The Foundations of Real Analysis
A Fundamental Course with 347 Exercises and Detailed Solutions 11/01/2015 |
This textbook covers the subject of real analysis from the fundamentals up through beginning graduate level. It is appropriate as an introductory course text or a review text for graduate qualifying examinations. Some special features of the text include a thorough discussion of transcendental functions such as trigonometric, logarithmic, and exponential from power series expansions, deducing all important functional properties from the series definitions. The text is written in a user-friendly manner, and includes full solutions to all assigned exercises throughout the text. |
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Geometry by Construction
Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries 02/19/2015 |
College geometry students, professors interested in undergraduate research and secondary geometry teachers will find three rich environments in this textbook. The first chapter contains many of the standards of Euclidean college geometry. The second and third chapters introduce non-Euclidean models where some Euclidean rules hold and others do not. With emphases on constructions and proofs, the reader is encouraged to create the objects under investigation and verify the results with reasoning. Since both models of “bent” spaces exist in Euclidean geometry, the reader gains facility with Euclidean moves through the whole book, even while exploring non-Euclidean spaces. The book itself is meant to be unpacked, expanded and taken further, just like the problems it contains. Geometry b... |
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Super Edge-Antimagic Graphs
A Wealth of Problems and Some Solutions 10/15/2008 |
Graph theory, and graph labeling in particular, are fast-growing research areas in mathematics. New results are constantly being discovered and published at a rapidly increasing rate due to the enormous number of open problems and conjectures in the field. This book deals mainly with the super edge-antimagic branch of graph labeling. It is written for specialists, but could be read also by postgraduate or undergraduate students with high school knowledge of mathematics and a vibrant interest in problem-solving. |
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08/31/2007 |
This is a course in boundary element methods for the absolute beginners. Basic concepts are carefully explained through the use of progressively more complicated boundary value problems in engineering and physical sciences. The readers are assumed to have prior basic knowledge of vector calculus (covering topics such as line, surface and volume integrals and the various integral theorems), ordinary and partial differential equations, complex variables, and computer programming. |
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A Brief Course in Linear Algebra
Matrices and Matrix Equations for Undergraduate Students in Applied Mathematics, Science and Engineering 06/15/2019 |
This book contains a brief course in elementary linear algebra with emphasis on solving systems of linear algebraic and ordinary differential equations. It is written for undergraduate students in the disciplines of applied mathematics, science and engineering. Topics covered include basics of matrices and vectors, systems of linear algebraic equations, matrix inverse, matrix determinant, eigenvalues and eigenvectors, matrix diagonalization, and systems of first order linear ordinary differential equations. The connections between the topics are carefully elucidated. Derivations or proofs are given in detail for all the main results in the book. Basic knowledge of the arithmetic of complex numbers and exposure to elementary functions and calculus are assumed. Problems are set at the end of... |
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04/01/2017 |
The Math Handbook has been developed for students with Dyscalculia and others who are struggling with mathematics. The book is based upon the Singapore Primary Mathematics curriculum, as well as the International Math curriculum. More than twenty topics are covered and explained step by step through visual representation to convey mathematical concepts. It has been specially developed for: • Students who have been diagnosed with Dyscalculia; other terms may include Mathematics Learning Disability, or Mathematics Disorder • Students who have been diagnosed with Dyslexia; as according to research more than fifty percent of those experience difficulties with mathematics. Some students may have Dyslexia and Dyscalculia as co-existing disorders • Students diagnosed with ADHD; as the... |
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Differential Inclusions in Modeling and Simulation
Interdisciplinary Applications, Reachable Sets, Uncertainty Treatment for Educators and Researchers of Computer Modeling and Simulation 12/01/2019 |
The purpose of this book is to reach a circle of readers in the field of modeling and simulation, and similar. The examples and applications are multidisciplinary because of the multidisciplinary nature of modeling and simulation (MS). The book is not aimed for mathematicians, though some theoretical issues are also included. One of the aims of the book is to call into question a common paradigm that prevails among MS specialists telling that everything in the real world what is continuous in time, can be described by the ordinary or partial differential equations (ODEs, PDEs). My point is that this is not exactly true. So, we should look for a wider set of modeling tools. Differential inclusions (DIs) are used as an generalization of the ODE models.An important topic of the book that appe... |
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How to Solve Large Linear Systems
Using a Stable Cybernetic Approach for Non-Cumulative Computation, Avoiding Underflow and Overflow, with Unconditional and Uniform Convergence 12/15/2019 |
