As educators, we understand the challenges you face in this course, and as authors, we have crafted a text that gives you the tools to meet them. This book has examples with clear explanations to help you learn how to logically solve mathematics problems. Read and work the examples and do the suggested NOW WORK Problems listed after them. Take advantage of the book's many features to help you to master calculus. Whether you are majoring in life sciences, business or economics, engineering or mathematics, this book has many applied exercises - some written by students like you - related to courses in a wide variety of majors. And a robust online support system includes a suite of easy-to-use and powerfully built learning tools, which include stepped-out examples, video tutorials, interactive figures, assessment quizzes, and hundreds of practice exercises with feedback and solutions.Achieve for Calculus redefines homework by offering guidance for every student and support for every instructor. Homework is designed to teach by correcting students' misconceptions through targeted feedback, meaningful hints, and full solutions, helping teach students conceptual understanding and critical thinking in real-world contexts.

This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation. The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

Bestselling historian William Dalrymple reinstates India as the great intellectual and philosophical superpower of Ancient Asia, tracing the cultural flow of its religion, science and mathematics.

For most of its modern history, India was fated to be on the receiving end of cultural influence from other civilisations. But this isn’t the complete story. A full millennium earlier, India’s major cultural exports – religion, art, technology, astronomy, mathematics, medicine, language and literature – were shaping civilisations, travelling as far as Afghanistan in the West and Japan in the East.

Out of India came pioneering merchants, astronomers and astrologers, scientists and mathematicians, surgeons and sculptors, as well as holy men, monks and missionaries. In The Golden Road, legendary historian William Dalrymple highlights India’s oft­forgotten position as a crucial economic and civilisational hub at the heart of the ancient and early medieval history of Eurasia.

From Angkor to Ayutthaya, The Golden Road traces the cultural flow of Indian religions, languages, artistic and architectural forms and mathematics throughout the world. In this groundbreaking tome, Dalrymple draws from a lifetime of scholarship to reinstate India as the great intellectual and philosophical superpower of ancient Asia.

Primary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace. Primary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire first level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work. - Packed with problem-solving, investigations and challenging problems - Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work - Worked examples and non-examples help pupils fully understand mathematical concepts - Includes intelligent practice that reinforces pupils' procedural fluency

This book gives a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures with an emphasis on ``bare hands'' approaches, combining differential-topological cut-and-paste procedures and applications of transversality. In particular, the smooth cobordism cup-product is defined from scratch and used as the main tool in a variety of settings. After establishing the fundamentals, the book proceeds to a broad range of more advanced topics in differential topology, including degree theory, the Poincare-Hopf index theorem, bordism-characteristic numbers, and the Pontryagin-Thom construction. Cobordism intersection forms are used to classify compact surfaces; their quadratic enhancements are developed and applied to studying the homotopy groups of spheres, the bordism group of immersed surfaces in a 3-manifold, and congruences mod 16 for the signature of intersection forms of 4-manifolds. Other topics include the high-dimensional $h$-cobordism theorem stressing the role of the ``Whitney trick'', a determination of the singleton bordism modules in low dimensions, and proofs of parallelizability of orientable 3-manifolds and the Lickorish-Wallace theorem. Nash manifolds and Nash's questions on the existence of real algebraic models are also discussed. This book will be useful as a textbook for beginning masters and doctoral students interested in differential topology, who have finished a standard undergraduate mathematics curriculum. It emphasizes an active learning approach, and exercises are included within the text as part of the flow of ideas. Experienced readers may use this book as a source of alternative, constructive approaches to results commonly presented in more advanced contexts with specialized techniques.

