Elementary Algebra
First published in the mid-19th century, Elementary Algebra by Charles Davies is a classic textbook on algebraic principles and techniques. Suitable for students at an introductory level, this book covers the basics of algebra, including equations, expressions, and functions. It also includes numerous examples and exercises to help students gain mastery over these concepts. Whether you are a student or an educator, Davies' Elementary Algebra remains an invaluable resource for mastering the fundamentals of algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Leonard Eugene Dickson
This classic text covers the theory of equations, including polynomials and their roots, algebraic equations, and more. Perfect for students of algebra and anyone interested in the foundations of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements of Algebra
This book provides a comprehensive introduction to algebra designed for common school students. With clear instruction and plenty of examples, students will gain a strong understanding of the fundamental principles of algebra. Written by George Roberts Perkins, this book also serves as a great introduction for more advanced algebraic concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Examples in Algebra
Whether you're a student or teacher of algebra, this comprehensive textbook has everything you need to excel in the subject. With over eight thousand exercises and problems, the book is carefully graded to provide a challenging but rewarding learning experience.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Complete Algebra
This comprehensive guide to algebra covers topics such as equations, proportions, polynomials, logarithms, and more. Suitable for students and teachers alike, this book contains clear explanations, worked examples, and practice problems with answers.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Key to the First Lessons in Algebra
This textbook provides a comprehensive introduction to algebra, with numerous worked examples and exercises. The book is aimed at students and teachers of mathematics, and offers a clear and accessible guide to the principles and techniques of algebraic manipulation.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise on Algebra for the Use of Schools and Colleges
In this comprehensive textbook, Stephen Chase provides a detailed overview of algebra, from basic concepts to advanced topics. His clear explanations and rigorous approach make this book an ideal resource for students and educators seeking a deeper understanding of algebra. With numerous examples and exercises, it is an essential tool for anyone interested in mathematics and education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Symbolic Algebra
Written by eminent mathematician William Cain, this book is a landmark in the development of algebraic geometry and number theory. With rigorous proofs and clear explanations, Cain lays out the foundations of symbolic algebra and explains how it can be used to solve complex mathematical problems. This book is a must-read for serious students and scholars of algebra and geometry alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Easy Algebra for Beginners
Venable provides readers with a clear and concise introduction to the basics of algebra. He introduces readers to key concepts such as equations, variables, and polynomials, and provides a variety of exercises to help students practice their skills. This book is an essential resource for anyone seeking to improve their understanding of algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Introd. to Algebra Upon the Inductive Method of Instruction
An Introd to Algebra Upon the Inductive Method of Instruction is a classic mathematical textbook, written by Warren Colburn. The book teaches algebra using the inductive method of instruction, which emphasizes problem-solving and discovery. This book is a must-read for anyone studying mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![Rudimentary Algebra [microform]](https://cdn.kingstone.com.tw/english/images/product/7099/9781020517099m.webp "Rudimentary Algebra [microform]")
Rudimentary Algebra [microform]
This is a practical and easy-to-follow guide to algebra, designed specifically for the needs of Canadian students and educators. The book covers all the essential topics of the subject, including equations, inequalities, polynomials, functions, and more, and provides plenty of examples and exercises to help students master the material. An invaluable resource for anyone who wants to improve their algebra skills and succeed in school and beyond.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Algebraic Difficulties Simplified
This accessible guide offers a clear and concise approach to solving common algebraic problems. With examples and explanations that are easy to understand, Arthur Lee Sparkes makes learning algebra a breeze for students and professionals alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Work-Life Balance in Europe
L'alg癡bre n'aura plus de secrets pour vous ! Ce manuel de r矇f矇rence, destin矇 aux 矇l癡ves de l'?cole Centrale des Quatre-Nations, vous guide pas ? pas dans l'apprentissage de cette discipline fondamentale.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Algebra
A thorough and accessible introduction to algebra, intended for high school and college students. The book includes clear explanations, ample exercises, and real-world applications, making it an ideal resource for self-study.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Key to the Last New-York Edition of Bonnycastle’s Algebra
This book offers a key to understanding the latest editions of Bonnycastle's Algebra. It contains solutions to all the questions and is presented in a clear and concise manner. This book is an essential resource for students and teachers of algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise On Algebra
George Peacock's classic treatise on algebra is a must-read for anyone interested in the history of mathematics and mathematical theory. With a clear and engaging writing style, Peacock presents complex concepts in a manner that is accessible and easy to understand, making this an essential resource for students and scholars alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Normal Elementary Algebra, Part 1
The Normal Elementary Algebra, Part 1 is an essential textbook for anyone studying algebra. Edward Brooks provides a clear and concise introduction to the subject, covering the fundamental concepts and techniques of algebra in a way that is accessible and easy to understand. This book is a must-read for anyone looking to gain a solid foundation in algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Key to the First Lessons in Algebra