Solving the linear equation system n x n can also be a problem for a computer, even when the number of equations and unknowns is relatively small (a few hundred). All existing methods are burdened by at least one of the following problems: 1) Complexity of computation expressed through the number of operations required to be done to obtaining solution; 2) Unrestricted growth of the size of the intermediate result, which causes overflow and underflow problems; 3) Changing the value of some coefficients in the input system, which causes the instability of the solution; 4) Require certain conditions for convergence, etc.In this paper an approximate and exact methods for solving a system of linear equations with an arbitrary number of equations and the same number of unknowns is presented. Al... |
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One-Sheet-A-Day Math Drills
Grade 2 Subtraction - 200 Worksheets (Book 4 of 24) 01/15/2018 |
This One-Sheet-A-Day math drill workbook is for 2nd grade students who want extra practice with two numbers, two digits subtraction. It contains 200 math practice sheets, one for each school day of the year. Upon completion, the student will be more competent in 2nd grade mathematics and ready to proceed with more difficult exercises. Unlike other math drill books, this is one of 24 workbooks created to establish a daily routine for each student to practice on their own from grades 1 through 7. It is specifically designed to gradually increase mathematic ability with the least amount of stress for both parent and student. Kids need to practice at home to support what they are learning in school, but finding resources to help with that goal can be daunting. It takes a lot of time searching... |
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One-Sheet-A-Day Math Drills
Grade 3 Addition - 200 Worksheets (Book 5 of 24) 01/15/2018 |
This One-Sheet-A-Day math drill workbook is for 3rd grade students who want extra practice with two numbers, three digits addition. It contains 200 math practice sheets, one for each school day of the year. Upon completion, the student will be more competent in 3rd grade mathematics and ready to proceed with more difficult exercises. Unlike other math drill books, this is one of 24 workbooks created to establish a daily routine for each student to practice on their own from grades 1 through 7. It is specifically designed to gradually increase mathematic ability with the least amount of stress for both parent and student. Kids need to practice at home to support what they are learning in school, but finding resources to help with that goal can be daunting. It takes a lot of time searching ... |
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Idolatry and Infinity
Of Art, Math, and God 08/11/2014 |
Some unwritten stories only exist in fragments. In this book, for the first time, the histories of the injunction against idolatry and the dread of infinity are uniquely woven into one. The spectre of idolatry has haunted the three Western religions since the biblical prohibition. The story of iconoclasm runs from ancient times, where Jews largely ignored the ban on images, through the iconoclastic episodes in Islam and Christianity, and into modern times during the French Revolution. A perhaps surprising thesis of this book is that a conceptual and secular form of iconoclasm continued as the revulsion of illusionism in Modern Art. More recently it flared-up in the dynamiting of two large statues of the Buddha by the Taliban in Afghanistan in 2001. The phobia of infinity arose from P... |
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Finding the Real Odds
Attrition and Time-to-Degree in the FSU College of Criminology and Criminal Justice 04/09/2009 |
Attrition and time-to-degree issues remain poorly understood in academia, and almost completely unexplored in criminology and criminal justice. Loss rates of fifty percent or more are common in the social sciences, while the success rates for criminal justice are unknown for most schools. This study attempts to investigate completion levels at the Florida State University (FSU) College of Criminology and Criminal Justice, using descriptive and inferential techniques, survival analysis, and questionnaires. Problems with data collection impeded analysis of even basic statistical operations, resulting in the exclusion of some independent variables due to unavailability of readily obtainable information. Both the Master's and Ph.D. programs had similar attrition rates, with nearly two-thirds o... |
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Some Recent Developments in Statistical Theory and Applications
Selected Proceedings of the International Conference on Recent Developments in Statistics, Econometrics and Forecasting, University of Allahabad, India, December 27-28, 2010 06/21/2012 |
This book is part of the proceedings of The International Conference on Recent Developments in Statistics, Econometrics and Forecasting 2010, which was organized to provide opportunities for academics and researchers to share their knowledge on recent developments in this area. The conference featured the most up-to-date research results and applications in statistics, econometrics and forecasting. The book has fifteen chapters contributed by different authors and can be divided into five parts: Time Series and Econometric Modelling, Linear Models, Non-parametrics, Statistical Applications and Statistical Methodology. This book will be helpful to graduate students, researchers and applied statisticians working in the area of time series, statistical and econometric modelling. |
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One-Sheet-A-Day Math Drills
Grade 2 Addition - 200 Worksheets (Book 3 of 24) 11/01/2017 |
