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Huge Numbers
How humanity's long pursuit of ever-larger numbers broke the boundaries of mathematics and propelled us into the Information Age "A charming tour"--Jordan Ellenburg, author of Shape What if, every time you wanted to write down 1,000,000, you had to draw a picture of a god? And what if that number were the biggest you had a symbol for? If you were doing math in ancient Egypt, those were the rules: anything bigger broke math. As mathematician Richard Elwes shows in Huge Numbers, this is the strange story of math. Even today, writing down some numbers is beyond us: try it with all the zeroes in a googolplex, or an outrageous alien number like TREE(3). Safer not to try: even harnessing every particle in the universe, you wouldn't come close. But this book is no mere bestiary of numerical monsters. It shows how, by hunting down and studying ever-bigger numbers, arithmetic has reshaped human thought and made our modern era of science and computation possible. Where many math books celebrate abstract algebra or ineffable infinities, Huge Numbers is both more practical and far weirder. It reveals a world where most numbers remain out of reach until we discover how to chase them down and tame them, and so remake our world again.
Algebra and Discrete Mathematics for Economics
Algebra and Discrete Mathematics are essential tools also for economists. Globalization makes that goods and services are exchanged worldwide. Input-output analysis uses the advantage of a relatively stable flow of commodities and services. The essential principles can be described by input-output tables. Such tables correspond to systems of linear equations, written as single equations consisting of matrices whose entries are non-negative rational numbers. The flow itself can be described by a directed edge-valued graph where the sets of values consist of positive rational numbers. Therefore numbers, especially non-negative rational numbers, multiple-partite graphs and matrices with non-negative rational entries play an important role in input-output analysis. Thus knowledge from Algebra and Discrete Mathematics becomes more and more useful in this area.We will consider a particular set of graphs, the so-called input-output graphs and a particular set of matrices, the input-output matrices, define a partial binary operation on each of these sets and prove that we obtain weakly isomorphic weakly partial semigroups. The result of considering this situation can be applied to multiple-step production processes, to material reqirements planning and to internal cost allocation of a business. The results show that Algebra and Discrete Mathematics are quite useful for mathematical modeling in Economy.
Simple Quadrature
An Illustrated Introduction to the Estimation of Surface Areas ( Quadrature ) with Example Applications drawn from Lake Geomorphology.The Book benefits from Extensive Mathematical Guidance with Equations and Computer Programs.
Math Mammoth Grade 1 Answer Keys
Math Mammoth Grade 1 Answer Keys contains the answers to the Grade 1-A worktext, Grade 1-B worktext, chapter tests, end-of-year test, and the cumulative review lessons from the Math Mammoth Grade 1 curriculum (2026 edition).
Math Mammoth Grade 1-B Worktext
Math Mammoth Grade 1-B worktext (Light Blue Series) is the student book for the second half of first grade mathematics studies in the Math Mammoth Grade 1 curriculum. This is the 2026 edition.In this part B, the main areas of study are: addition and subtraction facts within 0-10;geometric shapes, halves, and quarters;measuring length;adding and subtracting within 0-100; bar graphs;and counting coins.Features of the curriculum Math Mammoth focuses on conceptual understanding. It explains the "WHY", so the 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. The curriculum 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). A companion to this book, Math Mammoth Grade 1-A worktext covers the first half of 1st grade math (available separately). Also available are the answer keys and a book containing cumulative reviews and chapter tests.
Math Mammoth Grade 1 Tests and Cumulative Reviews
Math Mammoth Grade 1 Tests and Cumulative Reviews includes consumable student copies of: end-of chapter tests, the end-of-year test, andcumulative review lessons.The book also includes links to several downloadable board games that go along with the curriculum. It does not include answers; an answer key book is available separately.This is the 2026 edition.
What Are the Odds?
From bar bets to Nobel Prizes, viral outbreaks to lottery wins, how statistics shapes our choices, reveals hidden truths, and guides us toward certainty in uncertain times. We live in an uncertain world. Morning commutes, natural disasters, global pandemics--our lives are riddled with events whose outcomes we can never know with certainty. In What Are the Odds? Mark Prell reveals how statistical thinking empowers us to navigate this uncertainty with clarity and confidence. Whether weighing the benefits of different medications or deciding if home insurance is worth the steep cost, Prell shows that just as important as asking what the data says is asking how reliable it is. Describing the core concepts and methods of statistical thinking, he teaches us how to extract meaningful information from raw data, and crucially, to recognize data that's been cherry-picked, fabricated, or is simply wrong. As we ask if survey responses are truthful, estimate the number of deaths from the Covid pandemic, and plan for retirement, we develop a skill set to test and update our assumptions, to make more accurate forecasts, and above all, to assess the certainty of our conclusions. Through unforgettable stories of statistical ingenuity, Prell demonstrates that the underlying math can be intuitive and even fun. And as he turns us all into statisticians, he reminds us that statistics is about more than manipulating data--it's about joining a community of statisticians committed to truth and integrity.
