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Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus

Michael Spivak · 2 HN comments
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Amazon Summary
This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
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Hacker News Stories and Comments

All the comments and stories posted to Hacker News that reference this book.
You can try "Data Science from Scratch" [0] to get some taste. It uses Python to teach essentials of data science, and ML altorithms. The code quality is very good, and there is an introduction to Statistics, Maths and Python to start.

Then you can continue with improving your maths (Linear Algebra [1], Calculus [2], [3]) and moving on with Statistical Learning [4] [5]. I am personally going now through this plan.

[0] http://shop.oreilly.com/product/0636920033400.do

[1] http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mat...

[2] http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098...

[3] http://www.amazon.com/Calculus-Manifolds-Approach-Classical-...

[4] http://www-bcf.usc.edu/~gareth/ISL/

[5] http://statweb.stanford.edu/~tibs/ElemStatLearn/

misframer
An Introduction to Statistical Learning [0] is also good. It's a little less technical than The Elements of Statistical Learning. We used it for our statistical learning course at my university. The full PDF is available for free as well [1].

[0] http://www-bcf.usc.edu/~gareth/ISL/

[1] http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Fourth%20Printing....

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