Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering Ⅱ
The best works were selected after the conference titled "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM) II. The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering
The best works were selected after the conference "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM). The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
The Power of Probability
"The Power of Probability: Making Sense of Uncertainty" is a comprehensive exploration of probability theory and probabilistic reasoning. From its historical origins to its practical applications in diverse domains, the book delves into the fundamental concepts, methodologies, and implications of understanding uncertainty. Through engaging discussions and practical examples, readers are empowered to embrace probabilistic thinking, make informed decisions, and navigate complexities in an uncertain world.
Math-Ish
From Stanford professor, author of Limitless Mind, youcubed.org founder, and leading expert in the field of mathematics education Jo Boaler comes a groundbreaking guide to finding joy and understanding by adopting a diverse approach to learning math."Every once in a while, someone revolutionizes an approach to a difficult subject and changes it forever. That is what Jo Boaler has done for math. Fresh, smart, and inclusive, Jo Boaler's strategy eschews the one-size-fits-a-few approach and instead allows math to be seen and solved by everyone. A huge achievement. Math-ish is the only math book I've ever enjoyed reading in my entire life. Honestly." -Bonnie Garmus, author of Lessons in ChemistryMathematics is a fundamental part of life, yet every one of us has a unique relationship with learning and understanding the subject. Working with numbers may inspire confidence in our abilities or provoke anxiety and trepidation. Stanford researcher, mathematics education professor, and the leading expert on math learning Dr. Jo Boaler argues that our differences are the key to unlocking our greatest mathematics potential.In Math-ish, Boaler shares new neuroscientific research on how embracing the concept of "math-ish"--a theory of mathematics as it exists in the real world--changes the way we think about mathematics, data, and ourselves. When we can see the value of diversity among people and multi-faceted approaches to learning math, we are free to truly flourish. Utilizing the latest research on math education, Jo guides us through seven principles that can radically reframe our relationship with the subject: - The power of mindset on learning- Utilizing a visual approach to math- The impact of physical movement and communication on understanding- Understanding the value of an "ish" perspective - in mathematics and beyond- The importance of connected and flexible knowledge- New data on diverse teaching modes that work with different learning styles, not against them- The value of diversity in learning mathematics--and beyondWhen mathematics is approached more broadly, inclusively, and with a greater sense of wonder and play--when we value the different ways people see, approach, and understand it--we empower ourselves and gain a beneficial understanding of its value in our lives.
Combinatorics Problems and Solutions
This book will help you learn combinatorics in the most effective way possible - through problem solving. It contains 263 combinatorics problems with detailed solutions. Combinatorics is the part of mathematics that involves counting. It is therefore an essential part of anyone's mathematical toolkit. The applications of combinatorics include probability, cryptography, error correcting, games, music and visual art. In this new edition we have expanded the introductory section by more than twice the original size, and the number of problems has grown by over 30%. There are new sections on the pigeon hole principle and integer partitions with accompanying problems. Many of the new problems are application oriented. There are also new combinatorial geometry problems. Someone with no prior exposure to combinatorics will find enough introductory material to quickly get a grasp of what combinatorics is all about and acquire the confidence to start tackling problems.
Shrinkage for Stabilizing the Detection of Changepoints in Covariances for High-Dimensional Data
Diploma Thesis from the year 2012 in the subject Mathematics, grade: 1,0, University of Kaiserslautern (Fakult瓣t f羹r Mathematik), language: English, abstract: In mathematical statistics, detecting changes in parameters of real-life data series, known as change-point problems, is crucial. Originating in quality control during the 1950s, these problems have widespread applications today, spanning fields like economics, finance, medicine, and geology. In finance, fluctuations in asset returns can violate assumptions of constant variance, leading to inaccurate forecasts. Chapter 2 briefly discusses the univariate case, focusing on detecting changes in mean and variance parameters over time. The Cumulative Sums (CUSUM) test statistics, derived from likelihood ratios, serve as change-point estimators. However, their asymptotic distribution complexity and slow convergence limit applicability to small sample sizes. Nevertheless, asymptotic quantiles help determine if changes have occurred. Chapter 3 extends this analysis to the multivariate case, specifically addressing changes in covariance matrices. Estimating the covariance matrix, particularly in scenarios with many variables and few observations, poses challenges. Shrinkage estimators, like the Ledoit-Wolf (LW) estimator, offer improvements over sample covariance matrices, especially in small sample sizes. The Rao-Blackwell theorem leads to the development of the Rao-Blackwellized Ledoit-Wolf (RBLW) estimator, enhancing performance under Gaussian assumptions. A simulation study in Chapter 5 demonstrates the effectiveness of using these shrinkage estimators in detecting change-points, resulting in improved test power and accuracy. However, due to the absence of an asymptotic distribution for the test statistics, quantiles must be obtained through simulation.
