Philosophy of Mathematics
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today's mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally - First nonstandard steps Retrospection
Sudoku for beginners - 50 puzzles from Mio - think for yourself
The playing field is a 9x9 square, divided into smaller squares with a side length of 3 fields. The main goal of the game is to fill the empty cells with numbers from 1 to 9 so that each number appears only once in each row, column and 3x3 square. Can you fill in all the cells correctly?
Foundations of Information and Knowledge Systems
This LNCS conference volume constitutes the proceedings of the 13th International Symposium, FoIKS 2024, in Sheffield, UK, in April 2024. The 18 full papers together with 3 short papers included in this volume were carefully reviewed and selected from 42 submissions.The Symposium focuses on fundamental aspect of information and knowledge systems, including submissions that apply ideas, theories, or methods from specific disciplines to information and knowledge systems. Examples of such disciplines are discrete mathematics, logic and algebra, model theory, databases, information theory, complexity theory, algorithmics and computation, statistics, and optimization.
The Land Between
The Land Between is the first concise history of Slovenia and Slovenes written in English by leading scholars from the country. The authors base their arguments on Slovenian, former Yugoslav, and Western sources to provide a comprehensive account of Slovenes' political, social, economic and cultural history, from early Slav settlements to the present day. The authors focus on Slovenian history but, to their credit, manage to place it in a wider context of empires and states to which Slovenian lands had belonged throughout history. The book will be of use to students of Slovenia and East-Central Europe, to diplomats, journalists, tourists, and anyone interested in this part of the world. It represents a welcome addition to the historiography of Slovenia and former Yugoslavia as well as a unique insight into the state of scholarship in post-1991 Slovenia. Dejan Djokic, historian, National University of Ireland, Maynooth A study which makes the reader feel and understand that since the end of the Cold War there is a new lease of life for Central Europe. The former borderlands between East and West construct their new identities. Slovenia is one of the most successful new democratic societies in the middle of Europe. This book is an excellent history of Slovenia which maps the narrative of a small European people without falling into the traps of national mythmaking. Writing about a small European country with two million inhabitants which crave for Central European, Mediterranean and Balkan traditions at the same time is no simple task. The book makes fine reading for everybody interested in understanding the fascinating and creative complexities in the heart of Europe. Highly recommendable for history lovers and historians alike! Emil Brix, historian and ambassador, Director of the Diplomatische Akademie Wien - Vienna School of International Studies The book presents a concise and intelligible history of the Slovenes. The authors take into due consideration the history of the territory between the Eastern Alps and the Pannonian Plain, starting with the period that began long before the first Slavic settlements. Thus, they wish to emphasize that the Slovenes' ancestors did not settle an empty territory, but rather coexisted with other peoples and cultures ever since their arrival in the Eastern Alps. This has enabled them to build a community shaped by countless influences stemming from a long period of living alongside German, Romance, and South Slav neighbors in a melting pot of languages, cultures, and landscapes. The same reasons have most probably also contributed to the perception of their land as a "land in between." Constituting a link between Eastern and Western Europe, Slovenia has recently also been increasingly perceived as the meeting point of Central Europe and the Balkans. Today, history still occupies the central position in the life of the Slovenes. The heroic period of emancipation has been completed and the Slovenes will be bracing themselves for a no less turbulent period of challenging "essentialist" notions of identity in order to create a thoroughly open society.
Martingale Methods in Statistics
This gives a comprehensive introduction to the (standard) statistical analysis based on the theory of martingales and develops entropy methods in order to treat dependent data in the framework of martingales. The author starts a summary of the martingale theory, and then proceeds to give full proofs of the martingale central limit theorems.
Analysis of Longitudinal Data with Examples
Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas.Key Features: -Includes the most up-to-date methods-Use simple examples to demonstrate complex methods-Uses real data from a number of areas-Examples utilize R code
Origins and Varieties of Logicism
This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism.
Analysis of Distributional Data
In a time when increasingly larger and complex data collections are being produced, it is clear that new and adaptive forms of data representation and analysis have to be conceived and implemented. Distributional data, i.e., data where a distribution rather than a single value is recorded for each descriptor, on each unit, come into this framework. Distributional data may result from the aggregation of large amounts of open/collected/generated data, or it may be directly available in a structured or unstructured form, describing the variability of some features. This book provides models and methods for the representation, analysis, interpretation, and organization of distributional data, taking into account its specific nature, and not relying on a reduction to single values, to be conform to classical paradigms. Conceived as an edited book, gathering contributions from multiple authors, the book presents alternative representations and analysis' methods for distributional data of different types, and in particular, -Uni- and bi-variate descriptive statistics for distributional data-Clustering and classification methodologies-Methods for the representation in low-dimensional spaces-Regression models and forecasting approaches for distribution-valued variablesFurthermore, the different chapters -Feature applications to show how the proposed methods work in practice, and how results are to be interpreted, -Often provide information about available software.The methodologies presented in this book constitute cutting-edge developments for stakeholders from all domains who produce and analyse large amounts of complex data, to be analysed in the form of distributions. The book is hence of interest for companies operating not only in the area of data analytics, but also on logistics, energy and finance. It also concerns national statistical institutes and other institutions at European and international level, where microdata is aggregated to preserve confidentiality and allow for analysis at the appropriate regional level. Academics will find in the analysis of distributional data a challenging up-to-date field of research.
