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I think you should start working on your Math (Khan academy courses) and ML foundations (Andrew Ng's coursera course). Then Geoffrey Hinton's coursera course on Neural networks could be a gentle introduction to Neural networks, deep learning and their applications. Last but not least, do a small project on Deep learning or try out few kaggle competitions to deepen your understanding.

Links:

https://www.coursera.org/course/ml

https://www.khanacademy.org/math/linear-algebra

https://www.coursera.org/course/neuralnets

www.iro.umontreal.ca/~bengioy/papers/ftml.pdf

http://www.iro.umontreal.ca/~bengioy/dlbook/

http://techtalks.tv/talks/deep-learning/58122/




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