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What is the mathematical background required to start learning AI? What else should I also learn?

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Start with Andrew Ng's introduction to Machine Learning course on Coursera. There are not many prerequisites for that course, but you will learn how to make some useful things. And, more importantly, it will clearly show you which subjects you need to learn next.

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AI is quite large in scope and it sits at the intersection of several areas. However, there are a few essential fields or topics that you need to know

  1. Set theory
  2. Logic
  3. Linear algebra
  4. Calculus
  5. Probability and statistics

I would recommend you to first explore the AI algorithms that you might be interested in. I advise you to start with machine learning and deep learning.

Do not forget one very important prerequisite, passion, without it you are probably wasting your time!

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I would suggest you to

  1. start with Andrew Ng's Machine Learning course on Coursera. He provides the brief introduction to mathematics necessary for machine learning. Though not complete, it will be enough to cruise through the course.
  2. Next carefully learn logistic regression in the course. The sigmoid function will be widely used in neural networks.
  3. In the course, he will introduce you to neural networks and error minimization using back propagation. The back propagation will use optimization technique called Gradient Descent. It is a very important topic.
  4. After completing above steps try Geoff Hinton's neural networks course on Coursera.

If you want to go deep in math. Try these:

  • Linear algebra - Gilbert Strang
  • probability - khan academy

I would also like to suggest one of the best books for deep learning: Deep learning by Ian Goodfellow and Yoshua Bengio and Aaron Courville. http://www.deeplearningbook.org/

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Artificial Intelligence is a very broad field and therefore things will change accordingly.

Some Prerequisites: (Being a student of CS you should have fulfilled them)

  • Sound knowledge of algorithms and Data Structures. This skill will come in handy while solving problems that require use of alpha-beta pruning, minimax algorithm, etc.
  • Basic knowledge of programming languages like Java, Python. Python will help as it focuses more on the development part. For more info read this. Knowledge of LISP will be very helpful. Go through this answer.

The book, Artificial Intelligence: A Modern Approach (by Stuart J. Russell and Peter Norvig) is considered the Bible of AI. I strongly recommend you to read the complete book and solve the exercises. You can find the pdf of the book here. For solution manual visit this link. It will be better if you can buy a hardcopy of the book.

Knowledge of Computational Theory will greatly help you. Especially when you are working in the field of Natural Language Processing. Other sub-fields of AI that might interest you will be Machine Learning, Evolutionary Computing, Genetic Algorithms, Reinforcement Learning, Deep Learning etc. The list goes on.
Better your knowledge in Statistics, better it will be for Artificial Intelligence. Stay tuned to recent goings in the field via forums, websites, etc. Open AI website is also a very good source.

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In addition to Maheshwar's answer, once you feel you want to try more practical Machine Learning, I'd start with Weka. The software is free and effective, they have a good manual and relevant exercises and there are plenty of free videos available on Youtube!

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To complement the other answers:

I recommend you to take the Artificial Intelligence course from the AI micromaster given by Columbia on edx.

The course cover a wide range of AI problems and the most important is that give you a general framework to think with a mix of applications on python. Based on the book of Artificial Intelligence: A Modern Approach by Peter Norvig and Stuart Russell

From the perspective of machine learning as well said gokul, the Machine Learning course of Andrew Ng. on coursera is a good introductory course and very oriented to a potential practitioner.

I found useful to combine the study of some machine learning algorithms with the statistical programming language R to experiment with many algorithms to catch the concepts. Useful the following books: Elements of Statistical Learning and Introduction to Statistical Learning, both are available free on the authors websites.

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