Teaching and Research in Mathematics
The author's goal is to help the transition from graduate studies and make it less diffcult and time-consuming. Part I covers techniques on teaching and conducting research and in Part II, the author has introduced some modern research in mathematics in various industries.
Computational Framework for the Finite Element Method in Matlab(r) and Python
This book aims to provide a programming framework for coding linear FEM using matrix-based MATLAB language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible.
Functional Analysis
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
Advances in Architectural Acoustics
Satisfactory acoustics is crucial for the ability of spaces such as auditoriums and lecture rooms to perform their primary function. The acoustics of dwellings and offices greatly affects the quality of our life, since we are all consciously or subconsciously aware of the sounds to which we are daily subjected. Architectural acoustics, which encompasses room and building acoustics, is the scientific field that deals with these topics and can be defined as the study of generation, propagation, and effects of sound in enclosures. Modeling techniques, as well as related acoustic theories for accurately calculating the sound field, have been the center of many major new developments. In addition, the image conveyed by a purely physical description of sound would be incomplete without regarding human perception; hence, the interrelation between objective stimuli and subjective sensations is a field of important investigations.A holistic approach in terms of research and practice is the optimum way for solving the perplexing problems which arise in the design or refurbishment of spaces, since current trends in contemporary architecture, such as transparency, openness, and preference for bare sound-reflecting surfaces are continuing pushing the very limits of functional acoustics. All the advances in architectural acoustics gathered in this Special Issue, we hope that inspire researchers and acousticians to explore new directions in this age of scientific convergence.
Complex Variable Functions
The internationalization of mathematics education has become an inevitable trend, and bilingual education is the booster to realize the internationalization of mathematics education. For the freshmen majoring in science and engineering, it is not realistic to choose the first-year mathematics basic courses such as advanced mathematics and linear algebra as the bilingual teaching object; it is not the best choice for the bilingual teaching object compared with the senior mathematics courses, such as Function of Real Variables, Functional Analysis and Topology of Point Set, which are more difficult; "Complex Variable Functions" is a relatively easy mathematics course, which is the extension and supplement of higher mathematics. This book is divided into nine chapters, which systematically introduces the basic theory and methods of complex variable function, including complex number and complex variable function, analytic function, integral of complex variable function, power series representation of analytic function, Laurent expansion of analytic function and its isolated singularities, residue theory and its application, conformal mappings. This book is suitable for teachers and students of science and engineering major in colleges and universities all over the country, and can also be read and referenced by engineering and technical personnel.
Advances in Artificial Intelligence
The present book contains all the articles accepted and published in the Special Issue "Advances in Artificial Intelligence: Models, Optimization, and Machine Learning" of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of artificial intelligence and its subfields. These topics include, among others, deep learning and classic machine learning algorithms, neural modelling, architectures and learning algorithms, biologically inspired optimization algorithms, algorithms for autonomous driving, probabilistic models and Bayesian reasoning, intelligent agents and multiagent systems. We hope that the scientific results presented in this book will serve as valuable sources of documentation and inspiration for anyone willing to pursue research in artificial intelligence, machine learning and their widespread applications.
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions offers several topics from different mathematical disciplines and shows how closely they are related. The purpose of this book is to direct the attention of readers who have an interest in and talent for mathematics to engaging and thought-provoking problems that should help them change their ways of thinking, entice further exploration and possibly lead to independent research and projects in mathematics. In spite of the many challenging problems, most solutions require no more than a basic knowledge covered in a high-school math curriculum. To shed new light on a deeper appreciation for mathematical relationships, the problems are selected to demonstrate techniques involving a variety of mathematical ideas. Included are some interesting applications of trigonometry, vector algebra and Cartesian coordinate system techniques, and geometrical constructions and inversion in solving mechanical engineering problems and in studying models explaining non-Euclidean geometries. This book is primarily directed at secondary school teachers and college professors. It will be useful in teaching mathematical reasoning because it emphasizes how to teach students to think creatively and strategically and how to make connections between math disciplines. The text also can be used as a resource for preparing for mathematics Olympiads. In addition, it is aimed at all readers who want to study mathematics, gain deeper understanding and enhance their problem-solving abilities. Readers will find fresh ideas and topics offering unexpected insights, new skills to expand their horizons and an appreciation for the beauty of mathematics.
