Inverse Problems: Modelling and Simulation
This volume presents the latest theoretical and experimental advancements in the field of inverse problems in recent years. It includes outstanding research results that reflect current theoretical and numerical aspects of inverse problems and their various applications. The volume is a collection of selected contributions from nearly three hundred invited presentations at the International Conference "Inverse Problems: Modelling and Simulation" (IPMS 2024) held from May 26 to June 1, 2024, in Malta. The topics covered in this volume are closely related to emerging deterministic and stochastic models in the fields of medical imaging, biology, geophysics, radar, computer science, communication theory, signal processing, visualization, engineering, and economics. The contributions in this volume reflect a broad range of problems in the theory and applications of inverse problems that are useful for mathematicians, physicists, engineers, and researchers working with inverse problems.
Experimental Techniques in Medicinal Chemistry & Instrumental Analysis
"Experimental Techniques in Medicinal Chemistry and Instrumental Methods" is a comprehensive practical guide designed for pharmacy students and professionals. It integrates core laboratory techniques in organic chemistry with essential instrumental methods used in pharmaceutical analysis. The book is divided into two main sections: one focusing on the synthesis, purification, and identification of organic compounds, and the other covering instrumental techniques such as UV-Vis spectroscopy, IR, and chromatography. Each experiment includes clear objectives, step-by-step procedures, observations, and discussions to build both conceptual understanding and practical skills. Emphasis is placed on laboratory safety, analytical precision, and real-world applications. This manual is especially useful for BSC, MSC, B.Pharm and M.Pharm students, educators, and those working in pharmaceutical quality control, offering a solid foundation in experimental pharmaceutical chemistry.
The Asymptotic Behavior of Porous Systems
This book presents a rigorous and comprehensive treatment of the mathematical theory and real-world applications of porous systems, with a special focus on their asymptotic behavior. It combines analytical, numerical, and computational perspectives to bridge fundamental science and engineering applications, making it relevant to mathematicians, physicists, engineers, and material scientists. It also synthesizes the mathematical foundations, modeling strategies, and engineering practices of porous media systems with asymptotic behavior as a unifying theme, which empowers the readers to model, analyze, and design next-generation porous systems across diverse disciplines.
Existence and uniqueness of the weak solution for aP-Laplacian problem
In this work, we study the existence and uniqueness of weak solutions for a p-Laplacianproblem in RN of the form: -Δpu + m(x)up-2u = f(x, u(x)), (1)where 1
Impact of Awareness of Diabetes Mellitus
The book "Impact of Awareness of Diabetes Mellitus Among Individuals: A Mathematical Model-Based Study" explores the critical role of public awareness in controlling diabetes progression. Using mathematical modeling, it demonstrates how education and awareness influence diagnosis, treatment adherence, and disease burden reduction. The study confirms that sustained awareness campaigns significantly lower undiagnosed cases, improving healthcare outcomes and easing system strain. It provides data-driven insights for policymakers, recommending targeted interventions, digital health strategies, and behavioral tracking. The book highlights the power of mathematics in shaping public health initiatives, emphasizing the need for continuous engagement to prevent and manage diabetes effectively.
Reaching for the Extreme
From bestselling author and mathematician Ian Stewart, the fascinating story of the extreme problems that have driven math forward from antiquity to today "Stewart has a genius for explanation."--New Scientist Many of the deepest and most important areas of mathematics have emerged from questions about extremes--the shortest path between two points on a curved surface, the smallest area spanning a wire, or the fewest colors needed to make a map. Mathematicians have been pushing restlessly toward extremes for thousands of years. The isoperimetric problem, for example--which asks for the shortest route enclosing a given area--can be traced to ancient Carthage. By contrast, it was only in 2017 that the densest ways to pack identical spheres into a 24-dimensional space was proven. In Reaching for the Extreme, bestselling author Ian Stewart, one of the world's most popular writers on mathematics, presents a dazzling, wide-ranging tour of math's outer limits. Stewart tells the stories of sixteen superlative problems--their history, the struggles to solve them, and the uses of some of the results. From the biggest number to the smallest, the fastest fall to the weirdest symmetry, and the best fold to the shortest proof, these questions are either pure thought experiments or are motivated by real-world challenges. The Plateau problem, about the geometry of soap bubbles, led to the notion of a minimal surface--now used in cosmology, biology, and other fields. Meanwhile, the 2023 discovery of a single tile shape that covers the infinite plane without repeating the same pattern has no application--yet. Reaching for the Extreme illuminates how mathematicians drive knowledge forward by reaching for the edges and solving some of the world's most fascinating problems.