Mathematics of Information
Ausgehend vom Shannon-Wiener-Zugang zur mathematischen Informationstheorie beginnt das Buch mit einer Abgrenzung der Begriffe Nachricht und Information und der axiomatischen Zuordnung einer Informationsmenge zu einer Wahrscheinlichkeit. Im zweiten Teil werden abz瓣hlbare Wahrscheinlichkeitsr瓣ume untersucht, deren mittlere Informationsmenge zur Definition der Shannon-Entropie f羹hrt; dabei werden drei klassische Anwendungen der Shannon-Entropie in der statistischen Physik, der mathematischen Statistik und der Nachrichtentechnik vorgestellt, und es wird ein erster Einblick in den Bereich Quanteninformation gegeben. Der dritte Teil behandelt die informationstheoretische Analyse dynamischer Systeme.Das Buch baut auf Bachelor-Wissen auf und legt gro?en Wert auf exakte Beweisf羹hrung.
Disruptive Technologies and Optimization Towards Industry 4.0 Logistics
This contributed volume guides researchers and practitioners on resource collaborative management of supply chains and manufacturing enterprises within an industrial internet technological environment. The book comprises 10 chapters that cover two major topics in the subject of logistics 4.0, namely the utilization of both disruptive technologies and optimization techniques in smart logistic management. With global research on the book's topic expanding rapidly across various directions and disciplines, it provides a structured framework for international experts to showcase outstanding work and unique approaches. Researchers and students will find the comprehensive outline on collaborative optimization and management of smart manufacturing and production, warehousing, inventory, logistics, transportation, integrated supply chain, and supply network within the industrial internet platform a beneficial guide to understanding current and future practical problems that arise in manufacturing and supply chain management.
Physical and Physiological Analysis of Soya Seeds from the 2016/2017 Harvest
The use of high quality seeds allows access to genetic advances, with guarantees of quality and adaptation technologies in the various producing regions. The factors that influence seed quality can occur during the production phase in the field, during harvesting, drying, processing, storage, transport and sowing. Quality control must therefore be established, which includes analysing and certifying the seed in order to guarantee the genetic purity of the cultivars, thus assuring the farmer of a pure batch with high vigour, which can establish a uniform stand in the field. The quality of soya bean seed is essential for obtaining an adequate plant stand, because when the seed is placed in the soil to germinate and emerge, it usually encounters adverse conditions of humidity and temperature, among other factors. Considering the importance of seed for agricultural production and aiming to achieve higher levels of profitability, this study will present data on the physical and physiological quality of soya bean seeds from the 2017/2018 harvest in northern Rio Grande do Sul.
Journal of Applied Logics, Volume 11, Number 1, January 2024. Special Issue
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Cambridge IGCSE Complete Mathematics Core Student Book 6th E
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
Persistent Homology and Persistent Cohomology
Persistent homology has become an important tool in non-linear data reduction. Its sister theory, Persistent cohomology, has attracted less attention in the past eventhough it has many advantages. We surveyed several literatures and present a summary of the status quo in persistent (co)homology covering the theory, computations, representations in terms of cycles (for persistent homology) and cocycles (for persistent cohomology), lens (quotient) space and their equivalence. Moreover, we computed the persistent homology and persistent cohomology for the 2 - sphere both manually and computationally (Using Ripserer). In both cases, same result was obtained, particularly in the computation of their barcodes much more that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.