Algebraic Number Theory for Beginners
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.
Algebraic Number Theory for Beginners
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.
An Introduction to Statistical Learning
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform.Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.This Second Edition features new chapters on deep learning, survival analysis, and multiple testing, as well as expanded treatments of na簿ve Bayes, generalized linear models, Bayesian additive regression trees, and matrix completion. R code has been updated throughout to ensure compatibility.
Miniaturized Transistors, Volume II
In this book, we aim to address the ever-advancing progress in microelectronic device scaling. Complementary Metal-Oxide-Semiconductor (CMOS) devices continue to endure miniaturization, irrespective of the seeming physical limitations, helped by advancing fabrication techniques. We observe that miniaturization does not always refer to the latest technology node for digital transistors. Rather, by applying novel materials and device geometries, a significant reduction in the size of microelectronic devices for a broad set of applications can be achieved. The achievements made in the scaling of devices for applications beyond digital logic (e.g., high power, optoelectronics, and sensors) are taking the forefront in microelectronic miniaturization. Furthermore, all these achievements are assisted by improvements in the simulation and modeling of the involved materials and device structures. In particular, process and device technology computer-aided design (TCAD) has become indispensable in the design cycle of novel devices and technologies.It is our sincere hope that the results provided in this Special Issue prove useful to scientists and engineers who find themselves at the forefront of this rapidly evolving and broadening field. Now, more than ever, it is essential to look for solutions to find the next disrupting technologies which will allow for transistor miniaturization well beyond silicon's physical limits and the current state-of-the-art. This requires a broad attack, including studies of novel and innovative designs as well as emerging materials which are becoming more application-specific than ever before.
Teaching the Essentials of Arithmetic (Yesterday's Classics)
A thoughtful discussion of best practices for teaching arithmetic processes and the order in which to teach them. The author urges that methods adopted early on smooth the way for more advanced calculations taught later. Lots of food for thought for home educators as well as classroom teachers.
Pentagons and Pentagrams
A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon's wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist's discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon's impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost's superb illustrations provide sumptuous visual context, and the book's puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.
Introduction to Algebra and Geometry
Introduction to Algebra and Geometry introduces students to the concepts in algebraic relationships that can be applied to further study of math at the college level. Intended for college-level developmental math students, this book gives student the tools to understand and apply algebra and geometry to the fields of engineering, science, welding, diesel mechanics, and more. This book is a reprint of chapters from Douglas Gardner's Applied Algebra I and Applied Algebra II, packaged in a more condensed format.
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Structural Equation Modelling with Partial Least Squares Using Stata and R
This book presents PLS-SEM as a useful practical statistical toolbox that can be used for estimating many different types of research models. In so doing, the authors provide the necessary technical prerequisites and theoretical treatment of various aspects of PLS-SEM prior to practical applications.
Medical Risk Prediction Models
The backbone of medical decision making is prediction. Statistical prediction models can help in medical decision making. This book takes the viewpoint of the single patient and asks what does it mean that a risk prediction model performs well for a single individual?
Bayesian Analysis of Infectious Diseases
Bayesian Analysis of Infectious Diseases -COVID-19 and Beyond shows how the Bayesian approach can be used to analyze the evolutionary behavior of infectious diseases, including the coronavirus pandemic.
Real-World Evidence in Drug Development and Evaluation
This book concerns use of real world data (RWD) and real world evidence (RWE) to aid drug development across product cycle. RWD are healthcare data that are collected outside the constraints of conventual controlled randomized trials (CRTs); whereas RWE is the knowledge derived from aggregation and analysis of RWD.
Convolution-Like Structures, Differential Operators and Diffusion Processes
T​his book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms.The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.
Seduced by Mathematics: The Enduring Fascination of Mathematics
Seduction is not just an end result, but a process - and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people - not just those for whom math plays a key role in their day-to-day lives - have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," - because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.This book contains material capable of being appreciated by students in elementary school - as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.
Seduced by Mathematics: The Enduring Fascination of Mathematics
Seduction is not just an end result, but a process - and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people - not just those for whom math plays a key role in their day-to-day lives - have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," - because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.This book contains material capable of being appreciated by students in elementary school - as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.
