Prime Discoveries
Prime Discoveries is a discovery-driven mathematics book built to answer one question: What are prime numbers really doing?Prime numbers are the "atoms" of the integer world. They look simple, but their behavior controls an enormous part of mathematics. Gauss noticed a stunning pattern in how primes thin out as numbers grow - beautiful, clean, and still mysterious. But how?Then it gets even deeper when primes are taken into the complex world (imaginary numbers). We start from plain integers, and suddenly prime structure is encoded inside a function of a complex variable. Riemann built that bridge - and it works. It predicts. It shapes how we think about primes. But why? How is that even possible?This book is not a traditional textbook and not a literature survey. It is a discovery book, written using a strategy I call the Virgin Mindset: start at zero, avoid inherited explanations at the beginning, and build the tools from scratch until the subject becomes formulatable.The journey is structured and builds power step by step: Chapter 1: intuition and direction - no formulasChapters 2-3: the essentials of number theory and algebraUp to Chapter 7: modeling, reasoning, formulation, and the counting mindset needed to treat primes as a systemChapter 7 (turning point): the Number-Wave Framework - a wave language of spectra, shadows, and templatesFrom there, the framework becomes a method: it lets us depict prime structure and convert it into computable counting formulas.In the final chapter, we go straight for the famous patterns. We derive an exact Twin Prime Counting Function using inclusion-exclusion, study its behavior at infinity, and extend the same machinery to other prime patterns, including cousin primes, sexy primes, Sophie Germain primes, and prime triplets - with validation by direct enumeration at scale.This book is for readers who want more than results. It is for readers who want the construction - the path from zero to a working framework.Keep a pen beside you. You will not finish this book without thinking.NumbersDiscoveries.com
Math Mammoth Grade 7 Review Workbook
Math Mammoth Grade 7 Review Workbook is intended to give students a thorough review of seventh grade math (pre-algebra). It has both topical as well as mixed (spiral) review worksheets, and includes both topical tests and a comprehensive end-of-year test. You can use this workbook for various purposes: for summer math practice, to keep a student from forgetting math skills during other break times, or to prepare a student who is going into eighth grade or into high school math. The content follows a typical study for prealgebra or grade 7, so this workbook can be used no matter which math curriculum you follow.The topics reviewed in this workbook are: basics of algebraintegersone-step equationsrational numberslinear equations and inequalitiesratios and proportionspercentgeometryprobabilitystatisticsPlease 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 has not learned the topics at all. For those purposes, check out Math Mammoth Grade 7 Curriculum, which has all the necessary instruction and lessons.Note: the content for this workbook is taken from the Math Mammoth Grade 7 Curriculum (mixed reviews, cumulative reviews, tests). If you already own Math Mammoth Grade 7, and would like extra review for your student, we suggest you check out our Skills Review workbook series.
Elementary Number Theory
Elementary Number Theory offers a fresh and engaging exploration of one of mathematics' most timeless and beautiful fields. Designed for master's students and advanced undergraduates, it blends classical insights with modern perspectives to reveal the elegance and power of numbers-from ancient theorems to real-world applications. Drawing on over decades of classroom experience, the author presents a carefully sequenced development of topics, beginning with divisibility and congruences, moving through quadratic reciprocity, and culminating in contemporary themes such as cryptography. The text strikes a rare balance between rigor and accessibility, ensuring that readers not only master techniques but also develop a deep appreciation for the subject's underlying ideas. Notably, the book introduces abstract structures earlier than most standard texts, helping students build a strong conceptual framework from the outset. It also incorporates less commonly covered but highly valuable tools, such as p-adic valuations and matrix methods for continued fractions, which open doors to richer problem-solving strategies. Richly supported by classroom-tested exercises, worked examples, and intuitive explanations, Elementary Number Theory is as effective for guided learning in the classroom as it is for self- study. Whether you are preparing for advanced research or simply seeking to experience the intellectual beauty of number theory, this book offers a rewarding journey through one of mathematics' most fascinating landscapes.
The Spirit of Numbers
Most of us met numbers as exam questions, bank balances, and blood test results. Yet the same symbols that trigger anxiety have also been used to build temples, compose hymns, and describe the birth of stars. What if numbers are not only tools, but a quiet language of meaning? This book offers a guided walk through that language. It explores sacred numbers as more than lucky charms, showing how they structure stories, rituals, and memory across cultures. It treats numerology spirituality not as fortune-telling but as an instinctive human attempt to read significance in pattern. Along the way, it unfolds sacred geometry patterns in buildings and landscapes, inviting readers to see every circle, triangle, and spiral as a doorway into attention. Rather than teaching heavy theory, the chapters linger over everyday scenes: clocks, doorways, calendars, footsteps. They reveal how the symbolism of numbers shapes trust, fear, hope, and choice. Gentle reflections on pythagoras philosophy, meaning in mathematics, and mathematics and spirituality make abstract ideas feel personal and concrete. Practical suggestions show how to cultivate spiritual mathematics in daily habits, and how to notice symbolic number patterns without sliding into obsession. By the end, readers are invited to walk through life with fresh eyes, seeing even the simplest sums as part of a conversation between math and myth.