Foundations of Arithmetic
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like "A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance."This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise Of Geometry, Containing The First Six Books Of Euclid's Elements
"A Treatise Of Geometry, Containing The First Six Books Of Euclid's Elements, Together With the Elements of Solid Geometry" is a classic mathematical text meticulously presenting Euclid's foundational geometric principles. Authored by Daniel Cresswell, this treatise offers a rigorous exposition of plane geometry through the initial six books of Euclid's Elements, followed by an exploration of solid geometry. This work provides a comprehensive understanding of geometric concepts and theorems. This book is invaluable for students, scholars, and enthusiasts of mathematics and the history of science, offering both a historical perspective on the development of geometry and a solid foundation in the core principles of Euclidean geometry. Cresswell's clear and systematic approach makes this edition accessible to both beginners and advanced learners, solidifying its place as a timeless resource in the field of mathematical education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Proceedings Of The Cambridge Philosophical Society
This volume contains the proceedings of the Cambridge Philosophical Society, covering mathematical and physical sciences. It offers a detailed record of scholarly presentations and discussions from a pivotal era in scientific inquiry. The collection provides insights into the prevailing theories, methodologies, and debates shaping the scientific landscape. Researchers and historians of science will find this volume an invaluable resource for understanding the development of mathematical and physical sciences within an influential academic society.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Collineations in Space of Four Dimensions
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like "A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance."This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Numerical Linear Algebra with Applications
Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven't taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation. Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
Proposed Mathematical Model for Predicting Military Electronic Equipment Component Failure Rates and Isolating Underlying Failure Causes
A mathematical expression for combining the entire failure rate curve is derived based on the assumption that the failure population is composed of three subpopulations, early, chance, and wear out. A graphical method is provided for separating the subpopulations and determining the parameters of the model. The expression is then applied to observed failure data in three detailed examples and in each case the model is shown to represent the observed data at the.05 significance level using the Kolmogorov-Smirnov Test. Two BASIC language computer programs are provided to simplify the use of the proposed model.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Exercises in Algebra and Trigonometry
This book contains exercises that a student can complete to learn algebra and trigonometry. Though it is designed to serve as a companion to another book by the same author, namely Algebra and Trigonometry, the exercises herein are typical for the subjects and do not pertain exclusively to that particular text.
Proposed Mathematical Model for Predicting Military Electronic Equipment Component Failure Rates and Isolating Underlying Failure Causes
A mathematical expression for combining the entire failure rate curve is derived based on the assumption that the failure population is composed of three subpopulations, early, chance, and wear out. A graphical method is provided for separating the subpopulations and determining the parameters of the model. The expression is then applied to observed failure data in three detailed examples and in each case the model is shown to represent the observed data at the.05 significance level using the Kolmogorov-Smirnov Test. Two BASIC language computer programs are provided to simplify the use of the proposed model.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise Of Geometry, Containing The First Six Books Of Euclid's Elements
"A Treatise Of Geometry, Containing The First Six Books Of Euclid's Elements, Together With the Elements of Solid Geometry" is a classic mathematical text meticulously presenting Euclid's foundational geometric principles. Authored by Daniel Cresswell, this treatise offers a rigorous exposition of plane geometry through the initial six books of Euclid's Elements, followed by an exploration of solid geometry. This work provides a comprehensive understanding of geometric concepts and theorems. This book is invaluable for students, scholars, and enthusiasts of mathematics and the history of science, offering both a historical perspective on the development of geometry and a solid foundation in the core principles of Euclidean geometry. Cresswell's clear and systematic approach makes this edition accessible to both beginners and advanced learners, solidifying its place as a timeless resource in the field of mathematical education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Chaotic Maps, Fractals, and Rapid Fluctuations
This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems.
