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Kühnlein S: Algebra und Zahlentheorie

Algebra und Zahlentheorie

Ausgewählte Fragestellungen und wichtige Konzepte

Dieses Buch deckt alle relevanten mathematischen Themen eines Grundstudiums der Natur- oder Ingenieurwissenschaften ab, von der Analysis (inklusive einer ausführlichen Behandlung gewöhnlicher Differentialgleichungen mitsamt Modellierungsaspekten) und der linearen Algebra bis hin zu den wichtigsten Lösungsmethoden für partielle Differentialgleichungen. Das selbstständige Erlernen der Inhalte wird durch zahlreiche anwendungs- und praxisrelevante Beispiele motiviert und durch interaktive Aufgaben, verlinkte Videos und Repetitionsfragen gefördert. 
 Außerdem werden die Studierenden durch direkt in den entsprechenden Programmen bearbeitbare Dateien befähigt, mit den gängigsten Computer-Algebra-Systemen zu arbeiten, wodurch die eigene Auseinandersetzung mit der Materie weiter unterstützt wird.
 Insgesamt wird hier nicht nur eine äußerst geschickte didaktische Herangehensweise an die Mathematik umgesetzt, sondern die Themen werden zudem mit modernsten multimedialen Mitteln aufbereitet.&nbsp;&nbsp;Die AutorinDr. Laura Keller
 ist Senior Scientist an der ETH Zürich, also einerseits als Dozentin und andererseits als Forscherin tätig. Insbesondere hält sie seit mehreren Jahren Grundstudium-Mathematik-Vorlesungen für Studierende, die Mathematik nicht als Hauptfach belegen. Diese Vorlesungen sind bei den Studierenden nicht zuletzt wegen des großen didaktischen Geschicks der Dozentin und den vielen Praxisbezügen sehr geschätzt.

für Naturwissenschaftler, Ingenieure und Mediziner

Mathematik interaktiv und verständlich

Learn Calculus with Python

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis 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

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour

An engaging textbook for advanced undergraduates and beginning graduates covering the core subjects in linear algebra, with a unique emphasis on ideas from analysis. This edition includes over 200 new exercises and in-depth coverage of contemporary applications, including quantum mechanics, machine learning, data science, and quantum information.

A Concise Text with Contemporary Applications

Advanced Linear Algebra

Textbooks in Mathematics

Contemporary Abstract Algebra, 11e stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists.

Contemporary Abstract Algebra

Compact Textbooks in Mathematics

This textbook is designed for a first course in ring theory, module theory and category theory. Written following several decades of teaching experience, it stands out with its clear and engaging style, featuring thorough explanations and attention to detail. Carefully selected exercises encourage active learning and problem-solving.The textbook integrates elementary category theory with basic concepts and examples developed throughout the course. Although the primary focus is on rings and modules, relevant notions for other algebraic structures, such as groups and semigroups, are also discussed. Thus, this book aims at introducing students to noncommutative rings and modules within a broader algebraic context.Aimed at advanced undergraduates or master students in mathematics, this textbook is suitable both for use in the classroom and self-study. Whereas the first part of the book covers a basic course in ring and module theory, the latter part includes optional deepening topics.

Introduction to Ring and Module Theory

Synthesis Lectures on Engineering, Science, and Technology

This book provides an introductory overview of generating functions (GFs) and their applications. The authors begin by providing background information on the origin of GFs. The book then introduces the most commonly encountered GFs in engineering and applied sciences, such as ordinary GFs, exponential GFs, and probability GFs. This third edition includes an expanded discussion of the applications of GFs in a variety of applied science and engineering fields. The authors have also added two new chapters that cover the applications in mathematics and computer science, including algebra, combinatorics, geometry, graph theory, number theory, trigonometry, algorithm analysis, signal processing, and machine learning.In addition, this book:<ul><li>Provides readers with an essential overview of generating functions and their applications</li><li>Introduces the concepts at an appropriate level for beginners in applied science and engineering fields</li><li>Demonstrates the various applications of generating functions using practical problems and examples</li></ul>About the AuthorsRajan Chattamvelli, Ph.D., is a Professor in the School of Computer Science and Engineering at Amrita University, Amaravati. &nbsp;He has published more than 20 research articles in international journals, and his research interests include computational statistics, design of algorithms, parallel computing, cryptography, data mining, machine learning, and big data analytics.
 Ramalingam Shanmugam, Ph.D., is an Honorary Professor in the School of Health Administration at Texas State University, San Marcos.&nbsp; He is the Editor-in-Chief of several journals including&nbsp;
 Advances in Life Sciences; Global Journal of Research and Review; Journal of Obesity and Metabolism; 
 and the&nbsp;
 International Journal of Research in Medical Sciences
 . He has published more than 200 research articles and 120 conference papers.&nbsp; His research interests include&nbsp;theoretical and computational statistics, number theory, operations research, biostatistics, decision making, infectious disease modeling, patient risk management, cost-effective analysis and epidemiology.

Generating Functions in Engineering and the Applied Sciences

Synthesis Lectures on Mathematics & Statistics

<div>This book presents linear algebra in a concise and clear way, allowing beginner students to quickly attain the required proficiency. Existing books on the subject often cover too many topics, some of which are too complex and intimidating for a first course in linear algebra. This book presents the essential topics in a more user-friendly manner, benefiting both instructors and their students. The author devises an optimized order of topics that are adapted to the learning patterns of students. In addition, carefully designed examples are presented to enhance reader confidence to master the material and to avoid frequently observed frustration. This textbook is ideal for a one semester course on basic linear algebra for college students majoring in mathematics, engineering, and other sciences.</div>
<div> This book: • Presents a method to inspire quick grasps of algebraic key concepts and theorems • Includes relevant practice problems throughout at progressive levels of difficulty • Features intuitive examples throughout that clarify the presented concepts</div>
<div> About the Author Haiyan Tian, Ph.D., is a Professor of Mathematics at The University of Southern Mississippi (USM). Her research interests include nonlinear partial differential equations, applied analysis, computational mathematics, numerical analysis, and mathematical modeling. She has taught multiple mathematics subjects at both undergraduate and graduate levels. Dr. Tian is actively involved in math education. She started in 2007 to host the AMC contests at the USM campus to offer the talented Mississippi students an opportunity to participate in the national contests. She was the USM-AMC contest manager during 2007-2012. As the principal investigator, she received nine consecutive grants (2009-2017) from the U.S. Department of Education, through Mississippi Institutions of Higher Learning, for directing the USM Summer Math Institute for Mathematics Teachers.</div>

Key Ideas and Methods for a First Course

Linear Algebra

Oxford Graduate Texts in Mathematics

The theory of noncommutative Haagerup ¿¿ and Orlicz spaces is an important tool in both Quantum Harmonic Analysis and Mathematical Physics. Goldstein and Labuschagne provide a detailed account of the current theories in a way that is useful and accessible to a wide range of readers.

Noncommutative measures and Lp and Orlicz Spaces, with Applications to Quantum Physics

Proposes an in-depth formal framework for generalized Tonnetze, takes an algebraic approach, studies systems of k-chords in n-TET scales derived from a given k-mode through mode permutations and chord root translations, by combining key ideas of the neo-Riemannian Tonnetz theories with serial approaches to chordal structures.

Chord Transformations in Higher-Dimensional Networks

CRM Series in Mathematical Physics

16th International Symposium on Orthogonal Polynomials, Special Functions and Applications

Algebra und Zahlentheorie

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