General Combination Theorem and Selected Combinations
Document from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: So for combinations are discussed with different theorems in algebra. In this chapter I apply assembly analysis to get the theorems easy and memorable. After assembly analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. We have a full idea about combination. It indicates the outcome of arandom experiment. That is combination is the selection of M different components taken V at a time what is called usually a random experiment where order is not taken into account and repetitions are not allowed.
General Permutation Theorem and Selected Permutations
Document in the subject Mathematics - Algebra, language: English, abstract: We have permutations are discussed with different theorems in algebra. In this chapter I apply B system analysis to get the theorems easy and memorable. After B system analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. One usual theorem described with summation method and face new looks.
Exploring Unique Expressions of Positive Integers through Partitions and Theorems
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the realm of natural numbers and their expression as sums of other natural numbers, a concept known as partitions. Focusing on partitions originating from a positive integer and comprising positive integers, a systematic analysis is presented. Essential terms are defined to lay the groundwork, followed by the introduction of three key theorems and a consequential corollary. These theorems elucidate the uniqueness of expressions formed through arithmetic addition operations on such partitions, offering valuable insights into the structure and properties of positive integers. This exploration not only contributes to the theory of numbers but also holds implications for various mathematical and computational applications.
Analyzing Repartition Numbers of Parent Partitions. Theorems and their Implications
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the intricate realm of partition theory, specifically focusing on the repartition numbers of parent partitions. Through a systematic development of six theorems, insights into the distribution of repartitions, delineating distinct patterns for two separate parent partitions, are unveiled. Theorems are structured to elucidate the occurrences of repartitions based on the number of components involved, providing a comprehensive understanding of the repartition phenomena. The findings contribute to a deeper comprehension of partition theory and its implications across various domains.
Holy Trinity & Inverted Holy Trinity
The Trinities are all over the place!There is the positive Holy Trinity turned upwords... and there is the negative or Inverted Holy Trinity, turned upside down. From a Mathematical perspective. Applied Math to Life, Research. Bridge/Fusion between Mathematical Science & Spirituality.
Once Upon a Prime
A New York Times Book Review Editors' Choice "Wide-ranging and thoroughly winning." --Jordan Ellenberg, The New York Times Book Review "An absolute joy to read!" --Steven Levitt, New York Times bestselling author of Freakonomics For fans of Seven Brief Lessons in Physics, an exploration of the many ways mathematics can transform our understanding of literature and vice versa, by the first woman to hold England's oldest mathematical chair. We often think of mathematics and literature as polar opposites. But what if, instead, they were fundamentally linked? In her clear, insightful, laugh-out-loud funny debut, Once Upon a Prime, Professor Sarah Hart shows us the myriad connections between math and literature, and how understanding those connections can enhance our enjoyment of both. Did you know, for instance, that Moby-Dick is full of sophisticated geometry? That James Joyce's stream-of-consciousness novels are deliberately checkered with mathematical references? That George Eliot was obsessed with statistics? That Jurassic Park is undergirded by fractal patterns? That Sir Arthur Conan Doyle and Chimamanda Ngozi Adichie wrote mathematician characters? From sonnets to fairytales to experimental French literature, Professor Hart shows how math and literature are complementary parts of the same quest, to understand human life and our place in the universe. As the first woman to hold England's oldest mathematical chair, Professor Hart is the ideal tour guide, taking us on an unforgettable journey through the books we thought we knew, revealing new layers of beauty and wonder. As she promises, you're going to need a bigger bookcase.