This textbook provides a comprehensive introduction to algebra, with numerous worked examples and exercises. The book is aimed at students and teachers of mathematics, and offers a clear and accessible guide to the principles and techniques of algebraic manipulation.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Algebra
This textbook provides a comprehensive introduction to elementary algebra. It starts with the basics of arithmetic and then gradually introduces students to the concepts of variables, equations, and graphing. The author explains each step in a clear and concise way, making this book an excellent resource for students who are struggling with algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Algebra
This classic algebra textbook provides a straightforward introduction to this essential branch of mathematics. Covering the basics of algebraic operations, equations, and inequalities, as well as more advanced topics like factoring and quadratic equations, Sestini's textbook is a reliable guide for both students and teachers. Whether you're studying for your algebra exam or just looking to brush up on your math skills, this book is an invaluable resource.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Transmission of Information
In this pioneering work, Robert M. Fano presents a comprehensive study of information theory as the basis for communication with computers. The book examines the methods and limits of transmitting and receiving information, with practical applications in digital technology and communication engineering.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Cellular Automata and Groups
This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov-Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.
Algebra and Number Theory
In the two-volume set 'A Selection of Highlights' we present basics of mathematics in an exciting and pedagogically sound way. This volume examines fundamental results in Algebra and Number Theory along with their proofs and their history. In the second edition, we include additional material on perfect and triangular numbers. We also added new sections on elementary Group Theory, p-adic numbers, and Galois Theory. A true collection of mathematical gems in Algebra and Number Theory, including the integers, the reals, and the complex numbers, along with beautiful results from Galois Theory and associated geometric applications. Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested.
A First Course in Category Theory
This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to mastering its fundamental principles.Unlike traditional category theory books, which can often be overwhelming for beginners, this book has been carefully crafted to offer a clear and concise introduction to the subject. It covers all the essential topics, including categories, functors, natural transformations, duality, equivalence, (co)limits, and adjunctions. Abundant fully-worked examples guide readers in understanding the core concepts, while complete proofs and instructive exercises reinforce comprehension and promote self-study. The author also provides background material and references, making the book suitable for those with a basic understanding of groups, rings, modules, topological spaces, and set theory.Based on the author's course at the Vrije Universiteit Brussel, the book is perfectly suited for classroom use in a first introductory course in category theory. Its clear and concise style, coupled with its detailed coverage of key concepts, makes it equally suited for self-study.
Completely Regular Semigroup Varieties
This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object. The authors introduce various associated relations and operators on the lattice of varieties of completely regular semigroups. Following that, the book covers the sublattice of varieties of bands with a focus on the influence of that sublattice on the structure of the whole lattice. The book concludes with the remarkable theorem due to Pol獺k describing the whole lattice of varieties of completely regular as a subdirect product of lattices, some of which are well understood. The authors include recent advances, insights, results, and techniques throughout the book.
Linear Algebra and Geometry
This book originates from the lessons held by the author in university courses and is aimed at students who, for the first time, are approaching a course in linear algebra and geometry. Bearing in mind the difficulties that students usually encounter in the study of abstract topics such as those presented in this book, we have chosen to use a language that is as simple as possible, trying to motivate the introduction of the various abstract notions with concrete examples. Topics covered include the theory of vector spaces and linear functions, the theory of matrices and systems of linear equations, the theory of Euclidean vector spaces and, finally, the applications of linear algebra to the study of the geometry of affine space. Numerous figures, examples and exercises carried out in every detail have been included in order to facilitate the study and understanding of the topics presented.
Abstract Algebra
This book contains the basics of abstract algebra. In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations. Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts. The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
Compact Matrix Quantum Groups and Their Combinatorics
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Compact Matrix Quantum Groups and Their Combinatorics
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
The Algebrization of Mathematics during the 17th and 18th Centuries. Dwarfs and Giants, Centres and Peripheries
This book explores the major historical phenomenon of the algebraization of mathematics in the second half of the 17th and 18th centuries, offering a broader understanding of the consolidation of analytic geometry and infinitesimal calculus as disciplines. The authors examine the external (intellectual, geographical, and political) factors that influenced these transformations and shed light on the process of acquisition and integration of analytical mathematics into traditional curricula. Drawing on new trends in historiography of science, this book emphasizes the importance of "dwarfs", that is mathematicians but also technicians, artisans, military personnel, engineers, and architects, often ignored or marginalized in traditional histories, in the circulation of original mathematical knowledge, and of peripheral countries such as Italy and Spain as important sites for the appropriation and production of such knowledge.
