A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligence Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumor is cancerous, or deciding if someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics—the study of genomes, extrasolar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came on the scene. We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning, while suggesting intriguing links between artificial and natural intelligence. Might the same math underpin them both? As Ananthaswamy resonantly concludes, to make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible. Read more

The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook (with full solutions to every problem) to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:derivatives of polynomials, trig functions, exponentials, and logarithmsthe chain rule, product rule, and quotient rulesecond derivativeshow to find the extreme values of a functionlimits, including l’Hopital’s ruleantiderivatives of polynomials, trig functions, exponentials, and logarithmsdefinite and indefinite integralstechniques of integration, including substitution, trig sub, and integration by partsmultiple integralsThe goal of this workbook isn’t to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering. Read more

Step into a world where numbers defy expectations and embark on a thrilling adventure through the realm of the rare and mysterious—welcome to "The Transcendental Tangle." This captivating book is designed to take you on an enchanting exploration of transcendental numbers, those fascinating mathematical entities that exist beyond the boundaries of traditional algebraic understanding.Dive into the rich history of transcendental numbers, uncovering the delightful stories and endearing quirks of the mathematicians who dared to venture into this enigmatic realm. From ancient Greek geometrical puzzles to the bewildering mathematical concoctions of the 17th-century French mathematician Joseph Liouville, you'll encounter a treasure trove of whimsical anecdotes and intriguing personalities.Our journey will lead you through the captivating world of irrational numbers, the mathematical wildcards that cannot be expressed as a simple fraction. Delight in the mathematical beauty of famous constants like π and e, and unravel the perplexing intricacies of continued fractions, which have been used for centuries to capture the essence of these elusive numbers. Throughout the book, you'll also find a plethora of engaging problems and challenges designed to ignite your curiosity and fuel your passion for mathematics.But transcendental numbers aren't just a curiosity; they have profound implications for the very nature of mathematics and the fabric of reality itself. We'll delve into the philosophical underpinnings of these enigmatic numbers, exploring the intersections of Platonism, logicism, and intuitionism, and examining the impact of Gödel's incompleteness theorems on our understanding of the mathematical universe."The Transcendental Tangle" is more than just a book; it's an invitation to embark on your own mathematical journey. Through captivating narrative, engaging problems, and hands-on demonstrations, you'll be guided toward a deeper appreciation of the world of transcendental numbers and the vast potential they hold for discovery. Whether you're a seasoned mathematician, a student eager to broaden your horizons, or simply someone with a curious mind, this book offers an unforgettable voyage into the realm of the extraordinary.Prepare yourself for a whirlwind tour through the magical world of transcendental numbers, where you'll encounter mind-bending puzzles, charming anecdotes, and captivating mathematical beauty. So, grab your compass and your sense of wonder, and join us on this fantastical journey as we traverse the uncharted territories of mathematics, venturing beyond the bounds of the known into the exhilarating world of the transcendental. Read more

Dive into the realm of mathematical mastery with Silvanus P. Thompson's timeless guide, "Calculus Made Easy: Your Guide to Mastering Mathematical Concepts." Thompson's approachable style and clear explanations make calculus not just understandable but enjoyable.As Thompson demystifies complex mathematical concepts, you'll find yourself empowered with a newfound understanding of calculus. Gone are the days of confusion and frustration; welcome to a world where calculus becomes second nature.But here's the intriguing question that arises: What if mastering calculus isn't just about solving equations, but unlocking the secrets of the universe itself? Could calculus be the key to understanding the very fabric of reality?Unravel the intricacies of calculus through Thompson's expert guidance, where each concept builds upon the last, leading you on a journey of intellectual discovery. Embrace the challenge and uncover the beauty hidden within mathematical equations.Are you ready to embark on a journey that will forever change the way you see the world around you?Engage with bite-sized explanations that make even the most daunting calculus problems seem manageable. Thompson's clarity of thought illuminates the path to mathematical enlightenment.Here's your opportunity to not just learn calculus, but to master it. This book is more than a guide; it's a roadmap to mathematical brilliance. Will you seize the chance to unlock the power of calculus?Take the first step towards mathematical proficiency. Acquire your copy of "Calculus Made Easy: Your Guide to Mastering Mathematical Concepts" now, and embark on a journey that will forever transform your understanding of the mathematical universe. Read more

