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I have found from the internet that I need to know these topics for understanding Artificial Intelligence:

Matrix algebra: most machine learning models are represented as matrices and vectors. Concepts like eigenvectors and singular value decomposition appear all over the place.

Bayesian statistics: probability, Bayes' rule, common distributions (e.g., beta, Dirichlet, Gaussian), etc.

Multivariable calculus: most learning techniques use gradients and Hessians at their core to fit parameters. (If you want to get fancier, study numerical optimization.)

Information theory: entropy, KL divergence, etc. Just the basics here.

In limited cases, higher-level math can be useful. E.g., to understand manifold learning, you'll want to know some basic notions from geometry and topology. Occasionally abstract algebra is used (e.g., see "expectation semirings" for learning on hyper-graphs). I would learn these as-needed, but if you have a chance to learn them early it can't hurt.

Now whenever I want to learn these I got confused with symbols, functions, vectors, sets, subsets, etc. Provided I know only the basic math, how can I learn those? I am confused which things should I learn first and which second.

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We used "Pattern Classification" by "Duda, Hart and Stork". It is pretty good book.


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Your question is not an easy one, take my words as a naïve attempt while you catch the attention of someone more enlightened. I can give you a list of books, but if you are an computer science student, the curricula of your university should include some basic courses in linear algebra and calculus, you must start over there, guided tours in mathematics tend to be more successful for the ordinary people. Then you may be ready to basic undergraduate probability and statistics courses. That basic probability course is necessary in order to learn information theory, but mathematical maturity is also really useful.

It's okay to be confused with all those new symbols, you're learning a new language, you should keep that in mind. But most importantly, you must be perseverant, for if you really want to understand the most beautiful and exciting ideas about AI, you must learn to think in more abstract ways. That bunch of symbols is one of the most efficient ways to express these ideas.

Now, if you really insist in trying to do it by yourself:

  • Linear Algebra. Stephen H. Friedberg.
  • Introduction to Calculus and Analysis vol. I and II. Richard Courant.
  • First Course in Probability. Sheldon Ross.
  • Elements of Theory Information. Thomas M. Cover.

Also, this book is incredibly useful for computer scientists and mathematicians:

  • Concrete Mathematics: A Foundation for Computer Science. Donald Knuth.
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Is there a specific reason you would like to study AI without the prerequisites? Is there a focus area (AI for video games etc.) you are mostly interested in? I don't think you have to know all the listed math to be able to address specific problems with well established AI methods (e.g. A* search algorithm). I don't know your background, but I assume you have no experience with AI at all, and would like to jump into it as a freshman because its "cool", is that correct? For a generic overview about AI I believe the Russell & Norvig "Artificial Intelligence: A Modern Approach" is a good start.

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Actually i have not chosen those subjects and study is almost finished . but want to learn by self. I am a python programmer and want to learn heuristics , data mining and predictive modelling. what do i need to learn. i tried studying that books and i find it hard understanding math stuff – user825904 Oct 23 '12 at 9:16

In addition to the above answers/suggestions I think these books would also help you in your hunch of learning AI

  • Behavioral mathematics (by dave mark) - excellent book for AI based mathematical concepts
  • For probability - i recommend any college level Probability & Statistics book will help
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