Advertisement
| understanding mathematics from counting to calculus: A First Course in Calculus Serge Lang, 2012-09-17 This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions. |
| understanding mathematics from counting to calculus: Math Problems and Solutions Guide David Scheinker, 2009 |
| understanding mathematics from counting to calculus: From Counting to Calculus Michael F. Petras, 2016-12-27 A unified approach to mathematics covering all of the major topics from simple counting through calculus, including an introduction to differential equations. Starting with counting, all of the operations of arithmetic and the corresponding systems of numbers are developed as a single, interconnected framework. This framework is then used as a foundation for the construction of algebra and calculus. Each new topic is introduced as a logical extension of the topics that came before it, and is developed thoroughly and rigorously with the reader as if it was being invented for the first time. Although it is assumed that the reader is familiar with arithmetic and has had some exposure to algebra, proficiency with mathematics is not required. The conversational style and step-by-step approach make it easy to follow the flow of ideas, and numerous exercises sprinkled throughout allow readers to test their understanding before proceeding to the next topic. Among the topics covered are the additive and positional number systems, the operations of arithmetic, integer and non-integer exponents, fractions, rational and irrational numbers, real and complex numbers, algebraic solutions of equations, simultaneous equations, graphs and graphical solutions of equations, constructing polynomial equations from data, finding roots of polynomial equations, functions and inverse functions, differential calculus including the sum, product, and chain rules, integral calculus including proper and improper integrals, and an introduction to ordinary and partial differential equations, with applications to the physical sciences. Problems at the ends of the chapters, along with their solutions, provide the opportunity to practice methods discussed in the text, and explore important topics in more depth. The choice of subject matter and method of presentation makes this an ideal text for a high school or college level course, or as a self-teaching guide for the general reader interested in developing a deeper understanding of mathematics. |
| understanding mathematics from counting to calculus: Introduction to Calculus and Analysis II/1 Richard Courant, Fritz John, 2012-12-06 From the reviews: ...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students. --Acta Scientiarum Mathematicarum, 1991 |
| understanding mathematics from counting to calculus: Mathematics as Sign Brian Rotman, 2000 In this book, Rotman argues that mathematics is a vast and unique man-made imagination machine controlled by writing. It addresses both aspects—mental and linguistic—of this machine. The essays in this volume offer an insight into Rotman's project, one that has been called one of the most original and important recent contributions to the philosophy of mathematics. |
| understanding mathematics from counting to calculus: Mathematics for Everyman Egmont Colerus, 2013-02-04 This witty and engaging stylebook presents the fundamentals of mathematical operations: number systems, first steps in algebra and algebraic notation, common fractions and equations, and much more. 1958 edition. |
| understanding mathematics from counting to calculus: A Quick History of Maths Clive Gifford, 2020-03-31 A Quick History of Maths is 43,000 years of mathematical discoveries packed into one book, plus lots of jokes. |
| understanding mathematics from counting to calculus: Calculus Made Easy Silvanus Phillips Thompson, 1911 |
| understanding mathematics from counting to calculus: The Joy of X Steven Henry Strogatz, 2012 A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the New York Times. |
| understanding mathematics from counting to calculus: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| understanding mathematics from counting to calculus: Concrete Mathematics Ronald L. Graham, Donald E. Knuth, Oren Patashnik, 1994-02-28 This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. |
| understanding mathematics from counting to calculus: Introduction to Mathematical Thinking Keith J. Devlin, 2012 Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists.--Back cover. |
| understanding mathematics from counting to calculus: Discrete Calculus Carlo Mariconda, Alberto Tonolo, 2016-12-01 This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified. |
| understanding mathematics from counting to calculus: Count Like an Egyptian David Reimer, 2014-04-27 A lively collection of fun and challenging problems in ancient Egyptian math The mathematics of ancient Egypt was fundamentally different from our math today. 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. |
| understanding mathematics from counting to calculus: Math, Better Explained Kalid Azad, 2015-12-04 Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted. |
| understanding mathematics from counting to calculus: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| understanding mathematics from counting to calculus: Basic Mathematics Serge Lang, 1988-01 |
