Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.

    The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo MCMC. Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, and quantum mechanics. Indeed, linear algebra offers a powerful toolbox for modelling the real world.The NO BULLSHIT guide to LINEAR ALGEBRA shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy.The author has 15 years of tutoring experience, a B.Eng. in electrical engineering, a M.Sc. in physics, and a Ph.D. in computer science from McGill University.Preview: https://minireference.com/static/exce...Free tutorial: https://minireference.com/static/tuto... (4pp, PDF)

    Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.

    BRAND NEW, Exactly same ISBN as listed, Please double check ISBN carefully before ordering.

    Collected from the series of blog posts starting at: https://bartoszmilewski.com/2014/10/2...Hardcover available at: http://www.blurb.com/b/9008339-catego...

    If you're a reasonably proficient programmer who can think logically, you have all the background you'll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem. As you read this book, you'll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You'll also gain deep insight into the value of mathematics to programming--insight that will prove invaluable no matter what programming languages and paradigms you use. You will learn aboutHow to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiencyAncient paradoxes, beautiful theorems, and the productive tension between continuous and discreteA simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on itPowerful mathematical approaches to abstractionHow abstract algebra provides the idea at the heart of generic programmingAxioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you can learn from themHow practical implementations can exploit theoretical knowledge

    What will it take to turn this opportunity into reality in every classroom, school, and district? Continuing its tradition of mathematics education leadership, NCTM has defined and described the principles and actions, including specific teaching practices, that are essential for a high-quality mathematics education for all students. Principles to Actions: Ensuring Mathematical Success for All offers guidance to teachers, specialists, coaches, administrators, policymakers, and parents: Builds on the Principles articulated in Principles and Standards for School Mathematics to present six updated Guiding Principles for School MathematicsSupports the first Guiding Principle, Teaching and Learning, with eight essential, research-based Mathematics Teaching PracticesDetails the five remaining Principles--the Essential Elements that support Teaching and Learning as embodied in the Mathematics Teaching PracticesIdentifies obstacles and unproductive and productive beliefs that all stakeholders must recognize, as well as the teacher and student actions that characterize effective teaching and learning aligned with the Mathematics Teaching PracticesWith Principles to Actions, NCTM takes the next step in shaping the development of high-quality standards throughout the United States, Canada, and worldwide.

    This book starts with the notion of potential outcomes, each corresponding to the outcome that would be realized if a subject were exposed to a particular treatment or regime. In this approach, causal effects are comparisons of such potential outcomes. The fundamental problem of causal inference is that we can only observe one of the potential outcomes for a particular subject. The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. They lay out the assumptions needed for causal inference and describe the leading analysis methods, including, matching, propensity-score methods, and instrumental variables. Many detailed applications are included, with special focus on practical aspects for the empirical researcher.

    Updated for the relaunch of the primary national curriculum in autumn 2014, children can learn all about prime suspects, diabolical division, sneaky signs and much more.

    Murderous Maths: All Shapes and Sizes is full of facts, tricks and tips about why shapes are super and measurements are magic! Updated for the relaunch of the primary national curriculum in autumn 2014, children can learn all about tricky triangles, vicious circles, spangled angles and much more with simple explanations and hilarious characters.

    Updated for the relaunch of the primary national curriculum in autumn 2014, children can learn to become mathematical masters with simple explanations and hilarious characters.

    Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can't be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated--they technically didn't exist in the land of the pharaohs. You'll be counting like an Egyptian in no time, and along the way you'll learn firsthand how mathematics is an expression of the culture that uses it, and why there's more to math than rote memorization and bewildering abstraction.Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you'll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation--the precursor to our modern system--and compares ancient Egyptian mathematics to today's math, letting you decide for yourself which is better.

    It can be used by both students and practitioners in engineering, various sciences, finance, and other related fields. It provides a clear and intuitive approach to these topics while maintaining mathematical accuracy.The book covers:• Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods• Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities• Limit theorems and convergence• Introduction to Bayesian and classical statistics• Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion• Simulation using MATLAB and R (online chapters)The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications—such as engineering, finance, everyday life, etc.—are included to aid in motivating the subject. The digital version of the book, as well as additional materials such as videos, is available at probabilitycourse.com.