UPDATED EDITION: The new edition includes these updates:The updated edition numbers the questions and answers. This helps to easily find the correct answers in the back of the book.100% of the answers to the updated edition have been independently verified both by computer and by an international math whiz.AUTHOR: Chris McMullen earned his Ph.D. in physics from Oklahoma State University and currently teaches physics at Northwestern State University of Louisiana. He developed the Improve Your Math Fluency series of workbooks to help students become more fluent in basic math skills.CONTENTS: This Algebra Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental algebra skills - in particular, how to solve standard equations for one or more unknowns. These algebra 1 practice exercises are relevant for students of all levels - from grade 7 thru college algebra. This workbook is conveniently divided up into seven chapters so that students can focus on one algebraic method at a time. Skills include solving linear equations with a single unknown (with a separate chapter dedicated toward fractional coefficients), factoring quadratic equations, using the quadratic formula, cross multiplying, and solving systems of linear equations. Not intended to serve as a comprehensive review of algebra, this workbook is instead geared toward the most essential algebra skills. An introduction describes how parents and teachers can help students make the most of this workbook. Students are encouraged to time and score each page. In this way, they can try to have fun improving on their records, which can help lend them confidence in their math skills.PRACTICE: With no pictures, this workbook is geared strictly toward learning the material and developing fluency through practice.EXAMPLES: Each section begins with a few pages of instructions for how to solve the equations followed by a few examples. These examples should serve as a useful guide until students are able to solve the problems independently.ANSWERS: Answers to 100% of the exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes. All answers from the updated edition have been verified both by computer and independently by an international math whiz.PHOTOCOPIES: The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient if you have multiple children/students or if a child/student needs additional practice.NOTE: The answer key uses standard form. Fractions are expressed as reduced fractions, denominators are rationalized, and perfect squares are factored out of square roots. For example, if you receive an answer of 1 over root 8, the answer key will instead show root 2 over 4; both answers are the same, but the answer key uses standard form. Read more

Introducing the ultimate collection of 50 Logic Grid Puzzles for Adults, designed to challenge your brain and provide hours of entertainment! This logic puzzle book is perfect for those who enjoy solving logic puzzles, math games, and adult activity books. With a wide variety of puzzles and difficulty levels, this puzzle book is perfect for both beginners and experienced solvers alike.Each puzzle in this collection has been carefully crafted to provide a fun and challenging experience that will not only improve your logic and math skills but also give you a sense of accomplishment. This book makes a great gift for friends and family who enjoy brain teasers and logic puzzles. So, grab your copy of this adult logic puzzle book today and embark on a thrilling adventure of logic grid puzzles, perfect for game nights, quiet evenings, or daily brain exercises!Engaging and Challenging - Our 50 Logic Grid Puzzles for Adults book provides a variety of brain-teasing puzzles designed to sharpen your problem-solving skills and enhance your logical thinking abilities. The puzzles range from easy to difficult and involve a detailed solution example, perfect for both beginners and experienced solvers.Perfect for All Ages - Though specifically designed for adults, this logic puzzle book is also suitable for kids ages 12+. It's an excellent way to introduce young minds to the world of logic puzzles, math games, and brain teasers, fostering a love for learning and mental stimulation.Please note this is not an interactive book - you will have to draw the grids yourself using paper. Read more

