The Circle: A Mathematical Exploration beyond the Line [EPUB]
12 November 2016, 18:24
2016 | EPUB | 12.14MB
The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements.
The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry–leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves - many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry.
Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy [EPUB]
06 September 2016, 05:26
2016 | EPUB | 2.03MB
A former Wall Street quant sounds an alarm on the mathematical models that pervade modern life — and threaten to rip apart our social fabric
We live in the age of the algorithm. Increasingly, the decisions that affect our lives—where we go to school, whether we get a car loan, how much we pay for health insurance—are being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: Everyone is judged according to the same rules, and bias is eliminated.
But as Cathy O’Neil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated, and uncontestable, even when they’re wrong. Most troubling, they reinforce discrimination: If a poor student can’t get a loan because a lending model deems him too risky (by virtue of his zip code), he’s then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a “toxic cocktail for democracy.” Welcome to the dark side of Big Data.
Tracing the arc of a person’s life, O’Neil exposes the black box models that shape our future, both as individuals and as a society. These “weapons of math destruction” score teachers and students, sort résumés, grant (or deny) loans, evaluate workers, target voters, set parole, and monitor our health.
O’Neil calls on modelers to take more responsibility for their algorithms and on policy makers to regulate their use. But in the end, it’s up to us to become more savvy about the models that govern our lives. This important book empowers us to ask the tough questions, uncover the truth, and demand change.
30-Second Maths [EPUB]
30 May 2016, 13:34
2012 | EPUB | 4.14MB
From Rubik's cubes to Godel's incompleteness theorem, everything mathematical explained, with colour illustrations, in half a minute. Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was, or what he proved? The more you know about Maths, the less of a science it becomes.30 Second Maths takes the top 50 most engaging mathematical theories, and explains them to the general reader in half a minute, using nothing more than two pages, 200 words and one picture. Read at your own pace, and discover that maths can be more fascinating than you ever imagined.