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I am looking to brush up on my math skills so that I can use those skills when working with problems in machine learning, AI analyzing very large data sets. Most of the problems that I am likely to run into are related to analyzing user behavior on web applications to determine how users are using a system, and look for ways to optimize user interactions like have them find the right deal, or the right item, or the right x where x is something that the user cares about.

I graduated from a top tier Computer Science school in 2000 but I never paid attention to the math courses was much more interested in system programming. I have had a few university courses in Calculus, Linear Algebra, Stats and Probability but i have forgotten most of these and the courses were very focused on proving the core theorems of these fields rather than the industrial applications.

My goal is to brush up on these topics so that I can quickly whip them out when I need them. so I am looking for a list of the best books on these topics that would be great for self study with a large collection of practical problems in these books and a student solution manual of some kind.

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I assume you are already familiar with Machine Learning: An Algorithmic Perspective. Looks like great textbook on the topic with many examples –  com Nov 20 '11 at 15:31
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This course can also be useful for you. It's been quite famous over the years and the book Street Fighthing Mathematics can be downloaded from MIT's web site too.

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I have been impressed by the lecturing style used by Andrew Ng at ml-class.org (see also ai-class.org). There is no doubt you could cover the material vastly more quickly by simply reading some textbook on machine learning, rather than watching slow moving courses, but the overall perspective he brought looked valuable.

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for someone who's not fond of relabeling it's surprising to see you refer to Professor Andrew Ng as "Mr. Ng" ;) –  Chris Taylor Nov 15 '11 at 12:37
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