Probability and Statistics
Probability and Statistics: Theory and Exercises is a textbook focused on practical examples of probability theory and statistics, with the goal of giving readers a thorough understanding of mathematical relationships in these subjects. The book is designed for basic courses in probability and statistics, and is aimed primarily at non-specialists and beginner level students. The book is divided into 2 sections, respectively. Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws Statistics: Covers basic concepts of descriptive statistics Key features - Simple, clear language for easy comprehension of key concepts - Carefully chosen exercises with solutions for self-learning - Over 40 Illustrations for clear explanations - References for further reading and tutorials
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?
Tensor Analysis
Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics. ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates
Single Variable Calculus
The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. ContentsPrerequisites for calculusLimits and continuityThe derivativeApplications of the derivativeThe definite integralTechniques for integration and improper integralsApplications of the definite integralInfinite series, sequences, and approximations
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.
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.
Mathematicians Don't Work with Numbers
This book answers, in the form of short and entertaining vignettes, the question: "What do mathematicians really do?" Readers will learn that mathematicians use numbers in the same way that novelists use letters. The individual letters are typed while the author thinks on a much grander scale, invisible to the observer. Requiring only familiarity with the multiplication table (and that for only one vignette), the book makes accessible a variety of mathematical concepts, such as game theory, chaos, and traffic flow modelling. The author accomplishes this with a light, engaging style, and a range of real-world examples that includes everything from barbershops to President James Garfield. Mathematicians Don't Work With Numbers will be of interest to the large audience of people who have always assumed that mathematicians do, in fact, work with numbers.
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 Extended Student Book 6
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.
Paradoxes and Inconsistent Mathematics
Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
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.
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.
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.
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.
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.
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.
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.
Essays on Coding Theory
Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the basic ideas of these coding techniques, which tend not to be covered in the graduate curricula, including pointers to further reading. Written in an informal style, it avoids detailed coverage of proofs, making it an ideal refresher or brief introduction for students and researchers in academia and industry who may not have the time to commit to understanding them deeply. Topics covered include fountain codes designed for large file downloads; LDPC and polar codes for error correction; network, rank metric, and subspace codes for the transmission of data through networks; post-quantum computing; and quantum error correction. Readers are assumed to have taken basic courses on algebraic coding and information theory.
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.
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.
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.
The Daring Invention of Logarithm Tables
In the early 17th century, both Jost B羹rgi and John Napier dared to invent a logarithm table whose construction required tens of thousands of computing steps. These tables reduced computing effort for multiplication and division by an order of magnitude. Indeed, their invention launched a computing revolution that continues to this day. The book, which is the color edition of the original black and white edition published in 2020, tells the story of B羹rgi's and Napier's work, and how Henry Briggs built on Napier's idea, creating a table of logarithms that was easier to use. John Napier and Henry Briggs described their methods in detail; distribution of their results was widespread. In contrast, Jost B羹rgi did not leave detailed records of his work. Just a few copies of his table and terse handwritten instructions for its use have survived. To fill this gap, the book reconstructs B羹rgi's thinking leading up to his table. The reader looks over his shoulder, so to speak, and learns how B羹rgi came upon the idea, how he decided on the specific format of the table, and how his instructions should be interpreted. And so the reader experiences the magic of the invention of logarithms. The final chapters examine the question "Who invented logarithms?". For centuries, few people were aware of B羹rgi's work; John Napier was considered to be the sole inventor. This changed at the middle of the 19th century when Jost B羹rgi's work became more widely known. Since then there has been extensive debate whether B羹rgi should be considered an independent co-inventor. Careful parsing of the history of logarithm going back to Archimedes of antiquity then reveals that, without doubt, John Napier and Jost B羹rgi are independent co-inventors of logarithms.
