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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, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).&nbsp;&nbsp;<ul><li>Develops a theory of crossing and product cubic systems with a crossing-linear and self-quadratic product vector field;</li><li>Presents equilibrium series with hyperbolic-to-hyperbolic-scant flows and with paralleled hyperbolic flows;</li><li>Shows equilibrium series switching bifurcations by up-down hyperbolic upper-to-lower saddles, parabola-saddles, et al.</li></ul>

Crossing-linear and Self-quadratic Product Vector Field

Two-dimensional Crossing and Product Cubic Systems, Vol. II

Learn Calculus with Python

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

Linguistic Inquiry Monographs

"A mathematical explication of Chomsky's Merge theory of syntax"--

A mathematical formalization of Chomsky’s theory of Merge in generative linguistics. The Minimalist Program advanced by Noam Chomsky thirty years ago, focusing on the biological nature of human language, has played a central role in our modern understanding of syntax. One key to this program is the notion that the hierarchical structure of human language syntax consists of a single operation Merge. For the first time, Mathematical Structure of Syntactic Merge presents a complete and precise mathematical formalization of Chomsky’s most recent theory of Merge. It both furnishes a new way to explore Merge’s important linguistic implications clearly while also laying to rest any fears that the Minimalist framework based on Merge might itself prove to be formally incoherent. In this book, Matilde Marcolli, Noam Chomsky, and Robert C. Berwick prove that Merge can be described as a very particular kind of highly structured algebra. Additionally, the book shows how Merge can be placed within a consistent framework that includes both a syntactic-semantic interface that realizes Chomsky’s notion of a conceptual-intentional interface, and an externalization system that realizes language-specific constraints. The syntax-semantics interface encompasses many current semantical theories and offers deep insights into the ways that modern “large language models” work, proving that these do not undermine in any way the scientific theories of language based on generative grammar.

An Algebraic Model for Generative Linguistics

Mathematical Structure of Syntactic Merge

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

A Mathematical Tour

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.

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

Textbooks in Mathematics

This text focuses on the primary topics in a first course in Linear Algebra including additional advanced topics related to data analysis, singular value decomposition and connections to differential equations. This is a lab text that would lead a class through Linear Algebra using Mathematica demonstrations and Mathematica coding

This text focuses on the primary topics in a first course in Linear Algebra including additional advanced topics related to data analysis, singular value decomposition and connections to differential equations. This is a lab text that would lead a class through Linear Algebra using Mathematica demonstrations and Mathematica coding

Labs and Projects with Mathematica ®

Exploring Linear Algebra

Chapman Mathematical Notes

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.

The Mathematical and Philosophical Legacy of Alexander Grothendieck

Frontiers in Mathematics

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. 
 Shafarevich-Tate Groups
 will be a valuable resource to those interested in this active area of research.

Shafarevich-Tate Groups

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

The Mending of Broken Bones reveals that far from a set of mundane exercises, algebra is the delicate craft of untangling numerical puzzles to uncover the hidden patterns and surprising behaviors of the numbers themselves. As Paul Lockhart shows, you don't have to be a mathematician to experience the joy and creativity of mathematical discovery.

A Modern Guide to Classical Algebra

The Mending of Broken Bones

Algebra und Zahlentheorie

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