The Language Issue in the Teaching of Mathematics in South Africa
Lineare Algebra 1
Im vorliegenden Lehrbuch werden die Grundlagen der Linearen Algebra im Detail vorgestellt: Nachdem die grundlegenden Strukturen der Mathematik - die Gruppen, Ringe und K繹rper - eingef羹hrt sind, werden Vektorr瓣ume und lineare Abbildungen zwischen ihnen ausf羹hrlich vorgestellt. Wichtige Normalformen werden ebenso diskutiert wie die Determinante und das Problem der Diagonalisierung. Abschlie?end werden die Theorien der euklidischen und unit瓣ren Vektorr瓣ume parallel entwickelt.Dieses Buch ist der erste von zwei B瓣nden zur Linearen Algebra. Der Zugang der beiden B瓣nde ist einerseits eher klassisch: die formalen Aspekte der wissenschaftlichen Mathematik werden stark betont. Andererseits wird gerade aus den Anwendungen in der mathematischen Physik wichtige Motivation f羹r das Vorgehen gewonnen. Auf diese Weise ist das Lehrbuch f羹r Studierende der Mathematik und der Physik geeignet. Mehr als 200 umfangreiche ?bungen erleichtern das Selbststudium.
Numerical Linear Algebra and Matrix Factorizations
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results.Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Category Theory and Applications: A Textbook for Beginners (Second Edition)
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Linear Algebra
The book focuses on the development of the mathematical theory and also presents many applications to assist instructors and students to master the material and apply it to their areas of interest, whether it be to further their studies in mathematics, science, engineering, statistics, economics, or other disciplines.
Combinatorial Nullstellensatz
Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring.
X Marks the Spot
This book is written from the point of view of the users of maths. This book strives to give a guided tour of the development of various branches of mathematics (and what they're used for) that will give the reader this intuitive understanding.
Linear Algebra
Are you ready to dive into the vibrant world of linear algebra and see how it powers real-world applications? Welcome to this comprehensive guide, where traditional theory meets modern computational practices.Linear algebra is the magic behind many computational sciences -- machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and more. But here's a secret: the way it's taught in traditional textbooks isn't how professionals use it in the field.For instance, have you ever wondered about the practical importance of a matrix's "determinant"? You might be in for a surprise! This book bridges the gap between theoretical understanding and practical application, showing you not only the 'what' but also the 'how' of implementing linear algebra in real-world scenarios.What makes this book a must-have resource?Crystal clear explanations of linear algebra concepts and theories.Multiple angles to explain ideas, a proven technique to help cement your understanding.Vivid graphical visualizations to enhance your geometric intuition of linear algebra.Real-world implementations in MATLAB and Python. After all, in today's world, you seldom solve math problems by hand. Software is the way forward!A range of topics from beginner to intermediate levels, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.Emphasis on the application-oriented aspects of linear algebra and matrix analysis.Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.Ready-to-use codes in MATLAB and Python to bring linear algebra concepts to life on your computer. All codes can be downloaded from https: //github.com/mikexcohen/LinAlgBook.A unique blend of hand-solved exercises and advanced code challenges. Remember, math is not a spectator sport!Whether you're just starting your journey in linear algebra or seeking to apply these concepts to data analyses on computers (such as statistics or signal processing), this book is your go-to guide. With this book at your side, you won't just learn linear algebra; you'll experience it!