Locally Convex Spaces
This book provides an updated introductory textbook on the topic of locally convex topological vector spaces. Readers who enjoy combinations of topology, analysis and linear algebra will discover fascinating relevance in this work. The target audience is anyone, such as graduate students and researchers who have a typical background in one semester courses in topics like topology, and analysis of normed/Banach spaces. Several chapters are standard, with topics like basic properties of topological vector spaces and local convexity, the Hahn-Banach Theorem, the basics of duality, and some deep results such as the Banach-Steinhaus and Closed Graph theorems. Unique features of this book include the inclusion of examples from normed and Banach spaces that show how such spaces fit in within the larger context of locally convex spaces, the utility of sequences and series, examples of recent applications to results such as in distribution theory and optimization, and introductions to some atypical contexts of locally convex spaces such as convergence vector spaces and abstract duality pairs. Readers will find a colorful world of spaces and results that will be useful for starting research, or gaining insight into analysis and topology.
Math Mammoth Division 1
Math Mammoth Division 1 is a worktext that covers the concept of division, finding whole-number quotients within 0-100 (essentially, the basic division facts), and bar graphs and pictographs. It is most suitable for third grade, after the student knows the multiplication tables.The approach taken here to teach division facts is to simply base them on the multiplication tables, and not to teach them as a separate set of facts to memorize. This is very efficient and works well when the student knows the times tables. Several lessons in the book focus on this basic concept that division problems can be solved by thinking of multiplication.There are basically two ways to interpret division, and thus to illustrate it with concrete objects. The first way has to do with grouping. The problem 12 繩 3 is interpreted as, "How many groups of three items can you make out of 12 items?" This is also called measurement division.The second way to interpret division is equal sharing: we divide or share items equally between people or other items. For example, the problem 12 繩 3 can be interpreted as, "If you share 12 bananas equally between 3 people, how many bananas does each one get?"Both of these interpretations of division are important to understand so that the student can solve real-life and mathematical problems involving division.We also study division by zero. In that lesson, students should recognize that division by zero "does not work." The latter part of the book deals with bar graphs and pictographs. Earlier (in 2nd grade), students have drawn pictographs and bar graphs with single-unit scale. Now, they draw scaled pictographs and bar graphs from the given data, choosing the scale, or how many items one block in the bar graph or one picture in the pictograph signifies. This process provides practice in using both division and multiplication.This book will be relatively easy for students who have mastered the multiplication tables, since division facts are just multiplication tables "backwards". So, students can focus on another important skill: recognizing real-life situations in word problems that mathematically relate to either division or multiplication. This is very important to master so that the student can later on translate more complex situations into equations (modeling with mathematics).You can find free videos covering topics of this book at https: //www.mathmammoth.com/videos/ (choose 3rd grade, then division).The answer key is appended.
Numerical Analysis
Students completing a year of Calculus can find novel and practical challenges in mathematics using numerical analysis. This text follows the mathematician's process of examining a problem and deciding which algebraic or calculus techniques lead to reliable solutions. Each algorithm includes all developmental steps, illustrating the beauty of reducing complex systems to streamlined formulae. Accessible proofs using techniques beyond those in geometry are fully explained. All algorithms contain detailed examples of success and situational pitfalls. An exhaustive set of practice problems was meticulously developed by hand, not AI-generated, ensuring deviations at each stage of a particular algorithm. Many exercises highlight advantages and disadvantages of algorithms through comparison.
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.
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.
Open Mathematical Problems
The book presents much creative, original and stimulating ideas on the various approaches which could be taken to tackle five important open problems in mathematics, viz., the twin primes, Goldbach and Polignac's conjectures, and, the Navier-Stokes equations and turbulence, and the Riemann hypothesis which are both Millennium Prize problems. Technical areas such as calculus, differential equations, group theory/symmetry and complex analysis are covered, as well as logic and mathematical reasoning in general, and they are presented as clearly as possible for easier assimilation. For those who are interested in mathematical reasoning and logic, and researchers working on the open problems in mathematics, the book will offer much food for thought and inspire further advancement of the ideas presented in the book.