    Prolific polymath Clifford Pickover introduces the collection, which provides background on everything from the classic Mandelbrot set, to the infinitely porous Menger Sponge, to ethereal fractal flames. The following eye-popping gallery displays mathematical formulas transformed into stunning computer-generated 3D anaglyphs. More than 200 intricate designs, visible in three dimensions thanks to the enclosed 3D glasses, will engross math and optical illusions enthusiasts alike.

    Not only did he present a notoriously difficult subject in an engaging and accessible way, but in doing so, he attracted an incredibly broad readership. His correspondents ranged from academics like Roger Penrose and John Horton Conway to artists MC Escher and Salvador Dali to writer Isaac Asimov. His “Mathematical Games” column in Scientific American ran nearly every month for 26 years and was one of the most popular in the magazine’s history. Gardner would have celebrated his 100th birthday this October, and to mark the occasion we’ve created this eBook collection, Martin Gardner: The Magic and Mystery of Numbers. In this anthology, we strove to create a new “slice” through his wealth of material. Here, we focus on all flavors of number, from common integers and negative numbers to figurate numbers and the exotic random number, Omega, which can be described but not computed.Some of these columns are less well known than, say, his writings about flexagons, but they are no less fun. In true Gardner fashion, they leap from magic and games—as well as art, music, and literature—to flashes of deep mathematical insight. Lattice integers become a billiards challenge and surreal numbers spawn a host of related games. The “abracadabric number e,” quoting French entomologist Jean-Henri Fabre, leads to spiders’ webs and compounded interest. The binary Gray code inspires a poem and cracks the classic Chinese Rings puzzle. And binary numbers unlock mind-reading tricks and the Tower of Hanoi. Almost every column offers up problems for readers to solve and test their understanding—along with the answers for anyone easily frustrated. We hope that they will prove as inspirational to readers now as they did to earlier audiences.

    A wide range of physics notions such as the theory of motion, strength, force, and mechanics in general are still vague for beginners. Those “who do not know movement, do not understand nature” Aristotle once said. Although several pages of the author’s book “Physics for Entertainment” (2 volumes) are dedicated to mechanics’ problems, it very useful that he devoted a separate, but similarly written, book to mechanics. “Mechanics for Entertainment” is not a textbook. Instead it is a freestyle book with some entertaining experiments and descriptions of some exciting natural phenomena. I have included a number of mechanics laws applications in engineering, sports, circus performances and many other unexpected areas.

    Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus course Helps you refine your understanding of calculus Practice problems with answer explanations that detail every step of every problem The practice problems in 1001 Calculus Practice Problems For Dummies range in areas of difficulty and style, providing you with the practice help you need to score high at exam time.

    By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names!Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

    Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs., The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonne, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis.New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri's Principle, and, in many cases, the ability to see an integral result from measure theory., The presentation includes Vitali's Covering Lemma, density points - which are rarely treated in books at this level - and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.

    Each chapter is its own story about a number: why 12 is a sublime number, why 13 is unlucky and 7 lucky, and how imaginary numbers hold up buildings. The book tells the stories of ancient mathematicians, ground-breaking discoveries and mathematical applications that affect our world and our lives in so many ways.

    

    Over a century of development of principles and techniques in algebraic topology has of late crossed over to a variety of application domains. This text gives a completely novel introduction to these methods in the context of the applications. "Elementary Applied Topology" is short (250 pp. plus bibliography and index) and richly illustrated, with 268 figures. It is perfect for both self-study, and as the basis for a course in applied topology. This book is also well-suited for use as a supplementary text in a more traditional algebraic topology course, providing both context and motivation for the tools to be learned. The progression of mathematical techniques is a fresh approach. The book begins with a quick trip through manifolds and cell complexes. The segue to algebraic topology comes in the form of the Euler characteristic and the Euler calculus born from it. Passing from this to homology, exact sequences, and cohomology sets the stage for the innovative content to come. This is comprised of modern Morse theory (including discrete Morse theory, Conley index, and stratified Morse theory), sheaf theory (with an emphasis on cellular sheaves and cosheaves), and, finally, category theory and categorification. Every tool and topic is paired with an application. These range in scope across the biological, economic, engineering, material, physical, and statistical sciences. Of particular note are the applications to topological data analysis, including persistent homology and barcodes. "Elementary Applied Topology" is the first comprehensive text on applied algebraic topology for students of all mathematical sciences.