Why Transfinite Set-Theory is Wrong and an Alternative Theory of Numeric Structures
Set Theory is a formalization of the existence and fundamental properties of mathematical objects as collections of elements and/or elements included in collections. Its formulation is so basic and comprehensive that it has been postulated as the foundation of all mathematics. Perhaps, the major achievement of Set Theory is that, after being criticized by many reputable mathematicians and philosophers since its appearance, it is now commonly accepted as the primary explanation of the most basic components of mathematics: numbers; and not only the numbers we have needed or we may ever need but all the numbers that could potentially exist. In Set Theory, an infinite sequence of numbers exists not as the mere projection of a construction algorithm but as a complete and self-identical mathematical object: a set. In Set Theory the words infinite and infinity do not refer to the property of growing endlessly (potential infinity) but to a definite magnitude; a number; the actual infinity. As a result of such a conception, Set Theory arrives at the conclusion that there exist infinitely many infinities, each one with a different value. The set of postulates, proofs and theorems used to justify the existence of such infinities is commonly known as Transfinite Set-Theory. The first part of this work shows how some of the properties and theorems applied to infinite sets, in Set Theory, necessarily lead to internal and fundamental contradictions under classical logic, even when the idea of actual infinity is accepted. Throughout the second part, motivated by the necessity of an alternative to Transfinite Set-Theory, due to the incapacity of such a theory to explain some of the findings shown in the first part (especially the proof of the existence of as many rational as irrational numbers), the author develops a theory to provide a better understanding of infinite sequences of numbers.
Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.
Methods for the Summation of Series
This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered.
Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.
Game Theory and Applications
This textbook provides an overview of the fundamentals of game theory and its applications in various fields. It introduces game theory as an established toolkit for the mathematical analysis and evaluation of strategic decisions. Through applied exercises, it introduces the basic concepts of game theory and offers students from various disciplines the opportunity to practice the concepts through in-depth training. The textbook addresses advanced students of economics, business administration, and related disciplines, university graduates with basic mathematical training as well as interested readers from all fields. For this, it provides student-friendly explanations, a variety of exercises and problems, and useful references to further reading. The book is divided into a beginner-friendly theory section, in which the most important aspects are presented in a compact and clear manner, and an application-oriented problem section, in which the readers can directly check what they have learned and find many application examples. The latter can also be used as a source of inspiration for instructors.
A Model Theoretic Oriented Approach to Partial Algebras
No detailed description available for "A Model Theoretic Oriented Approach to Partial Algebras".
Theory of Functions on Complex Manifolds
No detailed description available for "Theory of Functions on Complex Manifolds".
Parametric Optimization and Related Topics
No detailed description available for "Parametric Optimization and Related Topics".
Finite Difference Methods on Irregular Networks
No detailed description available for "Finite Difference Methods on Irregular Networks".
Introductory Banach Space Operators
This book provides a concise introduction to the analysis of Banach space operators within the framework of Hilbert space theory. The guiding notion in this approach is that of operator properties. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in all chapters. Each chapter consists of varying sections and exercises at the end of each chapter.
The Arithmetic of Life and Death
Whether you realize it or not, numbers are everywhere--and integral to almost every facet of your life . . . from your next raise in pay to the inevitable rise of inflation, your weekly family budget to your end of the national debt. And as George Shaffner amazingly reveals, there are discerning answers (and a great measure of comfort) in numbers. In The Arithmetic of Life, he applies the basic principles of mathematics--addition, subtraction, multiplication, and division--to some of the most profound and just plain puzzling questions of our time. Illuminated with anecdotes, humor, and insight, each chapter explains a unique part of life that can be understood only through the magic of numbers. Whether it's an unconventional theory on why more things go wrong than right, a simple calculation of how much it will cost you to smoke for a lifetime, why crime (accumulatively) doesn't pay, or a glimpse into the probability of life after death, this enlightening and lucidly reasoned book will forever change the way you think about numbers--and the world around you.
Geometric Gems
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.
Introduction to Iso- Euclidean Geometry
The main purpose in this book is to represent some recent researches of Santilli iso-mathematics in the area of the plane geometry. This book is devoted to the iso-plane geometry. It summarizes the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The book contains five chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems. In Chapter 1 we introduce iso-real numbers with one and several iso-units. They are defined the basic operations with them and they are deducted some of their basic properties. In the chapter they are defined iso-matrices, iso-determinants and iso-trigonometric functions. Chapter 2 deals with straight iso-lines. It is defined iso-angle between two iso-vectors. They are introduced iso-lines and they are deducted the main equations of iso-lines. They are given criteria for iso-perpendicularity and iso-parallel of iso-lines. In Chapter 3 we introduce iso-motions: iso-reflections, iso-rotations, iso-translations and iso-glide iso-reflections. Chapter 4 is devoted on iso-circles. They are given the iso- parametric iso-representations of the iso-circles. In Chapter 5 they are introduced iso-parabolas, iso-ellipses and iso-hyperbolas. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of iso-mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.
A Compendium of Musical Mathematics
The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters.In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.
Geometric Gems
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.
Discrete-Valued Time Series
The analysis and modeling of time series has been an active research area for more than 100 years, with the main focus on time series having a continuous range consisting of real numbers or real vectors. It took until the 1980s for the first papers on discrete-valued time series to appear. In the 2000s, a rapid increase in research activity was noted, but only in the last few years was a certain maturity and consolidation of the area of discrete-valued time series observed. This reprint is a collection of articles on a wide range of topics on discrete-valued time series (especially count time series), covering stochastic models and methods for their analysis, univariate and multivariate time series, applications of time series methods to risk analysis, statistical process control, and many more. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples.
