The Heart of Mathematics: An Invitation to Effective Thinking, 3rd Edition [PDF]

The Heart of Mathematics: An Invitation to Effective Thinking, 3rd Edition [PDF]
The Heart of Mathematics: An Invitation to Effective Thinking, 3rd Edition by Edward B Burger, Michael Starbird
2010 | PDF | 40.18MB

Make mathematics fun and satisfying for everyone

Math can be a living source of powerful ideas that transcend mathematics; a window into mind-opening philosophical concepts such as infinity, fourth dimensions, chaos, and fractals; and a practical training ground for developing skills in analysis, reasoning, and thought—if you have the right approach and the right guide.

The Heart of Mathematics: An Invitation to Effective Thinking­—now in its third edition—transforms mathematics into an engaging, relevant experience even for the most math-phobic student. Infusing this book with humor and enthusiasm, Edward B. Burger and Michael Starbird—both recipients of the Mathematical Association of America’s foremost national teaching award and countless state, regional, and campus-wide teaching honors—introduce students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.

Richer and more rewarding than ever, this new edition features:

  • An emphasis on mathematical methods of investigation
  • Visualization techniques that make key concepts easier to understand
  • Accessible, friendly writing style that encourages critical thinking
  • "Life Lessons"-effective methods of thinking that students will retain and apply beyond the classroom
  • End of section Mindscape activities for the development of application, problem-solving, and argumentation skills

The Circle: A Mathematical Exploration beyond the Line [EPUB]

The Circle: A Mathematical Exploration beyond the Line [EPUB]
The Circle: A Mathematical Exploration beyond the Line by Alfred S Posamentier, Robert Geretschläger
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]

Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy [EPUB]
Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy by Cathy O'Neil
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.

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