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Kühnlein S: Algebra und Zahlentheorie

Algebra und Zahlentheorie

Ausgewählte Fragestellungen und wichtige Konzepte

1 Euklidischer Algorithmus und Teilbarkeit.
- 2&nbsp; Gruppen.
- 3 Ringe und Moduln.
- 4 Drei Exkurse.
- 5 Teilbarkeitslehre und Primelemente.
- 6 Mehr von Gruppen und Ringen.
- 7 Körpererweiterungen.

This book offers a comprehensive treatment of the core mathematical topics required for a modern engineering degree. The book begins with an introduction to the basics of mathematical reasoning and builds up the level of complexity as it progresses.

This book offers a comprehensive treatment of the core mathematical topics required for a modern engineering degree. The book begins with an introduction to the basics of mathematical reasoning and builds up the level of complexity as it progresses.

Mathematics for Engineers

Problem Solving in Mathematics and Beyond

This book offers high school teachers and students a broad and engaging look at an often-maligned subject - mathematics. Expanding beyond strictly defined curriculums, Fun Math: Problem Solving Beyond the Classroom explores additional topics that can inspire and motivate students to better appreciate the importance and beauty of mathematics.The first four chapters present novel examples in four integral areas of the mathematics curriculum, namely arithmetic, logic, algebra, and geometry. The last two chapters expose readers to topics in algebra and geometry that have been neglected at the secondary school level. Throughout the book, the focus is on introducing problem-solving techniques that will be useful in everyday life. With over 300 problems and carefully worked solutions, the book aims to foster a greater appreciation for mathematics through an exploration of useful and fascinating topics rarely addressed in the classroom. In other words, you can have fun with mathematics!

Fun Math: Problem Solving Beyond The Classroom

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

ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes.

ZAG Handbook of Modern Algebraic Geometry

Calculus for the Curious

A Textbook

Linear Algebra and Optimization for Machine Learning

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

Explore Set Theory, Abstract Algebra, and Category Theory with Functional Programming

The Book of Functions

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.

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

Linear Groups and Computation

Cambridge Tracts in Theoretical Computer Science

"This definitive treatment of results in category theory and theoretical computer science covers classical material from new viewpoints and develops a wealth of new topics. The centrepiece is a collection of existence theorems for initial algebras and terminal coalgebras. It will be the standard reference for years to come"--

This definitive treatment of results in category theory and theoretical computer science covers classical material from new viewpoints and develops a wealth of new topics. The centrepiece is a collection of existence theorems for initial algebras and terminal coalgebras. It will be the standard reference for years to come.

The Theory of Fixed Points of Functors

Initial Algebras and Terminal Coalgebras

This textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo.
This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving &nbsp;problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.

This textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo.This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving &nbsp;problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.

Analytical Methods in Physics

Non-commutative Ring Theory

Algebra und Zahlentheorie

Bibliografische Angaben

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Bibliografische Angaben

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