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Mathematics: quadratic equations.
"Quadratic Equations" is the first book of a series dedicated to mathematics. The book is also available in Italian. Using a fast, simple and complete method, you'll learn how to solve quadratic equations and what are the basics of this topic. In particular, here we explain the numerical, fractional and parametric equations, the Descartes' rule and the relation between the coefficients and solutions of a quadratic equation. If you need information, you can visit the website: www.mathsly.it, and by using the contact form, you can communicate directly with the author.
Beyond the Quadratic Formula
The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
Quadratic Diophantine Equations
This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.
Beyond the Quadratic Formula
A study guide to polynomials that goes beyond the familiar quadratic formula to cover cubic and quartic equations.
Algebraical Problems
None
A Journey Through The Realm of Numbers
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations...
Text-book of Algebra
None
Newton's Method Applied to Two Quadratic Equations in C2 Viewed as a Global Dynamical System
The authors study the Newton map $N:\mathbb{C 2\rightarrow\mathbb{C 2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things:
