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Dunham W: A Mathematician's Scrapbook

A Mathematician's Scrapbook

Highlights and Surprises from Across a Career

Mathe für Angeber

Monographs In Number Theory

The focus of this monograph is on the Jacobsthal sums of the title. These are quadratic character sums with polynomial arguments of a certain simple form. In addition to studying Jacobsthal sums on their own, the monograph explores their role in several topics of number-theoretical interest. A prominent theme is their use in counting solutions to equations over prime fields. Another aim is to construct representations of primes as sums of squares using Jacobsthal sums. Finally, Jacobsthal sums are applied to evaluate other quadratic character sums with polynomial arguments.This text is self-contained, with minimal technical prerequisites. We have strived for an engaging exposition, incorporating numerous examples and applications, carefully selected exercises, and historical notes and perspectives. Complete solutions to all exercises are provided.This monograph should be of interest to researchers studying character sums or counting solutions to equations over finite fields, as well as to graduate students and advanced undergraduates interested in these topics.

Jacobsthal Sums

Compact Textbooks in Mathematics

The main objective of the book is to teach how to practically construct periodic tessellations with stars and rosettes using an Interactive Geometry Software (IGS).Stars and rosettes are among the most characteristic geometric ornamental motifs of Islamic art. They are found on walls, ceilings, doors, and windows in both religious and secular buildings. Tessellations are repetitive patterns of shapes that fit together without gaps or overlaps, and they are periodic when they can be constructed by translations of a shape in two different directions. Periodic tessellations with stars and rosettes are complex and symmetrical compositions with rhythmic repetitions of profound beauty. An IGS allows to create and manipulate geometric constructions, producing accurate drawings. The book only assumes knowledge of basic geometric concepts and is self-contained while also providing all the necessary background information.Tessellations with Stars and Rosettes is aimed at students and graduates of mathematics, design, architecture, artists, and art historians, as well as anyone who wants to draw tessellations of stars and rosettes using IGS. It is suitable for a trimester or a semester course, and can also be used for self-study.

Practical Constructions with Interactive Geometry Software

Tessellations with Stars and Rosettes

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields This book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

Dieses Lese‐, Lern‐ und Nachschlagebuch stellt die Mathematik von den Basics bis zur Analysis anhand zentraler Fragen übersichtlich auf Einzelseiten dar.
Es ist für alle geschrieben,

die Mathe verstehen wollen oder müssen,
die das Wesentliche auf einen Blick finden wollen,
die visuell denken,
die nur das lesen wollen, was sie gerade brauchen.

Besonders an dem Buch ist,

dass jede Seite eine zentrale Frage behandelt und in sich abgeschlossen ist,
dass ich so schreibe, wie ich es dir mündlich erklären würde,
dass ich alles mithilfe möglichst einfacher Beispiele erkläre,
dass du links eine Erklärung findest und direkt rechts dazu Beispiele,
dass ich ganz am Anfang anfange, sodass du vorab nichts wissen musst.

Behandelt werden ganz grundlegende, aber auch fortgeschrittene Fragen – etwa:

Wie erweiterst und kürzt du Brüche?
Was bedeutet „genau dann, wenn“?
…
Wie bestimmst du die Ableitung der Umkehrfunktion?
Wann ist eine Funktion uneigentlich integrierbar?

Für die 3. Auflage wurde das Buch weiter optimiert und um zusätzliche Themen ergänzt. Nun kannst du es gut parallel zu einem Vorkurs oder Brückenkurs lesen. Es wird dir gefallen,

wenn du Schulstoff wiederholen willst,
wenn du dich auf die Mathematik im Studium vorbereiten willst, oder
wenn du dich einfach für Mathe interessierst.

Mit 130 ergänzenden Fragen und Antworten in der Springer-Nature-Flashcards-App kannst du dich spielerisch mit dem Stoff beschäftigen und deinen Lernerfolg überprüfen.
Die Autorin
Adriane Gründers (Pseudonym) hat in mathematischer Physik promoviert und ist in einem wissenschaftsnahen Unternehmen tätig. Die Vermittlung von Mathematik ist ihr ein Herzensanliegen. Sie ist fest davon überzeugt, dass viel mehr Menschen die Mathematik verstehen und dabei Freude haben können, als dies derzeit der Fall ist. Hierzu möchte das Buch einen Beitrag leisten.

