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Complex functions and integral transforms - Part I
This comprehensive textbook explores the theory and applications of complex functions in mathematics. Beginning with the foundations of complex numbers (z = x + iy), the book develops the geometric interpretation of the complex plane where these numbers reside. The core chapters examine mappings of complex numbers, covering linear transformations, M繹bius transformations, and conformal mappings, with special emphasis on the Riemann mapping theorem that allows conformally mapping any simply connected domain onto the unit disk.The text progresses to analytic functions, characterized by the Cauchy-Riemann equations, setting the groundwork for complex integration. The integration chapters develop the theory methodically, explaining path integrals, Cauchy's Integral Theorem (showing that integrals of analytic functions around closed contours equal zero), and path independence properties. Particular attention is given to function complex integration, covering contour deformation techniques, branch cuts for multi-valued functions, and integration on unbounded domains including Jordan's lemma.
High-Accuracy Methods for Singular Perturbation Problems
This book presents efficient numerical strategies for solving singular perturbation problems, particularly focus on differential-difference equations involving small delay parameters. Singular perturbation problems in various fields of engineering and applied sciences such as fluid dynamics, elasticity, quantum mechanics, electrical networks, are known for their boundary layer behavior, which challenges conventional numerical methods. This book reviews the theoretical background and existing literature before introducing two high-accuracy techniques: a Fourth-Order Adaptive Cubic Spline Method and a Variable Mesh Scheme. These methods are rigorously analyzed for stability, convergence, accuracy and are validated through extensive numerical experimentation. The work is motivated by the limitations of classical techniques and addresses the growing demand for robust computational methods in fields such as fluid dynamics, quantum mechanics, and reaction- diffusion process.
Structured Epistemic Truth Volume I
SEMT Volume I introduces the Structured Epistemic Model of Truth, a framework that unites logic, epistemology, and complexity theory to address core issues in bounded AI and knowledge verification. Drawing from G繹del, Turing, and modern AI debates, the book proposes a non-classical conception of truth suited to agents operating under cognitive and resource constraints. It redefines epistemic rigor for computationally limited reasoners.
2024-2025 Middle School Contest Materials
This book contains one year of mathleague.org middle school tests and answer keys: 6 qualifying-level test sets and one national-level test set. Each test set contains a Sprint, Target, Team, and Countdown test.
Developing Queue Network Model with Bulk Arrival
This book explores the steady state analysis of bi-serial servers with bulk arrival. The book consists of two chapters. In the first chapter bi serial servers linked to a common sever has been analysed. The arriving unit enters into the system at bi-serial servers in batches of fixed size. Various queue characteristics have been obtained using generating function technique.The second chapter studies the network model with probabilistic batch arrival under geometrical distribution. The queue characteristics of the model has been analysed for two parameters under geometrical distribution. Numerical analysis is also done to check the validity of the model.
Heat and Mass Transfer Analysis of Non-Newtonian Flow through Cylinder
The present trend follows the advanced technology in any part of life, also as the same cooling and heating is main concept in almost every industrial, engineering sector and so to enhance and reduce heat transfer rate there are several properties regarding heat transfer phenomena by nanoparticles. There is much development and necessity in the study of Nano-fluid flow over boundary layer through inclined cylinder. For that, we have numerous of active and passive technique that aids in enhancing the heat transfer characteristic of convectional fluids.
Portfolio Optimization
This comprehensive guide to the world of financial data modeling and portfolio design is a must-read for anyone looking to understand and apply portfolio optimization in a practical context. It bridges the gap between mathematical formulations and the design of practical numerical algorithms. It explores a range of methods, from basic time series models to cutting-edge financial graph estimation approaches. The portfolio formulations span from Markowitz's original 1952 mean-variance portfolio to more advanced formulations, including downside risk portfolios, drawdown portfolios, risk parity portfolios, robust portfolios, bootstrapped portfolios, index tracking, pairs trading, and deep-learning portfolios. Enriched with a remarkable collection of numerical experiments and more than 200 figures, this is a valuable resource for researchers and finance industry practitioners. With slides, R and Python code examples, and exercise solutions available online, it serves as a textbook for portfolio optimization and financial data modeling courses, at advanced undergraduate and graduate level.