Rings, Modules, and Closure Operations
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Basic Math Skills Rescue, Part 2
The Critical Foundations of AlgebraThere are three clusters of essential math skills that all students need to learn and master. These are the foundational skills that will gradually lead children to algebra. Students need to have a strong understanding of these topics. These skills are aptly called the Critical Foundations of Algebra.Students need to fully understand these skills conceptually.They need to be able to compute accurately with them.They need to be able to apply them to problem solving.Automatic recall of number facts is also vitally important.The concepts, computation, problem solving, and recall of facts are mutually supportive of one another.The Critical Foundations of AlgebraWhole Numbers.Fractions and decimals, including percents, integers and positive and negative fractions and decimals.Some aspects of measurement and geometry.With a strong background in these areas, students will be prepared for success in algebra and beyond. The importance of a student's success in algebra cannot be over-emphasized. Algebra is the gateway subject that will equip students to take more advanced math, science, and technical classes. Success in algebra opens many doors to a higher education and a rewarding career; lack of success in algebra will sadly result in these doors staying closed.Basic Math Skills Rescue Parts 1 and 2 will ensure mastery of these Critical Skills of Algebra.Part 1 consists of three complete books: Whole numbers & integersFractions DecimalsPart 2 consists of three complete books: GeometryProblem Solving using all the above skillsMore Advanced Pre-Algebra SkillsMath Essentials materials will teach students these vital math skills in the most effective way possible. Here are some of the parent/teacher/student friendly program highlights.Short, concise, non-intimidating, self-contained lessonsA "Helpful Hints" section as part of each lesson, which insures that parents and students alike will understand each new topicFree Access to Online Video Tutorials taught by the authorEach lesson is self-contained and easy to understand with no fluff or distractionsConsistent review is built into each lessonChapter tests and final examsFun and exciting . . . students feel successful and develop self-esteemThe end result . . . Success in Algebra!
Division Workbook Grade 3
Supercharge your child's math skills and help them master division!Do you want to help your child grow into a math whiz? Are you interested in supplementing their learning with a practical book to boost their division skills? Or are you searching for a way to bring them up to speed and help them strengthen weak areas in their learning? Then this book is for you!Designed to be the perfect accompaniment for a school course, curriculum, homework or a tutor, this brilliant 3rd-grade division workbook provides all the essential problems to help children master this crucial area of their math development.A child's early math skills forms the foundation of their long-term math success, so it's never been more important to make sure they're up to speed in this fundamental part of their education. Packed with a wealth of different problems, equations, graphs, exercises and puzzles, this wonderful workbook seeks to be both useful and fun!Book details: - Covers all Areas of 3rd Grade Division- Perfect as a Supplement For Homework, School Curriculum, and For Homeschoolers- Equations Deal With Numbers In The Tens, Hundreds, and Thousands- Includes Equal Divisions, Remainders, Long Division, Word Problems and More- Uses Graphs, Number Lines, and Puzzles To Make Learning Fun!- And Much More!So if you want to strengthen your child's math skills and help them become confident with numbers, then this workbook is for you. Combining challenging questions with engaging exercises, the Division Workbook Grade 3 empowers children to develop their math skills and excel in education!
Problem Based Journey from Elementary Number Theory to an Introduction to Matrix Theory, A: The President Problems
The book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Associative and Non-Associative Algebras and Applications
Part I: Algebraic and Analytic methods in associative and non-associative structures. Applications.- Behn, A., Casado Y. C. and Molina M. S: Isomorphisms of four dimensional perfect non-simple evolution algebras.- Ouattara, M. and Savadogo, S: Power-associative evolution algebras.- Cabrera-Padilla, M. G., Jim矇nez-Vargas A. and Villegas-Vallecillos, M: A survey on isometries between Lipschitz spaces.- Carmona, J., L籀pez-Mart穩nez, S. and Mart穩nez-Aparicio P. J: The principal eigenvalue for a class of singular quasilinear elliptic operators and applications.- Mart穩n, A. J. C., Dieme, B., and Izquierdo F. J. N: Non-commutative Poisson algebras admitting a multiplicative basis.- Garc穩a, M. C. and Palacios, ? . R: Multiplication algebras: algebraic and analytic aspects.- Oudghiri, M. and Souilah, K: Generalized Drazin inverse and commuting Riesz perturbations.- Louzari, M. and Reyes, A: Generalized rigid modules and their polynomial extensions.- Mart穩n, A. J. C., Gaye, B., and Izquierdo F. J. N: n-Ary k -actions between sets and their applications.- Badry, M. E., Abdallaoui, M. A., and Haily, A: Primary group rings.- Diop, Y., Mesmoudi, L. and Sow, D: Semi-ring based Gr繹bner-Shirshov bases over a noetherian valuation ring.- Haynou, M. and Mohammed Taous, M: The 4-rank of the class group of some real pure quartic number fields.- Part II: Homological and categorical methods in algebra.- Bulacu, D., and Torrecillas, B: Frobenius monoidal algebras and related topics.- Dembele, B., Maaouia M. B. F. and Sanghare, M: The functor SC-1 () and its relationship with homological functors T orn and E XT n.- Kaoutit, L. E.: BOCSES over small linear categories and corings.- Ammar, F., Ayadi, I., Mabrouk, S., and Makhlouf, A: Quadratic color Hom-Lie algebras.- Abdelalim, S., Chaichaa, A. and Garn, M. E: The extension property in the category of direct sum of cyclic torsion-free modules over a BFD.- Part III: History of Mathematics.- Azizi, A.: Arabic Scientific and technical Heritage in Morocco.