Mathematical Analysis for Sciences and Engineering
A real contribution to mathematical analysis, a discipline that requires a great deal of study and attention and finds interesting applications in many disciplines of sciences and engineering. This book is designed for graduate students in mathematics and engineering. From the first chapters, the book introduces real and complex numbers, the cornerstones of analysis. It explains in detail the properties of real numbers, such as the square root, absolute value. The analysis of sequences and series occupies a central place in this textbook. The reader discovers, step by step, the convergence through the study of real sequences, drawing on the concepts of Cauchy sequences and monotone sequences. The book also covers numerical series, presenting a variety of convergence criteria. The field of functions and asymptotic study of functions is treated with particular attention. The book contains proofs, numerous examples, and exercises with hints and solutions. The approach differs from similar books in that it is sequential, simplified concepts, and includes numerous solved examples and exercises that serve the reader, enabling them to understand the content well.
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.
The Language of Mathematics
A marvelous compendium of mathematical symbols and their fascinating histories Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Ra繳l Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, Ren矇 Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning.
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-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-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 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.
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.
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.
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.
Innovating Independently in Mathematics
The definitive collection of thoughts and essays by Hua Luogeng (1910-1985), the "Father of Modern Chinese Mathematics" and a pioneer in Analytic Number Theory. Hua Luogeng was a towering figure in 20th-century mathematics. A former professor at the University of Illinois (Urbana-Champaign) and member of the National Academy of Sciences (USA), Hua bridged the gap between Western mathematical research and China's scientific development. This volume, Innovating Independently in Mathematics, presents a comprehensive archive of his academic philosophy and contributions. Key highlights include: Theoretical Breakthroughs: Insights into his foundational work in Number Theory, Matrix Geometry, and the Theory of Complex Functions. Applied Mathematics: His revolutionary "Method of Optimization" (0.618 Method) that transformed industrial efficiency in China. Educational Legacy: His vision for mathematical education and the "self-taught" spirit that inspired generations. An essential primary source for collections in Number Theory, History of Mathematics, and Asian Scientific Development.
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.
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.
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.
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.
Math Mammoth Grade 7-A Worktext, Canadian Version
Math Mammoth Grade 7-A Worktext (2025 Edition, Canadian Version) 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.This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 7, only customized for the Canadian audience in these aspects: The curriculum uses mostly the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.
Math Mammoth Grade 7-B Worktext, Canadian Version
Math Mammoth Grade 7-B Worktext (2025 Edition, Canadian Version) 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.This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 7, only customized for the Canadian audience in these aspects: The curriculum uses mostly the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.
Math Mammoth Grade 7 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 7 Tests and Cumulative Reviews (2025 edition, Canadian Version) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 7 curriculum. Please note: The answer keys are not included. They are sold in a separate book that includes all answer keys for the Math Mammoth Grade 7 Complete Curriculum.
Math Mammoth Grade 7 Answer Keys, Canadian Version
Math Mammoth Grade 7 Answer Keys (2025 edition, Canadian Version) contains answers to Math Mammoth Grade 7-A and 7-B student worktexts, to chapter tests, to the end-of-year test, and to the cumulative review lessons. This is the full-color version.
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.
How to Do Good Mathematics
A definitive collection of essays, lectures, and reflections by the "Father of Modern Differential Geometry," Shiing-Shen Chern (1911-2004). Curated for mathematicians, historians of science, and educators, How to Do Good Mathematics provides a primary-source perspective on the evolution of 20th-century mathematics. As the founding director of the Mathematical Sciences Research Institute (MSRI) and a Wolf Prize laureate, Chern's influence extends far beyond the Chern Classes. This volume features: Historical Insight: Chern's personal account of the development of global differential geometry and his interactions with contemporaries like Andre Weil and Solomon Lefschetz. Educational Philosophy: His vision for mathematical education in China and the West, advocating for the integration of humanistic values in scientific research. Key Lectures: Including his seminal talks on the relationship between geometry and physics. An essential acquisition for academic libraries building collections in mathematical history, geometry, and scientific biography.
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.
Graph Theory
The author's passion for teaching core computer science courses, particularly discrete math and algorithms, inspired this book. Graphs are crucial in solving real-world problems, and this book aims to present graph theory gradually and accessibly. It provides a comprehensive overview of foundational and advanced concepts, starting with an introduction to graph theory, types of graphs, and their significance. The book covers key terms, properties, Eulerian and Hamiltonian graphs, isomorphism, subgraphs, and special graphs such as complete and bipartite graphs.The representation of graphs is discussed highlighting their practical applications and differences. A dedicated chapter showcases the use of graphs such as search engines, networks, and bioinformatics. Various graph algorithms are detailed, including Eulerian tours, shortest paths, minimum spanning trees, maximum flow, and matching. An appendix on algorithm complexity provides insights into analyzing algorithms, time complexity.This book is ideal for undergraduate and graduate students in mathematics, computer science, engineering, and those interested in mathematical structures. It is also valuable for software engineers and developers interested in modeling systems.