The Riemann Zeta Function
The Riemann zeta function plays a central role in many areas in which complex analysis is applied, such as number theory (e.g. generating irrational and prime numbers. It is also an important tool in signal analysis in many fields of contemporary practice and technology, cryptography. In condensed matter physics, for example, the famous Sommerfeld expansion, which is used to calculate the number of particles and the internal electron energy, includes the Riemann zeta function with even integer argument values. On the other hand, the spin-spin correlation function of isotropic spin-1/2 in the Heisenberg model is expressed by ln 2 and Riemann zeta function with odd integer arguments. The author has made a tremendous effort to provide the reader with a new, clear and innovative way of looking at the most important features of the Riemann zeta function. The proofs of the expressed theorems are completely original. The monography established a good theoretical basis for the problem of calculating multiple sums and integrals in which the Riemann function appears. A special method was developed to establish a connection between the values of the Riemann zeta function with odd and even integer arguments. Based on the results obtained by H. M. Srivastava in his study from 1988, related to several different groups of summation formulas with the series in which the Riemann zeta function appears (which was first investigated by Euler and Goldbach), the monograph dealt with the series of this type. A new formula will be offered for Riemann function for odd argument which has a more compact form and faster convergence than any of the relations described in the afore mentioned papers.
Partial Differential Equations Theory
Most modern textbooks on partial differential equations either contain proofs of fundamental results only in special cases, or proof outlines, or do not contain proofs at all. This textbook, despite its relatively small volume, provides all the main results with complete proofs. The foundation for the material in the textbook is the functional approach associated with the concept of a weak solution and Sobolev spaces. In this textbook, such an approach is demonstrated on second-order model equations: the Poisson equation, the heat equation, and the wave equation. However, it allows one to generalize the main results presented in the textbook to the case of more general equations of the corresponding type with variable coefficients. The theory of partial differential equations constructed on the basis of Sobolev spaces was earlier presented in a number of remarkable books. Although many of these sources have been used in preparing this textbook, its main difference however is the presentation of the semigroup theory with the application to evolutionary equations (thanks to this, mixed problems and the Cauchy problem are studied using a unified method), as well as the use of modern techniques, which made it possible to simplify the majority of proofs.
Mathematical Tools for Theoretical Physics
Mathematical Tools for Theoretical Physics provides a comprehensive and rigorous introduction to the mathematical foundations essential for modern theoretical physics. This self-contained volume systematically develops the mathematical language and techniques required to engage with cutting-edge research in quantum mechanics, general relativity, gauge theories, statistical mechanics, and beyond.The book is organized into seven carefully structured parts, each building upon the previous to create a unified framework for understanding the deep connections between mathematics and physics. Part I establishes the essential foundations in linear algebra, complex analysis, and real analysis, including modern topics such as distribution theory. Part II develops calculus on manifolds, covering differential geometry, differential forms, and Riemannian geometry with applications to general relativity. Part III explores algebraic structures and symmetry, with comprehensive treatments of group theory, Lie algebras, and fiber bundles-the mathematical language of modern gauge theories.Part IV provides a thorough introduction to functional analysis, including Hilbert spaces, spectral theory, and operator algebras, with direct applications to quantum mechanics. Part V covers differential equations from both classical and modern perspectives, including variational methods and Hamiltonian mechanics. Part VI addresses probability theory, stochastic processes, and statistical mechanics, bridging the gap between mathematical formalism and physical applications. Part VII presents advanced topics including topology, algebraic structures such as Clifford algebras and spinors, path integrals, and gauge theory.Each chapter balances mathematical rigor with physical intuition, featuring numerous worked examples that bridge abstract concepts to concrete applications. The 278 carefully graded exercises range from computational practice to challenging theoretical problems, allowing readers to test and deepen their understanding. Five comprehensive appendices provide essential reference material.Designed for advanced undergraduate and graduate students in physics and applied mathematics, this book also serves as an invaluable reference for researchers seeking a unified treatment of mathematical methods in theoretical physics.Key FeaturesComprehensive coverage progressing from foundations to frontier topicsEmphasis on geometric and algebraic structures underlying modern physicsDetailed treatment of Hilbert spaces, spectral theory, and quantum mechanical applicationsComplete chapters on fiber bundles, connections, and gauge transformationsRigorous development of path integrals and functional methodsExtensive index with over 1,100 entries for easy reference
Math Mammoth Grade 1-A Worktext
Math Mammoth Grade 1-A worktext (Light Blue Series) is the student book for the first half of first grade mathematics studies. This is the 2026 edition, and the full-color version.In this part A, the main areas of study are: * The concepts of addition and subtraction;* strategies for addition and subtraction facts; * addition and subtraction word problems;* two-digit numbers and place value; and* telling time (whole and half hours).Features of the curriculum: * Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.* Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.* The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.* There is a strong emphasis on mental math and number sense.* Requires very little teacher preparation.* The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.* After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.* For addition and subtraction facts, you can use our online practice program (free). Please note this is a student worktext and does not contain answers. A companion to this book, Math Mammoth Grade 1-B worktext covers the second half of 1st grade math (available separately). Also available are the answer keys and a book containing cumulative reviews and chapter tests.