Galois Theory and Advanced Linear Algebra
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley-Hamilton theorem, Galois groups, Sylvester's law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
Separation in Point-Free Topology
This book is the first systematic treatment of this area so far scattered in a vast number of articles. As in classical topology, concrete problems require restricting the (generalized point-free) spaces by various conditions playing the roles of classical separation axioms. These are typically formulated in the language of points; but in the point-free context one has either suitable translations, parallels, or satisfactory replacements. The interrelations of separation type conditions, their merits, advantages and disadvantages, and consequences are discussed. Highlights of the book include a treatment of the merits and consequences of subfitness, various approaches to the Hausdorff's axiom, and normality type axioms. Global treatment of the separation conditions put them in a new perspective, and, a.o., gave some of them unexpected importance. The text contains a lot of quite recent results; the reader will see the directions the area is taking, and may find inspirationfor her/his further work.The book will be of use for researchers already active in the area, but also for those interested in this growing field (sometimes even penetrating into some parts of theoretical computer science), for graduate and PhD students, and others. For the reader's convenience, the text is supplemented with an Appendix containing necessary background on posets, frames and locales.
Algebra Word Problems Made Simple
NEW from Math Essentials! The perfect companion to the popular No-Nonsense Algebra, Algebra Word Problems Made Simple gives additional help to those who struggle with word problems. Includes a handy glossary and Algebra Resource Center. FREE online video tutorials are available for each chapter.
A School Algebra
A School Algebra, by George A. Wentworth, brings Victorian-era rigour to clear, practical instruction in algebra. A classic text, still vital. Its orderly progression and emphatic focus on algebraic problem solving train the reader to reason with symbols and structure, not merely to memorise rules. Part classic algebra textbook and part foundational math guide, it lays out the mathematical principles study that underpins later work in calculus and beyond, demonstrating the Victorian commitment to methodical thought. The tone is plain and purposeful: definitions are stated, methods followed by examples, and problems are arranged to build confidence through steady practice. That steady pedagogy makes the book equally useful within the secondary school curriculum and for adults approaching self-study mathematics. Parents and tutors will find a dependable homeschool math resource here; hobbyists and curious minds will value an accessible window into nineteenth-century mathematics. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. As a historical math reference, A School Algebra reveals the priorities of Victorian-era education and helps historians, teachers and collectors trace the development of classroom practice. It sits naturally in the Wentworth algebra series of instructional works, and it also earns its place on the shelf of anyone assembling a principled math instruction collection. Equally at home on a student's desk as a study aid or on a collector's shelf as a piece of pedagogical history, this edition appeals to casual readers seeking lucid explanation and to classic-literature collectors who prize well-made educational books. Teachers will use it to compare contemporary classroom methods with period practice; historians can follow shifts in emphasis from rote computation to conceptual understanding. Collectors prize the measured language and instructive structure typical of nineteenth-century textbooks, while readers seeking sturdy, steady explanation will find the work refreshingly direct.
