Quantifying Life: A Symbiosis of Computation, Mathematics, and Biology [EPUB]

Quantifying Life: A Symbiosis of Computation, Mathematics, and Biology [EPUB]
Quantifying Life: A Symbiosis of Computation, Mathematics, and Biology by Dmitry A Kondrashov
2016 | EPUB | 15.04MB

Since the time of Isaac Newton, physicists have used mathematics to describe the behavior of matter of all sizes, from subatomic particles to galaxies. In the past three decades, as advances in molecular biology have produced an avalanche of data, computational and mathematical techniques have also become necessary tools in the arsenal of biologists. But while quantitative approaches are now providing fundamental insights into biological systems, the college curriculum for biologists has not caught up, and most biology majors are never exposed to the computational and probabilistic mathematical approaches that dominate in biological research.

With Quantifying Life, Dmitry A. Kondrashov offers an accessible introduction to the breadth of mathematical modeling used in biology today. Assuming only a foundation in high school mathematics, Quantifying Life takes an innovative computational approach to developing mathematical skills and intuition. Through lessons illustrated with copious examples, mathematical and programming exercises, literature discussion questions, and computational projects of various degrees of difficulty, students build and analyze models based on current research papers and learn to implement them in the R programming language. This interplay of mathematical ideas, systematically developed programming skills, and a broad selection of biological research topics makes Quantifying Life an invaluable guide for seasoned life scientists and the next generation of biologists alike.

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.

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