Negative Math (eBook)

How Mathematical Rules Can Be Positively Bent

Alberto A. Martínez (Autor)

eBook Download: PDF

2018
288 Seiten
Princeton University Press (Verlag)
978-0-691-18782-2 (ISBN)

Infos

A student in class asks the math teacher: "e;Shouldn't minus times minus make minus?"e; Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "e;impossible"e; numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features? Uses history, puzzles, and lively debates to devise new mathematical systems Shows how departures from rules can underlie new practical applications Clear and accessible Requires a background only in basic high school algebra

Autor

Alberto A. Martinez teaches history of science and mathematics at the University of Texas, Austin. He studies history to better understand scientific creativity and to clarify ambiguities in the elements of physics and algebra.

Produkt-Details

• Erscheint lt. Verlag: 5.6.2018
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: absolute value • abstract algebra • absurdity • Accuracy and precision • Addition • Algebra • Algebraic Curve • algebraic theory • Alternative algebra • Ambiguity • Analysis • arbitrariness • arithmetic • associative property • asymmetry • Augustus De Morgan • Axiom • Betterment • Big O notation • Binary logarithm • Blaise Pascal • Calculation • Closed-form expression • combination • commutative property • complex number • computer algebra system • conjecture • consistency • Contingency (Philosophy) • Contradiction • Counting • Descartes' rule of signs • Diagram (category theory) • Dimensional Analysis • Eclecticism • elementary arithmetic • Elements of Algebra • empty set • Equation • Ethnomathematics • Euclidean Vector • Eugenics • existential quantification • exponentiation • Extrapolation • Falsity • For All Practical Purposes • Foundations of mathematics • free algebra • Geometry • Hypercomplex number • Idolatry • imaginary number • Impossibility • Inequality (mathematics) • inference • Ingenuity • Intuitionism • Jean-Robert Argand • judicial astrology • Leonhard Euler • linear differential equation • logarithm • Mathematical instrument • mathematical practice • Mathematical Proof • Mathematical Sciences • mathematician • Mathematics • Metaphysics • Modern Physics • Monomial • Natural number • Negation • Negative number • New algebra • New Math • Nicholas Saunderson • Normal number • number line • Number Theory • Numerical Integration • philosophy of mathematics • physical mathematics • Plus and minus signs • Pseudovector • Pure Mathematics • Pythagorean Theorem • Quadratic equation • Quantity • quaternion • Racism • real number • Religion • result • resultant • Return to normalcy • Richard Dedekind • scientific notation • Sign (mathematics) • skepticism • Special case • square root • subtraction • Summation • Symbolic Computation • theoretical physics • theory • The Philosopher • Thomas Harriot • Thought • Traditional mathematics • truism • Variable (mathematics) • Vinculum (symbol) • William Kingdon Clifford • William Rowan Hamilton
• ISBN-10: 0-691-18782-7 / 0691187827
• ISBN-13: 978-0-691-18782-2 / 9780691187822