Which books /tutorials will be good for these topics for AI computer science student 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.
 A: We used "Pattern Classification" by "Duda, Hart and Stork". It is pretty good book.
Salahuddin
http://maths-on-line.blogspot.in/
A: 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.

A: 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.
A: 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

A: It is 6 years old question, I am still writing an answer in case anyone drifts here.
BACKGROUND: I am Software Engineer transitioning into Data Science and Machine Learning and hence I got stuck because every book I picked (Statistics or Probability) it talked using Calculus. Then LA (Linear Algebra) was a big part of everything in Data Science. To do all that, one needs to understand Algebra, which I have forgotten because I did it in my school some 20 years ago. I had to start all over again.
My Advice would be to watch videos online, read good books (you can find plenty of resources by searching archives here) which are:


*

*inclined more towards application than rigor.

*do lot of problems

*ask/search here whenever you get stuck

A: This is a surprisingly simple, old and quite frankly a very relevant question. Writing an answer anyways for others who might come here. 
Often if you get your references wrong you will get confused. This tends to happen if you read too many academic papers which prove theorems. It is important to do the following


*

*You must code. Python, R should get you going

*You must try out some practice problems and past competitions from places like Kaggle (now owned by Google). They give a very good insight into what real world data looks like.


To get started, you must keep things simple and start off with simple problems to code and practice. E.g. implement a simple Naive Bayes algorithm.
Here is a list of books that is worth owning.
