Mathematical Logic
The book "Mathematical Logic" has been meticulously prepared to serve the students of the B.A./ B.Sc./ B.Com. third semester (As per NEP-2020 new syllabus) Mathematics skill enhancement course under Dibrugarh University. Mathematical logic is a fundamental course in undergraduate mathematics, providing essential tools and concepts that are foundational for further studies in the field. This book covers all the topics outlined in the syllabus.
Euclid Transmogrified
This book tells the extraordinary story of how in the mid twentieth century, in a well-developed European country, a mathematically solid system of geometry was altered to such an extent that more than one million students were taught foundationally flawed geometry over more than a quarter of a century. The almost unbelievable situation came about in Ireland in the wake of early postcolonial developments that gave rise to an impressionable and unqualified civil service in a position of power over a nation's educational development. This is a multifaceted tale of a perfect storm within mathematics development in Ireland whose result was so destructive that its ramifications continue to be felt into the twenty-first century, forty years after a report of a Royal Irish Academy commission of professors of mathematics described the matter as a national scandal. Euclid Transmogrified: A National Scandal may be of interest to mathematics teachers, lecturers in mathematics, mathematical historians, lecturers in education, students of mathematical education, administrators of mathematical education, science administrators, science journalists and those educated in mathematics in Ireland, especially those born between 1954 and 2000. https: //sites.google.com/view/euclidtransmogrified1
Methods of Graph Decompositions
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Lexy and Kaylee's Advanced Nurikabe for Adults and Teens Volume Two
From the creators of Lexy and Kaylee's Canine Coloring Book for Children series now have put together an activity book for Adults and Teens. Inside there are 52 advanced 24x24 Nurikabe Puzzles in an easy to carry 6 x 9 format. Great for taking with you on plane and train rides or to sit at the beach or by the pool.Nurikabe is a logic puzzle that originated in Japan. The puzzle is named after a mythical creature from Japanese folklore, believed to create invisible walls to block travelers. Here's an overview of its history and how it has evolved: Origins and Development: The name "Nurikabe" is derived from a Japanese folklore creature that is said to appear as an invisible wall obstructing travelers' paths. This connection to the mythical creature adds a cultural layer to the puzzle's identity. The exact origins of the Nurikabe puzzle is not well-documented, but it is known to have been popularized by the Japanese puzzle company Nikoli. Nikoli has been instrumental in developing and spreading various types of logic puzzles, including Sudok. Nurikabe was first introduced in Nikoli's Puzzle magazine in the late 20th century. The puzzle quickly gained a following among puzzle enthusiasts in Japan and later internationally.Spread and Popularity: Like many other logic puzzles, Nurikabe became popular in Japan through Nikoli's publications. Japanese puzzle solvers appreciated its unique challenge and engaging nature. Nurikabe began to spread outside Japan in the early 21st century as puzzle enthusiasts and publishers in other countries discovered it. The rise of the internet and puzzle apps contributed significantly to its global popularity. Nurikabe is now available on various online puzzle platforms and mobile apps, allowing a global audience to enjoy the puzzle.Mechanics and Rules: Nurikabe is played on a rectangular grid, with some cells containing numbers. The goal is to shade specific cells to form a continuous "wall" while leaving the remaining cells as "islands."Cultural and Educational Impact: Nurikabe has a dedicated following among puzzle enthusiasts. It is often featured in puzzle magazines, websites, and competitions. The puzzle is also used in academic settings to teach logical reasoning and problem-solving skills. Its unique rules and requirements make it an excellent exercise in spatial awareness and deductive logic.Variations and Adaptations: Over time, different variations of Nurikabe have emerged, introducing new challenges and twists to the original rules. Some puzzles may have different grid shapes or additional constraints to increase difficulty. Nurikabe has also inspired hybrid puzzles that combine their elements with other logic puzzles, creating new and innovative challenges for solvers.Nurikabe is a logic puzzle deeply rooted in Japanese culture and folklore. It has grown in popularity both in Japan and internationally, thanks to its challenging nature and the efforts of puzzle publishers like Nikoli. Today, it continues to be a beloved puzzle enjoyed by many worldwide.