    While Nonlinear Systems was intended as a reference and a text on nonlinear system analysis and its application to control, this streamlined book is intended as a text for a first course on nonlinear control that can be taught in one semester. In Nonlinear Control, author Hassan K. Khalil employs a writing style that is intended to make the book accessible to a wider audience without compromising the rigor of the presentation. KEY TOPICS: Two-Dimensional Systems; Stability of Equilibrium Points; Time-Varying and Perturbed Systems; Passivity; Input-Output Stability; Stability of Feedback Systems; Special Nonlinear Forms; State Feedback Stabilization; Robust State Feedback Stabilization; Output Feedback Stabilization; Tracking and Regulation. MARKET A useful introduction to nonlinear control.

    Walker presents a compelling story of Black mathematical excellence in the United States. Much of the research and discussion about Blacks and mathematics focuses on underachievement; by documenting in detail the experiences of Black mathematicians, this book broadens significantly the knowledge base about mathematically successful African Americans. Beyond Banneker demonstrates how mathematics success is fostered among Blacks by mathematicians, mathematics educators, teachers, parents, and others, a story that has been largely overlooked by the profession and research community. Based on archival research and in-depth interviews with thirty mathematicians, this important and timely book vividly captures important narratives about mathematics teaching and learning in multiple contexts, as well as the unique historical and contemporary settings related to race, opportunity, and excellence that Black mathematicians experience. Walker draws upon these narratives to suggest ways to capitalize on the power and potential of underserved communities to respond to the national imperative for developing math success for new generations of young people.

    This book is a practical introduction for all those who don't want to miss out. In it you'll find down-to-earth explanations, detailed examples and interesting applications. Check out the sample for the table of contents and a taste of the action. From the author of "Mathematical Shenanigans" and the popular series "Great Formulas Explained". The second installment "Math Shorts: Integrals II" is now available for Kindle and contains advanced topics such as partial fractions, trigonometric and hyperbolic integrands, the Cauchy-Schwarz inequality and much more. A supplement to this book is available under the title "Exercises to Math Shorts - Integrals". It contains 30 exercises including detailed solutions. Important note: to enjoy the book, you need solid prior knowledge in algebra and calculus. This means in particular being able to solve all kinds of equations, finding and interpreting derivatives as well as understanding the notation associated with these topics.

    The aim is to present the fundamentals of linear algebra in the clearest possible way, and pedagogy is the main consideration.

    In fact, mathematics is noumenal (true) reality, and physics is phenomenal (illusory) reality. Mathematics tells you what things are in themselves, and physics tells you how they appear to us. Mathematics is the perfect ground of existence, defined by the God Equation. It’s the source of causation, determinism and objective reality; all of the things now formally denied by physics, which claims that observable reality is indeterministically born of unreal, probabilistic wavefunctions.It’s time to replace the scientific method with the mathematical method. It’s time to recognize that true reality is intelligible, not sensible; noumenal, not phenomenal; unobservable, not observable; metaphysical, not physical; hidden, not manifest; rationalist, not empiricist; necessary, not contingent. Physics is literally incapable of detecting true reality since true reality is an eternal, indestructible, dimensionless mathematical Singularity, outside space and time. The Singularity is a precisely defined Fourier frequency domain. There’s nothing “woo woo” about it. It's pure math. Physicists suffer from a disorder of the mind that causes them to believe that sensible, temporal objects have more reality than eternal, immutable Platonic mathematical objects, and to place more trust in their senses than in their reason, more trust in the scientific method of “evidence” than the mathematical method of eternal proof.Never forget that sensory objects are just ideas in the mind. According to quantum physics, objects are just the observable entities produced by the collapse of unreal wavefunctions, and don’t formally exist when they are not being observed. Niels Bohr, in response to Einstein, literally denied that the moon existed when it wasn’t being observed.The subject that comes after physics is metaphysics, and the true language of metaphysics is ontological mathematics. Physics is the phenomenal expression of noumenal mathematics.Mathematics has one final wonder to confer on us. It provides a complete definition of the human soul, which is, like the universe in itself, just an immaterial, dimensionless mathematical singularity defined by the God Equation. As above, so below. The soul is the microcosm and the universe the macrocosm.Anyone who denies that reality is 100% mathematical is simply too stupid for the truth. Truth is not a democracy. It’s not for everyone, only for humanity’s smartest individuals. As Robert Heinlein said, “Democracy can’t work. Mathematicians, peasants, and animals, that's all there is – so democracy, a theory based on the assumption that mathematicians and peasants are equal, can never work. Wisdom is not additive; its maximum is that of the wisest man in a given group.”This book comprehensively exposes the diabolical philosophical illiteracy, ignorance, bankruptcy and irrationalism of modern scientific “thinking”, most spectacularly evident in the paradox of Schrödinger’s cat, the standard interpretation of which is more or less indistinguishable from insanity, yet is taught as “fact” (but is nothing but an extremist expression of empiricist philosophy).Ontological mathematicians are vastly more intelligent than physicists. It’s all in the math!“Wisdom is sold in the desolate market where none come to buy.” – William BlakeThe God Series is entirely ignored by all but a handful of audacious souls with open minds.

