A groundbreaking treatise by one of the great mathematicians of our age, who outlines a style of thinking by which great ideas are conceived.What inspires and spurs on a great idea? Can we train ourselves to think in a way that will enable world-changing understandings and insights to emerge?Richard Hamming said we can. He first inspired a generation of engineers, scientists, and researchers in 1986 with “You and Your Research,” an electrifying sermon on why some scientists do great work, why most don’t, why he did, and why you can—and should—too. The Art of Doing Science and Engineering is the full expression of what “You and Your Research” outlined. It's a book about thinking; more specifically, a style of thinking by which great ideas are conceived.The book is filled with stories of great people performing mighty deeds—but they are not meant simply to be admired. Instead, they are to be aspired to, learned from, and surpassed. Hamming consistently returns to Shannon’s information theory, Einstein’s theory of relativity, Grace Hopper’s work on high-level programming, Kaiser’s work on digital filters, and his own work on error-correcting codes. He also recounts a number of his spectacular failures as clear examples of what to avoid.Originally published in 1996 and adapted from a course that Hamming taught at the US Naval Postgraduate School, this edition includes an all-new foreword by designer, engineer, and founder of Dynamicland Bret Victor, plus more than 70 redrawn graphs and charts.The Art of Doing Science and Engineering is a reminder that a capacity for learning and creativity are accessible to everyone. Hamming was as much a teacher as a scientist, and having spent a lifetime forming and confirming a theory of great people and great ideas, he prepares the next generation for even greater distinction. Read more

From the bestselling author of Quantum Computing for Everyone, a concise, accessible, and elegant approach to mathematics that not only illustrates concepts but also conveys the surprising nature of the digital information age.Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math, Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and, finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved.Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions. Read more

An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others. Read more

This text is geared toward assisting engineering and physical science students in cultivating comprehensive skills in linear static and dynamic finite element methodology. Based on courses taught at Stanford University and the California Institute of Technology, it ranges from fundamental concepts to practical computer implementations. Additional sections touch upon the frontiers of research, making the book of potential interest to more experienced analysts and researchers working in the finite element field. In addition to its examination of numerous standard aspects of the finite element method, the volume includes many unique components, including a comprehensive presentation and analysis of algorithms of time-dependent phenomena, plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. It also contains a systematic treatment of "weak," or variational, formulations for diverse classes of initial/boundary-value problems. Directed toward students without in-depth mathematical training, the text incorporates introductory material on the mathematical theory of finite elements and many important mathematical results, making it an ideal primer for more advanced works on this subject. Read more

Master essential logarithm and exponential skills through helpful explanations, instructive examples, and plenty of practice exercises with answers. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:logarithms of various bases and natural logarithmsthe change of base formulalogarithm rules like the sum and difference formulasexponential functionshyperbolic functions and their inversesgraphs of logarithms, exponentials, and hyperbolic functionsa concise review of exponents in the first chapterEuler’s numberapplications such as population growth, continuously compounded interest, and radioactive nuclear decaysan introduction to complex numbers in the last chapteran optional chapter covering the calculus of logarithms, exponentials, and hyperbolic functionsThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for working with logarithms and exponentials. Read more

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics. Read more

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Enhance your logic, reason, judgment, and wisdom. Increase your ability to create concise and reasoned arguments using data and evidence, to get a genuine conclusion.The Systems Thinker – Analytical Skills aims to raise the level of your mental performance by focusing on the fundamentals of how to use your mind effectively.This book will show you how to:• Increase your ability to analyze problems and to comprehend what you read, hear, experience in a logical manner.• Examine the logical structure of good and bad reasoning. • Look at what type of evidence are decisions commonly based on.• Detect common fallacies and rhetorical and psychological factors that can influence your thinking. The book presents the methods that good problem solvers use in understanding complex ideas. It provides practice in applying these methods to a variety of comprehension, analytical, and reasoning questions. It also includes a number of logical thinking problems to hone your logical thinking skills.Use these intellectual skills to analyze anything you might think about - questions, problems, disciplines.• The most widely used forms of analysis.• Guidance and practice to monitor your thoughts with the help of intellectual tools.• Learn to question purposes, problems, information, and concepts.• Interdisciplinary analytical tools to understand and assess your own reasoning, be it about a highly technical question or your everyday life. The Systems Thinker – Analytical Skills helps you to find the most fundamental logic of any discipline, problem, or thesis. Transfer your knowledge between and among subjects and fields of observation.• Learn four types of profound analysis.• Learn to read and create statistical charts.• Learn and correct the most frequent errors in reasoning.• Learn to complement your analytical thinking tools with synthetic, systemic, critical, and creative thinking tools.Good analytical thinking skills are deeply necessary if you are working in business, education, law, politics, and economics.Albert Rutherford is an internationally bestselling author whose writing derives from various sources, such as research, coaching, academic and real-life experience.Understanding the underlying structure of a problem can help you come up with the best solution. Adopt analytical thinking skills to make better decisions, assess situations more accurately, and persuade other people with more success to consider your point of view. This book serves as a springboard toward analytic proficiency. Read more