Harmonic Numbers and Open problems in Series
Problems involving harmonic numbers are so strange in solution way and those approaches or results are attracting the attention of students interested in mathematics as well as mathematicians and engineers, as there are many areas of application. In scientific and technological calculations that occur in various fields of mathematics and engineering, computational problems associated with various mathematical constants are often encountered, some of which are important tools for solving scientific and technological problems. There have been many open problems that have not been addressed before, due to the high level of scientific theory and the high performance of computer-based computing tools. Nevertheless, the world of mathematics still has a lot of problems to be discovered, so new and diverse methods are needed to solve these problems. This book contains open problems and challenging problems presented in several mathematical reference books and add their new generalizations written by us.
Primes and Particles
Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.
Supportive Foundation for High School Mathematics
This book is written to help students acquire a solid foundation in high school mathematics and enable them to develop problem-solving skills. Considerable effort has been devoted to ensure that the text is understandable and covers areas where learners have common difficulty. Numerous carefully selected examples are provided with detailed solutions to illustrate the mathematical concepts and enhance students understanding of the subject matter. The book has five chapters: (1) Relations and graphs of equations; (2) Functions with emphasis on linear, quadratic, and polynomial functions; (3) Exponential and logarithmic functions; (4) Topics of geometry that are basic to high school; (5) Trigonometric functions, trigonometric equations, and applications involving triangles.Undoubtedly, students who work through this manuscript will find that the book presents a comprehensive foundation to successfully understand high school mathematics. The other book of the author, namely, "Supportive Foundation for Basic Algebra" provides a comprehensive approach to the fundamental concepts and techniques of algebra and offers a useful supplementary background for enhanced mathematical competence.
Data and Process Visualisation for Graphic Communication
This book guides the reader through the process of graphic communication with a particular focus on representing data and processes. It considers a variety of common graphic communication scenarios among those that arise most frequently in practical applications. The book is organized in two parts: representing data (Part I) and representing processes (Part II). The first part deals with the graphical representation of data. It starts with an introductory chapter on the types of variables, then guides the reader through the most common data visualization scenarios - i.e.: representing magnitudes, proportions, one variable as a function of the other, groups, relations, bivariate, trivariate and geospatial data. The second part covers various tools for the visual representation of processes; these include timelines, flow-charts, Gantt charts and PERT diagrams. In addition, the book also features four appendices which cover cross-chapter topics: mathematics and statistics review, Matplotlib primer, color representation and usage, and representation of geospatial data. Aimed at junior and senior undergraduate students in various technical, scientific, and economic fields, this book is also a valuable aid for researchers and practitioners in data science, marketing, entertainment, media and other fields.
Calculus for Beginners
Foundations of Calculus: A Beginner's Comprehensive GuideCalculus for Beginners stands out as a pioneering educational tool, designed to demystify the complexities of calculus for novices. This book is crafted to cater to the needs of beginners, providing a clear and thorough foundation in calculus concepts, principles, and applications. Its unique structure and comprehensive coverage make it an indispensable resource for anyone looking to grasp the fundamentals of calculus.Empowering Learners with a Multifaceted ApproachCentral to this guide is its multifaceted approach to teaching calculus, which addresses the subject's inherent complexity and variations through a meticulously designed curriculum. Each chapter unfolds logically, guiding learners from basic principles to more intricate concepts. This pedagogical strategy is augmented by a wealth of resources aimed at reinforcing understanding and facilitating practical application.Highlights of the Book: Interactive Learning Experience: For each topic covered, the book includes a QR code and a dedicated link to an accompanying online course. This feature provides learners with instant access to detailed lessons, examples, exercises, video lessons, and worksheets, creating a rich, interactive learning environment.Comprehensive Curriculum: The book covers all fundamental aspects of calculus, including limits, derivatives, integrals, and differential equations, ensuring a solid foundation in each area. The content is presented in a clear, understandable language, making complex concepts accessible to beginners.Practical Application and Examples: Real-world applications and examples are woven throughout the text, illustrating how calculus principles are applied in various fields. This approach not only enhances comprehension but also demonstrates the relevance of calculus in solving practical problems.Enhanced Learning Tools: Each section is supplemented with exercises and worksheets, allowing learners to practice and apply what they have learned. Video lessons offer visual explanations of complex topics, catering to different learning styles.Accessible Solutions: A complete set of solutions for all exercises and questions is provided, enabling learners to check their work and understand the rationale behind each answer. This feedback mechanism is crucial for self-assessment and improvement. Calculus for Beginners is more than just a textbook; it is a comprehensive learning system that integrates traditional teaching methods with innovative digital resources. By offering a blend of written content, interactive online components, and practical exercises, this book ensures that learners not only understand calculus concepts but also know how to apply them in real-world contexts. Whether you are a student, a professional seeking to refresh your knowledge, or a curious mind venturing into the world of calculus for the first time, this guide offers the tools and guidance necessary to master calculus with confidence and ease. Ideal for self-study and classroom usage!