| understanding mathematics from counting to calculus: Mathematics for the General Reader E.C. Titchmarsh, 2017-04-19 A first-class mathematician's lucid, unhurried account of the science of numbers from arithmetic through the calculus. — James R. Newman, The World of Mathematics. This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do. Author E. C. Titchmarsh, who served for many years as Savilian Professor of Geometry at Oxford University, begins with counting and the fundamentals of arithmetic. He guides readers through the complexities of algebra, fractions, geometry, irrational numbers, logarithms, infinite series, complex numbers, quadratic equations, trigonometry, functions, and integral and differential calculus. Titchmarsh's graceful, fluid style helps make complicated topics easier to grasp, and his inclusion of numerous examples will prove especially helpful to readers with little or no background in mathematics. |
| understanding mathematics from counting to calculus: Book of Proof Richard H. Hammack, 2016-01-01 This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. |
| understanding mathematics from counting to calculus: Math with Bad Drawings Ben Orlin, 2018-09-18 A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark bad drawings, which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike. |
| understanding mathematics from counting to calculus: A Tour of the Calculus David Berlinski, 2011-04-27 Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others.--New York Times Book Review |
| understanding mathematics from counting to calculus: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| understanding mathematics from counting to calculus: The Pleasures of Counting Thomas William Körner, 1996-12-05 What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here. |
| understanding mathematics from counting to calculus: Advanced Mathematics Stanley J. Farlow, 2019-09-19 Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the rote-orientated courses of calculus to the more rigorous proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math. |
| understanding mathematics from counting to calculus: Inside Mathematics Mike Goldsmith, 2018-10 Think math is boring?Think again! Algebra to Calculus: Unlocking Math's Amazing Power tells the story of algebra and calculus to explore the surprising, fascinating and sometimes mind-boggling evolution of mathematics through the ages.How do you make a decision with numbers? You have to use a kind of math called Boolean algebra-it's a little strange because it only ever uses two numbers 1 or 0, and 1+1 always equals 1. Despite this weirdness, this algebra is used to create the nanoscale circuits in every microchip. Do you want to know more? Written to engage, entertain and enthuse readers young and old, Algebra to Calculus: Unlocking Math's Amazing Power takes an entirely new approach to the wonderful world of mathematics. Along the way, readers will meet with geniuses, such as Diophantus and Newton, who figured out how to turn math problems into general techniques that worked whatever the situation. Readers will not only learn how computer chips process their programs, but also how a smartphone knows where it is, what the link is between snowflakes, cannonballs and wine barrels, and how Carl Gauss figured out how to add up all the numbers between 1 and 100 in less than a minute-when he was just 10 years old! Algebra to Calculus: Unlocking Math's Amazing Power shows there is a lot more going on than just x + y = z. |
| understanding mathematics from counting to calculus: Applied Linear Algebra Lorenzo Adlai Sadun, 2007-12-20 Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises. |
| understanding mathematics from counting to calculus: Practical Mathematics Claude Irwin Palmer, Samuel Fletcher Bibb, 1952 |
| understanding mathematics from counting to calculus: A Quick Steep Climb Up Linear Algebra Stephen Davies, 2021-01-13 A Quick Steep Climb Up Lienar Algebra - and its companion site allthemath - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia! |
| understanding mathematics from counting to calculus: Advanced Problems in Mathematics Stephen Siklos, 2019-10-16 This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. |
| understanding mathematics from counting to calculus: Foundations of Differential Calculus Euler, 2006-05-04 The positive response to the publication of Blanton's English translations of Euler's Introduction to Analysis of the Infinite confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's Foundations of Differential Calculus as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community. |
| understanding mathematics from counting to calculus: Active Calculus 2018 Matthew Boelkins, 2018-08-13 Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface. |
| understanding mathematics from counting to calculus: Calculus for the Ambitious T. W. Körner, 2014-05-29 A short introduction perfect for any 16- to 18-year-old, about to begin studies in mathematics. |
| understanding mathematics from counting to calculus: Elliptic Tales Avner Ash, Robert Gross, 2012 Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture. |
| understanding mathematics from counting to calculus: Proofs from THE BOOK Martin Aigner, Günter M. Ziegler, 2013-06-29 According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such perfect proofs, those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics. |