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition. Read more

Unlock the mathematical engine that powers signal processing, quantum mechanics, and data science. This graduate‑level reference walks you step‑by‑step from the bedrock of measure theory to the cutting edge of Littlewood–Paley decompositions and wavelet frames—all in 44 tightly structured chapters engineered for rapid mastery.• From Lebesgue to Fourier – Build an unshakable foundation in Lᵖ spaces, orthogonality, and convergence theorems.• Transform‑Driven Insights – Master Fourier series, Fourier integrals, DFT, FFT concepts, multidimensional transforms, and the Poisson Summation Formula.• Core Operators Demystified – Conquer Hilbert and Riesz transforms, maximal functions, singular integrals, and fractional potentials.• Real‑World Connectivity – See rigorous proofs translate directly to signal reconstruction, uncertainty principles, spectral methods, and machine‑learning kernels.• Future‑Proof Skill‑Set – 400+ worked examples and tiered exercises turn abstract theory into practical expertise for research, teaching, or advanced industry work.Whether you’re sharpening your analytical toolkit or building curriculum, this single volume condenses decades of harmonic analysis into an accessible, engaging, and indispensable resource. Read more

This book covers a wide range of topics and techniques in Bayesian analysis, providing readers with a comprehensive understanding of this powerful statistical method and its practical applications.Starting with the fundamental concept of Bayes' theorem, the book dives into the mathematical foundation and definition, followed by its implementation in Python. You'll explore a variety of Bayesian modeling techniques, such as understanding prior and posterior distributions, likelihoods, and the application of conjugate priors.The book also covers advanced topics like Markov Chain Monte Carlo (MCMC) algorithms, including Gibbs Sampling, Metropolis-Hastings Algorithm, Hamiltonian Monte Carlo (HMC), and No-U-Turn Sampler (NUTS). With detailed explanations and step-by-step Python implementations, you'll gain valuable hands-on experience.Additionally, the book covers approximation methods like Approximate Bayesian Computation (ABC), Variational Inference, Expectation-Maximization (EM) Algorithm, Sequential Monte Carlo Methods (SMC), Particle Filters, and Kalman Filters. You'll also explore Bayesian modeling for linear regression, logistic regression, Gaussian processes, Dirichlet processes, latent Dirichlet allocation (LDA), hidden Markov models (HMM), Bayesian theorem networks, and hierarchical models.Throughout the book, you'll find practical code examples in Python, making it easy to apply the concepts to real-world scenarios. Whether you're a beginner or an experienced data scientist, this book will equip you with the necessary skills to confidently analyze and model data using Bayesian methods. Read more

This book is dedicated to the Dirac equation. The main arguments are: Dirac equation, gamma matrices in Dirac representation, properties of gamma matrices, covariance of the Dirac equation, Dirac Lagrangian and derivation of the Dirac equation from the equations of the Euler-Lagrange motion, Dirac equation in Hamiltonian form and free solutions in the rest and in any reference frame. Read more

The purpose of Blackjack for Blood, by Bryce Carlson, is to provide the reader with a comprehensive strategy for obtaining a winning edge at the game as it is commonly played in the casinos of Nevada and elsewhere, and also to entertain the reader with some sense of the glamour, excitement, and drama that are a part of the world of the professional gambler. For a Twenty-One game plan to be effective, it must address three fundamental and very different issues. First, it must show the player how to bet his money properly and how to play the hands accurately. Second, it must instruct the player on how to deal effectively with casino personnel. And third, a professional approach to the game requires the ability to deal with yourself, to maintain control under pressure and in situations loaded with stress. Read more

What knowledge should a calculus textbook cover? Are we able to tell the goals of learning on top of the content from the outline of the textbook? After every abstruse definition and theory, if there’s only one or two simple demonstrations, what then, is the root cause for students’ inability to solve those difficult practices, a lack of practice or the unfamiliarity of different practice variations? If there’s an exam starting minutes away, what content can be remembered from a closed textbook? There are five highlights in this textbook:First of all, readers can be aware of the learning goals of each chapter from the outline, allowing beginners to calculus to have clear understanding of the textbook’s structure.Secondly, before sample practices in each chapter, classic question variations are outlined with steps in solutions. Hence, after practicing, readers will be able to fully grasp the concepts and variation through steps of the solutions.Thirdly, the book contains more than 2,000 samples and each sample is demonstrated with the most thorough solution steps. Hence, readers will not find themselves confused with skipped steps.Fourthly, in hopes of allowing readers to understand the book as a whole, including relationships between chapters and significance in specific chapters, I’ve written the textbook as plain and straight-forward as possible. For instance, knowing where and how L'Hôpital's rule will be used in later chapters.Finally, in contrast with the simple explanations, each sample question is answered with great rigor and accuracy. Across all sample practices in the book, I’ve only used “Let”, “Then”, “Since”, “Thus”, and “Such that” to keep explanations simple and consistent. With all the above mentioned, I hope to present the most detailed context of calculus to all the readers. Read more

