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The Bayesian Way: Introductory Statistics For Economists And Engineers
by Svein Olav NybergA comprehensive resource that offers an introduction to statistics with a Bayesian angle, for students of professional disciplines like engineering and economics The Bayesian Way offers a basic introduction to statistics that emphasizes the Bayesian approach and is designed for use by those studying professional disciplines like engineering and economics. In addition to the Bayesian approach, the author includes the most common techniques of the frequentist approach. Throughout the text, the author covers statistics from a basic to a professional working level along with a practical understanding of the matter at hand. Filled with helpful illustrations, this comprehensive text explores a wide range of topics, starting with descriptive statistics, set theory, and combinatorics. The text then goes on to review fundamental probability theory and Bayes' theorem. The first part ends in an exposition of stochastic variables, exploring discrete, continuous and mixed probability distributions. In the second part, the book looks at statistical inference. Primarily Bayesian, but with the main frequentist techniques included, it covers conjugate priors through the powerful yet simple method of hyperparameters. It then goes on to topics in hypothesis testing (including utility functions), point and interval estimates (including frequentist confidence intervals), and linear regression. This book: Explains basic statistics concepts in accessible terms and uses an abundance of illustrations to enhance visual understanding Has guides for how to calculate the different probability distributions, functions , and statistical properties, on platforms like popular pocket calculators and Mathematica / Wolfram Alpha Includes example-proofs that enable the reader to follow the reasoning Contains assignments at different levels of difficulty from simply filling out the correct formula to the complex multi-step text assignments Offers information on continuous, discrete and mixed probability distributions, hypothesis testing, credible and confidence intervals, and linear regression Written for undergraduate and graduate students of subjects where Bayesian statistics are applied, including engineering, economics, and related fields, The Bayesian Way: With Applications in Engineering and Economics offers a clear understanding of Bayesian statistics that have real-world applications.
The Beauty and the Boost: Measurements of Higgs Boson Production at High Energy in Decays to Bottom Quarks and Their Interpretations with the ATLAS Experiment at the LHC (Springer Theses)
by Brian MoserPrecision measurements of the Higgs boson’s properties are a powerful tool to look for deviations from the predictions of the Standard Model (SM) of particle physics. The 139/fb of proton-proton collision data which have been collected by the ATLAS experiment during Run 2 of the LHC, offer an opportunity to investigate rare Higgs-boson topologies, which are particularly sensitive to new physics scenarios but experimentally difficult to access. Several such measurements, which target Higgs-boson decays to heavy-flavour quarks, as well as their combinations are presented in this thesis. A novel analysis that measures Higgs-boson production in association with a heavy vector boson V (VH, with V=W,Z) at high energies is presented. Dedicated Higgs-boson reconstruction techniques are applied to reconstruct the highly Lorentz-boosted Higgs-boson decays into pairs of bottom quarks. The measurement is subsequently combined with a VH cross-section measurement at low and intermediate pT(V) to provide a differential cross-section measurement in kinematic fiducial volumes over the largest possible pT(V) range. All cross-section measurements agree with the SM predictions within relative uncertainties that range from 30% to 300%. The results are furthermore interpreted as limits on the parameters of a SM effective field theory. Finally, a combination of measurements of Higgs decays to heavy-flavour quarks is used to experimentally determine that the Higgs-boson coupling to charm quarks is weaker than to bottom quarks, as predicted by the SM. The target audience for the thesis are physicists and physics students, in particular those with a background in high energy physics.
The Beauty of Mathematics in Computer Science
by Jun WuThe Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school. The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph theory and web crawler Pagerank for web search Matrix operation and document classification Mathematical background of big data Neural networks and Google’s deep learning Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.
The Beginner's Guide to Data Science
by Robert Ball Brian RagueThis book discusses the principles and practical applications of data science, addressing key topics including data wrangling, statistics, machine learning, data visualization, natural language processing and time series analysis. Detailed investigations of techniques used in the implementation of recommendation engines and the proper selection of metrics for distance-based analysis are also covered.Utilizing numerous comprehensive code examples, figures, and tables to help clarify and illuminate essential data science topics, the authors provide an extensive treatment and analysis of real-world questions, focusing especially on the task of determining and assessing answers to these questions as expeditiously and precisely as possible. This book addresses the challenges related to uncovering the actionable insights in “big data,” leveraging database and data collection tools such as web scraping and text identification.This book is organized as 11 chapters, structured as independent treatments of the following crucial data science topics:Data gathering and acquisition techniques including data creationManaging, transforming, and organizing data to ultimately package the information into an accessible format ready for analysisFundamentals of descriptive statistics intended to summarize and aggregate data into a few concise but meaningful measurementsInferential statistics that allow us to infer (or generalize) trends about the larger population based only on the sample portion collected and recordedMetrics that measure some quantity such as distance, similarity, or error and which are especially useful when comparing one or more data observationsRecommendation engines representing a set of algorithms designed to predict (or recommend) a particular product, service, or other item of interest a user or customer wishes to buy or utilize in some mannerMachine learning implementations and associated algorithms, comprising core data science technologies with many practical applications, especially predictive analyticsNatural Language Processing, which expedites the parsing and comprehension of written and spoken language in an effective and accurate mannerTime series analysis, techniques to examine and generate forecasts about the progress and evolution of data over timeData science provides the methodology and tools to accurately interpret an increasing volume of incoming information in order to discern patterns, evaluate trends, and make the right decisions. The results of data science analysis provide real world answers to real world questions. Professionals working on data science and business intelligence projects as well as advanced-level students and researchers focused on data science, computer science, business and mathematics programs will benefit from this book.