| understanding mathematics from counting to calculus: Practical Algebra Peter H. Selby, Steve Slavin, 1991-09-03 Practical Algebra If you studied algebra years ago and now need arefresher course in order to use algebraic principles on the job,or if you're a student who needs an introduction to the subject,here's the perfect book for you. Practical Algebra is an easy andfun-to-use workout program that quickly puts you in command of allthe basic concepts and tools of algebra. With the aid of practical,real-life examples and applications, you'll learn: * The basic approach and application of algebra to problemsolving * The number system (in a much broader way than you have known itfrom arithmetic) * Monomials and polynomials; factoring algebraic expressions; howto handle algebraic fractions; exponents, roots, and radicals;linear and fractional equations * Functions and graphs; quadratic equations; inequalities; ratio,proportion, and variation; how to solve word problems, andmore Authors Peter Selby and Steve Slavin emphasize practical algebrathroughout by providing you with techniques for solving problems ina wide range of disciplines--from engineering, biology, chemistry,and the physical sciences, to psychology and even sociology andbusiness administration. Step by step, Practical Algebra shows youhow to solve algebraic problems in each of these areas, then allowsyou to tackle similar problems on your own, at your own pace.Self-tests are provided at the end of each chapter so you canmeasure your mastery. |
| understanding mathematics from counting to calculus: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| understanding mathematics from counting to calculus: Understanding Basic Calculus S. K. Chung, 2014-11-26 Understanding Basic CalculusBy S.K. Chung |
| understanding mathematics from counting to calculus: What is Mathematics? Richard Courant, Herbert Robbins, 1978 |
| understanding mathematics from counting to calculus: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-03-08 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. |
| understanding mathematics from counting to calculus: Math Without Numbers Milo Beckman, 2021-01-07 'The whizz-kid making maths supercool. . . A brilliant book that takes everything we know (and fear) about maths out of the equation - starting with numbers' The Times 'A cheerful, chatty, and charming trip through the world of mathematics. . . Everyone should read this delightful book' Ian Stewart, author of Do Dice Play God? The only numbers in this book are the page numbers. The three main branches of abstract math - topology, analysis, and algebra - turn out to be surprisingly easy to grasp. Or at least, they are when our guide is a math prodigy. With forthright wit and warm charm, Milo Beckman upends the conventional approach to mathematics, inviting us to think creatively about shape and dimension, the infinite and the infinitesimal, symmetries, proofs, and all how all these concepts fit together. Why is there a million dollar prize for counting shapes? Is anything bigger than infinity? And how is the 'truth' of mathematics actually decided? A vivid and wholly original guide to the math that makes the world tick and the planets revolve, Math Without Numbers makes human and understandable the elevated and hypothetical, allowing us to clearly see abstract math for what it is: bizarre, beautiful, and head-scratchingly wonderful. |
UNDERSTANDING Definition & Meaning - Merriam-Webster
The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use …
UNDERSTANDING Definition & Meaning - Dictionary.com
Understanding definition: mental process of a person who comprehends; comprehension; personal …
UNDERSTANDING definition and meaning | Collins Englis…
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, …
Understanding - Definition, Meaning & Synonyms - Vocab…
The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding …
UNDERSTANDING Definition & Meaning - Merriam-Webster
The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. …
UNDERSTANDING Definition & Meaning - Dictionary.com
Understanding definition: mental process of a person who comprehends; comprehension; personal interpretation.. See examples of UNDERSTANDING used in a sentence.
UNDERSTANDING definition and meaning | Collins English …
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, you are kind and forgiving. Her boss, who was very …
Understanding - Definition, Meaning & Synonyms
The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding person doesn't take a lot of studying …
UNDERSTANDING definition | Cambridge English Dictionary
UNDERSTANDING meaning: 1. knowledge about a subject, situation, etc. or about how something works: 2. a particular way in…. Learn more.
understanding noun - Definition, pictures, pronunciation and …
Definition of understanding noun from the Oxford Advanced Learner's Dictionary. [uncountable, singular] understanding (of something) the knowledge that somebody has about a particular …
What does Understanding mean? - Definitions.net
Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support …
understanding - definition and meaning - Wordnik
noun The ability by which one understands; intelligence. noun The quality or condition of one who understands; comprehension: synonym: reason. noun Individual or specified judgment or …
Understanding - definition of understanding by ... - The Free …
1. the mental process of a person who understands; comprehension; personal interpretation. 2. intellectual faculties; intelligence. 3. knowledge of or familiarity with a particular thing. 5. a …