Calculus: Essential Skills Practice Workbook with Full Solutions - Derivatives, Limits and Integrals 2022 EditionThis workbook has been written to provide you all the help you need to master the essential calculus skills of evaluating derivatives, limits and integrals quickly and accurately. For achieving this objective, it guides you step-by-step through the essential tool set - rules, methods and formulas - with the help of clear discussions of topics, thoroughly explained solved examples and exercises with complete solutions. In order to inculcate full student confidence, this user-friendly workbook does not shy away from clarifying even ‘simple’ calculation skills like addition of fractions, multiplication/division of exponents, use of trigonometric identities and so on.What is inside? The subject matter of the workbook has been divided into twenty one chapters with each chapter dealing with a particular topicTable of Contents 1 - Basic Differentiation Rules and the Derivatives of Polynomials2 - The Chain Rule3 - The Product Rule4 - The Quotient Rule5 - Derivatives of Trigonometric Functions6 - Derivatives of Inverse Trigonometric Functions7 - Derivatives of Exponential Functions8 - Derivatives of Logarithmic Functions9 - Derivatives of Hyperbolic Functions10 - Derivatives of Implicit Functions11 - Second Order Derivatives12 - Extreme Values-Maxima and Minima13 - Limits and L’Hôpital’s Rule14 - Indefinite Integrals and Integrals of Polynomials15 - Definite Integrals16 - Integrals of Trigonometric Functions17 - Integrals of Exponential, Logarithmic and Hyperbolic Functions18 - Integration by Polynomial Substitution19 - Integration by Trigonometric Substitution20 - Integration by Parts21 - Multiple IntegralsEach chapter of the workbook begins with a concise yet self-contained discussion of the topic of the chapter supplemented by formulas, identities and properties of various functions, their derivatives and anti-derivatives. This is followed by a number of examples that are solved step by step with explanation of every step.At the end of every chapter, a variety of practice exercises are provided to test your problem solving skills as well as your comprehension and retention of the topic.Full solution of every practice exercise can be found at the back of the workbook to allow you to check your answers. An effort is made to provide really detailed answers without skipping any steps.Who this workbook is forStudents taking introductory calculus course in high schools, colleges and universities who can use it as a text book or a supplementary bookThose from various fields like sciences, engineering, economics, medicine and others who wish to learn or to brush up their knowledge about derivatives and integrals, which they need to solve myriad problems in their respective fields.All those in home study programs, parents wanting to help their kids and other adults of all ages who wish to have a handle on differentiation and integration.About the AuthorSudhir K. Sood obtained his Ph.D. degree in fundamental particle physics. As research scientist and Professor of Physics at Universities in France, Canada and India, Dr. Sood has taught a number of courses both at introductory and advanced graduate level. He has lectured at international Physics conferences and authored numerous well-cited research papers that are published in reputed peer reviewed journals. More recently, for more than a decade, he has taught physics and mathematics to students who wish to specialize in engineering, medicine and physical science courses. Read more

This math workbook, authored by Chris McMullen, Ph.D., is focused on essential prealgebra skills. It includes examples, plenty of practice problems, answers, and full solutions to most problems. Topics include:order of operations; PEMDASfractions, decimals, and percentsexponents and square rootsa beginning introduction to working with variablesratios and ratesnegative numbersother prealgebra skillsThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for applying arithmetic and prealgebra skills. Read more

The bestselling book that has helped millions of readers solve any problemA must-have guide by eminent mathematician G. Polya, How to Solve It shows anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can help you attack any problem that can be reasoned out—from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it’s not just for the classroom. Generations of readers from all walks of life have relished Polya’s brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem. Read more

A comprehensive new illustrated guide to geometry—from New York Times bestselling cartoonist Larry GonickWhat's the point of points? Where do we draw the line? If there are two sides to everything, then what's up with triangles, squares, and polygons?Once again, mathematician-turned-cartoonist Larry Gonick uses his unique gift for witty, lively, and clear exposition to demystify another complex subject: geometry.Moving from the most basic geometrical concepts—planes, lines, and points—through elementary postulates and to elaborate proofs, The Cartoon Guide to Geometry is a comprehensive primer on all the essentials of plane geometry: angles, triangles, area, similarity, and, yes, the Pythagorean theorem. Carefully tailored to the curriculum standards and standardized testing guidelines of the subject, the book provides innovative visuals that develop proofs and constructions with sequential graphics rather than single illustrations. The reader emerges with a deep grasp of key ideas—and has fun getting there. Read more