This One-Sheet-A-Day math drill workbook is for 2nd grade students who want extra practice with two numbers, two digits addition. It contains 200 math practice sheets, one for each school day of the year. Upon completion, the student will be more competent in 2nd grade mathematics and ready to proceed with more difficult exercises. Unlike other math drill books, this is one of 24 workbooks created to establish a daily routine for each student to practice on their own from grades 1 through 7. It is specifically designed to gradually increase mathematic ability with the least amount of stress for both parent and student. Kids need to practice at home to support what they are learning in school, but finding resources to help with that goal can be daunting. It takes a lot of time searching on... |
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One-Sheet-A-Day Math Drills
Grade 3 Subtraction - 200 Worksheets (Book 6 of 24) 01/15/2018 |
This One-Sheet-A-Day math drill workbook is for 3rd grade students who want extra practice with two numbers, three digits subtraction. It contains 200 math practice sheets, one for each school day of the year. Upon completion, the student will be more competent in 3rd grade mathematics and ready to proceed with more difficult exercises. Unlike other math drill books, this is one of 24 workbooks created to establish a daily routine for each student to practice on their own from grades 1 through 7. It is specifically designed to gradually increase mathematic ability with the least amount of stress for both parent and student. Kids need to practice at home to support what they are learning in school, but finding resources to help with that goal can be daunting. It takes a lot of time searchi... |
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One-Sheet-A-Day Math Drills
Grade 3 Multiplication - 200 Worksheets (Book 7 of 24) 01/15/2018 |
This One-Sheet-A-Day math drill workbook is for 3rd grade students who want extra practice with two numbers, one or two digits multiplication. It contains 200 math practice sheets, one for each school day of the year. Upon completion, the student will be more competent in 3rd grade mathematics and ready to proceed with more difficult exercises. Unlike other math drill books, this is one of 24 workbooks created to establish a daily routine for each student to practice on their own from grades 1 through 7. It is specifically designed to gradually increase mathematic ability with the least amount of stress for both parent and student. Kids need to practice at home to support what they are learning in school, but finding resources to help with that goal can be daunting. It takes a lot of time... |
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05/07/2009 |
The purpose of this qualitative study was to measure the effectiveness of a new reusable learning object design model for elementary mathematics. This study was motivated by the lack of general reusable learning object design models and, specifically, elementary mathematics design models that include both technical and learning specifications. The research design method was a qualitative Delphi technique and included participants across the United States and other countries. Ten participants were provided the design model and a questionnaire to analyze the effectiveness of the model on the online instructional design process. Two rounds of questionnaire responses and model refinements were conducted, at which point a consensus was reached. As a result of the data collected, the elementary ... |
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01/31/1999 |
Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to pro... |
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02/17/2002 |
The thesis starts with a short description of the credit derivatives' place in the credit risk management. Then it proceeds by outlining the basic forms of credit derivatives, their applications, and their contract elements. A short description of the two common pricing frameworks for credit derivatives, the Firm's Value Models and the Credit Rating Transition Models is given. The major approach reviewed in this thesis is the one of Duffie-Singleton for valuing credit derivatives with term structure models. This framework is also applied in a simulation and examines the importance of the different parameters on the outcome. Also examples for the valuation of Default Digital Swaps and Puts as well as Credit Default Swaps and Puts are given. |
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03/26/1999 |
The study of Multivariate Time Series has always been more difficult at the modeling stage than the univariate case. Identification of a suitable model, questions of stability, and the difficulties of prediction are well recognised. A variety of methods appear to be worth examining. This thesis is concerned with the proposal of an useful tool which is to apply canonical analysis to a realisation of a Multivariate Time Series and concentrates it's attention on k-variate ARMA(p,q) models. The multivariate series is partitioned into two overlapping or non-overlapping sets of different sizes. The left set is kept at lag 0 (without loss of generality) and the right set at a sequence of lags s=0,1,... . The model includes the possibility that the same subset of variables belong to the left set a... |
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03/31/1998 |
In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space.Based on these results we introduce an operator on H^2 which we study in some detail. We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements. On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations of the bounded and compact ones in terms of the behavior of the inducing maps. |
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03/31/1998 |