Modeling of biomechanical heat transfer in human physiology
This book explores the intricate connections between various disciplines such as anatomy, physiology, neurology, and the biomechanical aspects of heat transfer within the human body. It highlights the significant overlap between kinesiology, the systematic study of human movement, and biomechanics, particularly in analyzing movement patterns, enhancing physical performance, and addressing mechanical factors underlying injuries and diseases. The primary objectives include optimizing physical performance and understanding injury processes for prevention strategies. Biomechanics, as delineated in the book, comprises two principal sections: kinematics and kinetics. Kinematics involves the detailed description of motion, encompassing movement patterns and the sequencing of body segments that influence coordination and performance outcomes. In contrast, kinetics investigates the causes of motion, particularly the forces acting on the body. This distinction underscores kinetics' focus on force analysis, setting it apart from kinematics which primarily concerns itself with describing motion patterns.
Contributions to the Theory of Special Functions and Number Theory
The author has given a brief introduction of an all-time great Mathematician Srinivasa Ramanujan, the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including Mathematical analysis, Infinite series, Continued fractions, Number theory and Game theory.He has established new general theorems for the explicit evaluations of Ramanujan's remarkable product of theta function and their new explicit assessment.He has also established several new P - Q eta-function identities which were obtained, leading to several new modular relations for the Ramanujan-G繹llnitz-Gordon continued fraction.He has obtained a continued fraction of order 12 and evaluated several new identities analogous to the Rogers-Ramanujan continued fraction and Ramanujan's cubic continued fraction.He has derived some new modular equations of degree 5 for the ratios of Ramanujan's theta function and new modular relations for Ramanujan's parameters related to Rogers-Ramanujan's continued fraction were also established along with their explicit evaluations.
Some Studies on Theta Functions and Their Related Identities
The author has given a brief introduction of an all-time great Mathematician Srinivasa Ramanujan, the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including Mathematical analysis, Infinite series, Continued fractions, Number theory and Game theory.He has established several interesting and new explicit evaluations for newly defined parameters by using Ramanujan Weber class invariants, modular equations and mixed-modular equations.He has established several new explicit evaluations of Ramanujan's remarkable product of theta-function.He has established some new general theorems for explicit evaluations of the product of theta-function.He has derived several general formulas for explicit evaluations of Ramanujan's cubic continued fractions, reciprocity theorems, two formulas connecting V(q) and V(q3) and also established some explicit evaluations using the values of the remarkable product of theta-function.He has obtained a modular transformation formula for the theta-function.
Advanced Probability and Statistics
The chapters in this book deal with: Basic formulation of waveguide cavity resonator equations The reviews of basic statistical signal processing The Hartree-Fock equations
Evolutionary Optimization Algorithms
The text covers evolutionary optimizing algorithms with the help of MATLAB and Python programming in a comprehensive manner. It will be an ideal reference text for readers in diverse engineering fields including electrical, electronics and communication, computer science and mechanical engineering.
Fluid Waves
The book covers mathematical basis for fluid waves in science and engineering illustrating basis to undertake pertinent calculations in varied areas. It covers fundamentals of fluid dynamics including chapters explaining specialized applications. All concepts are supported by narrative examples, illustrations, and case studies.
Mathematical Methods for Operations Research Problems
This reprint of the Special Issue in the journal Mathematics presents research in the area of Operations Research. The subjects addressed in the 15 research papers cover a broad spectrum of subjects, such as machine learning, scheduling, timetabling, or graph theory.
Selected Topics in Statistical Inference
This book focuses exclusively on the domain of parametric inference and that, too, from a reader's perspective, i.e., covering only point estimation of parameter(s). It covers those topics in parametric inference which need clarity of exposure to students, researchers, and teachers alike; mere statements of theorems and proofs may not always reveal the inner beauty and significance of some aspects of inference. To ensure clarity, the book discusses the following topics at an advanced level-(1) sequential (unbiased) point estimation of 'p' and its functions; generalization to trinomial and tetranomial populations; (2) some aspects of the use of additional resources in finite population inference; (3) the concept of sufficiency vis-?-vis the notion of sufficient experiments and comparison of experiments; (4) estimation of the size of a finite population with special features; and (5) unbiased estimation of reliability in exponential samples and other settings. This book provides a platform for thought-provoking, creative, and challenging discussions on a variety of topics in statistical estimation theory, it is also ideal for research methodology course for statistics research scholars, and for clarification of basic ideas in topics discussed at basic/advanced levels.