Foundations of Arithmetic
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like "A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance."This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Advances Statistic Inference Process Driven Fraction Process
One of the important problems in studying stochastic phenomena is to develop stochastic models and understand their implications behind the phenomenon. Long range dependence is an important stochastic phenomena and it needs study of special type of stochastic processes for modelling. My earlier book on Statistical Inference for Fractional Diffusion Processes (2010) dealt with several aspects for modelling by fractional Brownian motion. This book will contain my work on parametric and nonparametric inference for processes driven by fractional processes such as fractional Brownian motion, mixed fractional Brownian motion, sub-fractional Brownian motion, alpha-stable noise, fractional Levy process and Gaussian processes.
Proceedings Of The Cambridge Philosophical Society
This volume contains the proceedings of the Cambridge Philosophical Society, covering mathematical and physical sciences. It offers a detailed record of scholarly presentations and discussions from a pivotal era in scientific inquiry. The collection provides insights into the prevailing theories, methodologies, and debates shaping the scientific landscape. Researchers and historians of science will find this volume an invaluable resource for understanding the development of mathematical and physical sciences within an influential academic society.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Projective Groups of Perspective Collineations in the Plane Treated Synthetically
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Projective Groups of Perspective Collineations in the Plane Treated Synthetically
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Collineations in Space of Four Dimensions
The University of Kansas (KU) is a public research university and the largestuniversity in the state of Kansas. Created by the staff of the KU libraries, KU ScholarWorks is the digital repository of the University. It contains scholarly workcreated by KU faculty and staff, as well as material from the University Archives. KUScholarWorks makes important research and historical items available to a wideraudience and helps assure their long-term preservation. The University of Kansas's KU ScholarWorks Pre-1923 Theses and Dissertationcollection was digitized by the Scholarly Communications program staff in the KULibraries' Center for Digital Scholarship. These theses and dissertations range from 1883 - 1921 and reflect topics from Engineering and History to Economics and Chemistry, including titles like "A Study of Terpeneless Lemon Extracts, English Interest in the Abolition of the Slave Trade, and Aspects of the Gothic Romance."This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Increasing Unit Effectiveness in a Dynamic Environment by Implementing a Leadership Mathematical Model
The Ukrainian Army is in a transition period which requires flexible, adaptive leadership with a contemporary vision. The problem of improving unit effectiveness is now very topical, because old leadership does not correspond to modern requirements and does not facilitate rapid development. The lack of understanding the need for a change in a dynamic environment makes a military unit ineffective. To explain the procedure of how to lead subordinates in a dynamic environment and give recommendations for commanders is valuable, because it will adapt the current leadership for modern requirements and make a military unit effective in any operational environment. The purpose of this research is to find an improved leadership model that will significantly increase unit effectiveness in a dynamic environment. This is a model that could be used as the foundation for a change in the leadership culture of the Ukrainian Army. The originality of this work will be its use of mathematical formulas to explain the key leadership methods/ideas proposed within the study.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Art of Mathematical Research
This book is based on lecture notes from the author's general elective course, Mathematical Methodology, at Sun Yat-sen University. It is organized into ten chapters that cover key mathematical methods, including reduction, analogy, induction, association, intuition, abstraction, reasoning, modeling, experimentation, and aesthetics. Additionally, the book explores notable mathematical conjectures and classic research methods in mathematics. This book serves as a valuable resource for both undergraduate and graduate students across various disciplines, providing insights into fundamental research methods in mathematics. It is also a useful reference for individuals engaged in mathematical research, offering an in-depth exploration of essential methodologies that support rigorous study and innovation in the field.