Grade 3 Review Workbook
Math Mammoth Grade 3 Review Workbook is intended to give students a thorough review of third grade math. It has both topical as well as mixed (spiral) review worksheets, and includes both topical tests and a comprehensive end-of-the-year test. The tests can also be used as review worksheets, instead of tests.You can use this workbook for various purposes: for summer math practice, to keep a child from forgetting math skills during other break times, to prepare students who are going into fourth grade, or to give third grade students extra practice during the school year.The topics reviewed in this workbook are: mental addition and subtractionregrouping and roundingmultiplication concept and tablesclockmoneyplace value with thousandsdivisionmeasuringgeometryfractionsThe content for these is taken from Math Mammoth Grade 3 Complete Curriculum, so it works especially well to prepare students for grade 4 in Math Mammoth. However, the content follows a typical study for grade 3, so this workbook can be used no matter which math curriculum you follow.Please note this book does not contain lessons or instruction for the topics. It is not intended for initial teaching. It also will not work if the student needs to completely re-study these topics (the student has not learned the topics at all). For that purpose, please consider Math Mammoth Grade 3 Complete Curriculum, which has all the necessary instruction and lessons.This is the 2025 edition.
New Models of SUDOKU
The author of New Models of Sudoku, Nael Qutub, is a well-versed and experienced math teacher of various programmes at middle and high schools. He wanted the puzzles not only to entertain, but also to stimulate the thinking skills of puzzle-solvers while reinforcing simple math concepts by placing the right number in the right place while going around and across the 9x9 grid.The author offers a unique and enjoyable way to engage reasoning through a new style of Sudoku while avoiding stress. It is the kind of puzzle that contributes to memory improvement and mental clarity.New Models of Sudoku is an excellent tool for challenging and enhancing the mindset and logic of individuals. It takes Sudoku a step further, whereby the numbers used have a meaning. Incorporating mathematical elements will make the puzzle a rewarding experience for those who embrace changes and challenges.While most Sudoku puzzles have three levels, New Models of Sudoku, to the contrary, has six levels ranging from Beginner to Expert levels to accommodate all sorts of abilities and skills. Calculators are NOT needed. TRY TO SOLVE THE NEW MODELS!
Regularity for the 3D Navier-Stokes Equations with Damping
This book is concerned with the 3D Navier-Stokes equations with damping(DNS). We've obtained some important results such as the uniqueness of the weak solutions and the existence of the strong solutions while studying DNS for several years.In the current edition, we synthesis and analysis these results as well as make our effort to give the proofs of them in detail and perfectly. However, in this process, we have benefited enormously.In conclusion, I hope that the interested scientist will enjoy this book and derive great benefit from reading it just as I did while writing it.
A mathematical analysis of the corruption dynamics model
This book presents a comprehensive mathematical analysis of a corruption dynamics model, integrating optimal control strategies to mitigate corruption in various systems. The research explores the underlying mechanisms of corruption, examining how it spreads and affects societal structures. By employing advanced mathematical techniques, the study develops a model that captures the dynamics of corruption and identifies effective control measures. The findings provide valuable insights for policymakers and researchers, offering a framework for understanding and addressing corruption through strategic interventions. This work contributes to the field of applied mathematics by demonstrating the practical application of mathematical modeling in social issues, making it a significant resource for scholars, practitioners, and students interested in the intersection of mathematics and social sciences.
Notes, Problems and Solutions in Differential Equations
This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm-Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.
Unlocking Data with SPSS
Unlocking Data with SPSS: From Curiosity to Competence is a complete and practical guide designed to lead students, researchers, and professionals from the basics of SPSS to advanced statistical techniques. Beginning with an intuitive introduction to SPSS software, readers learn how to define variables, manage data, and conduct essential descriptive statistics and visualizations. As the book progresses, it builds a strong foundation in inferential statistics, including hypothesis testing, t-tests, ANOVA, regression analysis, and non-parametric methods. Advanced topics like factor analysis, reliability testing, and multivariate techniques are also thoroughly explained with step-by-step SPSS procedures. Special emphasis is placed on applying SPSS in academic research, reporting results according to APA standards, and exploring discipline-specific applications across psychology, business, and health sciences. Real-world case studies ensure practical understanding and reinforce the connection between theory and application. Whether for thesis writing, professional research, or general skill-building, this book empowers readers to unlock the full potential of their data using SPSS.