Jerome Cardan
This book has been considered important throughout the human history, and so that this work is never forgotten we have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies and hence the text is clear and readable.
Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting
In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0 (t real) where the operators A_t periodically depend on t and the function u takes values in a UMD Banach space X.We impose a suitable condition on the operator family (A_t) and their common domain, in particular a decay condition for certain resolvents, to obtain the central result that all exponentially bounded solutions can be described as a superposition of a fixed family of Floquet solutions.
Simultaneous Tracking and Shape Estimation of Extended Objects
This work is concerned with the simultaneous tracking and shape estimation of a mobile extended object based on noisy sensor measurements. Novel methods are developed for coping with the following two main challenges: i) The computational complexity due to the nonlinearity and high-dimensionality of the problem, and ii) the lack of statistical knowledge about possible measurement sources on the extended object.
Polynomials, Dynamics, and Choice
This book is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes.
Veech Groups and Translation Coverings
A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
Backseat Driver
Buying the safest car for your family shouldn't be up for debate. Yet for decades, car safety advocates, manufacturers, and lawmakers in the United States have clashed over whether to make automobiles safer. All sides armed themselves with data in the hopes of winning the great car safety debates. In this way, crash statistics and the analysts who studied them made history. But data were always in the backseat, merely supporting different points of view. That is, until now. With car safety, it's the value we place on every human life that counts. Automobile safety expert Dr. Norma Faris Hubele delivers a lively discussion of the role data play in protecting you and your family on the road. You'll gain a greater appreciation for how: A World War I pilot's near-death experience birthed the U.S. car safety movement Data from real car crashes helped create the first vehicle safety standards A shift toward fuel-efficient cars affected fatality risk in the 1970s-1980s versus now Vehicle size has changed, and the problems that creates for you and others sharing the road Car safety rating systems, even when limited, empower consumers and motivate manufacturers Federal regulators decide whether to issue a safety recall on your vehicle Data's role is evolving with the advent of driver-assist and self-driving technologies Further information can be found on the book's website: www.TheAutoProfessor.com/book [US only].
Invariants of complex and p-adic origami-curves
Origamis (also known as square-tiled surfaces) are Riemann surfaces which are constructed by glueing together finitely many unit squares. By varying the complex structure of these squares one obtains easily accessible examples of Teichm羹ller curves in the moduli space of Riemann surfaces.Different Teichm羹ller curves can be distinguished by several invariants, which are explicitly computed. The results are then compared to a p-adic analogue where Riemann surfaces are replaced by Mumford curves.
Discrete Time Analysis of Consolidated Transport Processes
The objective of this work is to develop models for the analysis of consolidated transport processes. With the discrete time queuing models developed for inventory and vehicle consolidation, in particular milkrun systems, a detailed performance evaluation of different design scenarios can be conducted faster than with simulation. Moreover, it is demonstrated how the models can be connected with each other in form of a network analysis, in order to analyze hub-and-spoke networks.
Strategic power plant investment planning under fuel and carbon price uncertainty
The profitability of power plant investments depends strongly on uncertain fuel and carbon prices. In this doctoral thesis, we combine fundamental electricity market models with stochastic dynamic programming to evaluate power plant investments under uncertainty. The application of interpolation-based stochastic dynamic programming and approximate dynamic programming allows us to consider a greater variety of stochastic fuel and carbon price scenarios compared to other approaches.
Backseat Driver
Car safety advocates, manufacturers, and lawmakers have clashed over whether to make automobiles safer. All sides armed themselves with data in the hopes of winning the great car safety debates.In this way, crash statistics and the analysts who studied them made history.
The factorization method for inverse scattering from periodic inhomogeneous media
This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.
Boundary Elements and other Mesh Reduction Methods XLV
Advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences are reported in the papers that form this volume.As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process.The maturity of BEM since 1978 has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general.The included papers originate from the 45th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) and describe theoretical developments and new formulations, helping to expand the range of applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments.
Discrete Time Analysis of Multi-Server Queueing Systems in Material Handling and Service
In this doctoral thesis, performance parameters of multi-server queueing systems are estimated under general stochastic assumptions. We present an exact calculation method for the discrete time distribution of the number of customers in the queueing system at the arrival moment of an arbitrary customer. The waiting time distribution and the sojourn time distribution are estimated exactly, as well. For the calculation of the inter departure time distribution, we present an approximation method.
