1. I want to learn maths for artificial intelligence. I heard that main areas of mathematics for AI are Multivariable Calculus, Linear Algebra, Probability and Statistics and Discrete Mathematics. But what level of these subjects do I need?
For example the easy level is like Calculus of Gilbert Strang and 18.01 Calculus from MIT Open Course Ware. The hard level is Apostol's or Spivak's Calculus.
Do I need easy level of maths or hard level to be good at artificial intelligence and its areas (machine learning, pattern recognition).

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3. You're going to need as much probability and statistics as you can handle. You can probably get by with a bit less of everything else.(Linear algebra is probably second most important, but not that close of a second.)

4. Hey, my advice is defintely to get really grounded in discrete math first. You need everything in a good basic discreet math book. Then you want to zoom in on probability and communications/information theory. This will take you into linear algebra land.

There's no solid answer of what level you need because AI is still an evolving field. With Newtonian physics, some one could tell you exactly what level of math you need because its a closed field. But with AI, the next breakthrough could come from really simple math, or something really advanced. There's just no telling. The key is for you to get a math toolkit that feels empowering for you and lets you read and understand the papers of others. Discrete math, deep probability and basic linear algebra will go a long way toward that.

My personal advice from looking at this field for awhile is to zoom in on theories of compression, and information theory and communication. I say this because when I read a good novel, an author can build an entire scene in my mind with just one page. That's amazing compression, to be able to communciate so much with so little. The brain is in the compression business, and object recognition is a big part of that. Object recognition is why you need to study communications theory, to see how many things can be embedded in one. For instance, all the cell phone conversations on a single tower can come in on a single frequency, through something called CDMA multiplexing. The cell phone tower can break that single signal down to all the different conversations. An AI needs to do the same with a video or a photo. It needs to break it down to see the actual objects, as differenent channels multiplexed into one channel, in order to get meaning from the photo. But this is just my opinion.

But yeah, generally, get as much math as you can have fun and be creative with it. That's what open an advancing fields are all about!

5. I'm only an artificial intelligence student, but if you're planning to work with robots, then you will mostly need simple math such as the pythagoras functions to correctly move the actual robots, while using statistics for things like pattern recognition. To be honest though, math is to artificial intelligence, what a good diet is to an athlete. It's important that you know how things work "pretty much", but when you actually need to use something you can just look it up.