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career.Learn how to:Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learningUnderstand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargonPerform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significanceManipulate vectors and matrices and perform matrix decompositionIntegrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networksNavigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market Read more

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logicIn 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science. Read more

Logic is the backbone of Western civilization, holding together its systems of philosophy, science and law. Yet despite logic's widely acknowledged importance, it remains an unbroken seal for many, due to its heavy use of jargon and mathematical symbolism.This book follows the historical development of logic, explains the symbols and methods involved and explores the philosophical issues surrounding the topic in an easy-to-follow and friendly manner. It will take you through the influence of logic on scientific method and the various sciences from physics to psychology, and will show you why computers and digital technology are just another case of logic in action. Read more

A marvelous compendium of mathematical symbols and their fascinating historiesGalileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one.In dozens of lively and informative entries, Raúl Rojas shows how today’s mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, René Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time.An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning. Read more

Does the complexity of calculus in machine learning leave you feeling lost in a thicket of equations? Are you eager to find a guide that maps out this territory with clarity and ease? Enter a unique exploration where the world of calculus is demystified through the fascinating biology of bees, offering a perspective on mathematics that is as enlightening as it is unexpected.In this book, I take you on a journey through the mathematical landscapes of derivatives, gradients, and algorithms, illuminated by the natural wisdom of bees. Drawing parallels between the meticulous behaviors of these remarkable insects and the principles of calculus, I present a narrative that is rich with insight and alive with humor.This is not a mere textbook—it's a dialogue. It's a story told through the lens of bee biology, where every concept from gradient descent to neural networks is related back to the intuitive understanding of nature's own algorithms. Together we will find the connections between the disciplined dance of bees and the structured world of mathematics.Here's what to expect:A fresh take on calculus, viewing complex concepts through the simplicity and order of bee behavior.An engaging journey from the basics of calculus to its application in machine learning algorithms like RMSprop, Momentum, and ADAM.Key algorithms like linear regression and neural networks.Coding exercises and practical tasks that mirror the principles you'll learn.Prepare to embark on a transformative journey into the heart of calculus. With bees as our guides, we'll unlock the secrets of machine learning and reveal the mathematical patterns that underpin the digital world. Let's take flight on this adventure together, where the buzz of bees brings mathematics to life.Grab your copy today! Read more

Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits.With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network.In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.  Read more

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Be prepared for exam day with Barron’s. Trusted content from AP experts!Barron’s AP Calculus Premium, 2025 includes in‑depth content review and practice for the AB and BC exams. It’s the only book you’ll need to be prepared for exam day. Written by Experienced EducatorsLearn from Barron’s‑‑all content is written and reviewed by AP expertsBuild your understanding with comprehensive review tailored to the most recent examsGet a leg up with tips, strategies, and study advice for exam day‑‑it’s like having a trusted tutor by your sideBe Confident on Exam DaySharpen your test‑taking skills with 12 full‑length practice tests‑‑3 AB practice tests and 3 BC practice tests in the book, including one diagnostic test each for AB and BC to target your studying‑‑and 3 more AB practice tests and 3 more BC practice tests online–plus detailed answer explanations for all questionsStrengthen your knowledge with in‑depth review covering all units on the AP Calculus AB and BC examsReinforce your learning with dozens of examples and detailed solutions, plus a series of multiple‑choice practice questions and answer explanations, within each chapterEnhance your problem‑solving skills by working through a chapter filled with multiple‑choice questions on a variety of tested topics and a chapter devoted to free‑response practice exercisesRobust Online PracticeContinue your practice with 3 full‑length AB practice tests and 3 full‑length BC practice tests on Barron’s Online Learning HubSimulate the exam experience with a timed test optionDeepen your understanding with detailed answer explanations and expert adviceGain confidence with scoring to check your learning progress  Read more

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