The Principia is "justly regarded as one of the most important works in the history of science". The Mathematical Principles of Natural Philosophy, often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of mathematical Principles of natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny that" (out of the Principia) "a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally." In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities. In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I contrive no hypotheses"). Read more

Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs—all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant discipline—its long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors’ extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher-level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1–5 introduce the fundamentals of abstract mathematics and chapters 6–8 apply the ideas and techniques, placing the earlier material in a real context. Readers’ interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments. Read more

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Discrete Mathematics for Computer Science Made EasyEmbark on a journey through the essential concepts of discrete mathematics with "Discrete Mathematics for Computer Science Made Easy," a definitive guide designed to empower computer science students and professionals. This book breaks down the complexities of discrete math into digestible, easy-to-understand sections, making it accessible to learners at all levels.Key Features:Comprehensive Coverage: From foundational principles like sets, logic, and proofs to advanced topics such as graph theory, number theory, and formal languages, this book covers all the essential topics in discrete mathematics.Practical Examples and Applications: Real-world examples and applications demonstrate how discrete mathematics underpins core computer science concepts, including algorithms, data structures, cryptography, and more.Clear and Concise Explanations: Complex topics are presented in a straightforward manner, with clear explanations and minimal jargon, making it easy to grasp even the most challenging concepts.Visual Aids: Diagrams, charts, and tables are used throughout to enhance understanding and provide visual representations of key ideas.Exercises and Solutions: Each chapter includes exercises designed to reinforce learning and provide hands-on practice, with solutions available to check your work.Who Should Read This Book?Students: Ideal for undergraduate and graduate computer science students seeking a solid foundation in discrete mathematics.Professionals: A valuable resource for software engineers, data scientists, cybersecurity experts, and other professionals looking to deepen their understanding of the mathematical principles that underpin their work.Enthusiasts: Anyone with an interest in the mathematical foundations of computer science will find this book engaging and informative.Unlock the Potential of Discrete MathematicsWith "Discrete Mathematics for Computer Science Made Easy," you'll gain the knowledge and skills needed to excel in the dynamic field of computer science. Whether you're preparing for exams, tackling complex projects, or simply looking to enhance your mathematical toolkit, this book is your go-to resource for mastering discrete mathematics. Read more

The Lottery Code: Unveiling the Secrets to Winning Big" is an engaging and insightful non-fiction book that takes readers on a captivating journey into the mysterious world of lottery winning strategies. With millions dreaming of hitting the jackpot, this illuminating guide aims to demystify the lottery by providing practical tips and uncovering the hidden secrets behind successful winners.Drawing from extensive research, expert interviews, and real-life stories of individuals who have struck it rich, this book uncovers the patterns, statistics, and strategies that can dramatically increase the odds of winning. From analyzing previous winning numbers to understanding the psychology behind playing the lottery, "The Lottery Code" equips readers with the knowledge needed to make informed decisions when participating in this game of chance.Beyond mere luck, the author explores various approaches to playing the lottery strategically. Explaining different types of games, odds calculations, and mathematical formulas used by avid players, aspiring winners will learn how to maximize their chances of success. Additionally, the book delves into innovative techniques such as number selection methods, syndicate play, and understanding ticket purchasing patterns.While emphasizing the importance of responsible gambling, "The Lottery Code" also addresses common misconceptions about lotteries and dispels myths surrounding winning strategies. Through engaging stories and evidence-based insights, readers will gain a comprehensive understanding of the inner workings of lotteries and how to align their efforts with proven techniques.More than just a guide for potential winners, this book encourages readers to think critically about their relationship with lotteries and money. It provides valuable insights into managing newfound wealth, including financial planning advice, tips for avoiding common pitfalls, and inspiring stories of individuals who have made a positive impact after hitting the jackpot."The Lottery Code: Unveiling the Secrets to Winning Big" is a must-read for anyone intrigued by lotteries or eager to improve their chances of winning big. With its well-researched information and practical guidance, this book serves as an empowering resource that will transform lottery participation from blind hope into an informed pursuit towards greater success. Read more

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems.This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'. Read more