    The absence of a book, explaining the techniques in a simple language, has been felt acutely for a long time. This book has been written using a step-by-step approach, and attempts to fill the existing void. It includes several solved problems in addition to 1000 practice problems with answers. It also includes a special chapter which shows the application of the techniques to problems set in competitive exams like CAT, CET etc. People from all walks of life including school and college students, teachers, parents and also those from non-mathematical areas of study will discover the joys of solving mathematical problems using the wonderful set of techniques called Vedic Maths.

    Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

    Her notes on the engine include what is recognised as the first algorithm intended to be carried out by a machine. Because of this, she is often described as the world's first computer programmer. This book published in 1842 has been reformatted for the Kindle and may contain an occasional defect from the original publication or from the reformatting.

    

    The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

    

    Book of Extremes is a tour of the current reality as seen through the lens of complexity theory the only theory capable of explaining why the Arab Spring happened and why it will happen again; why social networks in the virtual world behave like flashmobs in the physical world; why financial bubbles blow up in our faces and will grow and burst again; why the rich get richer and will continue to get richer regardless of governmental policies; why the future of economic wealth and national power lies in comparative advantage and global trade; why natural disasters will continue to get bigger and happen more frequently; and why the Internet invented by the US -- is headed for a global monopoly controlled by a non-US corporation. It is also about the extreme innovations and heroic innovators yet to be discovered and recognized over the next 100 years.Complexity theory combines the predictable with the unpredictable. It assumes a nonlinear world of long-tailed distributions instead of the classical linear world of normal distributions. In the complex 21st century, almost nothing is linear or normal. Instead, the world is highly connected, conditional, nonlinear, fractal, and punctuated. Life in the 21st century is a long-tailed random walk Levy walks -- through extreme events of unprecedented impact. It is an exciting time to be alive."

    MYTH OF INVARIANCE explores the unifying symbolism of music and number so the reader can understand the secrets from Babylon, Egypt, Greece and the Bible - secrets hidden for centuries.

    Numerous exercises, examples and applications are included.D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.ContentsIntroductionPart One - Prologue: The foundations of analysis1 - The axioms of set theory2 - Number systemsPart Two - Functions of a real variable3 - Convergent sequences4 - Infinite series5 - The topology of R6 - Continuity7 - Differentiation8 - Integration9 - Introduction to Fourier series10 - Some applicationsAppendix A - Zorn's lemma and the well-ordering principleIndexIntroductionPart Three - Metric and topological spaces11 - Metric spaces and normed spaces12 - Convergence, continuity and topology13 - Topological spaces14 - Completeness15 - Compactness16 - ConnectednessPart Four - Functions of a vector variable17 - Differentiating functions of a vector variable18 - Integrating functions of several variables19 - Differential manifolds in Euclidean spaceAppendix B - Linear AlgebraAppendix C - Exterior algebras and the cross productAppendix D - Tychonoff's theoremIndexIntroductionPart Five - Complex Analysis20 - Holomorphic functions and analytic functions21 - The topology of the complex plane22 - Complex integration23 - Zeros and singularities24 - The calculus of residues25 - Conformal transformations26 - ApplicationsPart Six - Measure and Integration27 - Lebesgue measure on R28 - Measurable spaces and measurable functions29 - Integration30 - Constructing measures31 - Signed measures and complex measures32 - Measures on metric spaces33 - Differentiation34 - ApplicationsIndex