The Bending Theory of Fully Nonlinear Beams
by Angelo Marcello Tarantino Luca Lanzoni Federico Oyedeji FalopeThis book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semi-inverse approach, the book formulates a three-dimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of cross-sections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book’s closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams.
The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics (Static & Dynamic Game Theory: Foundations & Applications)
by Mindia E. Salukvadze Vladislav I. ZhukovskiyThe goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: “Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.
The Bergman Kernel and Related Topics: Hayama Symposium on SCV XXIII, Kanagawa, Japan, July 2022 (Springer Proceedings in Mathematics & Statistics #447)
by Takeo Ohsawa Kengo Hirachi Shigeharu Takayama Joe KamimotoThis volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel. The symposium took place in Hayama and Tokyo in July 2022. Each article is closely related to the Bergman kernel, covering topics in complex analysis, differential geometry, representation theory, PDE, operator theory, and complex algebraic geometry. Specifically, some papers address the L2 extension operators from a newly opened viewpoint after solving Suita's conjecture for the logarithmic capacity. They are also continuations of quantitative solutions to the openness conjecture for the multiplier ideal sheaves. The study involves estimates for the solutions of the d-bar equations, focusing on the existence of compact Levi-flat hypersurfaces in complex manifolds. The collection also reports progress on various topics, including the existence of extremal Kähler metrics on compact manifolds, Lp variants of the Bergman kernel, Wehrl-type inequalities, homogeneous Kähler metrics on bounded homogeneous domains, asymptotics of the Bergman kernels, and harmonic Szegő kernels and operators on the Bergman spaces and Segal-Bargmann spaces. Some of the papers are written in an easily accessible way for beginners. Overall, this collection updates how a basic notion provides strong insights into the internal relationships between independently found phenomena.
The Best American Infographics 2016
by Gareth Cook Robert Krulwich“When it comes to infographics…the best work in this field grabs those eyes, keeps them glued, and the grip is sensual—and often immediate. A good graphic says ‘See what I see!’ and either you do or you don’t. The best ones…pull you right in, and won’t let you go.” —From the introduction by Robert Krulwich The year’s most “awesome” (RedOrbit) infographics reveal aspects of our world in often startling ways—from a haunting graphic mapping the journey of 15,790 slave ships over 315 years, to a yearlong data drawing project on postcards that records and cements a trans-Atlantic friendship. The Best American Infographics 2016 covers the realms of social issues, health, sports, arts and culture, and politics—including crisp visual data on the likely Democratic/Republican leanings of an array of professions (proving that your urologist is far more likely to be a Republican than your pediatrician). Here once again are the most innovative print and electronic infographics—“the full spectrum of the genre—from authoritative to playful” (Scientific American). ROBERT KRULWICH is the cohost of Radiolab and a science correspondent for NPR. He writes, draws, and cartoons at Curiously Krulwich, where he synthesizes scientific concepts into colorful, one-of-a-kind blog posts. He has won several Emmy awards for his work on television, and has been called “the most inventive network reporter in television” by TV Guide.
The Best Apple Crisp in the World
by Charnan SimonJake wants to learn how to make his grandmother’s apple crisp! The only problem is she doesn’t use a recipe. With his uncle’s help, he must figure out the ingredients and measurements.
The Best Bug Parade (MathStart #Level 1)
by Stuart J. MurphyA variety of different bugs compare their relative sizes while going on parade
The Best Writing on Mathematics 2010 (The Best Writing on Mathematics #1)
by Mircea PiticiThis anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it's headed.
The Best Writing on Mathematics 2011
by Freeman Dyson Mircea PiticiThis anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The Best Writing on Mathematics 2012 (The Best Writing on Mathematics #3)
by Mircea PiticiThe year's finest writing on mathematics from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The Best Writing on Mathematics 2013 (The Best Writing on Mathematics #4)
by Mircea PiticiThe year's finest writing on mathematics from around the world, with a foreword by Nobel Prize–winning physicist Roger PenroseThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more.In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
The Best Writing on Mathematics 2014
by Mircea PiticiThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more.In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes an introduction by editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
The Best Writing on Mathematics 2015 (The Best Writing on Mathematics #14)
by Mircea PiticiThe year's finest writing on mathematics from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates.Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
The Best Writing on Mathematics 2021 (The Best Writing on Mathematics #20)
by Mircea PiticiThe year’s finest mathematical writing from around the worldThis annual anthology brings together the year’s finest mathematics writing from around the world—and you don’t need to be a mathematician to enjoy the pieces collected here. These essays—from leading names and fresh new voices—delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today’s hottest mathematical debates.Here, Viktor Blåsjö gives a brief history of “lockdown mathematics”; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of “dark data”—information that is missing or ignored. And there is much, much more.