Graph Path
★ Graph Paper Composition Notebook, 8.5" x 11", 100 Sheets 5X5, Quad Ruled, Large Graph Paper Journal, Grid Paper Notebook, Math and Science Notebook ♥ The graph paper notebook you'll love to use for your projects!Our graph paper composition notebook is a nice book of grid paper. It is great for school, it has good quality and the paper is nice. It is very much like a regular composition book just with grid paper Our grid notebook can be used for drawing, writing, journaling, taking notes at school and so much more. It can be used by kids and adults - students, teachers, artists, architects. ♥ Click buy to get one for your activities and projects. ★ Our graph paper notebook has the following features: Large: 8.5" x 11" 100 Sheets 5X5 High-quality paper and glossy cover for a perfect experience.
Affine, Vertex and W-Algebras
This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac-Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
Skew Pbw Extensions
This monograph is devoted to a new class of non-commutative rings, skew Poincar矇-Birkhoff-Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gr繹bner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin-Schelter regular algebras, and the noncommutative Zariski cancellation problem. The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.
Ring Theory 2019
Since 1991, the group of ring theorists from China and Japan, joined by Korea from 1995 onwards, took turns to hold the quadrennial international conferences (sometimes also referred to as symposiums). As the proceedings of the eighth conference held in Nagoya, Japan in 2019, this volume consists of a collection of articles by invited speakers (survey) and general speakers (survey and original), all of which were refereed by world experts.The survey articles show the trends of current research and offer clear, thorough explanations that are ideal for researchers also in other specialized areas of ring theory. The original articles display new results, ideas and tools for research investigations in ring theory.The articles cover major areas in ring theory, such as: structures of rings, module theory, homological algebra, groups, Hopf algebras, Lie theory, representation theory of rings, (non-commutative) algebraic geometry, commutative rings (structures, representations), amongst others.This volume is a useful resource for researchers - both beginners and advanced experts - in ring theory.
Involutive Category Theory
This monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge applications. Additionally, the author's own recent advances in the area are featured, never having appeared previously in the literature. The opening chapters offer an introduction to basic category theory, ideal for readers new to the area. Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author's state-of-the-art research. Chapters on coherence of involutive symmetric monoidal categories, and categorical GNS construction follow. The last chapter covers involutive operads and lays important coherence foundations for applications to algebraic quantum field theory. With detailed explanations and exercises throughout, Involutive Category Theory is suitable for graduate seminars and independent study. Mathematicians and mathematical physicists who use involutive objects will also find this a valuable reference.
Elements of Linear and Multilinear Algebra
This set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the most elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes - to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as "proposition", "example", "theorem", "exercise", and "corollary", if not followed by a proof (and proofs here are very rare) or a reference to a proof, are invitations to verify the assertions made.These notes are intended to accompany an (academic) year-long course at the advanced undergraduate or beginning graduate level. (With judicious pruning most of the material can be covered in a two-term sequence.) The text is also suitable for a lecture-style class, the instructor proving some of the results while leaving others as exercises for the students.This book has tried to keep the facts about vector spaces and those about inner product spaces separate. Many beginning linear algebra texts conflate the material on these two vastly different subjects.
Lectures in Algebraic Combinatorics
Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia's inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.
Mathematics of Convex and Linear Optimization
Discover the practical impacts of current methods of optimization with this approachable, one-stop resource Linear and Convex Optimization: A Mathematical Approach delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them. Experienced researcher and undergraduate teacher Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms. The book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout. Linear and Convex Optimization contains a wide variety of features, including: Coverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates Enhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion An emphasis on the formulation of large, data-driven optimization problems Inclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts Presentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management Ideal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training.Software to accompany the text can be found here: https: //www.gordon.edu/michaelveatch/optimization
Advanced Algebra Study Guide
This book was written to better solve algebra problems using text, graphs, diagrams, rules, combined to show several approaches ofsolving algebra in a real life environment.
Exercises in Numerical Linear Algebra and Matrix Factorizations
To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students' learning process. This book provides precisely this type of supporting material for the textbook "Numerical Linear Algebra and Matrix Factorizations," published as Vol. 22 of Springer's Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.
Semilocal Categories and Modules with Semilocal Endomorphism Rings
This book collects and coherently presents the research that has been undertaken since the author's previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material.In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research.Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.
Lectures on Orthogonal Polynomials and Special Functions
Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
Exercises and Problems in Linear Algebra
This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.
Desingularization: Invariants and Strategy
This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka's Theory. The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references. Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.