Frontiers of Fractal Analysis
This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.
Multivariate Statistical Modeling in Engineering and Management
The book focuses on problem solving for practitioners and model building for academicians under multivariate situations. This book helps readers in understanding the issues, such as knowing variability, extracting patterns, building relationships, and making objective decisions.
High Dimensional Space to Formulate Marriage and Birth Functions
The reaction-diffusion system describes the fertility decline process, elaborating where and when fertility declines and analyzes how to slow down the fertility decline using Brittany as a testing ground. The model used suggests that our behaviors are not governed by our conscious wills but by surrounding environment.
Multi-Fractal Traffic and Anomaly Detection in Computer Communications
This book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks.
Compressible Flow with Applications to Engines, Shocks and Nozzles
This book is part of the series "Mathematics and Physics Applied to Science and Technology." The book presents the mathematical theory of partial differential equations. It includes applications to acoustic, elastic, water, electromagnetic and other waves, to the diffusion of heat, mass and electricity, and to their interactions.
Fuzzy Optimization Techniques in the Areas of Science and Management
This book helps to enhance the application of fuzzy logic optimization in the areas of science and engineering. It includes implementation and modeling paradigms such as path planning and routing design for different wireless networks, organization behavior strategies modeling, and so forth.
Select Topics in Signal Analysis
This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail.The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan's Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory.The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.
Predictive Analytics
Predictive analytics refers to making predictions about the future based on different parameters which are historical data, machine learning, and artificial intelligences. This book provides the most recent advances in the field along with case studies and real-world examples.
Mathematical Gnostics
The focus of the book will be concentrated to the step-by-step explanation of applications of the algorithms to real data which are met in daily practice by all data analysts, with particulr focus on chemcial engineering. The book will lead readers through all relevant tasks on one-dimensional, two-dimensional, and multi-dimensional data analysis.
Skew-Normal Model Theories and Their Applications
This book focuses on several skew-normal mixed effects models, and systematically explores the statistical inference theories, methods, and applications of parameters of interest. This book is of academic value, since it helps to establish a series of statistical inference theories and methods for skew-normal mixed effects models.
Robust Engineering Designs of Partial Differential Systems and Their Applications
This book focusses on partial differential systems (PDS) from an engineering perspective covering robust stabilization control, filter, and reference tracking design in signal processing, control, and biological systems.
Tilings in Hyperbolic Space in an Arbitrary Dimension
Of a special interest are tilings in hyperbolic n-space. The present work studies tilings in hyperbolic n-space of arbitrary dimension by polytopes. The best behaved tilings are the face-to-face tilings by convex polytopes. The main results of this publication are obtained for tilings (isohedral, non-isohedral, face-to-face, non- face-to- face) in the hyperbolic n-space of arbitrary dimension for any n, (n >= 2) by compact and non-compact polytopes and we describe their discrete isometry groups and properties. Torsion free groups are especially important.
Quantitative Literacy Through Games and Gambling
This book was developed to address a need. Quantitative Literacy courses have been established in the mathematics curriculum for decades now. The students in these courses typically dislike and fear mathematics, and the result is often a class populated by many students that are unmotivated and uninterested in the material.