Discrete and Algebraic Structures
This textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation. Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly. Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists. Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids. This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation.
Algebra
This book has been carefully designed in accordance with the model syllabus prescribed by the University Grants Commission (UGC), India, for courses in Algebra and Linear Algebra. It is well-suited for undergraduate and postgraduate students of mathematics across Indian universities and other institutions offering similar curricula.To ensure comprehensive understanding, the book begins with a preliminary chapter on Set Theory, providing the foundational concepts necessary for a deeper grasp of abstract algebraic structures. The content then progresses to cover a wide range of essential topics including integers, groups, rings, and fields, as well as polynomials, vector spaces, linear transformations, matrices, and Boolean algebra.Written in a clear and accessible language, the book emphasizes conceptual clarity through illustrative examples and real-world applications. Special attention has been given to demonstrating how abstract algebraic concepts are relevant and useful in number theory and the theory of equations, particularly in understanding the roots of polynomials.To enhance the utility of the text, an additional chapter on fuzzy set theory has been included. This modern topic introduces students to a broader perspective on set-related concepts and logical structures, offering them insight into emerging mathematical frameworks.Overall, the book serves as a valuable and self-contained resource for academic learning and exam preparation in algebra and linear algebra.
Discrete Mathematics
This book has been carefully structured in accordance with the model syllabus prescribed by the University Grants Commission (UGC), India. It is ideally suited for undergraduate students pursuing B.Tech in Computer Science and Engineering or Mathematics, as well as postgraduate students enrolled in M.C.A. (Master of Computer Applications) or M.Sc. Mathematics programs.To make the book self-contained and accessible, it begins with foundational chapters on Mathematical Logic and Set Theory, which are essential components of the curriculum. Building upon these basics, the book introduces a wide array of key topics relevant to both Computer Science and Mathematics, including Combinatorics, Graph Theory, and Algebraic Structures such as Groups, Rings, and Boolean Algebra.In addition to traditional topics, the book includes important subjects like Finite State Machines (Theory of Computation) and Probability, making it a comprehensive guide for students navigating the intersection of mathematics and computer science.The content is presented in a simple, lucid, and student-friendly manner, with numerous examples and applications that demonstrate the practical relevance of abstract concepts, especially in the domain of Computer Science.To enhance its academic scope, the book also offers a final chapter on Fuzzy Set Theory-a modern extension of classical set theory-introducing students to contemporary topics in mathematical reasoning and logic. Overall, it is an excellent academic and reference resource.
Number Theory
This book is designed to serve as a comprehensive textbook for undergraduate and postgraduate students across various academic disciplines. It is particularly well-suited for B.A. and B.Sc. (Pass and Honours) students, as well as M.A. and M.Sc. candidates enrolled in universities throughout India. Additionally, the book caters to second and third-year undergraduate students at universities in North America and Europe, making it a versatile resource for a global audience.The content is structured to support students undertaking an elementary course in Real Analysis or an advanced course in Calculus. It also complements elementary courses in Modern Abstract Algebra, providing foundational knowledge crucial for further studies in mathematics and related fields.To ensure the book is self-contained and accessible to readers with varying backgrounds, basic concepts of Set Theory and Abstract Algebra are thoughtfully included in the appendices. These appendices help bridge gaps in prerequisite knowledge and allow students to grasp advanced topics with greater ease.The book's clear explanations, systematic progression of topics, and inclusion of supplementary material make it an ideal choice for both classroom use and self-study. It balances theoretical rigor with practical applications, enabling students to develop a strong conceptual understanding and problem-solving skills.Overall, this text stands out as a valuable educational tool, empowering students to master core mathematical concepts essential for academic success and future research.
