(Redacted from an answer I gave at AIDL.)
It depends on the chapters you are at. The first two parts are better to be supplementary material of lectures/courses. For example, if you are reading deep learning with watch all videos from Karpathy and Socher's class, you would learn much more than other students. I think the best lecture to go with is Hinton's "Neural Network".
Part 1 tries to power you through the Math necessary. If you never have at least a class of machine learning, those material are woefully inadequate. Consider to study matrix algebra or more importantly matrix differentiation first. (Abadir's Matrix Algebra is perhaps the most relevant.) Then you will make through the Math more easily. Saying so, Chapter 4's example on PCA is quite cute. So read them if you are comfortable with the Math.
Part 3 is tough, and for the most part it is a reading for researchers in *unsupervised learning*, which many people believe it is the holy grail of the field. You will need to be comfortable with energy-based model. For which I suggest you go through Lecture 11 to 15 of Hinton's deep learning first. Me think: if you don't like unsupervised learning, you could skip Part 3 for now. Reading Part 3 is more about knowing what other people are talking about in unsupervised learning.
Finally, it's how you see this book, while deep learning is a hot field, make sure you don't abandon other ideas in machine learning. e.g. I found reinforcement learning and genetic algorithm very useful (and fun). Learning theory is deep and can explain certain things we experienced in machine learning. IMO, those topics are at least as interesting as Part 3 of deep learning. (Thanks Richard Green at AIDL for his opinion.)
Further reading: Some Quick Impression of Browsing "Deep Learning".
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