Squigonometry The Study Of Imperfect Circles

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Squigonometry: The Study of Imperfect Circles

Robert D. Poodiack,William E. Wood
Squigonometry The Study of Imperfect Circles Book PDF

Author : Robert D. Poodiack,William E. Wood
Publisher : Springer Nature
Page : 292 pages
File Size : 54,6 Mb
Release : 2022-12-15
Category : Mathematics
ISBN : 9783031137839

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Squigonometry: The Study of Imperfect Circles by Robert D. Poodiack,William E. Wood Pdf

This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric worlds might be. Comprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of π, two deeper dives into parameterizing the squigonometric functions, and integration. Applications include a celebration of Piet Hein’s work in design. From here, more technical pathways offer further exploration. Topics include infinite series; hyperbolic, exponential, and logarithmic functions; metrics and norms; and lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout, along with historical anecdotes, engaging exercises, and wry humor. Squigonometry: The Study of Imperfect Circles invites readers to extend familiar notions from trigonometry into a new setting. Ideal for an undergraduate reading course in mathematics or a senior capstone, this book offers scaffolding for active discovery. Knowledge of the trigonometric functions, single-variable calculus, and initial-value problems is assumed, while familiarity with multivariable calculus and linear algebra will allow additional insights into certain later material.

Joins and Intersections

H. Flenner,Liam O'Carroll,W. Vogel
Joins and Intersections Book PDF

Author : H. Flenner,Liam O'Carroll,W. Vogel
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 47,8 Mb
Release : 1999-10-08
Category : Mathematics
ISBN : 3540663193

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Joins and Intersections by H. Flenner,Liam O'Carroll,W. Vogel Pdf

Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei! [Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non singular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, co workers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have ex cess dimension. The first, by W. Fulton [Full] (recently revised in updated form), used a geometrical theory of deformation to the normal cone, more specifically, deformation to the normal bundle followed by moving the zero section to make the intersection proper; this theory was due to the author together with R. MacPherson and worked generally for intersections on algeb raic manifolds. It represents nowadays the standard approach to Intersection Theory. The second, by W. Vogel [Vogl], employed an algebraic approach to inter sections; although restricted to intersections in projective space it produced an intersection cycle by a simple and natural algorithm, thus leading to a Bezout theorem for improper intersections. It was developed together with J. Stiickrad and involved a refined version of the classical technique ofreduc tion to the diagonal: here one starts with the join variety and intersects with successive hyperplanes in general position, laying aside components which fall into the diagonal and intersecting the residual scheme with the next hyperplane; since all the hyperplanes intersect in the diagonal, the process terminates.

Mathematica®: A Problem-Centered Approach

Roozbeh Hazrat
Mathematica A Problem Centered Approach Book PDF

Author : Roozbeh Hazrat
Publisher : Springer
Page : 318 pages
File Size : 50,8 Mb
Release : 2016-01-04
Category : Computers
ISBN : 9783319275857

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Mathematica®: A Problem-Centered Approach by Roozbeh Hazrat Pdf

This textbook introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked-out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool. This new edition has been extensively revised and updated, and includes new chapters with problems and worked examples.

Normal Forms and Unfoldings for Local Dynamical Systems

James Murdock
Normal Forms and Unfoldings for Local Dynamical Systems Book PDF

Author : James Murdock
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 54,9 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387217857

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Normal Forms and Unfoldings for Local Dynamical Systems by James Murdock Pdf

This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the necessary theory 'from scratch' in just the form that is needed for the application to normal forms, with as little unnecessary terminology as possible.

From Natural Numbers to Quaternions

Jürg Kramer,Anna-Maria von Pippich
From Natural Numbers to Quaternions Book PDF

Author : Jürg Kramer,Anna-Maria von Pippich
Publisher : Springer
Page : 277 pages
File Size : 44,5 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9783319694290

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From Natural Numbers to Quaternions by Jürg Kramer,Anna-Maria von Pippich Pdf

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

It's a Nonlinear World

Richard H. Enns
It s a Nonlinear World Book PDF

Author : Richard H. Enns
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 50,9 Mb
Release : 2010-10-14
Category : Mathematics
ISBN : 9780387753409

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It's a Nonlinear World by Richard H. Enns Pdf

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.