Cryptographic Algorithms
This book explores cryptographic techniques by integrating Elliptic and Jacobian Elliptic Curve Cryptography with Ancient Indian Mathematics, optimizing security and computational efficiency. As digital security becomes vital, the rich mathematical heritage of ancient India offers profound insights into cryptography, bridging historical wisdom with cutting-edge security solutions.Key frameworks- algebra, analysis, and optimization- enhance point operations like addition and doubling in cryptographic protocols. The book explores trilinear pairing and cryptographic schemes over specialized rings, leveraging projective geometry and algebraic structures to enhance encryption and decryption methods. Covering foundational concepts, algorithms, and applications, the book highlights how ancient Indian insights can improve Elliptic Curve Cryptography, Jacobian Elliptic Curve Cryptography, and trilinear pairing.Applications span secure vehicular communication using fog computing, blockchain-based authentication, and cloud security. It is targeted at cryptographers, mathematicians, and computer scientists and provides algorithmic innovations, security proofs, structured exercises, and real-world case studies.
Math Mammoth Grade 7 Answer Keys, International Version
Math Mammoth Grade 7 Answer Keys (International Version, 2025 Edition) contains answers to Math Mammoth Grade 7-A and 7-B worktexts, tests, and cumulative reviews. This is the full-color version.
Math Mammoth Grade 7-A Worktext, International Version
Math Mammoth Grade 7-A Worktext (International Version, 2025 Edition) is the student book for the first half of 7th grade mathematics studies or the first half of a pre-algebra course (Math Mammoth grade 7 is a pre-algebra curriculum). This is the full-color version of the worktext. Please note: The worktext does not include the answer key. The answer keys for grade 7 are sold as a separate book.The main areas of study in Math Mammoth Grade 7-A are: introduction to basic algebra conceptsintegers and their operationssolving one-step equations, including with negative numbersoperations with negative rational numberssolving linear equations and writing equations for word problemsFeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation required.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 7-B Worktext, International Version
Math Mammoth Grade 7-B Worktext (International Version, 2025 Edition) is the student book for the latter half of 7th grade mathematics studies or the latter half of a pre-algebra course (Math Mammoth Grade 7 is a pre-algebra curriculum). This is the full-color version of the worktext. Please note: The worktext does not include the answer key. The answer keys for grade 7 are sold as a separate book.The main areas of study in Math Mammoth Grade 7-B are: ratios, rates, proportions, and percentgeometry: angle relationships, compass & ruler constructions, drawing problems, pi and the area and circumference of a circle, cross-sections formed when cutting solids, surface area, and volumeprobabilitystatisticsFeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is very little teacher preparation required.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 7 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 7 Tests and Cumulative Revisions (International Version, 2025 Edition) contains chapter tests and additional cumulative review lessons to accompany Math Mammoth Grade 7 curriculum. This is the full-color version.
Time Scales Analysis
In Chapter 1, time scales are defined and some examples are given. Forward jump operators, backward jump operators, forward graininess functions and backward graininess functions are defined and some of their properties are given. The induction principle and dual induction principle are introduced. Chapter 2 deals with the delta differential calculus for one variable functions on time scales. The basic definition of delta differentiation is due to Hilger. We have included several examples on delta differentiation and the delta Leibniz formula for the nth delta derivative of a product of two functions. Nabla derivatives are introduced. We present delta mean value results. They are given sufficient conditions for delta convexity and delta concavity of one variable functions. It is stated a sufficient condition for completely delta differentiability of one variable function. Several versions ofdelta chain rules and delta L'H^opitals rules, which do not appear in the usual form, are included. In Chapter 3 are introduced the main concepts for regulated, delta rd-continuous and delta pre-differentiable functions. They are defined indefinite delta integral and the Riemann delta integral and they are deducted some of their properties. The basic delta monomials are defined and investigated. In the chapter are represented different variants of Taylor's formula. Improper integrals of the first and the second kind are defined and some of their properties are deduced. A survey on nabla integrals is done. Chapter 4 is devoted to the Hilger complex plane and the basic operations circle plus and circle minus. They are defined the basic delta elementary functions: delta exponential function, delta trigonometric functions and delta hyperbolic functions. Some of their properties are deduced.
Mathematical Cryptology
This text offers a comprehensive introduction to cryptology, based on elementary number theory and essential numerical algorithms. It covers core mathematical topics --number theory, algebraic structures, matrices, determinants, and polynomials --through their use in cryptography. Symmetric-key cryptography and practical techniques are introduced, followed by algorithms and computational complexity. Public-key systems based on integer factorization and discrete logarithms, as well as hash functions and digital signatures, are discussed. Advanced topics include elliptic curve and multivariate polynomial cryptography, primality testing, and integer factorization are also explored. The book is self-contained, with all necessary proofs, theory, and tools to analyze cryptographic security and attacks.
Calculus of One Variable
This book is a textbook about calculus of one variable. It contains proofs of all the theorems, propositions etc but also Python codes in order to solve many calculus problems. To produce these codes we use AI and show to the reader how to do that. This book aims to supplement the existing bibliography concerning single-variable calculus. Material including Python code for both symbolic and approximate computations. Our goal is to appropriately use artificial intelligence to generate this code and demonstrate to students how this is approximately done. This book is extremely useful for first-year science students, their professors, and others.
Mathematics of Deep Learning
This course aims at providing a mathematical perspective to some key elements of the so-called deep neural networks (DNNs). Much of the interest on deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g. introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics. The book focuses on deep learning techniques and introduces them almost immediately. Other techniques such as regression and SVM are briefly introduced and used as a steppingstone for explaining basic ideas of deep learning. Throughout these notes, the rigorous definitions and statements are supplemented by heuristic explanations and figures. The book is organized so that each chapter introduces a key concept. When teaching this course, some chapters could be presented as a part of a single lecture whereas the others have more material and would take several lectures.