Mathews' Matriculation Mathematics
"Mathews' Matriculation Mathematics" is a comprehensive collection of arithmetic and algebra examination papers from 1844 to 1878. This historical compilation offers a unique glimpse into the mathematical education and testing standards of the time. Compiled by E.H. Mathews, the book provides a valuable resource for students, educators, and historians interested in the evolution of mathematical curricula.Featuring a wide range of problems and exercises, this volume showcases the mathematical knowledge expected of students during the mid-19th century. With answers included, "Mathews' Matriculation Mathematics" serves as an important reference for understanding the development of mathematical education and assessment practices.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practical Mathematics
"Practical Mathematics, Volume 3: Being The Essentials Of Arithmetic, Geometry, Algebra And Trigonometry" offers a comprehensive exploration of fundamental mathematical principles. This volume, authored by Claude Irwin Palmer, is designed to provide a solid foundation in essential mathematical concepts. Covering arithmetic, geometry, algebra, and trigonometry, the book aims to equip readers with practical mathematical skills. This book is a valuable resource for students, educators, and anyone seeking to enhance their understanding of mathematics. Palmer's approach emphasizes clarity and practicality, making complex topics accessible to a wide audience. Explore the core principles of mathematics with this meticulously crafted volume.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![An Introduction To Arithmetic. [with] Key](https://cdn.kingstone.com.tw/english/images/product/6487/9781024686487m.webp?Q=9ba4c "An Introduction To Arithmetic. [with] Key")
An Introduction To Arithmetic. [with] Key
"An Introduction To Arithmetic," complete with its answer key, is a comprehensive mathematics textbook intended for students learning the fundamentals of arithmetic. Authored by John Newark, this educational resource offers a structured approach to understanding and mastering essential arithmetic concepts. The book is designed to provide a solid foundation in basic mathematical operations and problem-solving techniques. With its detailed explanations and a dedicated key for checking answers, this book supports independent learning and effective classroom instruction.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practical Mathematics
"Practical Mathematics, Volume 3: Being The Essentials Of Arithmetic, Geometry, Algebra And Trigonometry" offers a comprehensive exploration of fundamental mathematical principles. This volume, authored by Claude Irwin Palmer, is designed to provide a solid foundation in essential mathematical concepts. Covering arithmetic, geometry, algebra, and trigonometry, the book aims to equip readers with practical mathematical skills. This book is a valuable resource for students, educators, and anyone seeking to enhance their understanding of mathematics. Palmer's approach emphasizes clarity and practicality, making complex topics accessible to a wide audience. Explore the core principles of mathematics with this meticulously crafted volume.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Industrial Mathematics Practically Applied
"Industrial Mathematics Practically Applied" by Paul V. Farnsworth is a comprehensive guide designed for students in manual training, industrial, and technical schools, as well as for home study. This book offers practical instruction and serves as a valuable reference for understanding the application of mathematics in industrial settings. The book covers a range of topics relevant to various trades and industries, providing clear explanations and examples to aid comprehension. Farnsworth's work emphasizes the importance of mathematical principles in real-world scenarios, making it an essential resource for anyone looking to enhance their skills in industrial mathematics. Originally published in the early 20th century, this book remains a valuable resource for those seeking a practical understanding of mathematics in industrial applications.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
On Twisted Quintic Curves