Functional Differential Equations and Dynamic Equations on Time Scales
Machine Learning and Soft Computing
This two part-volume CCIS constitutes the refereed proceedings of 9th International Conference, ICMLSC 2025, in Tokyo, Japan in January 24-26, 2025. The 39 full papers and 13 short papers included in this book were carefully reviewed and selected from 121 submissions. They follow the topical sections as below: Part I: Multimodal Data Analysis and Model Optimization; Basic Theories of Machine Learning and Emerging Application Technologies; and Intelligent Recommendation System Design and Privacy Security. Part II: Deep Learning Models and High-performance Computing; Data-driven Complex System Modeling and Intelligent Optimization Algorithms; and Image Analysis and Processing Methods based on AI.
Intelligent Computers, Algorithms, and Applications
This book constitutes the proceedings of the 4th BenchCouncil International Symposium on Intelligent Computers, Algorithms, and Applications, IC 2024, held in Guangzhou, China, during December 4-6, 2024. The 16 full papers included in this book were carefully reviewed and selected from 31 submissions. They were organized in topical sections as follows: Algorithms; Education; Evaluation; System.
Math Mammoth Grade 7 Answer Keys
Math Mammoth Grade 7 Answer Keys (2025 edition) contains answers to Math Mammoth Grade 7-A and 7-B student worktexts, to chapter tests, to the end-of-year test, and to the cumulative review lessons. This is the full-color version.
Math Mammoth Grade 7 Tests and Cumulative Reviews
Math Mammoth Grade 7 Tests and Cumulative Reviews (2025 edition) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 7 curriculum. Please note: The answer keys are not included. They are sold in a separate book that includes all answer keys for the Math Mammoth Grade 7 Complete Curriculum.
Intuitionistic Fuzzy Digital Spaces
This book is intended to define and analyse the geometrical and topological properties among the digital subsets of the digital images such as convexity, convex envelopes, continuity, connectedness and r-simplexes with the background of intuitionistic fuzzy logic. As an example automated detection of diabetic retinopathy using intuitionistic fuzzy digital convex envelope segmentation algorithm is propounded. As the co-extension of the above notions, some of the maps between the digital images such as continuous maps, connected maps, C-maps and enfolding maps are presented and investigated with intuitionistic fuzzy logic. Finally, intuitionistic fuzzy digital topology is framed up. Under this notion, CS - filtered spaces and Hausdorff CS - filtered spaces are instigated.
Business Analytics
This book covers key topics related to business analytics like descriptive, predictive, and prescriptive analytics, data exploration, visualization, and preparation. There is emphasis on practical application, including advanced Excel features like pivot tables and lookup functions, alongside Python's capabilities for data preparation, regression analysis, and predictive modeling. Each chapter integrates examples, coding exercises, and step-by-step instructions. The primary purpose of this book is to equip readers with the knowledge and skills required to decode data using Advanced Excel and Python. It will not only simplify their business decision-making process but also enable them to predict future trends. It serves as a practical guide for students, educators, and professionals. Readers will learn about the three pillars of analytics: descriptive, predictive, and prescriptive, and understand why they're indispensable in organisational growth trajectories.
Analytical Study of Air Traffic Using ARFIMA Time Series Models
While time series forecasting techniques have been widely developed, the self-similar structure of data has not been adequately addressed. This research focuses on investigating self-similar structures in real-time air traffic data from Air India and Indigo's scheduled domestic flights, aiming to develop a suitable forecasting model for self-similar time series. Self-similarity has proven valuable, particularly in processes like ARFIMA, long-range dependence, and the Hurst parameter. This study explores the current understanding of self-similarity, its concepts, definitions, and applications, offering a roadmap for future research. The book consolidates past works on air traffic modeling using methods such as Box-Jenkins, Exponential Smoothing, and Artificial Neural Networks. It aims to present a comprehensive overview of time series forecasting developments, focusing on air traffic modeling, long-range dependence through self-similarity, and fitting ARFIMA to identify the most effective forecasting model.
