculate their age. This is easy of course, just subtraction. A slightly harder example would be, say you're given a person's location in latitude/longitude. Maybe you think the relevant feature to your application is the distance to your store. – Alexander Gruber May 05 '20 at 06:05
  • So, then, you have to be able to write a distance formula. There are a lot more complicated examples in data preparation, usually you'll want some statistics there (e.g. what is the correlation matrix between person A's behavior and person B's? or maybe you want the probability they will do a certain action, compared to others of similar demographics?). The neural network won't do that data prep for you. Neural networks are black boxes and they're magic but the quality of the results you get depends heavily on the quality of the data you feed them and how you featurize it. – Alexander Gruber May 05 '20 at 06:13
  • Let us continue this discussion in chat. – noviceFedora May 05 '20 at 19:37

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