The Logic of Partitions
This book is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (direct-sum decompositions or DSDs) on a vector space. Partitions of a set are categorically dual to subsets of a set. Thus the logic of partitions is, in that sense, the dual to the Boolean logic of subsets (usually presented as the special case of propositional logic).Since partitions can be seen as the inverse image partitions of random variables or numerical attributes, partition logic is the logic of random variables or numerical attributes (abstracted from the actual values). On the lattice of partitions of an arbitrary unstructured set, there is a rich algebraic structure of dual operations of implication and co-implication - resembling a non-distributive version of Heyting and co-Heyting algebras.
Four Famous Numbers
WE DELVE DEEP INTO THE SCIENCE AND INTER-RELATIONSHIPS OF FOUR FAMOUS MATHEMATICAL CONSTANTS: EULER'S NUMBER, e, THE LUDOLPHINE CONSTANT, ( pi ), PYTHAGORAS' CONSTANT AND THE RATIO OF PHIDIAS ( phi ). ALONG THE WAY WE ASSESS THE USEFULNESS OF DIVERSE METHODS OF COMPUTING THESE NUMBERS, TECHNIQUES DATING FROM THE BRONZE AGE TO THE TWENTY-FIRST CENTURY. FROM THE EARLIEST DAYS OF VISIBLE LIFE TO OUR OWN TIMES, TINY ANIMALS HAVE PLOWED AND BURROWED THE DEEP SEA FLOOR IN SYSTEMATIC, GEOMETRICAL PATHS. THEY OFTEN SEEMED TO HAVE CONFORMED TO THE MATHEMATICS OF OUR FAMOUS NUMBERS! CAN THIS REALLY BE TRUE? WE CONSIDER THE EVIDENCE. THIS SECOND EDITION, CORRECTED AND EXTENDED, IS PROFUSELY ILLUSTRATED AND HAS ORIGINAL RESEARCH, ALGEBRAIC DERIVATIONS, FULL ACADEMIC REFERENCES, AND A COMPREHENSIVE INDEX. "FOUR FAMOUS NUMBERS" WILL APPEAL TO ENTHUSIASTS, UNDERGRADUATES AND TEACHERS IN HIGHER EDUCATION.
Nonlinear Control Systems with Recent Advances and Applications
In the rapidly evolving landscape of nonlinear control systems, this reprint stands as a beacon of knowledge, showcasing the remarkable progress made over the last few decades. With a focus on design methodologies and their applications, this text employs various mathematical tools to address the myriad challenges inherent in nonlinearly controlled systems.This reprint extends its reach beyond traditional boundaries, presenting applications of nonlinear control across diverse fields such as energy, health care, robotics, biology, and big data research. As technology continues to advance, nonlinear control emerges as a critical player in shaping the future of theory and technology adoption across these domains.Despite the wealth of the existing literature, synthesizing control strategies for a broader class of nonlinear systems, especially those integrated with emerging technologies in communication and computation, remains a formidable task. This reprint addresses this gap, providing a cutting-edge collection of articles that push the boundaries of both theoretical background and practical applications. With its emphasis on novel developments and the broader class of applications, this reprint opens doors to new possibilities, making it a must-read for anyone seeking to navigate the intricate challenges of nonlinear control systems in the 21st century.
Mathematical Logic
Presents an introduction to of formal mathematical logic and set theoryPresents simple yet nontrivial results in modern model theoryProvides introductory remarks to all results, including a historical background