Euclid Transmogrified
This book tells the extraordinary story of how in the mid twentieth century, in a well-developed European country, a mathematically solid system of geometry was altered to such an extent that more than one million students were taught foundationally flawed geometry over more than a quarter of a century. The almost unbelievable situation came about in Ireland in the wake of early postcolonial developments that gave rise to an impressionable and unqualified civil service in a position of power over a nation's educational development. This is a multifaceted tale of a perfect storm within mathematics development in Ireland whose result was so destructive that its ramifications continue to be felt into the twenty-first century, forty years after a report of a Royal Irish Academy commission of professors of mathematics described the matter as a national scandal. Euclid Transmogrified: A National Scandal may be of interest to mathematics teachers, lecturers in mathematics, mathematical historians, lecturers in education, students of mathematical education, administrators of mathematical education, science administrators, science journalists and those educated in mathematics in Ireland, especially those born between 1954 and 2000. https: //sites.google.com/view/euclidtransmogrified1
Lectures on Differential Geometry
This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
Lectures on Differential Geometry
This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
The Extension of Fixed Point Theorems in Various b-Metric Spaces
This book entitled "The Extension of Fixed Point Theorems in Various b-Metric Spaces" is divided into following 8 chapters Chapter - I: The first chapter is an introductory part of our research work which includes the brief introduction of our topic.Chapter - II: Our second chapter titled as "Fixed Point Results for Various Contractions in b-Metric Spaces." Chapter - III: The chapter third having the title "Common Fixed Point Theorem in b-Metric Spaces for Compatible Mapping of Type (A)"Chapter - IV: The fourth chapter titled as, "Common Fixed Point Theorems for Two Self Compatible Mapping Satisfying an Implicit Relation of b-Metric Spaces." Chapter - V: The Chapter five titled as, "Existence of Fixed Point Theorem of Integral Type Contractions in b-Metric Spaces". Chapter - VI: Chapter six titled as "Coupled Coincidence Fixed Point Theorem in Two Weakly Compatible Mapping in b-Metric Spaces ".Chapter - VII: The seventh chapter titled as "Coincidence and Common Fixed Point Theorem using Compatible Mapping of Type (P) in Intuitionistic Fuzzy b-Metric Spaces" Chapter - VIII: Our last chapter titled as "Some Generalized Theorems of q-Contraction in Symmetric Nb-Fuzzy Metric Spaces".
Series and functional series associated with harmonic numbers
The book has five chapters. Chapter 1 gives the basic knowledge needed to understand the contents of this book. Chapter 2 describes several interesting formulas related to harmonic numbers. In Chapter 3, the series problems involving several kinds of harmonics in the general terms are shown together with the solution to these problems can be found in mathematical references dealing with difficult problems. Chapter 4 presents the problem of multiple series involving several kinds of harmonics in general terms with solutions. Chapter 5 presents interesting challenges and open problems involving harmonic numbers in general terms.Since we have raised a number of interesting problems and various technical problems to solve them, this book will be a good reference not only for those specializing in mathematics, but also for those specializing in physics or other natural sciences.
Handbook on Affective Interest in Mathematics
In Nigeria, mathematics holds a pivotal role as a mandatory subject in both primary and secondary education. Mathematics, as an academic discipline, delves into the realms of numbers, shapes, patterns, and their intricate relationships. It equips learners with the vital ability to communicate using symbols and logical reasoning, fostering logical thinking, precision, and spatial awareness (Arhin & Yanney, 2020). Mathematics is regarded as one of the core prime instruments for understanding and exploring the scientific, technological, economic, and social and information world. Science, Technology, Engineering and Mathematics (STEM). Mathematics education is considered as a precious way to make the education system keep up with the developments and to meet the expectations of 21st century skills (Kazu & Cemre, 2021; Ghazali, & Yusof, 2022).
Digital resources in mathematics teaching
This book shows the work of designing and then implementing a Virtual Teaching and Learning Space (EVEA) that allows students to learn mathematical knowledge through the appropriate use of different technological resources. This proposal is aimed at 4th year students of the Oriented Cycle and is intended to teach with technology, through an easily accessible platform such as Classroom, organizing knowledge by topics and providing interactive resources where students, through ICT and virtual classes, are expected to acquire autonomy and commitment in their work, giving account of the concepts learned through the different activities proposed. In this way, students are expected to play an active role in their learning process, the teacher being a mediator of knowledge and a moderator in the proposed classes. We seek to design pedagogical actions by means of technological resources that allow the acquisition of minimum knowledge in conjunction with the students' interests, promoting activities that allow the construction of significant knowledge.
Topics in Contemporary Mathematical Analysis and Applications
This book covers contemporary topics of mathematical analysis in the form of new ideas, methods, techniques, algorithms, as well as applications of tools in various engineering and scientific fields. It discusses various problems and offers ways to create models to solve those problems.