Nonlinear Convection in Earth’s Outer Core
I worked on linear and weakly non-linear theories on magneto convection in a rotating fluid with isotropic/anisotropic diffusivities using analytical methods. In linear stability analysis, we have determined the marginal stability curves at the onset of stationary and oscillatory convection using one-term Galerkin method. In weakly nonlinear analysis, a two dimensional non-linear amplitude equation near the onset of stationary and oscillatory convection has been derived. Conditions for the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities are studied. Also, stability regions of travelling waves and standing waves are studied.
Forced Convection Heat Transfer Inparallel Plate Channels Partially Fi
This book explains the hydrodynamic and thermal behavior of laminar Newtonian fluid flow in channels partially filled with porous material, symmetrically distributed at the walls. Using the Successive Accelerated Replacement (SAR) numerical scheme, the analysis explores the influence of porous fraction (γₚ), Darcy number (Da), Peclet number (Pe), and Brinkman number (Br) on flow and heat transfer. Results show that axial conduction significantly affects temperature profiles at low Pe (
The Statistical Methods
This book acquaints the readers with the mathematical and statistical aspects extensively used in a variety of disciplines of social, biological and engineering sciences. The statistical models find tremendous applications through their use in facilitating economic evaluation and in a number of decision-making contexts. In the present era, the applications of statistical techniques to a variety of disciplines including economics, commerce, biology, chemistry and physics are of great importance and the present book meets the requirements of these researchers.
Three Body Scattering Problem
This book introduces the classical three-body problem, highlighting its complexity, non-integrability, and relevance in celestial mechanics. Discusses types of three-body systems and basic solution approaches. Applies the restricted three-body model to analyze the Moon's motion under the gravitational influence of Earth and the Sun, including effects like orbital perturbations and tidal interactions. This book explores temporary interactions among three bodies, focusing on scattering, capture, and escape phenomena. Describes chaotic behavior and energy exchanges during close encounters. Analyzes how binaries interact with a third body, leading to outcomes like binary disruption, exchange, or tightening. Crucial in stellar dynamics and compact object interactions. Examines how giant molecular clouds gravitationally perturb Oort Cloud comets, triggering inward migration and potential comet showers in the solar system.
Mathematical Study of Epidemic Models
This book covers mathematical study of epidemic model and explores mathematical modeling techniques for infectious disease dynamics, focusing on stability, bifurcation analysis, stochastic influences, diffusion, and optimal control. It begins with an introductory overview of epidemiological concepts, historical modeling approaches, and methodologies. The subsequent chapters present the author's original contributions, analyzing various epidemic models under deterministic, delayed, stochastic, and controlled frameworks.
New Method for Time Series Forecast-Application of Rainfall Prediction
An overview of the conventional time series forecasting methods, including AR, MA, ARMA, ARIMA, SARIMA, ARCH, and GARCH models, is provided in this book. The trend pattern of rainfall in India is described in detail in Chapter 1, the traditional forecast models are described in Chapter 2, and the innovative way of building a time series model is discussed in Chapter 3. The validity of this method is tested using an appropriate data set of Indian rainfall.
The Silent Struggle
This book examines the systematic marginalisation of Hindus in West Bengal, tracing its roots from pre-Partition Bengal to modern-day socio-political dynamics. It explores political appeasement, Islamic radicalism, demographic shifts, and cultural erosion, supported by historical analysis and real-life case studies.The book concludes with a call to action for Hindus to reclaim their rights, heritage, and future.
The Formula for Growth
This book explores the integration of mathematics, data, and psychology as essential tools for driving sustainable business growth. It provides business leaders with strategies for optimizing operations, improving customer engagement, and scaling effectively across diverse markets. The book emphasizes the importance of using predictive analytics and data-driven decision-making to anticipate trends and enhance business performance, while also highlighting the role of psychological insights in fostering customer loyalty and understanding consumer behavior. With real-world case studies and practical frameworks, the book offers actionable strategies for building resilient, growth-oriented business models that can adapt to future challenges. By combining these three disciplines, businesses can create a holistic approach to growth that is both innovative and sustainable.
