Just picked up this book recently, so my review is more so based on the first couple hundred pages.
I have to tell you that I'm really enjoying this book so far. As someone who comes from a math background, this book does provide a fair amount of intuition--many graduate math text books are terse and don't always give you the intuition behind theorems, definitions and examples. So from that perspective, this book is good. Still, I can see where someone without much math experience may need an alternative that is less rigorous to pick up the intuition. From my experience, if you want to understand the math, don't study anything much more advanced than what you are comfortable with. You'll be able to do the math but may not have the intuition.
So my recommendation is if you have taken the following classes (or have exposure to the material), you can go ahead and start with this book:
1. Real Analysis
2. Linear Algebra (at the bear minimum you should at least have learned what a a vector space, and a linear transformation and what the dimension of a Vector Space is...however if you have seen abstract algebra and not much linear algebra, you still should be good to read this book)
3. Optimization. Hopefully you have taken a class in Convex Optimization that talks about Karush Khun Tucker or something like the Simplex Method.
If you haven't, I'd say start with Simon and Blume. They give more intuition and examples. The disadvantage being that it contains less advanced material. The advantage being the material that is covered has more room for understanding with plenty of examples to get intuition.
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