Creative Activities in Mathematics - Book 1
Problem-based learning is a powerful alternative to drill-and practice or skills-based learning, especially within maths, but it can be difficult to source rich materials that engage an entire class.The Creative Activities in Mathematics series provides a wealth of investigations and open-ended active learning activities, designed to engage students with mathematics and develop their problem solving, collaboration and mathematical skills.Book One provides 12 different class activities suitable for students in lower and middle primary school (Foundation to Year 4), along with teaching notes and staged lesson plans. Each activity is a whole-class investigation with open-ended answers that takes a particular scenario and develops it over three levels. This enables it to be used both at different year levels and with students of differing ability in the same class. All activities are firmly rooted in the Australian Curriculum: Mathematics and linked to the content descriptors of the Number and Algebra, Measurement and Geometry, and Statistics and Probability strands.
Stochastic and Fuzzy Analysis of Parallel and Biserial Queuing Model
This book is an attempt to analyze the bi-serial and parallel queue network models with Priority discipline. The proposed Queuing Models have been analyzed in Stochastic as well as in Fuzzy Environment. The Chapman- Kolmogorov equations (CKE) are used to define the joint probability distributions with associated probabilities and satisfied all required conditions for the existence of time - independent solutions in stochastic process. The present study is useful to reduce congestions and idle period of service systems. The applicability of the study finds in banking sectors, medical, registrations and administrations and many other fields with assumptions of high priority visitors gets special treatment over the common (low priority) visitors.
Some Perspectives on Prime Number Theory and Its Relationship to Number Theory
What if the age-old Goldbach Conjecture harbors more than a simple additive truth? In this groundbreaking work, Samuel Bonaya Buya explores the conjecture through three powerful interpretations-viewing every integer greater than one as the mean of two primes, framing every even number as a difference of primes, and introducing a novel prime gap formulation with geometric depth. This book presents a bold reimagining of prime behavior through algebraic, analytic, and geometric lenses. With accessible derivations, radical new formulations, and thought-provoking implications, the author illuminates how the conjecture interweaves with the deepest structures in prime number theory. From symmetry in prime distributions to insights into prime gaps and additive partitions, this book is not just a study of Goldbach-it is a compelling journey through the hidden architecture of the integers. Designed for both researchers and advanced enthusiasts, this volume redefines how we approach one of mathematics' most enduring unsolved problems.
Numerical Analysis
Internationalization of mathematics education has become an inevitable trend, and bilingual education is a booster for achieving internationalization of mathematics education. Due to the vast territory of our country, there are significant differences in the foreign language proficiency and mathematical thinking ability of students in different regions and universities. Therefore, we cannot blindly establish unified standards for all mathematics courses in universities and choose some mathematics courses as bilingual teaching objects. In terms of content, "Numerical Analysis" is the most ideal choice for implementing bilingual education, and numerical analysis originates from practice. It is a discipline with a systematic theoretical system and is widely used as a powerful tool in many natural science fields such as automation control, communication and control, and electronic engineering. This book is divided into six chapters, which systematically introduces the basic theory and methods of numerical analysis, including mathematical foundations and error analysis, calculus review, error sources and precision control, direct/iterative methods for solving systems of linear equations, interpolation and polynomial approximation, curve fitting, numerical differentiation and integration, convergence, and precision. This book is suitable for teachers and students of science and engineering major in colleges and universities all over the country, and can also be read and referenced by engineering and technical personnel.
Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research
Decision-making is a constant feature in the lives of individuals and organizations. Choices, whether simple or complex, are shaped by preferences, experiences and available data, and often involve reconciling multiple points of view. Formally, a decision is the selection of a course of action based on information to solve a problem. In this context, Multicriteria Decision Analysis (MCDA) plays a vital role in evaluating options to identify the most favorable alternative or to rank them. MCDA is fundamental in allocating finite resources in the face of competing interests, a daily challenge in organizational and domestic environments. This Reprint presents new methods and applications that support decision-making in various organizational contexts, such as law enforcement agencies and the education sector, featuring the integration of multi-criteria methods, and contextualizes the theory through application to real-world problems.
Enterprise Transformation
Hello, I'm Jerry Torres. Over 75% of all enterprise transformation initiatives fail. This means they're halted before solutions are delivered but not before substantial time, money, resources and confidence are lost and wasted. Those that do succeed are mostly second, third or fourth go-rounds of previously failed efforts. Transformation program failure doesn't discriminate. It's common to both public and commercial sector enterprises and to every business space regardless of the initiative's size, location, complexity, cost or objectives.Whether you're transforming the fundamental ways you conduct and carry out business processes or procedures or enforce standards of performance; redefine your organizational or team structures; integrate emerging or cutting edge technologies such as Artificial Intelligence (AI), Robotics or Quantum solutions; transition from traditional Data Center or Network Operation Center (NOC) to Cloud Based Computing (CBC) architectures; or re-define your business cultures, values or belief systems, your enterprise faces momentous challenges and roadblocks to success. This book provides the magic you need to achieve your transformational objectives. This book is a practical methodological guide that defines how to deliver transformational enterprise solutions right the first time. This approach, named "Enterprise Transformation Methodology" (ETM), details proven practices that consistently result in comprehensive, sustained, precise and predictable results. It also describes the forces and dynamics that cause initiatives to fail and explains how to avoid, mitigate and manage them. Initiatives that succeed almost always protect themselves against these challenges, while those that fall victim to them fail.
