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A comment on Level-Up Your Machine Learning. Parent comment
For mathematical foundations of ML, I would recommend the book "Understanding Machine Learning: From Theory to Algorithms" by Shai Shalev-Shwartz.
A brief version of the book is available to download on the author's website: http://www.cs.huji.ac.il/~shais/Handouts.pdf
At the same time, it's the only book I've seen that covers online learning well. Can you think of any others?
For mathematical foundations of ML, I would recommend the book "Understanding Machine Learning: From Theory to Algorithms" by Shai Shalev-Shwartz.
A brief version of the book is available to download on the author's website: http://www.cs.huji.ac.il/~shais/Handouts.pdf