In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of s...

If you're looking for a gentle introduction to basic mathematics, look no further. This book picks you up at the very beginning and guides you through the foundations of algebra using lots of examples and no-nonsense explanations. Each chapter contains well-chosen exercises as well as all the solutions. No prior knowledge is required.Topics include: Exponents, Brackets, Linear Equations and Quadratic Equations. For a more detailed table of contents use the "Look Inside" feature. Fr...

The Foundations of GeometryGeometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. The choice of the axioms and the investigation of their relations to one another is a problem which, since the time of Euclid, has been discussed in numerous excellent memoirs to be found in the mathematical literature.This problem is tantamount to the ...

New York Times bestselling author Danica McKellar makes it a breeze to excel in high school geometry!Hollywood actress and math whiz Danica McKellar has completely shattered the “math nerd” stereotype. For years, she’s been showing girls how to feel confident and ace their math classes—with style! With Girls Get Curves, she applies her winning techniques to high school geometry, giving readers the tools they need to feel great and totally “get” ev...

This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation.Some of the turning points considered are the rise of the axiomatic method (m...

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad.Numerous strategies and techniques are presented that can be used ...

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is ...

To a large extent, it lies, no doubt, in what is presented in this work under the title of ‘meta lever‘, a method which it is certainly interesting to develop and further refine. There exists in mathematics courses a strange prudery which forbids one to ask questions such as, ‹‹ Why are we doing this? », ‹‹ At what is the objective aimed? », whereas it is usually easy to reply to such questions, to keep them in mind, and to show that one can challenge these questions and modify the objecti...

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix s...

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on top...

Since the publication of this book’s bestselling predecessor, Mathematica® has matured considerably and the computing power of desktop computers has increased greatly. The Mathematica® typesetting functionality has also become sufficiently robust that the final copy for this edition could be transformed directly from Mathematica R notebooks to LaTex input.Incorporating these aspects, CRC Standard Curves and Surfaces with Mathematica®, Third Edition is a virtual enc...

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert functi...