"On Twisted Quintic Curves" delves into the intricate world of algebraic geometry, focusing specifically on the properties and characteristics of twisted quintic curves. This work by Elmer Clifford Colpitts explores the mathematical structures underlying these complex curves, offering insights into their geometric and algebraic nature. Suitable for advanced students and researchers in mathematics, this book provides a rigorous examination of the subject matter. It contributes to a deeper understanding of quintic curves and their significance within the broader field of algebraic geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Mathews' Matriculation Mathematics
"Mathews' Matriculation Mathematics" is a comprehensive collection of arithmetic and algebra examination papers from 1844 to 1878. This historical compilation offers a unique glimpse into the mathematical education and testing standards of the time. Compiled by E.H. Mathews, the book provides a valuable resource for students, educators, and historians interested in the evolution of mathematical curricula.Featuring a wide range of problems and exercises, this volume showcases the mathematical knowledge expected of students during the mid-19th century. With answers included, "Mathews' Matriculation Mathematics" serves as an important reference for understanding the development of mathematical education and assessment practices.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practical Mathematics Part Iv
"Practical Mathematics Part IV: Trigonometry and Logarithms" offers a comprehensive exploration of these essential mathematical concepts. Designed for practical application, this book provides clear explanations and numerous examples to aid understanding. Beginning with the fundamentals of trigonometry, it progresses through trigonometric functions, identities, and their applications in solving real-world problems. The section on logarithms covers their properties, computations, and uses in various fields. This book is a valuable resource for students, engineers, and anyone seeking a solid foundation in trigonometry and logarithms.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![An Introduction To Arithmetic. [with] Key](https://cdn.kingstone.com.tw/english/images/product/2083/9781024682083m.webp?Q=ebb1f "An Introduction To Arithmetic. [with] Key")
An Introduction To Arithmetic. [with] Key
"An Introduction To Arithmetic," complete with its answer key, is a comprehensive mathematics textbook intended for students learning the fundamentals of arithmetic. Authored by John Newark, this educational resource offers a structured approach to understanding and mastering essential arithmetic concepts. The book is designed to provide a solid foundation in basic mathematical operations and problem-solving techniques. With its detailed explanations and a dedicated key for checking answers, this book supports independent learning and effective classroom instruction.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Integral Calculus For Beginners
"Integral Calculus For Beginners" is a comprehensive introduction to integral calculus, designed for students and learners with little to no prior knowledge of the subject. Authored by Alfred Lodge, this book presents the fundamental concepts and techniques of integration in a clear and accessible manner. Starting with basic definitions and progressing through various integration methods, the book provides numerous examples and exercises to reinforce understanding. This book aims to build a solid foundation in integral calculus, enabling readers to tackle more advanced topics and applications. Suitable for self-study or classroom use, this book is an invaluable resource for anyone seeking to master integral calculus.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Recent Trends in AI Enabled Technologies
This book constitutes the refereed proceedings of the Second International Conference on Recent Trends in AI Enabled Technologies, ThinkAI 2024, which took place in Hyderabad, India, during December 27-28, 2024. The 18 full papers in this book were carefully reviewed and selected from 75 submissions. These papers focus on topics of AI enabled technologies, including machine learning, soft computing, and deep learning algorithms.
