High School: G11 & 12 - TOK: AOK Mathematics

Reveals the impact chance has on a person's day-to-day life, explaining how wine ratings, school grades, political polls, health, and other factors of daily life are based more on chance than reliable information and examining how psychological factors have led people to underestimate the power of chance.

A Masterpiece of Classic Science Fiction: Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884. Written pseudonymously by "A Square",the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. Physicists and science popularizers Carl Sagan and Stephen Hawking have both commented on and postulated about the effects of Flatland. Sagan recreates the thought experiment as a set-up to discussing the possibilities of higher dimensions of the physical universe in both the book and television series Cosmos, whereas Hawking notes the peculiarity of life in two-dimensional space. A Must Read Classic for Lovers of Science Fiction!

A comprehensive survey of many different fields of mathematics, including geometry, development of Sudoku, and number theory.

The author argues that there has not been a breakthrough in the foundations of physics for more than four decades due to the standard physicists use to separate popular theories from disposable ones, assuming that the best theories are beautiful, natural, and elegant. She asserts that this false assumption conflicts with scientific objectivity and urges physicists to rethink theoretical methods.

How a little mathematics goes a long way in helping you not to be wrong. Ellenberg explores the mathematician's way of analysing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely.

"Where does math come from? From a textbook? From rules? From deduction? From logic? Not really, Eugenia Cheng writes in Is Math Real?: it comes from curiosity, from instinctive human curiosity, 'from people not being satisfied with answers and always wanting to understand more.' And most importantly, she says, 'it comes from questions:': not from answering them, but from posing them. Nothing could seem more at odds from the way most of us were taught math: a rigid and autocratic model which taught us to follow specific steps to reach specific answers. Instead of encouraging a child who asks why 1+1 is 2, our methods of education force them to accept it. Instead of exploring why we multiply before we add, a textbook says, just to get on with the order of operations"--Provided by publisher.

An introduction to calculus that features manga illustrations, and provides exercises and explanations on approximates, derivatives, differentiation, polynomials, mean value theorem, and the chain rule; and also describes how to integrate functions, achieve a series expansion, and more.

Jason Padgett discusses how a violent mugging forever altered the way his brain works, giving him unique gifts. His ability to understand math and physics skyrocketed, and he developed the astonishing ability to draw the complex geometric shapes he saw everywhere"--Provided by publisher.

Mathematics, that breathtaking invention of ours that reveals the tiniest particles of matter and takes us to the outermost reaches of the cosmos, is found by many people to be intimidating. In The Universe and the Teacup, K. C. Cole demystifies mathematics and shows us-with humor and wonderfully accessible stories-why math need not be frightening. Using the O. J. Simpson trial, the bell curve, and Emmy Noether, the nineteenth-century woman scientist whose work was essential for Einstein'stheory of relativity, Cole helps us see that more than just being a tool, math is a key to understanding the beauty of everything from rainbows to relativity.