Geometry and Discrete Mathematics
In the two-volume set 'A Selection of Highlights' we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis and enhanced the chapter on Graph Theory for solving further classical problems such as the Traveling Salesman Problem.
On Length Spectra of Lattices
The aim of this work is to study Schmutz Schaller's conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume.Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.
Dynamic Time Series Models Using R-Inla
This Book is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework.
Applied Mathematical Problems in Geophysics
This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes.This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.
Fractional Differential Equations
This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.
Smooth Functions and Maps
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor's formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor's formula in a nonconvex area (Chapter I, 禮8), Whitney's extension theorem for smooth function (Chapter I, 禮11) and some of its corollaries, global diffeomorphism theorem (Chapter II, 禮5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
Coalgebraic Methods in Computer Science
This book constitutes the thoroughly refereed post-conference proceedings of the 16th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2022, colocated with ETAPS 2022, held in Munich, Germany, in April 2022. The 9 revised full papers were carefully reviewed and selected from 12 submissions. The papers cover a wide range of topics in the theory, logics, and applications of coalgebras.
AI Age Knowledge
Peter Chew theorem is AI age knowledge because the theorem can help convert all Quadratic Surds . In addition, the theorem can help convert easier and faster than current method. Applying Peter Chew theorem in AI age calculator, PCET calculator can help the calculator solve all problem of Quadratic Surds. This will cause students to increase their interest in using PCET calculator and increase the promotion of effective mathematics learning. When the future epidemics such as Covid-19 occur in the future, it can effectively help mathematics teaching, especially for students studying at home. Presenting numbers in surd form is quite common in science and engineering especially where a calculator is either not allowed or unavailable, and the calculations to be undertaken involve irrational values. Therefore, the application of Peter Chew theorem in Mechanical Engineering can make the teaching and learning of Mechanical Engineering easier. About the Author: Peter Chew is Mathematician, Inventor and Biochemist from National University Of Malaysia (UKM). Global issue analyst and Reviewer for Eliva Press. Peter Chew also is CEO PCET, Malaysia, PCET is a long research associate of IMRF (International Multidisciplinary Research Foundation), Institute of higher Education & Research with its HQ at India and Academic Chapters all over the world.Peter Chew obtain the Certificate of appreciation from Malaysian Health Minister Datuk Seri Dr. Adam Baba(2021), PSB Singapore. National QC Convention STAR AWARD (2 STAR), IMRF Outstanding Analyst Award 2019, IMFR Inventor Award 2020, the Best Presentation Award ICEMP 2019 in Ningbo, China . Invited speaker at the ATCM 2019, China. iCon-MESSSH'20 and iCon-MESSSH'21 Special Talk Speaker the 100th CONF of the IMRF, Goa, India. Keynote Speaker of the ICCEMS 2019 and the ICPCE 2020.
The Art of Mathematics - Take Two
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.
Gradient Descent, Stochastic Optimization, and Other Tales
The goal of this book is to debunk and dispel the magic behind the black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This book doesn't shy away from addressing both the formal and informal aspects of gradient descent and stochastic optimization methods. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these algorithms.Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize machine learning tasks. Its stochastic version receives attention in recent years, and this is particularly true for optimizing deep neural networks. In deep neural networks, the gradient followed by a single sample or a batch of samples is employed to save computational resources and escape from saddle points. In 1951, Robbins and Monro published A stochastic approximation method, one of the first modern treatments on stochastic optimization that estimates local gradients with a new batch of samples. And now, stochastic optimization has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this article is to give a self-contained introduction to concepts and mathematical tools in gradient descent and stochastic optimization.
Approximation Theory and Analytic Inequalities
This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss-Jacobi and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam's stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Detection and characterization of inclusions in impedance tomography
The topic of this work are two further developments of the Factorization method for electrical impedance tomography.We present a modification of this method that is capable of detecting mixed inclusions, i.e. both inclusions with a higher as well as inclusions with a lower conductivity than the background medium. In addition, we derive a new method to compute the conductivity inside inclusions after they have been localized.