Multigrid Methods
This book introduces the theory and application of multigrid methods for the fast numerical solution of linear and weakly nonlinear elliptic PDE. No previous exposure to numerical discretization methods is assumed. All that is required of the reader is curiosity and some basic knowledge of matrix theory and the theory of finite-dimensional vector spaces.We use an axiomatic, mostly-matrix-based approach in the book, both as a way of presenting the theory in a natural and simple setting, and as a means for translating the theory into practical codes. We deviate a little from the matrix-based-approach in the presentation of the framework for nonlinear problems in the latter part of the book. That nonlinear analysis, based on subspace decompositions, represents an area of current research. In fact, the book takes the reader all the way from the basics and simple implementation issues to the front lines of multigrid research.Coding the multigrid method is notoriously difficult. The current book, which contains several sample codes in the finite element and cell-centered finite difference frameworks, will train the interested reader in the construction of sophisticated, efficient multigrid codes using the simple but powerful MATLAB(c) programming environment.
Mathematical Biology
Very Short Introductions: Brilliant, Sharp, Inspiring Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumours. In this Very Short Introduction Philip K. Maini describes the art of modelling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach - verbal reasoning - is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Analysis with Mathematica(r)
A computer algebra system such as Mathematica(R) is able to do much more than just numerics: This revised text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica(R) represents domains, qualifiers and limits to implement actual proofs - a requirement to unlock the huge potential of Mathematica(R) for a variety of applications.
Functional and Harmonic Analysis
This book provides a comprehensive exploration of weighted function spaces, a fundamental topic in modern analysis. Beginning with the basics of weighted Lebesgue spaces, it systematically develops key properties such as duality, convexity, and interpolation. It delves into Muckenhoupt weights, Hardy and Carlson inequalities, and Calder籀n-Zygmund decompositions, highlighting their applications in harmonic analysis. With a structured and didactic approach, this work serves as an essential reference for researchers and graduate students in mathematical analysis, functional spaces, and related areas.
The Great Math War
A stirring account of the mathematicians who went looking for the bedrock philosophical foundations of their field and witnessed a house of cards collapse instead "A fascinating romp through one of the most consequential conflicts of the early 20th century."--Johnjoe McFadden, author of Life on the Edge As the nineteenth century ended, mathematicians were celebrating a century of triumphs that--surprisingly--made clear how little they knew: What is the nature of infinity? Is math free from self-contradiction? And what does math have to do with reality? This was the Foundational Crisis in mathematics. In The Great Math War, Jason Socrates Bardi tells the story of three competing efforts by mathematicians to resolve it--and the firefight that ensued. Bertrand Russell thought we could achieve certainty if we treated math as an extension of logic. David Hilbert believed redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition--and that math is not based on logic but rather logic is based on math. It was a bitter struggle, intellectually and personally, as the three vied to set the course for mathematics in the twentieth century. Set against the backdrop of international warfare unfolding alongside it, The Great Math War brings the Foundational Crisis to radiant life--and shows how it indelibly shaped twentieth-century intellectual life.
The Indisputable Existence of Santa Claus
In The Indisputable Existence of Santa Claus, two distinguished mathematicians explain, with humor and clarity, mathematical concepts through one very merry motif: Christmas. Lighthearted and diverting with Christmasy diagrams, sketches and graphs, equations, Markov chains, and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingsful of mathematical marvels. How do you apply game theory to select who should be on your Christmas shopping list? What equations should you use to decorate the Christmas tree? Will calculations show Santa is getting steadily thinner--shimmying up and down chimneys for a whole night--or fatter--as he munches on cookies and milk in billions of houses across the world? In their quest to provide mathematical proof for the existence of Santa, the authors take readers on a festive journey through a traditional holiday season. Every activity, from wrapping presents to playing board games to cooking the perfect turkey, is analyzed through the lens of math. Because who hasn't always wondered how to set up a mathematically perfect Secret Santa? This book belongs under your Christmas tree if you enjoy a spice of math in your eggnog.
Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3)
A hidden cornerstone of algebra returns rediscovered, restored, and reborn by Alpha Editions. Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3) is a rigorous, illuminating classic in mathematical group theory that probes the fine architecture of p-groups and their internal symmetries. This compact yet deep work guides readers through a precise analysis of order P^M groups, centering on P^(M-3) subgroup analysis and the role of cyclic subgroups in shaping algebraic structures. With clear proofs, carefully classified cases, and thoughtful exploration of cyclic group properties, Neikirk s group theory investigation advances subgroup classification and group order analysis in ways that still inform contemporary research. Scholars will find exacting results and techniques; curious learners will discover the logic and beauty behind abstract algebra. Historically significant and long out of print, this edition has been restored for today s and future generations. Alpha Editions presents more than a reprint this is a collector s item and a cultural treasure, prepared for mathematicians, libraries, and lovers of classic mathematical research alike. Whether you re assembling a reference shelf or seeking clarity on advanced mathematics, this volume offers enduring insight into algebraic structures and the foundations of subgroup theory. Rediscover Neikirk s contributions to mathematical group theory a must-have for anyone passionate about cyclic subgroups, subgroup classification, and the anatomy of p-groups.