Commutative Algebra
The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth).
Exercises in Algebra and Trigonometry
This book contains exercises that a student can complete to learn algebra and trigonometry. Though it is designed to serve as a companion to another book by the same author, namely Algebra and Trigonometry, the exercises herein are typical for the subjects and do not pertain exclusively to that particular text.
100 Comprehensive Solutions in Algebra
This compilation presents comprehensive and step by step progressive solutions involving Algebra Problems. Covers major topics in algebra which include solving word problems involving age, mixture, investment, work, motion, arithmetic and geometric sequences, exponential and logarithmic functions, quadratic functions, variations, circle, parabola, ellipse, imaginary numbers, rational and quadratic equations.
Mathematics for the Practical Man
First published in 1910, this book aims to present and explain, in simple terms, all the elements of algebra, geometry, trigonometry, logarithms, coordinate geometry, and calculus. Mathematics For The Practical Man constitutes the ideal introduction to some of mathematics more tricky elements, and it is not to be missed by collectors of vintage literature of this ilk. The contents include: - Fundamentals of Algebra. Addition and Subtraction - Fundamentals of Algebra. Multiplication and Division, I - Fundamentals of Algebra. Multiplication and Subtraction, II - Fundamentals of Algebra. Factoring - Fundamentals of Algebra. Involution and Evolution - Fundamentals of Algebra. Simple Equations Many vintage books such as this are becoming increasingly scarce and expensive. We are republishing this volume now in an affordable, high-quality, modern edition complete with the original text and images.
Inverse Problems - Recent Advances and Applications
Inverse Problems - Recent Advances and Applications examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used. It consists of five chapters divided into two sections. Section 1, "Modeling and Formulations of Inverse Problems", discusses new approaches to modeling and formulations of inverse problems in some physical systems. Section 2, "Some Computational Aspects", contains research related to mathematical methods of solving some inverse problems.
The Square Root of Two to One Million Digits
A conundrum faced ancient mathematicians. Which number to use for the square root of 2? Ancient Babylonians used the fraction 305470/216000. This was accurate to about six decimal places. Ancient Indians used the fraction 577/408. This fraction is accurate to five decimal places. Today, mathematicians understand that the square root of 2 is irrational, its digits go on forever without repeating. It is calculated using an infinite series. This book lists the first million digits of the square root of 2.
Geometry of Continued Fractions
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics.The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Algebra 1 Through Stories
Unravel the Mysteries of AlgebraStep into a thrilling mathematical escapade with "Algebra 1: The Mystery of the Algebraic Artifact"! This dynamic guide offers a unique spin on mastering Algebra 1 concepts, making it an excellent supplementary resource for students aged 11-13 (8th-9th grade) and a compelling teaching tool for educators.A Novel Approach to LearningNo more wading through old-fashioned, dry textbooks! This book cleverly intertwines vital algebraic ideas into an exciting story that captures students' attention, making learning a captivating and effortless process.Essential Topics UncoveredOur journey uncovers all the key Algebra 1 concepts. The 19 exciting chapters delve into: Equations and ExpressionsInequalitiesLinear FunctionsExponents and PolynomialsQuadratic EquationsSystems of EquationsCompound InequalitiesReinforce and Validate UnderstandingEach chapter includes a comprehensive review and a carefully selected range of practice problems that reinforce understanding and allow the application of newly gained knowledge in various situations. These end-of-chapter exercises empower students to flex their algebraic muscles and gain confidence in their understanding.Ideal For"Algebra 1: The Mystery of the Algebraic Artifact" is a valuable resource for: 8th-9th graders studying Algebra 1, aiming to supplement their learning with an engaging twist.Parents looking for innovative methods to encourage and support their child's math education.Teachers in search of an engaging, narrative-driven technique to illuminate algebra concepts.With "Algebra 1: The Mystery of the Algebraic Artifact", algebra becomes an epic quest filled with adventure and intrigue. Join us as we unlock the wonders of Algebra 1 and make math an exciting mystery to solve!
Application-Inspired Linear Algebra
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, oneof which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors' website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Matrix Mathematics
Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.
Algebraic Curves and Surfaces
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Character Map in Non-Abelian Cohomology, The: Twisted, Differential, and Generalized