Hyperbolic Dynamics and Brownian Motion illustrates the interplay between distinct domains of mathematics. There is no assumption that the reader is a specialist in any of these domains: only basic knowledge of linear algebra, calculus and probability theory is required. The content can be summarized in three ways: Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group. The Lorentz group plays, in relativistic space-time, a role analogue to the rotations in Euclidean space. The hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of the hyperbolic space is defined as the set of light rays. Special attention is given to the geodesic and horocyclic flows. Hyperbolic geometry is presented via special relativity to benefit from the physical intuition. Secondly, this book introduces basic notions of stochastic analysis: the Wiener process, Ito's stochastic integral, and calculus. This introduction allows study in linear stochastic differential equations on groups of matrices. In this way the spherical and hyperbolic Brownian motions, diffusions on the stable leaves, and the relativistic diffusion are constructed. Thirdly, quotients of the hyperbolic space under a discrete group of isometries are introduced. In this framework some elements of hyperbolic dynamics are presented, as the ergodicity of the geodesic and horocyclic flows. This book culminates with an analysis of the chaotic behaviour of the geodesic flow, performed using stochastic analysis methods. This main result is known as Sinai's central limit theorem.

An introduction to statistical data mining, Data Analysis and Data Mining is both textbook and professional resource. Assuming only a basic knowledge of statistical reasoning, it presents core concepts in data mining and exploratory statistical models to students and professional statisticians-both those working in communications and those working in a technological or scientific capacity-who have a limited knowledge of data mining. This book presents key statistical concepts by way of case studies, giving readers the benefit of learning from real problems and real data. Aided by a diverse range of statistical methods and techniques, readers will move from simple problems to complex problems. Through these case studies, authors Adelchi Azzalini and Bruno Scarpa explain exactly how statistical methods work; rather than relying on the "push the button" philosophy, they demonstrate how to use statistical tools to find the best solution to any given problem. Case studies feature current topics highly relevant to data mining, such web page traffic; the segmentation of customers; selection of customers for direct mail commercial campaigns; fraud detection; and measurements of customer satisfaction. Appropriate for both advanced undergraduate and graduate students, this much-needed book will fill a gap between higher level books, which emphasize technical explanations, and lower level books, which assume no prior knowledge and do not explain the methodology behind the statistical operations.

Now available with Macmillan's new online learning tool Achieve, Introduction to the Practice of Statistics, 10th edition, prepares students for the application of statistics in the real world by using current examples and encouraging exploration into data analysis and interpretation. The text enforces statistical thinking by providing learning objectives and linked exercises to help students master core statistics concepts and think beyond the calculations.Achieve for Introduction to the Practice of Statistics integrates outcome-based learning objectives and a wealth of examples with assessment in an easy-to-use interface. Students are provided with rich digital resources that solidify conceptual understanding, as well as homework problems with hints, answer-specific feedback, and a fully worked solution.

Linear Algebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations. The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life. Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.

A groundbreaking, flexible approach to computer science anddata science The Deitels' Introduction to Python for ComputerScience and Data Science: Learning to Program with AI, Big Data and the Cloudoffers a unique approach to teaching introductory Python programming,appropriate for both computer-science and data-science audiences. Providing themost current coverage of topics and applications, the book is paired withextensive traditional supplements as well as Jupyter Notebooks supplements.Real-world datasets and artificial-intelligence technologies allow students towork on projects making a difference in business, industry, government andacademia. Hundreds of examples, exercises, projects (EEPs) and implementationcase studies give students an engaging, challenging and entertainingintroduction to Python programming and hands-on data science. The book's modular architecture enables instructors toconveniently adapt the text to a wide range of computer-science anddata-science courses offered to audiences drawn from many majors.Computer-science instructors can integrate as much or as little data-scienceand artificial-intelligence topics as they'd like, and data-science instructorscan integrate as much or as little Python as they'd like. The book aligns withthe latest ACM/IEEE CS-and-related computing curriculum initiatives and withthe Data Science Undergraduate Curriculum Proposal sponsored by the NationalScience Foundation.

Thomas' Calculus: Early Transcendentals goes beyond memorizing formulas and routine procedures to help you develop deeper understanding. It guides you to a level of mathematical proficiency, with additional support if needed through its clear and intuitive explanations, current applications and generalized concepts. Technology exercises in every section use the calculator or computer for solving problems, and Computer Explorations offer exercises requiring a computer algebra system like Maple or Mathematica. The 15th Edition adds exercises, revises figures and language for clarity, and updates many applications.