240 Themen zum Nachlesen und Verstehen auf jeweils einer Seite

Mathe übersichtlich: Von den Basics bis zur Analysis

Mathematik kompakt

Dieses Buch richtet sich an Studierende in Studienrichtungen der Informatik zu Beginn ihres Studiums. Vorausgesetzt werden daher lediglich Kenntnisse der Schulmathematik.Behandelt werden grundlegende Themen aus dem Bereich der Diskreten Mathematik, mit besonderem Augenmerk auf Algorithmen und Anwendungen. Der Begriff "Diskrete Mathematik" ist hierbei weiter gefasst, als es in Deutschland zumeist üblich ist, und beinhaltet auch Teilbereiche der Zahlentheorie, Logik und erzeugender Funktionen. Selbstverständlich werden mit Abzählmethoden und Graphen auch klassische Themen der Diskreten Mathematik diskutiert.Zahlreiche Beispiele und Übungsaufgaben bieten eine optimale Vertiefung zum Verständnis der Materie an.

Diskrete Mathematik für die Informatik

Lecture Notes in Computer Science

This book constitutes the refereed post-conference proceedings of the 4th International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2024, held in Szczecin, Poland, during June 24–26, 2024.
The 9 full papers and 2 invited papers presented in this book were carefully reviewed and selected from 12 submissions. They were organized in topical sections as follows: invited talks; elliptic curves in cryptography; number theory; algebraic structures and public-key cryptography.

4th International Conference, NuTMiC 2024, Szczecin, Poland, June 24–26, 2024, Revised Selected Papers

Number-Theoretic Methods in Cryptology

Revised Third Edition

Introduction to Modern Cryptography

Vienna Circle Institute Library

Kurt Gödel (1906-1978) created a sensation by his incompleteness theorems of 1931, now seen as one of the high points of 20th century mathematics and science more generally. His professor at the University of Vienna Hans Hahn decided to organize a seminar on mathematical logic for the academic year 1931/32, with Gödel in charge for most of the practical side. The seminar proceedings, given in English translation in this book, are a unique witness of the state of research in logic and foundations of mathematics right after Gödel's theorems. They also add an important aspect to the intellectual history of these times in Vienna, both Hahn and Gödel having been members of the Vienna Circle. One fourth of the seminars were dedicated to Gödel's results: First the doctoral thesis about the completeness of predicate logic, then incompleteness, and last his results on intuitionistic logic. The seminars explain all these results in detail, in contrast to Gödel's publications of the time that often were quite laconic and extremely short. This book also contains Gödel's trial lecture on intuitionistic logic &nbsp;held in Vienna in 1933. The manuscript, recently found among the Gödel papers kept in Princeton, is preserved in Gödel's forgotten German shorthand and published here in an English translation.&nbsp;

Mathematical Logic in Vienna

Selected Chapters Of Number Theory: Special Numbers

Eulerian Numbers

Problem Solving in Mathematics and Beyond

Geometry Workbook for Anyone: Learn, Recap, Practice, Discover, Enjoy!This new volume focuses on problem-solving in plane geometry topics and is suitable for any reader with elementary geometrical knowledge at the secondary school level. The author has assembled an exceptional collection of geometry exercises with approximately equal weight allocated among different types of problems: proofs, calculations, and geometric straightedge-and-compass constructions.The book is divided into seven chapters, with sets of problems arranged in approximate order of increasing difficulty. The first chapter is devoted to a discussion of several useful strategies and techniques for approaching geometric problems. The next chapter presents warm-up exercises to 'stretch' geometric muscles and refresh the very basic facts about topics covered in subsequent chapters. Each of the following chapters: 'Triangles, ' 'Quadrilaterals, ' 'Circles, ' and 'Areas' has three sections (A, B, and C), starting with simple problems and questions (section A), progressing to intermediate problems (section B), and ending with more advanced and complex challenges (section C), some of which were offered in math Olympiads and various math contests. The final chapter is a mixture of challenging problems comprising material covered in previous chapters.At the end of the book, the 'Solutions and Answers' section provides detailed explanations and solutions for all the problems. In that section, for many interesting problems, the author reveals not just one but multiple alternative solutions, compares them, and discusses their effectiveness. The emphasis is on how to acquire insight and develop different strategies for tackling geometrical challenges. By solving these problems, readers discover fascinating links between them, unlock geometrical secrets, build self-confidence, and -- for many skeptics -- discover that learning geometry can be fun and enjoyable!

Learning Geometry Through Problem Solving

Routledge Focus on Mental Health

In The Mind of Complex Numbers and the Subject in Analyses, Raul Moncayo uses the complex plane to evaluate analytic outcomes. Moncayo's approach provides a study of the process and outcome of singular analyses that does not rely on the methods and questionnaires of psychotherapy or medical research.

The Mind of Complex Numbers and the Subject in Analyses

A Mathematician's Scrapbook

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