Mordechai Ben-Ari - Böcker

This book approaches mathematics based on the needs of computer science students, teaching logic by means of the method of semantic tableaux. The third edition is entirely rewritten, and includes new chapters on SAT solvers and model checking.

Principles of Spin is an introductory book, the only requirement is a background in programming. The Spin model checker is not only a widely used professional tool but it is also a superb tool for teaching important concepts of computer science such as verification, concurrency and nondeterminism.

Ada is the programming language of choice for high integrity software systems and is used extensively in industries such as transportation and aerospace. Special features of the book include: Object-oriented programming, concurrency, and embedded and real-time systems are emphasized. Ada for Software Engineers explains the language concepts and the terminology of the standards document, the Ada Reference Manual (ARM). Extracts from the ARM are used throughtout and there are extensive cross references to the ARM. A comprehensive glossary and technical quizzes assist the reader in developing the ability to use the ARM as a practical reference. Comparisons with familiar languages like C and Java are given to facilitate the transition to Ada. The features of Ada 2005 are used routinely, but they are carefully identified, so that programmers using Ada 95 will also find the textbook useful. The companion website contains the full source code of nearly 100 case studies and 100 technical quizzes.

This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction.Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss'spurely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.Supplementary material to the book can be found at https://github.com/motib/surprises.

Dieses Buch ist Open-Access und bietet viele mathematische Überraschungen. Es gibt viele faszinierende Ergebnisse, die nicht in Lehrbüchern erscheinen, obwohl sie mit guten Kenntnissen der Sekundarschulmathematik zugänglich sind. Dieses Buch stellt eine Auswahl dieser Ergebnisse vor, darunter die mathematische Formalisierung von Origami, Konstruktionen mit Lineal und Zirkel (und anderen Instrumenten), die Fünf- und Sechs-Farben-Theoreme, eine Kostprobe der Ramsey-Theorie und wenig bekannte Theoreme, die durch mathematische Induktion bewiesen werden.Zu den überraschendsten Theoremen gehören das Mohr-Mascheroni-Theorem, das besagt, dass alle klassischen Konstruktionen die mit Lineal und Zirkel ausgeführt werden können, tatsächlich sogar nur mit einem Zirkel ausgeführt werden können, und das Steinersche Theorem, das besagt, dass ein Lineal allein ausreicht, wenn ein einziger Kreis gegeben ist. Der Höhepunkt des Buches ist eine detaillierte Darstellung des rein algebraischen Beweises von Gauß, dass ein regelmäßiges Heptadekagon (ein regelmäßiges Polygon mit siebzehn Seiten) mit Lineal und Zirkel konstruiert werden kann.Obwohl die in diesem Buch verwendete Mathematik elementar ist (euklidische und analytische Geometrie, Algebra, Trigonometrie), werden Schüler und Studenten an weiterführenden Schulen und Hochschulen, Lehrer und andere interessierte Leser gerne die Gelegenheit nutzen, sich der Herausforderung zu stellen, diese überraschenden Theoreme zu verstehen.

This open access book is intended to give a bird's-eye view of ellipses and planetary orbits. The only background required is secondary-school Euclidean geometry, analytic geometry, and trigonometry. That doesn't mean that the theorems and proofs are easy; to the contrary, many are very challenging.Although Isaac Newton invented the calculus and used it to study motion, from the time of the Greeks, proof meant proof by geometry. The book contains Newton's detailed geometric proof of the inverse-square law of orbits, based on Conic Sections Treated Geometrically, a widely used textbook from the nineteenth century written by William H. Besant. An important feature of the book is the numerous diagrams that are much more detailed than those appearing in the textbooks from the nineteenth century.Turning to planetary orbits, the book presents Kepler's equation for computing the position, speed and direction of a planet in its orbit, followed by the computation of Lagrange points, which are points in the solar system where a spacecraft can be placed so that the period of its orbit is the same as the Earth's.The history of mathematics has (or should have) an important place in mathematics education. Euclid is well-known but mathematicians were equally familiar with Conics by Apollonius of Perga. Some of his results are given in modern notation, although the presentation is faithful to his style. In addition, Kepler's own geometric proof of his First Law is given.The final chapter presents challenging theorems on ellipses: the Steiner inellipse, Marden's Theorem, the theorems of Pascal and Brianchon, and Newton's Ellipse Theorem.