A Textbook of Partial Differential Equation
Partial differential equations provide a generic description of the majority of physical events, whether they are related to heat flow, fluid dynamics, electricity, magnetism, mechanics, or optics. Such equations are, in fact, essential to mathematical physics. Even if these equations can be simplified to become ordinary differential equations, the full description of physical systems can be found in the general field of partial differential equations. This extremely helpful literature demonstrates to the reader how to create a mathematical model of the physical problem, how to generate a partial differential equation from it, and how to solve the equation (along with initial and boundary conditions).This succinct guide is devoted to assisting engineering students in solving problems in their profession that include partial differential equations and only requires a basic understanding of ordinary differential equations. Questions of existence, uniqueness, and convergence are not emphasised; instead, the treatment concentrates solely on the useful solution of partial differential equations. The more prevalent partial differential equations related to phenomena, including vibration, heat transport, electricity, and elasticity, are derived.For more details, please visit https: //centralwestpublishing.com
Multiple Integrals in Calculus
The book consists of eight chapters, each focusing on different aspects of multiple integrals and related topics in mathematical analysis.In Chapter 1, multiple integrals are defined and developed. The Jordan measure in n-dimensional unit balls is introduced, along with the definition and criteria for multiple integrals, as well as their properties. Chapter 2 delves into advanced techniques for computing multiple integrals. It introduces the Taylor formula, discusses linear maps on measurable sets, and explores the metric properties of differentiable maps. In Chapter 3, we focus on improper multiple integrals and their properties. The chapter deduces criteria for the integrability of functions of several variables and develops concepts such as improper integrals of nonnegative functions, comparison criteria, and absolute convergence. Chapter 4 investigates the Stieltjes integral and its properties. Topics covered include the differentiation of monotone functions of finite variation and the Helly principle of choice, as well as continuous functions of finite variation. Chapter 5 addresses curvilinear integrals, defining line integrals of both the first and second kinds. It also discusses the independence of line integrals from the path of integration. In Chapter 6, surface integrals of the first and second kinds are introduced. The chapter presents the Gauss-Ostrogradsky theorem and Stokes' formulas, along with advanced practical problems to practice these concepts.
Foundations of Numerical Methods and Data Analysis
This book offers a comprehensive journey into the world of numerical methods, beginning with the essential mathematical preliminaries: calculus, vectors, matrices, and programming concepts before moving into deeper areas such as error analysis, curve fitting, interpolation, and the numerical solution of ordinary and partial differential equations. Advanced chapters extend into systems of equations, finite element methods, and spectral techniques, ensuring that readers not only understand the fundamentals but also gain exposure to methods at the frontier of computational practice. A distinguishing feature of the book is the integration of theory with practice. Each concept is accompanied by carefully chosen examples, figures, and end- of-chapter exercises designed to strengthen understanding and encourage hands-on application. Historical notes and bibliographical references enrich the discussion, situating modern numerical methods in their broader intellectual context. In addition, the book pays special attention to the use of contemporary computational tools such as MATLAB, Python, and other numerical libraries, thereby bridging traditional methods with current software-driven practice. In short, it is both a textbook and a reference, meant to serve readers across different stages of their academic or professional journey. For more details, please visit https: //centralwestpublishing.com
Advanced Analytical and Numerical Methods with their Application to Industrial Problems
This book covers the models of different real-world problems that include the models using ordinary and partial differential equations and dynamical systems, uncertainty quantifications using fuzzy systems, computational methods for differential equations, modern control theory and applications, neural networks and neural computing, computational heat and mass transfer and computational fluid dynamics. It also includes various research problems on developing advanced analytical and numerical methods for solving real-world situations, with its theoretical derivations and engineering and science applications. For more details, please visit https: //centralwestpublishing.com
Evidence for Dark Numbers
This book contains several arguments for the existence of dark numbers, i.e., numbers which cannot be manipulated as individuals but only collectively. Their existence depends on the premise of actual infinity. Whether actually infinite sets exist is unknown and cannot be proven; it can only be assumed as an axiom. But if actually infinite sets exist then dark elements are unavoidable. This concept helps to explain many paradoxes of set theory like Zeno's paradox or the paradox of the binary tree or the completely scattered space of the real axis.
Compound Poisson Distributions
This book presents a comprehensive overview of compound Poisson distributions. All of the distributions listed in this book were derived, or invented, by the original authors as ""new"" statistical distributions, to fit a dataset(s) of experimental data. The properties of each newly proposed distribution were derived ab initio, sometimes with much effort by the original authors. Hence the title and motivation for this book: the primary focus here is the compound Poisson distributions themselves. We show that they are all exemplars of a common underlying formalism. General formulas (this includes both exact results and recurrences) are presented which apply to all compound Poisson distributions. In individual chapters, we apply that underlying formalism to selected compound Poisson distributions. We also derive new formulas not published in the literature. Having said the above, this book also presents a new technique for parameter estimation for a set of widely used compound Poisson distributions. The new technique is applied to several published experimental datasets, i.e. real data, not simulations. It yields equal or better fits to the data than those obtained by the original authors (in some cases, significantly better). Numerous graphs are plotted, to demonstrate the good/better fits obtained by the new technique. Hence this book contains not only pure theory, but also visually demonstrates the merits of the new formalism for fitting experimental data.