Mathematical Modeling and Computation of Real-Time Problems
This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems.
G Families of Probability Distributions
Statistical distributions are important tools to model the characteristics of data sets observed in different applied sciences such as engineering, medicine, and finance, among others. This book will help future and current researchers in the field of G families of probability distributions.
Textile Engineering
Overall theme of the book is analysis and interpretation of the textile data for improving the quality of textile process and product using various statistical techniques. This volume covers statistical techniques, design of experiments and stochastic modeling in textile engineering supported by practical examples and end-of-chapter exercises.
Recent Advances in Time Series Forecasting
Future predictions are always a topic of interest. Precise estimates are crucial in many activities as forecasting errors can lead to significant financial loss. The sequential analysis of data and information gathered from past to present is called time series analysis. This book covers the recent advancements in time series forecasting.
Mathematical Modeling and Soft Computing in Epidemiology
This book describes the use of different Mathematical Modeling and Soft Computing techniques used in Epidemiology for experiential research in projects such as how infectious diseases progress to show the likely outcome of an epidemic, and to contribute to public health interventions.
Finitely Presented Groups
This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Visualisation and Epistemological Access to Mathematics Education in Southern Africa
This book demonstrates that using visualisation processes in mathematics education can help to enhance teaching and learning and bridge the inequality gap that exists between well-resourced and under-resourced schools in Southern Africa. Drawing on classroom research conducted in the Southern African region, it examines how epistemological access in a context of gross inequality can be constructively addressed by providing research-based solutions and recommendations. The book outlines the visualisation process as an integral but often overlooked process of mathematics teaching and learning. It goes beyond the traditional understanding of visualisation processes such as picture forming and using tools and considers visualisation processes that are semiotic in nature and includes actions such as gestures in combination with language. It adds value to the visualisation in mathematics education research discourse and deliberation in Africa.With a unique focus on Southern Africa and open avenues for further research and collaboration in the region, it will be a highly relevant reading for researchers, academics and post-graduate students of mathematics education, comparative education and social justice education.
Homogeneous Projective Varieties and Invariant Theory
The general theme of this book is the interplay between the geometry of homogeneous complex projective varieties, the structure and representation theory of their symmetry groups, and more specifically, invariant theory related to subgroups of the symmetry groups. The framework is based on the Borel-Weil theorem and the Geometric Invariant Theory of Hilbert-Mumford. The setting is classical and the basic objects of interest are widely studied. A source of unanswered questions lies in the notorious nonconstructiveness of Hilbert's theorem asserting the existence of a finite generating set for the ring of invariants in the homogeneous coordinate ring of a complex projective variety endowed with a reductive group action. The goal of this work is to contribute to the effort for further development of the structure theory of reductive Lie groups, aiming to bound and explore the variation of certain parameters related to generating sets of invariants. Particular attention is given to the geometry of unstable loci - the zero-loci of the invariants of positive degree.
Logic as a Tool
This textbook, written in a concise yet user-friendly style, will guide the reader in understanding and mastering the use of classical logic as a tool for performing logically correct reasoning. It offers a systematic and precise exposition of classical logic on both propositional and first-order level with many examples and exercises and only the necessary minimum of theory. Most of the exercises are provided with answers or detailed solutions.The book explains the grammar, semantics, and use of classical logical languages and teaches the reader how to grasp the meaning and translate the formulae of classical logic to and from natural language. It illustrates with many detailed examples the use of the most popular deductive systems - axiomatic systems, semantic tableaux, natural deduction, and resolution - for formalizing and automating logical reasoning and provides the reader with the technical skills needed for practical derivations. Systematic guidelines are offered on how to carry out logically correct and well-structured reasoning using the proof strategies and techniques that these deductive systems employ.The book is accompanied with a set of detailed slides available online and can be used as a textbook for introductory or intermediate courses in classical logic for students in mathematics, computer science, philosophy, or related disciplines, as well as for self-study.
Pulling Rabbits Out of Hats
Pulling Rabbits Out of Hats: Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences focuses on those assumptions made during applied mathematical modeling in which the phenomenological data and the model predictions are self-consistent.