Combinatorial Games are a generalization of real numbers. Each game has a recursively defined complexity (birthday). In this paper we establish some game bounds. We find some limit cases for how big and how small a game can be, based on its complexity. For each finite birthday, N, we find the smallest positive number and the greatest game born by day N, as well as the smallest and the largest positive infinitesimals. As for each particular birthday we provide the extreme values for those types of games, these results extend those in [1, page 214]. The main references in the theory of combinatorial games are ONAG [1] and WW [2]. We'll use the notation and some fundamental results from WW---mainly from its first six chapters---to establish some bounds to the size of the games. |
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01/02/2012 |
Information Systems Analysis and Design presents essential knowledge about management information systems development, while providing a good balance between the core concepts and secondary concepts. It is intended for four-year university/college students who study information systems analysis and design. Students will learn the information systems development strategies, the systems acquisition approach to information systems development, and the process of information systems development. The book highlights the most important methods for information systems acquisition development, such as process modeling and systems acquisition design. To maintain a well-rounded approach to the topic, both fundamental knowledge about information systems development and hands-on material are presen... |
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12/15/2008 |
Data Envelopment Analysis (DEA) represents a milestone in the progression of a continuously advancing methodology for data analysis, which finds extensive use in industry, society and even in education. This book is a handy encyclopedia for researchers, students and practitioners looking for the latest and most comprehensive references in DEA. J.K. Mantri has specifically selected 22 research papers where DEA is applied in different fields so that the techniques discussed in this book can be used for various applications. In A Bibliography of Data Envelopment Analysis (1978-2001), Gabriel Tavares states that DEA is a mathematical programme for measuring performance efficiency of organizations popularly named as decision-making units (DMU). The DMU can be of any kind such as manufacturing ... |
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12/16/2004 |
Radiative transfer of photons though a random distribution of scatterers is considered. The Boltzmann transport eq is used to develop a program to obtain real values of intensity based on a set of discrete time intervals. A Newton-Raphson method is used to determine a set of eigenvalues based on the boundary conditions and system geometry. A numerical method due to Lanczos is used to approximately invert a Laplace transform. The algorithm is designed for easy modification to more general problems. PART II: Eigenvalues for the intensity distribution from the one speed Boltzmann transport equation can be computed using an iteration method with the roots and coefficients for the zeros of the Legendre polynomials and the results converge to the known values based on a Newton-R... |
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11/09/2010 |
A High School First Course in Euclidean Plane Geometry is intended to be a first course in plane geometry at the high school level. Individuals who do not have a formal background in geometry can also benefit from studying the subject using this book. The content of the book is based on Euclid's five postulates of plane geometry and the most common theorems. It promotes the art and the skills of developing logical proofs. Most of the theorems are provided with detailed proofs. A large number of sample problems are presented throughout the book with detailed solutions. Practice problems are included at the end of each chapter and are presented in three groups: geometric construction problems, computational problems, and theorematical problems. The answers to the computational problems ar... |
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08/10/2005 |
Introduction to Quantum Computation is an introduction to a new rapidly developing theory of quantum computing. The book is a comprehensive introduction to the main ideas and techniques of quantum computation. It begins with the basics of classical theory of computation: NP-complete problems, Boolean circuits, Finite state machine, Turing machine and the idea of complexity of an algorithm. The general quantum formalism (pure states, qubit, superposition, evolution of quantum system, entanglement, multi-qubit system ...) and complex algorithm examples are also presented. Matlab is a well known in engineer academia as matrix computing environment, which makes it well suited for simulating quantum algorithms. The (Quantum Computer Toolbox) QCT is written entirely in the Matlab and m-files ar... |
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Proof in Alonzo Church's and Alan Turing's Mathematical Logic
Undecidability of First Order Logic 10/25/2012 |
When in 1900 David Hilbert produced a list of 23 mathematical problems and expressed optimism in the power of the human mind to proffer positive solutions to them, little did he know that it would take much of the century for solutions to be found for some of the problems. The problems numbered 1, 2, and 10 which concern mathematical logic and which gave birth to what is called the entscheidungsproblem or the decision problem were eventually solved though in the negative by Alonzo Church and Alan Turing in their famous Church-Turing thesis. Given any fixed machine M and input n, there are gamma (a set of formulas) and D (a single formula) such that M halts on input n is identical to (gamma) (superset) D. So, if there were an effective means of deciding in first-order-logic in general wheth... |
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01/28/2008 |
The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black... |
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05/05/2011 |
This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite par... |