Book of Proof by Richard Hammack.
From the webpage:
This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics’ Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews.
The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) The two editions can be used interchangeably, except for the last few pages of Chapter 13. (But you can download them here.)
Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Click here for a pdf copy of the entire book, or get the chapters individually below.
From the Introduction:
This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.
For a 300+ page book, almost a steal at Amazon for $13.75. A stocking stuffer for Math/CS types on your holiday list. For yourself, grab the pdf version. 😉
Big data projects are raising the bar for being able to think critically about data and the mathematics that underlie its processing.
Big data is by definition too large for human inspection. So you had better be able to think critically about the nature of the data en masse and the methods to be used to process it.
Or to put it another way, if you don’t understand the impact of the data on processing, or assumptions built into the processing methods, how are you going to evaluate big data results?
Just accept them as ground level truth? Ignore them if they contradict your “gut?” Use a Magic 8-Ball?, a Ouija Board?
I would recommend none of the above and working on your data and math critical evaluation skills.
You?
I first saw this in a tweet by David Higginbotham.