Concrete Mathematics: A Foundation for Computer Science (2nd Edition)
Concrete Mathematics: A Foundation for Computer Science (2nd
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. ...
- Brand: Graham, Ronald L.
- ASIN: 0201558025
- UPC: 785342558029
GMAT Foundations of Math: 900+ Practice Problems in Book and Online (Manhattan Prep GMAT Strategy Guides)
GMAT Foundations of Math: 900+ Practice Problems in
Developed for test-takers who need a refresher, GMAT Foundations of Math provides a user-friendly review of basic math concepts crucial for GMAT success.Designed to be user-friendly for all students, GMAT Foundations of Math provides:* Easy-to-follow explanations of fundamental math concepts* Step-by-step application of concepts to example problems* 700+ practice problems and 10 chapters* Purchase of this book includes one year of online access to the Foundations of Math Homework Banks with 400+ extra practice questions and detailed explanations not included in the book.GMAT Foundations of Math is an invaluable resource for any student who wants to cement their understanding and build their basic math skills for the GMAT.
- Brand: Manhattan Prep Publishing
- ASIN: 1506207642
Foundations of Game Engine Development, Volume 1: Mathematics
Foundations of Game Engine Development, Volume 1:
The first volume of Foundations of Game Engine Development discusses the mathematics needed by engineers who work on games or other types of virtual simulations. The book begins with conventional treatments of topics such as linear algebra, transforms, and geometry. Then, it introduces Grassmann algebra and geometric algebra to provide a much deeper understanding of the subject matter and highlight the places where traditional arithmetic with vectors, matrices, quaternions, etc., isn't quite correct. Includes exercises.Chapter 1: Vectors and Matrices1.1 Vector Fundamentals1.2 Basic Vector Operations1.2.1 Magnitude and Scalar Multiplication1.2.2 Addition and Subtraction1.3 Matrix Fundamentals1.4 Basic Matrix Operations1.4.1 Addition, Subtraction, and Scalar Multiplication1.4.2 Matrix Multiplication1.5 Vector Multiplication1.5.1 Dot Product1.5.2 Cross Product1.5.3 Scalar Triple Product1.6 Vector Projection1.7 Matrix Inversion1.7.1 Identity Matrices1.7.2 Determinants1.7.3 Elementary Matrices1.7.4 Inverse Calculation1.7.5 Inverses of Small MatricesChapter 2: Transforms2.1 Coordinate Spaces2.1.1 Transformation Matrices2.1.2 Orthogonal Transforms2.1.3 Transform Composition2.2 Rotations2.2.1 Rotation About a Coordinate Axis2.2.2 Rotation About an Arbitrary Axis2.3 Reflections2.4 Scales2...
- ASIN: 0985811749
The Foundations of Mathematics
The Foundations of
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The ...
- Brand: Oxford University Press USA
- ASIN: 019870643X
Philosophy of Mathematics (Princeton Foundations of Contemporary Philosophy)
Philosophy of Mathematics (Princeton Foundations of Contemporary
A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholarsMathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics.Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, D...
- Brand: University Press Group Ltd
- ASIN: 0691161402
Foundation Mathematics for Computer Science: A Visual Approach
Foundation Mathematics for Computer Science: A Visual
John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications.Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts.Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-tim...
- ASIN: 3319214365
Foundations of Mathematics: Algebra, Geometry, Trigonometry and Calculus (Essentials of Mathematics)
Foundations of Mathematics: Algebra, Geometry, Trigonometry and Calculus
Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption.Features:•Covers the basics of algebra, trigonometry, geometry, and calculus•Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics•Uses numerous examples and exercises to reinforce concepts
- ASIN: 1942270755
Foundations of Higher Mathematics
Foundations of Higher
This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking.
- ASIN: 053495166X
Building a Foundation in Mathematics
Building a Foundation in
Real-world, on-the-job scenarios and a clear, straightforward approach bring to life the fundamental mathematical concepts that readers will learn with BUILDING A FOUNDATION IN MATHEMATICS, 2nd EDITION. This latest edition begins with deliberate and thorough coverage of the simplest topics, like whole numbers and fractions, before delving into more advanced areas. By the time the book has progressed to complex subjects like binary numbers and Boolean algebra, readers have been armed with such a solid foundation of the basics that comprehension is easy. Added value is found in the practical examples that encompass typical situations electricians face every day, providing a concrete context for learning and making this book an indispensable resource for anyone seeking the mathematical skills necessary for work in the electrical field. Check out our app, DEWALT Mobile Pro™. This free app is a construction calculator with integrated reference materials and access to hundreds of additional calculations as add-ons. To learn more, visit dewalt.com/mobilepro.
- Brand: Brand: Cengage Learning
- ASIN: 1435488547
Introduction to the Foundations of Mathematics: Second Edition (Dover Books on Mathematics)
Introduction to the Foundations of Mathematics: Second Edition
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.