Practical Solid Geometry
"Practical Solid Geometry" provides a comprehensive exploration of the principles and applications of solid geometry. Designed for students and instructors alike, this book offers a clear and accessible approach to understanding geometric concepts in three dimensions.Herbert Gilbert presents a systematic treatment of various topics, including the properties of lines, planes, polyhedra, and curved surfaces. With numerous examples and exercises, readers can develop their skills in visualizing and solving geometric problems. This book serves as an invaluable resource for anyone seeking a deeper understanding of spatial reasoning and its practical applications.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Observations On A Passage In Mr. Playfair's Letter To The Lord Provost Of Edinburgh Relative To The Mathematical Pretensions Of The Scottish Clergy
In "Observations On A Passage In Mr. Playfair's Letter To The Lord Provost Of Edinburgh Relative To The Mathematical Pretensions Of The Scottish Clergy," Thomas Chalmers offers a detailed response to criticisms regarding the mathematical abilities and education of the Scottish clergy. Chalmers, a prominent figure in Scottish religious and intellectual life, carefully examines and refutes the claims made by Mr. Playfair, providing insights into the standards of education and the intellectual pursuits of clergymen in Scotland during the period.This work sheds light on the intersection of religion, science, and education in early 19th-century Scotland, offering a valuable historical perspective on the intellectual climate of the time and the role of the clergy within it. It provides a nuanced view of the debates surrounding mathematical knowledge and its relevance to religious leadership.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Longmans' School Trigonometry
This is a comprehensive textbook on trigonometry, intended for school use. "Longmans' School Trigonometry" covers the fundamental principles and applications of trigonometry, providing a solid foundation for students. It includes detailed explanations, numerous examples, and exercises designed to enhance understanding and skill development. This book is an invaluable resource for students learning trigonometry and for teachers seeking a reliable and thorough instructional tool.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Struggles of BSE-Math Student-Parent in the Online Learning Approach
The outbreak of the pandemic COVID-19 resulted to school closures occurred on such a large scale and in such a way that learning and teaching were disrupted. Students and parents suffer from shortage of resources, how much more are the student-parents? This study was conducted to evaluate the struggles of BSE-Math student-parent when learning mathematics online. This study used phenomenology as a qualitative research method, a purposive sampling technique was used to select five participants, and a descriptive-evaluative design with thematic analysis was used in utilizing the qualitative data analysis. Findings showed that the participants experience the struggles in online learning approach, specifically with the following themes: time management, stability of internet connection, health problems, and cognitive aspect.
A Gentle Introduction to Quantum Machine Learning
Quantum machine learning (QML) is revolutionizing artificial intelligence by leveraging the power of quantum computing to access previously unimaginable computational possibilities. However, the field remains fragmented--balancing rigorous quantum theory with practical AI applications remains a challenge. This book bridges this gap, offering a systematic, hands-on guide for AI researchers, ML practitioners, and computer scientists eager to explore this emerging frontier. It provides a cohesive roadmap, covering everything from fundamental quantum computing principles to state-of-the-art QML techniques. Readers will explore quantum kernel methods, quantum neural networks, and quantum Transformers, gaining insight into their theoretical foundations, performance advantages, and practical implementations. The book's code demonstrations offer hands-on experience, ensuring that readers can move beyond theory to real-world applications. Designed for those with an AI or ML background, this tutorial does not assume prior expertise in quantum computing. Instead, it presents complex concepts with clarity, making it an essential resource for researchers, graduate students, and industry professionals eager to stay ahead in the quantum AI revolution. Whether you seek to understand quantum speedups, develop quantum-based models, or explore future research directions, this book provides the foundation you need to engage with QML and shape the future of intelligent computing.
The Magic Theorem
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things. Begun as a standard second edition by the original author team, it changed in scope following the passing of John Conway. This version of the book fulfills the original vision for the project: an elementary introduction to the orbifold signature notation and the theory behind it.The Magic Theorem features all the material contained in Part I of The Symmetries of Things, now redesigned and even more lavishly illustrated, along with new and engaging material suitable for a novice audience. This new book includes hands-on symmetry activities for the home or classroom and an online repository of teaching materials avaialble at themagictheorem.com
Observations On A Passage In Mr. Playfair's Letter To The Lord Provost Of Edinburgh Relative To The Mathematical Pretensions Of The Scottish Clergy
In "Observations On A Passage In Mr. Playfair's Letter To The Lord Provost Of Edinburgh Relative To The Mathematical Pretensions Of The Scottish Clergy," Thomas Chalmers offers a detailed response to criticisms regarding the mathematical abilities and education of the Scottish clergy. Chalmers, a prominent figure in Scottish religious and intellectual life, carefully examines and refutes the claims made by Mr. Playfair, providing insights into the standards of education and the intellectual pursuits of clergymen in Scotland during the period.This work sheds light on the intersection of religion, science, and education in early 19th-century Scotland, offering a valuable historical perspective on the intellectual climate of the time and the role of the clergy within it. It provides a nuanced view of the debates surrounding mathematical knowledge and its relevance to religious leadership.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Graduate Course in Probability
This book grew out of the notes for a one-semester basic graduate course in probability. As the title suggests, it is meant to be an introduction to probability and could serve as textbook for a year long text for a basic graduate course. It assumes some familiarity with measure theory and integration so in this book we emphasize only those aspects of measure theory that have special probabilistic uses.The book covers the topics that are part of the culture of an aspiring probabilist and it is guided by the author's personal belief that probability was and is a theory driven by examples. The examples form the main attraction of this subject. For this reason, a large book is devoted to an eclectic collection of examples, from classical to modern, from mainstream to "exotic". The text is complemented by nearly 200 exercises, quite a few nontrivial, but all meant to enhance comprehension and enlarge the reader's horizons.While teaching probability both at undergraduate and graduate level the author discovered the revealing power of simulations. For this reason, the book contains a veiled invitation to the reader to familiarize with the programing language R. In the appendix, there are a few of the most frequently used operations and the text is sprinkled with (less than optimal) R codes. Nowadays one can do on a laptop simulations and computations we could only dream as an undergraduate in the past. This is a book written by a probability outsider. That brings along a bit of freshness together with certain "naiveties".