The Hidden Poetry & Music of Mathematics for Teaching Professionals
When poetry and music are interlinked with mathematics to provide phenomenal strategies to teaching mathematics. This would invite a plethora of thinking beyond classical frames to exceptional intelligent practice for teaching mathematics, including thinking outside classical frames to innovatively and creatively teach mathematics. This book is an open invite to all teaching professionals of mathematics.
Wonderlic Math Workbook
Complete math workbook, prepared by exam experts, with over 200 questions. You have arrived!Here is everything you need to pass the WONDERLIC(R)! We have helped thousands of students and we can help you!WONDERLIC(R) Basic Skills Math Practice Questions and Tutorials for: Fractions, Decimals and PercentWord ProblemsBasic AlgebraBasic GeometryWonderlic is a registered trademark of WONDERLIC, INC CORPORATION, who are not involved in the pro-duction of, and do not endorse this product. You also receive: - Math Multiple-Choice Strategy - How to Study for a Math Test - How to make a WONDERLIC(R) study plan - How to Take a TestHere is what the WONDERLIC(R) Math Workbook can do for you: - Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the WONDERLIC(R) - Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.- Practice reduces test anxiety, one of the main reasons for low marks on an exam. - Learn powerful multiple-choice strategies designed by exam experts! Includes tips and multiple-choice strategies to increase your score you won't find anywhere else!You can get a Great Score with the Least Amount of Studying! Study Smarter, Not Harder!You receive the benefit of our dedicated team of exam experts. All the material in the math workbook, including every practice question, are designed increase your score on the WONDERLIC(R) exam with the least amount of studying. Heard it all before? Maybe you have read this kind of thing before, and maybe feel you don't need it, and you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students. Even if our test tips increase your score by a few percentage points, isn't that worth it?I will be honest - it will require real effort and dedication, but if you are willing to focus your energy and devote the study time necessary, (don't worry - we help every step of the way) then before you know it you will be opening that letter of acceptance to the school or the job of your dreams. Do everything to get the best score on the WONDERLIC(R)!
Complex Function Theory
The text book gives a clear and concise analysis of the fundamentals of complex function theory. It presents various illustrative and motivating examples to make the concepts clearer and to help the students to acquire a basic understanding of the subject and learn the techniques of problem solving, which will help him/her enormously in the examinations like GATE, NET, CSIR etc.We hope this book would appeal not only to post graduate students of Mathematics and Physics (including research mathematicians) but also to those engineering students who are highly motivated.Salient Features* The concepts are emphasized in each chapter to make the students learn them thoroughly.* Applications of most of the theorems are shown through various solved examples.* Theorems and Propositions are stated in the maximum possible generality and much stress has been given to help the readers to compare and understand how vastly different the subjects Complex Analysis and Real Analysis are.* The exercise sets given at the end of each chapter shall sharpen the student's intellectual ability.* Nearly 80 figures are drawn to illustrate the results which will help the students for visualization.* The book is more exhaustive than most of the existing books.* The solved examples and exercises will better prepare students for different competitive examinations like GATE, NET, CSIR, NBHM etc.
TASC Math Mastery
TASC Math Mastery: Complete Tutorials & Practice Workbook with 200+ QuestionsYou have arrived!Here is everything you need to pass this tough test!We have helped thousands of students and we can help you! Over 200 TASC math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! TASC Math Practice Questions and Tutorials for: Basic MathScientific NotationExponents and Radicals Square RootFractions, Decimals and PercentMeans, Median and ModesAlgebra Solve real world problems with ratio and proportion Solve one and two variable equations Identify and solve quadratic equations given values or graphs Solve quadratic using different methods Translate real world problems into quadratic equa-tions and solve Basic Geometry Slope of a line Identify linear equations from a graph Calculate perimeter, circumference and volume Solve problems using the Pythagorean theorem Determine geometric transformations Solve real world problems using the properties of geometric shapesTASC(R) is a registered trademark of the Educational Testing Service (ETS), who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
SSAT Math Workbook
Over 200 SSAT(R) math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! You have arrived! We have helped thousands of students and we can hlep you!SSAT(R) Math Practice Questions and Tutorials for: AlgebraBasic MathGeometryWord ProblemsProbabilityStatisticsSSAT(c) and the Specialized High School Admissions Test(c) are administered by the New York Department of Education, who are not involved in the produc-tion of, and do not endorse this publication.You also receive: - Math Multiple Choice Strategy - How to Study for a Math Test - How to make a SSAT(R) study plan - How to Take a TestHere is what the SSAT(R) Math Workbook can do for you: - Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the SSAT(R) math test.- Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.- Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.SSAT(R) Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.- Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.- Learn powerful multiple choice strategies designed by exam experts! Includes tips and multiple choice strategies to increase your score you won't find anywhere else!Practice Really Does Make Perfect! The more questions you see, the more likely you are to pass the test. And between our study guide and practice tests, you'll have over 200 practice questions that cover every category. Our SSAT(R) Math practice test questions have been developed by our dedicated team of experts. All the material in the study guide, including every practice question, are designed to engage your critical thinking skills needed to pass the test! Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
NLN PAX Math Workbook
Over 200 NLN PAX math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple-choice strategies! ou have arrived! We have helped thousands of students and we can help you! Practice questions and tutorials for: Basic MathFractions and DecimalsWord ProblemsMetric ConversionBasic AlgebraGeometrySpeed, Force and MomentumMode, Mean and MedianAnd more!NLN PAX and the National Nursing League are not involved in the production of, and do not endorse this publication.You also receive: Math Multiple Choice StrategyHow to Study for a Math TestHow to make a NLN PAX study planHow to Take a TestPlease note that the PAX RN is administered by the National League of Nursing which is not involved in the production of, and does not endorse, this product. Here is what the NLN PAX Math Workbook can do for you: Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the NLN PAX math test.Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.NLN PAX Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book.Remember though, it only a few percentage points divide the PASS from the FAIL students!Even if our test tips increase your score by a few percentage points, isn't that worth it?