An Introduction to Infinite Products

Charles H. C. Little,Kee L. Teo,Bruce van Brunt
An Introduction to Infinite Products Book PDF

Author : Charles H. C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer Nature
Page : 258 pages
File Size : 50,6 Mb
Release : 2022-01-10
Category : Mathematics
ISBN : 9783030906467

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An Introduction to Infinite Products by Charles H. C. Little,Kee L. Teo,Bruce van Brunt Pdf

This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

Elementary Differential Geometry

A.N. Pressley
Elementary Differential Geometry Book PDF

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 47,9 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781848828919

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Elementary Differential Geometry by A.N. Pressley Pdf

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul

A Journey Through The Realm of Numbers

Menny Aka,Manfred Einsiedler,Thomas Ward
A Journey Through The Realm of Numbers Book PDF

Author : Menny Aka,Manfred Einsiedler,Thomas Ward
Publisher : Springer Nature
Page : 344 pages
File Size : 49,5 Mb
Release : 2020-10-03
Category : Mathematics
ISBN : 9783030552336

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A Journey Through The Realm of Numbers by Menny Aka,Manfred Einsiedler,Thomas Ward Pdf

This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

Introduction to Lie Algebras

K. Erdmann,Mark J. Wildon
Introduction to Lie Algebras Book PDF

Author : K. Erdmann,Mark J. Wildon
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 51,5 Mb
Release : 2006-09-28
Category : Mathematics
ISBN : 9781846284908

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Introduction to Lie Algebras by K. Erdmann,Mark J. Wildon Pdf

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Cryptography

Simon Rubinstein-Salzedo
Cryptography Book PDF

Author : Simon Rubinstein-Salzedo
Publisher : Springer
Page : 259 pages
File Size : 42,5 Mb
Release : 2018-09-27
Category : Mathematics
ISBN : 9783319948188

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Cryptography by Simon Rubinstein-Salzedo Pdf

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book. Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.

Recent Advances in Harmonic Analysis and Applications

Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Recent Advances in Harmonic Analysis and Applications Book PDF

Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 43,9 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445647

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Recent Advances in Harmonic Analysis and Applications by Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick Pdf

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.

B-Series

John C. Butcher
B Series Book PDF

Author : John C. Butcher
Publisher : Springer Nature
Page : 310 pages
File Size : 54,9 Mb
Release : 2021-04-01
Category : Mathematics
ISBN : 9783030709563

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B-Series by John C. Butcher Pdf

B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods can be assessed. Runge–Kutta methods, in particular, depend on B-series for a clean and elegant approach to the derivation of high order and efficient methods. However, the utility of B-series goes much further and opens a path to the design and construction of highly accurate and efficient multivalue methods. This book offers a self-contained introduction to B-series by a pioneer of the subject. After a preliminary chapter providing background on differential equations and numerical methods, a broad exposition of graphs and trees is presented. This is essential preparation for the third chapter, in which the main ideas of B-series are introduced and developed. In chapter four, algebraic aspects are further analysed in the context of integration methods, a generalization of Runge–Kutta methods to infinite index sets. Chapter five, on explicit and implicit Runge–Kutta methods, contrasts the B-series and classical approaches. Chapter six, on multivalue methods, gives a traditional review of linear multistep methods and expands this to general linear methods, for which the B-series approach is both natural and essential. The final chapter introduces some aspects of geometric integration, from a B-series point of view. Placing B-series at the centre of its most important applications makes this book an invaluable resource for scientists, engineers and mathematicians who depend on computational modelling, not to mention computational scientists who carry out research on numerical methods in differential equations. In addition to exercises with solutions and study notes, a number of open-ended projects are suggested. This combination makes the book ideal as a textbook for specialised courses on numerical methods for differential equations, as well as suitable for self-study.

Groups, Rings and Fields

David A.R. Wallace
Groups Rings and Fields Book PDF

Author : David A.R. Wallace
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447104254

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Groups, Rings and Fields by David A.R. Wallace Pdf

This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

Numerical Linear Algebra

Folkmar Bornemann
Numerical Linear Algebra Book PDF

Author : Folkmar Bornemann
Publisher : Springer
Page : 153 pages
File Size : 49,5 Mb
Release : 2018-01-29
Category : Mathematics
ISBN : 9783319742229

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Numerical Linear Algebra by Folkmar Bornemann Pdf

This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.