Objective Bayesian Inference
Bayesian analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.
Comparative Genomics
This book constitutes the proceedings of the 21st International Conference on Comparative Genomics, RECOMB-CG 2024, which was held in Boston, MA, USA, during April 27-28, 2024. The 13 full papers presented in this book were carefully reviewed and selected from 21 submissions. The papers are divided into the following topical sections: phylogenetic networks; homology and phylogenetic reconstruction; tools for evolution reconstruction; genome rearrangements; and genome evolution.
Volatility Estimation
These notes have been written with the precisely purpose of summarizing the more often encountered and implemented volatility estimation techniques, to describe the realized volatility surface and its term structure, for example in developing Option Pricing libraries. The common and accepted assumptions behind the random fashion, that each quoted and traded asset follows, there are stochastic differential equations (SDEs) characterized by two main terms: one is the drift and the other one is the diffusion term or volatility. If the drift term is set uniquely by the definition of the martingale measure, imposing the drift's value under such risk neutral measure, to be equal to the free interest rate; on the other side, the diffusion term or volatility is not estimated or defined uniquely. Indeed, the latter is estimated involving several different approaches, that over the time have been developed, trying to catch a better fit with the observed options' quotation.
So You Think You Have Brains?
Really Challenging Mathematical Puzzles Newspapers and similar media often feature crossword puzzles, word-searches, general knowledge quizzes, problems on word games like Scrabble and other puzzles, typically on 'brain' games like chess and bridge. As one who has always been fascinated by mathematics, the author offers testing examples from the world of numbers which will require a fair amount of brain-work if you are to find correct solutions. The world of numbers displays much variety and some strange traits. That world forms the first of our group of problems and then the book focuses attention on the three "p's" palindromes, primes, and powers. Later, geometry problems and examples where numbers can be substituted for letters conclude the book. We hope readers enjoy being challenged!
Polytopes and Graphs
This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.
A Primer on Smooth Manifolds
Differential Geometry is one of the major branches of current Mathematics, and it is an unavoidable language in modern Physics. The main characters in Differential Geometry are smooth manifolds: a class of geometric objects that locally behave like the standard Euclidean space.The book provides a first introduction to smooth manifolds, aimed at undergraduate students in Mathematics and Physics. The only prerequisites are the Linear Algebra and Calculus typically covered in the first two years. The presentation is as simple as possible, but it does not sacrifice the rigor.The lecture notes are divided into 10 chapters, with gradually increasing difficulty. The first chapters cover basic material, while the last ones present more sophisticated topics. The definitions, propositions, and proofs are complemented by examples and exercises. The exercises, which include part of the proofs, are designed to help the reader learn the language of Differential Geometry and develop their problem-solving skills in the area. The exercises are also aimed at promoting an active learning process. Finally, the book contains pictures which are useful aids for the visualization of abstract geometric situations. The lecture notes can be used by instructors as teaching material in a one-semester course on smooth manifolds.
Understanding the Language of Mathematics
Alexander Firestone always wanted to be a teacher but felt that in order to know what was important to teach, he should be out in the real world to see what he was able to do with his present education. Upon graduation from the University, he secured a position as a Research Physicist working on new types of rocket propulsion for deep space exploration. In the first week, he realized that his present education ill-equipped him as a problem-solver working on new ideas. This was the beginning of What, How, and Why. After successfully working on the projects he was assigned, he realized he was ready for teaching. Over the last 50 years he has used his teaching and classroom experiences as a laboratory, developing What, How, and Why learning.I still get telephone calls this very evening (student from Westmount College in Christchurch) former students wanting to know how I'm doing and sharing their classroom experiences with me as a teacher. That was nearly 40 years ago. I'm a very passionate teacher who has taught for over 40 years and still teaches casually full-time. I am probably the oldest Mathematics teacher in Australia who is a passionate Mathematics teacher and is still able to teach full time. My teaching positions include classroom teacher, HOD mathematics, Principal, University lecturer in China. I have over 8 years of part-time experience doing post-graduate university study on What, How, and Why. Three in China and five at Griffith University in Queensland. I have presented papers and given Talks at International Education Conferences in Australia, and New Zealand.
Functional Analysis Revisited
'Functional Analysis Revisited' is not a first course in functional analysis - although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'
Functional Analysis Revisited
'Functional Analysis Revisited' is not a first course in functional analysis - although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'
Fundamentals of Abstract Algebra
Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained.Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
Extreme Values in Random Sequences
The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry. The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.