Linear Algebra
Praise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications."--Electric Review Learn foundational and advanced topics in linear algebra with this concise and approachable resource A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features: A new application section on section on Google's Page Rank Algorithm. A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC). Many other illuminating applications of linear algebra with self-study questions for additional study. End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB code Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
Exercises and Problems in Linear Algebra
This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.
Profinite Semigroups and Symbolic Dynamics
This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.
Complex Semisimple Quantum Groups and Representation Theory
This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincar矇-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.
No Bullshit Guide to Linear Algebra
Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, quantum mechanics, and countless other applications. Indeed, linear algebra offers a powerful toolbox for modelling the real world.The No Bullshit Guide to Linear Algebra shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy to speed up tedious matrix arithmetic tasks."The book explains the concepts in a way that gives a strong intuitive understanding." - Joe Nestor, student"It's very well written and a fun read!" - Felix Kwok, professor"I used this book in multiple big data courses when I needed a deeper understanding of the material." - Zane Zakraisek, studentThe author, Ivan Savov, combines 17 years of tutoring experience with a B.Eng. in electrical engineering, an M.Sc. in physics, and a Ph.D. in computer science from McGill University.
Summit Math Algebra 2 Book 6
This textbook series supports both independent study and classroom learning, empowering students to learn at their own pace, whether working individually or collaboratively. The author makes each concept easy to understand and actively engages students in a step-by-step process of building genuine understanding, rather than memorizing formulas without knowing why they work. With careful pacing, clear explanations, and a detailed answer key for timely feedback and helpful guidance, the uniquely scaffolded approach allows students to learn math anywhere, at school or at home. Written by a teacher with over 20 years of experience, each feature is designed to benefit students. Published as separate books instead of a single textbook, students feel a sense of achievement when they finish each book, making learning feel less intimidating. Each lightweight book has 2 parts. The first half uses small steps to guide students through the process of constructing each concept, while the second half provides additional practice to reinforce learning and improve retention. Every section includes an answer key to provide teacher-like feedback that helps students keep moving forward. This curriculum is named Summit Math to reflect the author's belief that learning is like hiking. Anyone can reach the summit, at their own pace, if they keep taking small steps. Book description: In this book, students review what they learned about solving systems of linear equations in the Algebra 1 course. They will use the strategies of substitution and elimination to solve word problems that involve systems of linear equations. Linear inequalities are also included in this book. Students will then apply what they have learned about factoring as they solve nonlinear systems of equations. They will also learn how to solve 3-variable systems of equations and then use this skill to find the equation of a parabola when they know 3 points on the parabola. This book builds on Algebra 1: Books 5 and 6 and Algebra 2: Book 3. Book 6 Contents: Review graphing systems, substitution, and eliminationScenarios involving linear systemsSystems of linear inequalitiesNonlinear systemsSystems with 3 variablesWriting the equation for a parabola, given 3 pointsCumulative ReviewAnswer Key
Recent Developments in Commutative Algebra
- Defining Equations of Blowup Algebras. - Koszul Modules. - Gr繹bner Degenerations. - Adams Operations in Commutative Algebra.
Elements of algebra. Translated from the French, with the notes of Bernoulli and the additions of De La Grange To Which Is Prefixed a Memoirs of the Life and Character of Euler
John Hewlett's translation of the Elements of Algebra brings eighteenth century mathematics into sharp, usable form. Clear reasoning survives the ages. Part classic algebra textbook and part foundational mathematics text, the work lays out the principles of algebra with a patient, example-led voice that doubles as a mathematics students guide and a primer in mathematical problem solving. Readers will find a steady progression from arithmetic into algebraic method and number theory basics, set in the clear pedagogical tone that distinguished French mathematical works of the period. The edition preserves the scholarly commentary that historians prize: the notes of Bernoulli and the additions of De La Grange (the Bernoulli and Lagrange notes) sit alongside a prefixed memoir of the life and character of Euler, a concise Leonhard Euler biography that places the ideas in human context. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. Accessible to curious readers and to those seeking a rigorous reference, it functions as a homeschool math resource and as a supportive mathematics students guide in formal study. The clear exposition illuminates the principles of algebra while leading gently into number theory basics, and the editorial context - Bernoulli and Lagrange notes, the memoir of Euler - places the methods within the culture of French mathematical works. Students of mathematical problem solving will find models of disciplined reasoning; readers of intellectual history gain a lucid historical math treatise that captures a turning point in eighteenth century mathematics. The effect is both practical and literary: useful to learners, satisfying to collectors of classic algebra textbooks and admirers of Leonhard Euler alike. Elegantly presented and thoughtfully annotated, this edition suits study, teaching and the shelves of classic-literature collectors alike.