Application of Bayesian Model Averaging to Carbon Emissions in Nigeria
In this book, the application of Bayesian Model Averaging in Environmental Statistics, were discussed. Uncertainties of variables in the model and elicitation of parameters were also extensively looked into. Series of literature were reviewed, especially those focusing on parameter prior elicitation and sensitivity in Bayesian Model Averaging as applicable to various milieus of science. To this end, three modified g-parameter priors were elicited and their asymptotic properties were derived in Bayesian Model Averaging. Specifically the modified g-parameter priors elicited are consistent in both the Posterior Model Probabilities and Bayes factor for the model. In addition, the sensitivities of these modified g-parameter priors were investigated using both the simulated results and data sets from carbon emissions in Nigeria from 1975 - 2015.
Analysis of Numerical Schemes to Singular Perturbation Problems
The primary goal of this book is to present, evaluate, and analyze efficient numerical methods for solving a specific class of singularly perturbed differential equations characterized by boundary and interior layer behaviors. Organized into six chapters, the book begins with a detailed overview of definitions, motivations, singular perturbation problems, differential-difference equations, boundary layers, and a comprehensive literature review. Subsequent chapters introduce advanced numerical methods, such as adaptive splines, numerical integration on specialized meshes, trigonometric splines, and fitted numerical schemes using the backward Euler method, to address interior layer problems, differential-difference equations, and singularly perturbed parabolic differential-difference equations. These studies underscore the significance of developing numerical techniques for singularly perturbed differential-difference equations. The research emphasizes creating simple, non-asymptotic, user-friendly, and efficient methods that are easily adaptable for computer implementation with minimal preparation.
Numerical Study of Multi Parameter Boundary Layer Problems
This book aims to present, analyze, and evaluate various straightforward and effective numerical methodologies for addressing two-parameter boundary layer problems, also referred to as singularly perturbed two-parameter boundary value problems, which exhibit dual boundary layer characteristics in their solutions. The book comprises five chapters. Chapter -1 delves into elucidating the definition and rationale behind singular perturbation problems, as well as singularly perturbed two parameters boundary value problems. A fourth order computational scheme with an exponential spline, a numerical scheme using an adaptive cubic spline function, a completely exponential fitted second order finite difference method, a completely exponential fitted modified upwind finite difference method for the solution of two parameters singularly perturbed two-point boundary value problems having dual layers are proposed in the remaining four chapters. These approaches may be applied to solve differential-difference equations with several parameters, as well as higher order order singular perturbation problems. The approaches proposed are efficient for doing computations with minimal computing effort.
Mathematics of Machine Learning
Build a solid foundation in the core math behind machine learning algorithms with this comprehensive guide to linear algebra, calculus, and probability, explained through practical Python examplesPurchase of the print or Kindle book includes a free PDF eBookKey Features: - Master linear algebra, calculus, and probability theory for ML- Bridge the gap between theory and real-world applications- Learn Python implementations of core mathematical conceptsBook Description: Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you'll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts.PhD mathematician turned ML engineer Tivadar Danka-known for his intuitive teaching style that has attracted 100k+ followers-guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you'll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors.By the end of this book, you'll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.What You Will Learn: - Understand core concepts of linear algebra, including matrices, eigenvalues, and decompositions- Grasp fundamental principles of calculus, including differentiation and integration- Explore advanced topics in multivariable calculus for optimization in high dimensions- Master essential probability concepts like distributions, Bayes' theorem, and entropy- Bring mathematical ideas to life through Python-based implementationsWho this book is for: This book is for aspiring machine learning engineers, data scientists, software developers, and researchers who want to gain a deeper understanding of the mathematics that drives machine learning. A foundational understanding of algebra and Python, and basic familiarity with machine learning tools are recommended.Table of Contents- Vectors and vector spaces- The geometric structure of vector spaces- Linear algebra in practice spaces: measuring distances- Linear transformations- Matrices and equations- Eigenvalues and eigenvectors- Matrix factorizations- Matrices and graphs- Functions- Numbers, sequences, and series- Topology, limits, and continuity- Differentiation- Optimization- Integration- Multivariable functions- Derivatives and gradients- Optimization in multiple variables- What is probability?- Random variables and distributions- The expected value- The maximum likelihood estimation- It's just logic- The structure of mathematics- Basics of set theory- Complex numbers
Scalable Monte Carlo for Bayesian Learning
A graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC), as applied broadly in the Bayesian computational context. The topics covered have emerged as recently as the last decade and include stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment. A particular focus is on cutting-edge methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI. Examples are woven throughout the text to demonstrate how scalable Bayesian learning methods can be implemented. This text could form the basis for a course and is sure to be an invaluable resource for researchers in the field.