    

    It covers the most basic material from KS3, plus some important topics and skills from KS2, making it ideal for less confident Maths students. Along with the questions, there are thought-provoking investigation tasks for each topic, and there’s a glossary at the back that explains all the crucial maths terminology. Answers to every question are included.

    Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, or computer, the online component works in conjunction with the book to polish your skills and confidence in preparation for calculus.Calculus-level math proficiency is required for college STEM majors. Pre-calculus introduces you to the concepts you'll learn in calculus, and provides you with a solid foundation of methods and skills that are essential to calculus success. 1,001 Pre-Calculus Practice Problems For Dummies gives you the practice you need to master the skills and conquer pre-calculus. Companion website includes:All 1,001 practice problems in multiple choice format Customizable practice sets for self-directed study Problems ranked as easy, medium, and hard Free one-year access to the online question bank Math is notorious for giving students trouble, and calculus is the #1 offender. Fear not! Pre-calculus is the perfect calculus prep, and 1,001 Pre-Calculus Practice Problems For Dummies gives you 1,001 opportunities to get it right.

    Firstly, the book gives a historical overview of Africa and its contribution to Mathematics. Secondly, the book provides the teacher and the learner with study materials that can be used in the classroom. Thirdly, the book introduces some of the numerical patterns and puzzles that has fascinated one of the authors John Matthews. Fourthly, the book introduces the lectures, classes and workshops that the two authors teach on these subjects. Mathematics has an interesting history in Africa. This history forms the first part of the book. The earliest known mathematical artefact in human history is the Lebombo Bone. Thought to be 37,000 years old, it was discovered by archaeologists in South Africa. Scholars believe that the number system carved into the bone represents a lunar calendar. Later mathematical evidence comes from the Ishango region of Central Africa, Ancient Egypt, Medieval North Africa, Ethiopia, Medieval West Africa and Medieval Central Africa. Mathematics teachers have asked for material that can be used in the classroom where these African mathematical ideas can be used, tested or even challenged. To this aim, the second part of the book presents classroom material that can engage children. Each lesson demonstrates a mathematical principle followed by classroom exercises that the pupils can attempt. We have provided perhaps 22 hours worth of teaching and learning material. The third part of this book was written wholly by John Matthews, a secondary school mathematics teacher. It contains a sample of his tips and short cuts that any pupil of mathematics can profitably use to improve their engagement with number. Mr Matthews also believes that students of mathematics should enjoy detecting patterns in number sequences. In the fourth part of the book he presents a sample of his own discoveries in this area. He also presents classroom exercises that the pupils can attempt.

    

    Learn the basic concepts on a pretend computer screen! Playful cats fill the pages of this activity book, which encourages children to slide the tabs to count from 1 to 10, identify colors and shapes, and even lift the flaps to play a matching game.• Early learning concepts• Hands-on play with flaps and pull-tabs• Sturdy board book is ideal for travel with built-in handleFans of My First Computer will also enjoy other books in the series, including Let's Bake a Cake!, Let's Grow Vegetables!, My First Toolbox, and Let's Care for Baby!.• Great family read-aloud• Books for babies-3 years old• Books for preschool

    The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

    The focus is on introducing recursive methods--an important part of every economist's set of tools--and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models.The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. The book goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the book's website. A solutions manual for students is available for sale from the MIT Press; a downloadable instructor's manual is available to qualified instructors.

    Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be apluralist or relativist about logic. One of these is an extended argument that words and phrases like valid and logical consequence are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the debates in the literature betweeninferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order.A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers anumber of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure.The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the samemeaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to someprominent considerations concerning open texture, vagueness, and verbal disputes.Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes withdifferent logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

    

    This book offers the definitive guide to the theory and practice of disaster robotics. It can serve as an introduction for researchers and technologists, a reference for emergency managers, and a textbook in field robotics. Written by a pioneering researcher in the field who has herself participated in fifteen deployments of robots in disaster response and recovery, the book covers theory and practice, the history of the field, and specific missions.After a broad overview of rescue robotics in the context of emergency informatics, the book provides a chronological summary and formal analysis of the thirty-four documented deployments of robots to disasters that include the 2001 collapse of the World Trade Center, Hurricane Katrina, the 2010 Haiti earthquake, the Deepwater Horizon oil spill, the 2011 Japanese earthquake and tsunami, and numerous mining accidents. It then examines disaster robotics in the typical robot modalities of ground, air, and marine, addressing such topics as robot types, missions and tasks, and selection heuristics for each modality. Finally, the book discusses types of fieldwork, providing practical advice on matters that include collecting data and collaborating with emergency professionals.The field of disaster robotics has lacked a comprehensive overview. This book by a leader in the field, offering a unique combination of the theoretical and the practical, fills the gap.

    This practical book from bestselling author Dr. Nicki Newton explains why Math Workshops are effective and gives you step-by-step instructions for implementing and managing your own workshop.You'll find out how to...create a math-rich environment;use anchor charts effectively;manage the workshop;begin a workshop with activities;lead whole-group mini-lessons;make workstations meaningful and engaging;create guided math groups;implement "the Share" effectively; andensure balanced assessments.Each chapter offers a variety of charts and tools that you can use in the classroom immediately, as well as reflection questions and key points. The book also features a handy Quick-Start Guide to help you as you implement your own workshop.

    Hall discusses the esoteric aspects of Pythagorean thought; with its profound (and heretofore not completely grasped) influence on our understanding of the cosmos; as well as further implications. Custom-formatted for Kindle and checked for typos.

     Mathematics can be fun, exciting, surprising, and stunningly beautiful. But too few people ever experience this, associating it instead with boring and apparently pointless exercises in trigonometry and solving equations. This guide will take you on an emotional journey, starting from very simple ideas, and exploring some surprising and intricately beautiful behaviors of the very simple mathematics that underlies the famous Mandelbrot fractal. You won't need anything more than basic school mathematics. Part 1 is about ideas. It introduces the mathematical ideas underlying the Mandelbrot fractal, gently with lots of illustrations and examples. Part 2 is practical. It introduces the popular and easy to learn Python programming language, and gradually builds up a program to calculate and visualise the Mandelbrot fractal. Part 3 extends these ideas. It reveals the related Julia fractals, creates 3-dimensional landscapes and shows how even more interesting images can be made using mathematical filters. The fractal image on the cover of this book is created using only the ideas and code developed in this book.

    The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations.With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis.Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.

    It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.

    The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual."Key Features"" " Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms."Logic and Discrete Mathematics: A Concise Introduction" is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.

    A dynamic table of contents enables to jump directly to the chapter selected. Table of Contents -01- About this book -02- ON GEOMETRICAL DEMONSTRATION -03- FOOTNOTES

    Written in an engaging style that renders complex concepts accessible to a wide readership, and with more than 450 exercises, this textbook introduces the basics of real analysis as well as more advanced topics such as measure theory and Lebesgue integration.

    Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.

    It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy ofmathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Godel's theorems, interpretability, the hierarchyof sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and realnumbers and have some background in formal logic."

    Edwards of the University of Florida, brings the basic concepts of calculus together in a much deeper and more powerful way. This course is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an eye-opening intellectual exercise for teachers, retired professionals, and anyone else who wants to understand the amazing applications of 3-D calculus.

    Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems.Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:- Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers - Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods - A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations - Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts - A chapter-by-chapter review to clarify the most crucial concepts coveredCombinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.

    Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, or computer, the online component works in conjunction with the book to polish your skills and confidence in preparation for calculus. Calculus-level math proficiency is required for college STEM majors. Pre-calculus introduces you to the concepts you'll learn in calculus, and provides you with a solid foundation of methods and skills that are essential to calculus success. 1,001 Pre-Calculus Practice Problems For Dummies gives you the practice you need to master the skills and conquer pre-calculus. Companion website includes: All 1,001 practice problems in multiple choice format Customizable practice sets for self-directed study Problems ranked as easy, medium, and hard Free one-year access to the online question bank Math is notorious for giving students trouble, and calculus is the #1 offender. Fear not! Pre-calculus is the perfect calculus prep, and 1,001 Pre-Calculus Practice Problems For Dummies gives you 1,001 opportunities to get it right.

    Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

    Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critical dynamics for graduate students and researchers across many disciplines within physical and life sciences.

    The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage.The book is organised around Godel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Godel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Godel's attempt to go far beyond intuitionism.The four central essays are Monads and sets', On the philosophical development of Kurt Godel', Godel and intuitionism', and Construction and constitution in mathematics'. The first analyses and criticises Godel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Godel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Godel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his published writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Godel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Godel envisaged, and concludes that it does not.The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references."

    How would you teach the concept of odd and even numbers to a child?What is the probability of throwing a three on a six-sided die?How could you help a child who is confusing ratio and proportion?By seamlessly combining subject knowledge and pedagogy, the second edition of Understanding and Teaching Primary Mathematics will not only build your own confidence in mathematics, but also equip you with the curriculum understanding and pedagogical know-how to excel at teaching maths to children of any age.Written in a clear and accessible way, the book guides you through the fundamental ideas which are at the heart of teaching and learning maths, with special focus on observation and assessment of primary and early years children. Hallmark featuresLinks to the classroom and research are provided throughout to help you relate educational theory to your own teaching practice. Portfolio and audit tasks allow you to assess your own subject knowledge and build up a portfolio of evidence to gain Qualified Teacher Status.The accompanying extra resources offers topic-specific self-audits for you to monitor your progress, exemplar lesson plans, a range of Portfolio Tasks mapped directly to current teacher standards and web-links to up-to-date online resources. New to this editionResource Inspiration boxes give inviting examples of different activities to do with your class to provide inspiration for your own teaching.High quality videos with corresponding discussion, have been expertly selected from Teachers TV help to widen your skills and develop your practice, offering tips, lesson ideas and classroom resources.

    

    This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

    Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects.Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text.

    This updated edition describes the engineering elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices.This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises.This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs.

    All the programs and graphics of the book have been developed using free software, which you can obtain free and legally on the internet, so it is not necessary to buy any software. Python is currently the most popular language for teaching introductory computer science courses at top-ranked U.S. universities. You can freely write Python programs whether you are a Windows user or whether you prefer Mac or Linux. A free pdf excerpt is available at our website www.pysamples.com. The buyers of the book can also download the code of the Python programs. The book consists of a detailed introduction to Python, followed by ten chapters of mathematics with its corresponding Python programs, results and graphs.

    Jason Rosenhouse, the editor of Four Lives, has provided an Introduction, in addition to compiling numerous tributes from former students, friends, and others saluting this celebrated professor, author, and logic scholar hailed by Martin Gardner as "the most entertaining logician and set theorist who ever lived."

    The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical modelbuilding.The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features:An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

    This book is a gentle introduction to the rich world of differential equations filled with no-nonsense explanations, step-by-step calculations and application-focused examples. College level math has never been easier. From the author of "Mathematical Shenanigans" and the popular series "Great Formulas Explained". Important note: to enjoy the book, you need solid prior knowledge in algebra and calculus. This means in particular being able to solve all kinds of equations, finding and interpreting derivatives, evaluating integrals as well as understanding the notation associated with these topics.

    Mathematical Understanding of Nature

    It starts with the basic Python knowledge outlined in Python for Biologists and introduces advanced Python tools and techniques with biological examples. You'll learn: - How to use object-oriented programming to model biological entities - How to write more robust code and programs by using Python's exception system - How to test your code using the unit testing framework - How to transform data using Python's comprehensions - How to write flexible functions and applications using functional programming - How to use Python's iteration framework to extend your own object and functions Advanced Python for Biologists is written with an emphasis on practical problem-solving and uses everyday biological examples throughout. Each section contains exercises along with solutions and detailed discussion.

    Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models.The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features:A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.