BTG Math Middle School Workbook
The BTG Math Middle School Workbook is a supplemental resource that could be used to bridge the learning gaps of students. Our curriculum is geared towards the essential readiness standards that are needed for students to successfully transition from 6th grade through 8th grade.
Theory and Applications of Ordered Fuzzy Numbers
This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Theory and Applications of Ordered Fuzzy Numbers
This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Sch羹lervorstellungen Zu Geradengleichungen in Der Vektoriellen Analytischen Geometrie
Die vorliegende qualitative Interviewstudie geht der Frage nach, welche Vorstellungen Sch羹lerinnen und Sch羹ler mit einer Geradengleichung in Vektorform verbinden. Insgesamt 22 Sch羹lerinnen und Sch羹ler der gymnasialen Oberstufe werden mit Hilfe eines leitfadengest羹tzten, problemzentrierten Interviews zu Geradengleichungen in Vektorform aus unterschiedlichen Perspektiven befragt. Die Auswertung der Interviews erfolgt mit einer an die Grounded Theory angelehnten Kategoriengenerierung und einer typenbildenden qualitativen Inhaltsanalyse, die die Bildung von 6 verschiedenen Typen erm繹glicht.
Topics in Galois Fields
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields.We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm.The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.
Arbeitsbuch Lineare Algebra
Dieses Arbeitsbuch enth瓣lt die Aufgaben, Hinweise, L繹sungen und L繹sungswege des Werks Karpfinger/Stachel, Lineare Algebra. Durch die stufenweise Offenlegung der L繹sungen ist das Werk bestens geeignet zum Selbststudium, zur Vorlesungsbegleitung und als Pr羹fungsvorbereitung. Inhaltlich decken die Aufgaben den Stoff der linearen Algebra aus den ersten beiden Semestern ab.
H繹here Mathematik Kompakt
Dieses Buch enth瓣lt die wesentlichen Themen der h繹heren Mathematik f羹r Ingenieure und Naturwissenschaftler, wie sie beispielsweise an Fachhochschulen und Berufsakademien gelehrt werden. Es behandelt einerseits die Analysis, beginnend bei den elementaren Funktionen 羹ber die Differenzial- und Integralrechnung bis hin zur mehrdimensionalen Analysis, und andererseits die lineare Algebra mit der Vektor- und Matrizenrechnung. Auf die 羹bersichtlich dargestellten Definitionen und S瓣tze folgen Beispielrechnungen und Bemerkungen, die die Inhalte zueinander in Bezug setzen. Zu zahlreichen Abschnitten und Fragestellungen gibt es ausf羹hrliche Erkl瓣rvideos, in denen die dargestellten Themen m羹ndlich erl瓣utert und vertieft werden, sowie Visualisierungen, mit denen LeserInnen die mathematischen Methoden und Anwendungsbeispiele interaktiv erfahren k繹nnen. Ferner gibt es ein auf das Buch abgestimmtes Arbeitsbuch h繹here Mathematik mit Aufgaben und vollst瓣ndig durchgerechneten L繹sungen. Damit eignet sich dieses Werk bestens als vorlesungsbegleitende Literatur, zur Pr羹fungsvorbereitung oder zum Selbststudium.
Combinatorial Structures in Algebra and Geometry
This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past - for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic propertiesof line bundles in geometry and multiplier ideals in algebra.This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).
Generalized Ordinary Differential Equations in Abstract Spaces and Applications
GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book's descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and App-lications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