Artificial Intelligence Technologies for Education
This Reprint presents a collection of cutting-edge research and reviews on the application of artificial intelligence (AI) technologies in education, focusing on both theoretical advancements and practical implementations. It examines how AI can be leveraged to enhance personalized learning, support adaptive assessment, enable intelligent learning environments, and facilitate more effective human-computer interaction in educational contexts. The contributions cover a broad spectrum of topics, including student and cognitive modeling, educational data mining, natural language processing for educational purposes, learning analytics, and the design of automated assistants and intelligent tutoring systems.The works featured in this Reprint address key challenges and opportunities in integrating AI into diverse educational domains. They explore innovative methods and tools for analyzing learning data, delivering targeted instructional support, and adapting pedagogical strategies to meet the needs of individual learners. The collection also highlights the interplay between AI-driven systems and educators, emphasizing collaborative and human-centered approaches to technology-enhanced learning. By bringing together original research, comprehensive surveys, and case studies, this Reprint provides valuable insights into the evolving role of AI in shaping the future of education, making it a useful resource for researchers, practitioners, and policymakers alike.
HOAE PSB Math Workbook
Over 200 PSB math practice questions, prepared by a dedicated team of exam experts!You have arrived! We have helped thousands of students and we can help you! Practice questions and tutorials for: Basic Math Fractions and DecimalsWord ProblemsMetric ConversionBasic AlgebraGeometrySpeed, Force and MomentumMode, Mean and MedianAnd more!The PSB Health Occupations Aptitude Exam is administered by the Psychological Services Bureau, who are not involved in the production of this book and do not endorse this product. You also receive: Math Multiple Choice StrategyHow to Study for a Math TestHow to make a PSB study planHow to Take a TestHere is what the PSB Math Workbook can do for you: Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the PSB math test.Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.PSB Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.Learn powerful multiple-choice strategies designed by exam experts! Includes tips and multiple-choice strategies to increase your score you won't find anywhere else!Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Calculus I
This Calculus I workbook is designed to provide structure to the Peer-Led Team Learning (PLTL) Workshop. These materials, originally developed from courses at the University of Maine, Morehouse College, and Prince George's Community College in Maryland, have been tested and provide students with many valuable tools for success.Each unit in this publication falls into one of three categories: (1) a discovery workshop, best offered before discussion of a concept occurs in class, with the goal that your learning will be enhanced through discovering an idea with peers; (2) an exploratory workshop, best offered after a concept is discussed in class so you can explore concepts in more depth with the goal of deepening your understanding of the idea; (3) a review workshop that is offered so you can practice important skills. You may be asked to complete the entire workshop, or selected parts because of the extensive nature of the topic and/or time constraints.
Blueprints
"A stunning book ... a thrilling read" (Peter Frankopan) that reveals how creative people can harness the profound and productive relationship between mathematics and the arts When Shakespeare has the Three Witches cast Macbeth's lot, he uses something very weird to do it: not simply "eye of newt and toe of frog," but the number seven. And when Hamlet claims, "To be or not to be, that is the question," Shakespeare reaches for eleven. For Shakespeare, prime numbers were magical. And he is not alone. As Marcus du Sautoy showcases in Blueprints, creativity is inseparable from mathematics. The designs of Le Corbusier and Leonardo; the music of Glass, Bach, and Debussy; the wild visions of Dali, the choreography of Laban, the animation of Pixar--all are shot through with mathematics, from primes and fractals to the weirder worlds of Hamiltonian cycles and hyperbolic geometry. And Du Sautoy argues that the relationship runs both ways. Just as mathematics inspires new art, the artistic mindset is a necessity for discovering new mathematics. Blueprints will expand your mind, but more importantly, it shows how to ignite your imagination. Anyone who wants to create needs this book.
Master HiSET Math
HiSET Math Mastery: Complete Tutorials & Practice Workbook with 200+ QuestionsYou have arrived! We have helped thousands of students and we can help you! Over 200 HiSET math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! HiSET Math Practice Questions and Tutorials for: Basic MathScientific NotationExponents and Radicals Square RootFractions, Decimals and PercentMeans, Median and ModesAlgebra Real world problems with ratio and proportion One and two variable equations Solve quadratic equations given values or graphs Quadratic using different methods Basic Geometry Slope of a line Linear equations from a graph Perimeter, circumference and volume Pythagorean theorem Geometric transformations Real world problems using the properties of geometric shapesYou also receive: Math Multiple Choice Strategy- How to Study for a Math Test- How to make a study plan- How to Take a TestHiSET(R) is a registered trademark of the Educational Testing Service (ETS), who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