The Best of All Possible Worlds: A Life of Leibniz in Seven Pivotal Days
by Michael KempeA biography of the polymath Gottfried Wilhelm Leibniz told through seven critical days spanning his life and revealing his contributions to our modern world. Gottfried Wilhelm Leibniz (1646–1716) was the Benjamin Franklin of Europe, a “universal genius” who ranged across many fields and made breakthroughs in most of them. Leibniz invented calculus (independently from Isaac Newton), conceptualized the modern computer, and developed the famous thesis that the existing world is the best that God could have created. In The Best of All Possible Worlds, historian and Leibniz expert Michael Kempe takes us on a journey into the mind and inventions of a man whose contributions are perhaps without parallel in human history. Structured around seven crucial days in Leibniz’s life, Kempe’s account allows us to observe him in the act of thinking and creating, and gives us a deeper understanding of his broad-reaching intellectual endeavors. On October 29, 1675, we find him in Paris, diligently working from his bed amid a sea of notes, and committing the integral symbol—the basis of his calculus—to paper. On April 17, 1703, Leibniz is in Berlin, writing a letter reporting that a Jesuit priest living in China has discovered how to use Leibniz’s binary number system to decipher an ancient Chinese system of writing. One day in August 1714, Leibniz enjoys a Viennese coffee while drawing new connections among ontology and biology and mathematics. The Best of All Possible Worlds transports us to an age defined by rational optimism and a belief in progress, and will endure as one of the few authoritative accounts of Leibniz’s life available in English.
The Best of Corwin: Differentiated Instruction in Literacy, Math, and Science
by Leslie E. LaudContent-specific DI guidance from the best minds in education In this collection, current research on the most effective differentiation practices for differentiating instruction in literacy, mathematics, and scienceis brought alive through the many strategies and examples. Topics covered include: Reading and writing: A comprehensive array of models for differentiating reading instruction; gradual release of responsibility to accelerate progress; and multi-tiered writing instruction Mathematics: Support for both low- and high-achieving students, including interventions and challenges, and the implementation of RTI in math instruction Science: Models and methods for increasing student achievement through differentiated science inquiry
The Best of Times: Math Strategies That Multiply
by Greg Tang Harry BriggsNEW YORK TIMES bestselling author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers WITHOUT memorization. Four is very fast to do when you multiply by 2. Here's a little good advice -- please just always double twice! BEST OF TIMES gives kids an intuitive understanding of multiplication, encouraging them to arrive at answers on their own rather than memorizing the times tables. A child who can multiply by two, for instance, can multiply by four and even eight! Likewise, times six builds on times two and times three. With his common-sense approach, Greg Tang encourages kids to solve problems creatively, building both their skills and their confidence.
The Best of Times: Math Strategies that Multiply
by Greg TangNEW YORK TIMES bestselling author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers WITHOUT memorization.Four is very fast to do when you multiply by 2.Here's a little good advice --please just always double twice!BEST OF TIMES gives kids an intuitive understanding of multiplication, encouraging them to arrive at answers on their own rather than memorizing the times tables. A child who can multiply by two, for instance, can multiply by four and even eight! Likewise, times six builds on times two and times three.With his common-sense approach, Greg Tang encourages kids to solve problems creatively, building both their skills and their confidence.
The Bicentennial Census: 30th Anniversary Edition
by Constance F. CitroIn 1982 the Census Bureau requested the Committee on National Statistics to establish a panel to suggest research and experiments, to recommend improved methods, and to guide the Census Bureau on technical problems in appraising contending methods with regard to the conduct of the decennial census. In response, the panel produced an interim report that focused on recommendations for improvements in census methodology that warranted early investigation and testing. This report updates and expands the ideas and conclusions about decennial census methodology.
The Big Bang of Numbers: How to Build the Universe Using Only Math
by Manil SuriAn engaging and imaginative tour through the fundamental mathematical concepts—from arithmetic to infinity—that form the building blocks of our universe. Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing—no matter, no cosmos, not even empty space—could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try. In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa’s asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can. Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math.
The Big Book of Real Analysis: From Numbers to Measures
by Syafiq JoharThis book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the study of measures and how one can construct the Lebesgue integral as an extension of the Riemann integral. This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.
The Big Brain Puzzle Book: Entertaining Sudoku, Kakuro, And Brainteasers For Every Day (Little Bathroom Book Ser.)
by Terry StickelsGive your brain a series of workouts that'll make it bigger and better! This colossal collection of more than 200 puzzles simultaneously provides a relaxing atmosphere for mental play and stimulates brain activity. Created by an internationally renowned puzzle-maker, the challenges involve creative thinking, mathematics, logic, language and wordplay, visuals, and general knowledge.Kick start your neurons at Level 1 with puzzles involving hidden words, math calculations, and logical conundrums. At Level 2, fire up your synapses with cryptograms, scrambled sentences, and visual challenges. And activate your brain at Level 3 with fill-in-the-blanks, search-a-words, magic squares, and much more. If you get stumped, an answer key with complete solutions appears at the end.