Discrete Stochastic Models and Applications for Reliability Engineering and Statistical Quality Control
This book provides real-life examples and illustrations of models in reliability engineering and statistical quality control and establishes a connection between the theoretical framework and their engineering applications.
Ordinary Differential Equations. Exercises and Problems
This book presents a variety of methods of analytic solution of ordinary differential equations and features a wealth of examples, both solved in detail and proposed. The goal of this work is to give a broad training in techniques of solution of equations and problems involving differential equations, which are important both in mathematics and applications.The book is aimed primarily at undergraduate students of mathematics, natural sciences and engineering, who need a solid knowledge of differential equations in their professional activities. The text contains many examples of scientific problems solved by constructing models involving differential equations, which introduce students to a number of interesting aspects of applications.The proposed material can also be useful for professors and instructors of differential equations courses, since the text contains an exposition of all the principal analytic techniques usually studied in undergraduate programs, which are illustrated with numerous examples. In this way, teachers/instructors can use this book both to teach classes and to administer exams/tests on the studied subjects.
G繹del's Incompleteness Theorems
In 1931, the mysterious-sounding article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" shook the mathematical world. In this article, Kurt G繹del proved two incompleteness theorems that have fundamentally changed our view of mathematics. G繹del's theorems manifest that the concept of truth and the concept of provability cannot coincide. Since their discovery, the incompleteness theorems have attracted much attention, and a flood of articles and books have been devoted to their striking consequences. For good reasons, however, hardly any work deals with G繹del's article in its original form: His complex lines of thought described with meticulous precision, the many definitions and theorems, and the now largely outdated notation turn G繹del's historical masterpiece into a difficult read. This book explores G繹del's original proof in detail. All individual steps are carefully explained and illustrated with numerous examples. However, this book is more than just an annotated version of the historical article, as the proper understanding of G繹del's work requires a solid grasp of history. Thus, numerous excursions take the reader back to the beginning of the twentieth century. It was the time when mathematics experienced one of its greatest crises, when type theory and axiomatic set theory were taking shape, and Hilbert's formalistic logic and Brouwer's intuitionistic mathematics were openly confronting each other. This book is the revised translation of the second edition of the author's German language book "Die G繹del'schen Unvollst瓣ndigkeitss瓣tze".
Statistics of Extremes and Records in Random Sequences
Rare events such as earthquakes, tsunamis, and floods fortunately do not occur every day, but when they do, their effects are devastating. Such rare events are particularly important in understanding and characterizing global warming and climate changes. In addition to natural catastrophes, rare events such as big financial crashes also play a significant role in the economy. In the absence of predictive models, the best way forward is to analyse the statistics of these extreme events and draw conclusions about the probability of their occurrences. Extreme value statistics (EVS) and the statistics of records in a random sequence are examples of a truly interdisciplinary topic, spanning from statistics and mathematics on one side to physics of disordered systems on the other. They have tremendous importance and practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, and random matrices. Statistics and mathematical literature have explored the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics, in particular in disordered systems. This has led to a plethora of activities, both in the statistical physics and in the mathematics communities over the last few decades. This book develops the theory of rare events, both for the classical uncorrelated as well as for correlated sequences, in terms of simple models and examples. Statistics of Extremes and Records in Random Sequences is a pedagogical book with examples illustrating the basic tools and techniques that are essential to a student starting to work in this interesting and rapidly developing field.
Mesure et int矇gration. Cours et exercices corrig矇s.
Ce livre est un ouvrage, principalement destin矇 aux 矇tudiants de troisi癡me ann矇e LMD math矇matiques. Le contenu de ce livre, correspond au programme de la mati癡re Mesure et Int矇gration enseign矇 en troisi癡me ann矇e. Le livre s'articule autour de quatre chapitres. A la fin de chaque chapitre on pourra trouver une s矇rie d'exercices. A la fin de ce manuscrit, nous avons donn矇 quelques bibliographies de base classiques. Nous esp矇rons que ce livre r矇ponde aux attentes des 矇tudiants et qu'il les aidera ? r矇ussir.Le programme du cours est le suivant.1. Tribus et mesures.2. Fonctions mesurables, variables al矇atoires.3. Fonctions int矇grables.4. Produit d'espaces mesur矇s.