High-Accuracy Finite Difference Methods
Scientific computing plays a critically important role in almost all areas of engineering, modeling, and forecasting. The method of finite differences (FD) is a classical tool that is still rapidly evolving, with several key developments barely yet in the literature. Other key aspects of the method, in particular those to do with computations that require high accuracy, often 'fall through the cracks' in many treatises. Bengt Fornberg addresses that failing in this book, which adopts a practical perspective right across the field and is aimed at graduate students, scientists, and educators seeking a follow-up to more typical curriculum-oriented textbooks. The coverage extends from generating FD formulas and applying them to solving ordinary and partial differential equations, to numerical integration, evaluation of infinite sums, approximation of fractional derivatives, and computations in the complex plane.
Magic, Mathematics, and Playing Cards
Drawing from their collective experience as math enthusiasts, the authors, who are co-founders of Mathematical Circus, have compiled a collection of mathematical activities centered around a standard deck of cards. This book presents a range of self-working card tricks, each rooted in mathematical principles, explained in a clear and straightforward manner. Designed to be both educational and entertaining, the book makes these mathematical concepts accessible to readers of all backgrounds.
Fundamentals of Ordinary Differential Equations
This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling. Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study.
Magic, Mathematics, and Playing Cards
Drawing from their collective experience as math enthusiasts, the authors, who are co-founders of Mathematical Circus, have compiled a collection of mathematical activities centered around a standard deck of cards. This book presents a range of self-working card tricks, each rooted in mathematical principles, explained in a clear and straightforward manner. Designed to be both educational and entertaining, the book makes these mathematical concepts accessible to readers of all backgrounds.
Partially Observed Markov Decision Processes
Covering formulation, algorithms and structural results and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. In light of major advances in machine learning over the past decade, this edition includes a new Part V on inverse reinforcement learning as well as a new chapter on non-parametric Bayesian inference (for Dirichlet processes and Gaussian processes), variational Bayes and conformal prediction.
Discrete and Computational Geometry, 2nd Edition
The essential introduction to discrete and computational geometry--now fully updated and expanded Discrete and Computational Geometry bridges the theoretical world of discrete geometry with the applications-driven realm of computational geometry, offering a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. Beginning with polygons and ending with polyhedra, it explains how to capture the shape of data given by a set of points, from convex hulls and triangulations to Voronoi diagrams, geometric duality, chains, linkages, and alpha complexes. Connections to real-world applications are made throughout, and algorithms are presented independent of any programming language. Now fully updated and expanded, this richly illustrated textbook is an invaluable learning tool for students in mathematics, computer science, engineering, and physics.Now with new sections on duality and on computational topologyProject suggestions at the end of every chapterCovers traditional topics as well as new and advanced materialFeatures numerous full-color illustrations, exercises, and fully updated unsolved problemsUniquely designed for a one-semester classAccessible to college sophomores with minimal backgroundAlso suitable for more advanced studentsOnline solutions manual (available to instructors)
Bioinspired Algorithms and Applications in Image Fusion
The preying strategies in animals and other living creatures have motivational intelligence which can be implemented significantly in computer algorithms designed for image fusion which is an eminent image processing technique. The research contributed in this book is the designing of few methodologies for the pixel type fusion of two magnetic resonance images harnessing the traits of different genres of discrete wavelet transform and Bayesian model. The parameters of this estimation model are then optimized employing distinctive nature encouraged optimization algorithms, for instance bird swarm algorithm (BSA), etc. to have an optimized fused image with peerless performance.
