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.

A snapshot of my bookshelf's "math" section, which really hasn't changed much since I was in high school and hadn't taken calculus:

W.W. Sawyer, What is Calculus About? and Mathematician's Delight

Courant and Robbins, What is Mathematics?

Hogben, Mathematics for the Million

Steinhaus, Mathematical Snapshots

Ivars Peterson, The Mathematical Tourist

Davis and Hersh, The Mathematical Experience

Polya, How to Solve It

Huff, How to Lie With Statistics

McGervey, Probabilities in Everyday Life

Raymond Smullyan: The Lady or the Tiger, Alice in Puzzle-Land, others

Anything by Martin Gardner. I happen to have picked up Mathematical Magic Show and Mathematical Circus, but I'm sure there are many other collections.

I also recommend cryptography stuff. David Kahn's The Codebreakers is not really a math book, but it is awesome and it stars mathematicians, as does Simon Singh's The Code Book. You could read Schneier's Applied Cryptography.

This is HN, so I would be remiss if I didn't point out that you can learn a lot of fun and useful math by reading SICP, Knuth, or any good algorithms book.

If anybody out there knows a good, spirited statistics book addressed to someone who knows calculus, tell me. I keep planning to go through Fundamentals of Applied Probability Theory but I never get around to it; see "Related Resources" here:

Having said all of that: I have a Ph.D. in physics/EE, so I've got to tell you, if you haven't tried calculus you haven't lived. ;) I'm not sure how to go about learning calculus in a fun way for a mathematician -- I took fairly standard first- and second-year college courses in calculus and physics and learned it that way. The folks on Amazon seem kind of enthusiastic about Spivak:

Most books have problems and most have solutions guides for about half of the problems. I'm surprised nobody's mentioned Spivack yet:
http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098...

https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/091409...

one of my favorite text books ever. (tho it was paired w/ one of my favorite teachers ever, which i'm sure helped a lot.)

Many consider the book's presentation of the topic utterly beautiful, bordering even on the spiritual.

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://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/

W.W. Sawyer,

What is Calculus About?andMathematician's DelightCourant and Robbins,

What is Mathematics?Hogben,

Mathematics for the MillionSteinhaus,

Mathematical SnapshotsIvars Peterson,

The Mathematical TouristDavis and Hersh,

The Mathematical ExperiencePolya,

How to Solve ItHuff,

How to Lie With StatisticsMcGervey,

Probabilities in Everyday LifeRaymond Smullyan:

The Lady or the Tiger,Alice in Puzzle-Land, othersAnything by Martin Gardner. I happen to have picked up

Mathematical Magic ShowandMathematical Circus, but I'm sure there are many other collections.I also recommend cryptography stuff. David Kahn's

The Codebreakersis not really a math book, but it is awesome and it stars mathematicians, as does Simon Singh'sThe Code Book. You could read Schneier'sApplied Cryptography.This is HN, so I would be remiss if I didn't point out that you can learn a lot of fun

anduseful math by reading SICP, Knuth, or any good algorithms book.If anybody out there knows a good, spirited statistics book addressed to someone who knows calculus, tell me. I keep planning to go through

Fundamentals of Applied Probability Theorybut I never get around to it; see "Related Resources" here:http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Compute...

Having said all of that: I have a Ph.D. in physics/EE, so I've

gotto tell you, if you haven't tried calculus you haven't lived. ;) I'm not sure how to go about learning calculus in afunway for amathematician-- I took fairly standard first- and second-year college courses in calculus and physics and learned it that way. The folks on Amazon seem kind of enthusiastic about Spivak:http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098918/...