Noncommutative Measures and LP and Orlicz Spaces, with Applications to Quantum Physics
The theory of noncommutative Haagerup ����sup����/sup and Orlicz spaces is an important tool in both Quantum Harmonic Analysis and Mathematical Physics. Indeed, noncommutativity is arguably the raison-d'礙tre of the Heisenberg approach to quantum mechanics. Just as classical analysis formed the foundation for classical mechanics, a mature response to the challenges posed by quantum mechanics (from the Heisenberg perspective) similarly needs to be built on a well-developed foundation of noncommutative analysis. In the passage from the classical to the quantum setting, functions get replaced with (possibly noncommuting) operators. Von Neumann himself realised early on that some sort of noncommutative integral calculus tailored to this setting is therefore needed to meet this challenge. This book seeks to help address this need. The noncommutative Orlicz spaces presented here help in dealing with observable quantities and entropy. Goldstein and Labuschagne provide a detailed account of the current theories in a way that is useful and accessible to a wide range of readers, from graduate students to advanced users. Beginning with some foundational examples intended to build intuition for the theory to follow, including the theory of noncommutative decreasing arrangements, as developed by Fack and Kosaki, and of Orlicz spaces for general von Neumann algebras. The authors then present the theory of the more accessible tracial case, followed by that of the more demanding general (type III) case. The final part of the book is devoted to advanced theory and applications.
Number Theory
This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers congruences, the Euclidean algorithm, linear Diophantine equations, the Chinese Remainder Theorem, Mobius inversion formula, Pythagorean triplets, perfect numbers and amicable pairs, Law of Quadratic Reciprocity, theorems on sums of squares, Farey fractions, periodic continued fractions, best rational approximations, and Pell's equation. Results are applied to factoring and primality testing including those for Mersenne and Fermat primes, probabilistic primality tests, Pollard's rho and p-1 factorization algorithms, and others. Also an introduction to cryptology with a full discussion of the RSA algorithm, discrete logarithms, and digital signatures. Chapters on analytic number theory including the Riemann zeta function, average orders of the lattice and divisor functions, Chebyshev's theorems, and Bertrand's Postulate. A chapter introduces additive number theory with discussion of Waring's Problem, the pentagonal number theorem for partitions, and Schnirelmann density.
Empowering Young Minds
Many metaheuristics are inspired by natural intelligence, particularly in how living species adapt and collaborate for survival. Swarm intelligence-based algorithms mimic the collective behaviour of animals and insects, and this book explores four such algorithms: Cat Swarm, Chicken Swarm, Bird Swarm, and Elephant Search. The authors have created engaging games to help children understand these algorithms through hands-on activities. With this interactive experience, the authors hope children can learn creative problem-solving skills while enjoying the amazing strategies that living creatures use in nature.
