Andrew Ng's Coursera course simply titled "Machine Learning" is good - it addresses the mathematics of fundamental algorithms and concepts while giving practical examples and applications:
https://www.coursera.org/learn/machine-learningRegarding books, there are many very high quality textbooks available (legitimately) for free online:
Introduction to Statistical Learning (James et al., 2014) http://www-bcf.usc.edu/~gareth/ISL/
the above book shares some authors with the denser and more in-depth/advanced
The Elements of Statistical Learning (Hastie et al., 2009) http://statweb.stanford.edu/~tibs/ElemStatLearn/
Information Theory: Inference & Learning Algorithms (MacKay, 2003) http://www.inference.phy.cam.ac.uk/itila/p0.html
Bayesian Reasoning & Machine Learning (Barber, 2012) http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=...
Deep Learning (Goodfellowet al., 2016) http://www.deeplearningbook.org/
Reinforcement Learning: An Introduction (Sutton & Barto, 1998) http://webdocs.cs.ualberta.ca/~sutton/book/ebook/the-book.ht...
^^ the above books are used on many graduate courses in machine learning and are varied in their approach and readability, but go deep into the fundamentals and theory of machine learning. Most contain primers on the relevant maths, too, so you can either use these to brush up on what you already know or as a starting point look for more relevant maths materials.
If you want more practical books/courses, more machine-learning focussed data science books can be helpful. For trying out what you've learned, Kaggle is great for providing data sets and problems.