- ASIN: 0486488209
- UPC: 800759488209
Burn Math Class: And Reinvent Mathematics for Yourself
Burn Math Class: And Reinvent Mathematics for
A manifesto for a mathematical revolutionForget everything you've been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math--with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire.Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically--and it becomes fun!Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so...
- Brand: Basic Books
- ASIN: 0465053734
Foundations of Applied Mathematics, Volume 1: Mathematical Analysis
Foundations of Applied Mathematics, Volume 1: Mathematical
This book provides the foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analy...
- ASIN: 1611974895
Foundations of GMAT Math, 5th Edition (Manhattan GMAT Preparation Guide: Foundations of Math)
Foundations of GMAT Math, 5th Edition (Manhattan GMAT
Developed for test-takers who need a refresher, Foundations of Math provides a user-friendly review of basic math concepts crucial for GMAT success.Manhattan GMAT'â€™s Foundations of Math book provides a refresher of the basic math concepts tested on the GMAT. Designed to be user-friendly for all students, this book provides easy-to-follow explanations of fundamental math concepts and step-by-step application of these concepts to example problems. With ten chapters and over 700 practice problems, this book is an invaluable resource to any student who wants to cement their understanding and build their basic math skills for the GMAT. Purchase of this book includes one year of online access to the Foundations of Math Homework Banks consisting of over 400 extra practice questions and detailed explanations not included in the book.
- ASIN: 1935707590
Foundations of Applied Mathematics
Foundations of Applied
This classic text in applied mathematics, suitable for undergraduate- and graduate-level engineering courses, is also an excellent reference for professionals and students of applied mathematics. The precise and reader-friendly approach offers single-volume coverage of a substantial number of topics along with well-designed problems and examples. The five-part treatment begins with an exploration of real variable theory that includes limit processes, infinite series, singular integrals, Fourier series, and vector field theory. Succeeding sections examine complex variables, linear analysis, and ordinary and partial differential equations. Answers to selected exercises appear in the appendix, along with Fourier and Laplace transformation tables and useful formulas.
- ASIN: 0486492796
- UPC: 800759492794
Logic, Mathematics, and Computer Science: Modern Foundations with Practical Applications
Logic, Mathematics, and Computer Science: Modern Foundations with
This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory. The focuses is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided.Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material? Additio...
- ASIN: 1493932225
Remarks on the Foundations of Mathematics [Bemerkungen Uber Die Grundlagen Der Mathematik]
Remarks on the Foundations of Mathematics [Bemerkungen Uber
2014 Reprint of 1956 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Published in English and German with each text presented on opposing pages. "Remarks on the Foundations of Mathematics" are Wittgenstein's notes on the philosophy of mathematics. It has been translated from German to English by G.E.M. Anscombe, edited by G.H. von Wright and Rush Rhees, and published first in 1956. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937-1944 and a few passages are incorporated in the "Philosophical Investigations" which were composed later. Wittgenstein's philosophy of mathematics is exposed chiefly by simple examples on which further skeptical comments are made. The text offers an extended analysis of the concept of mathematical proof and an exploration of Wittgenstein's contention that philosophical considerations introduce false problems in mathematics. Wittgenstein in the "Remarks" adopts an attitude of doubt in opposition to much orthodoxy in the philosophy of mathematics. Wittgenstein's influence has been felt in nearly every field of the humanities and the social sciences, though many of his views remain controversial. Wittgenstein's work remai...
- ASIN: 1614276501
Kurt Godel and the Foundations of Mathematics: Horizons Of Truth
Kurt Godel and the Foundations of Mathematics: Horizons
This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers.
- ASIN: 1107677998
Foundations of the Theory of Probability: Second English Edition (Dover Books on Mathematics)
Foundations of the Theory of Probability: Second English
This famous little book was first published in German in 1933 and in Russian a few years later, setting forth the axiomatic foundations of modern probability theory and cementing the author's reputation as a leading authority in the field. The distinguished Russian mathematician A. N. Kolmogorov wrote this foundational text, and it remains important both to students beginning a serious study of the topic and to historians of modern mathematics.Suitable as a text for advanced undergraduates and graduate students in mathematics, the treatment begins with an introduction to the elementary theory of probability and infinite probability fields. Subsequent chapters explore random variables, mathematical expectations, and conditional probabilities and mathematical expectations. The book concludes with a chapter on the law of large numbers, an Appendix on zero-or-one in the theory of probability, and detailed bibliographies.
- ASIN: 0486821595
- UPC: 800759821594
Introduction to the Foundations of Applied Mathematics (Texts in Applied Mathematics)
Introduction to the Foundations of Applied Mathematics (Texts
FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.
- ASIN: 0387877495
Concrete Mathematics: A Foundation for Computer Science
Crisis in the Foundation of Mathematics | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -- it de...
Kurt Gödel & the Limits of Mathematics
Kurt Gödel and his famous Incompleteness Theorems are discussed by Mark Colyvan, Professor of Philosophy and Director of the Sydney Centre for the Foundations of Science. This is from Key Thinkers (Sydney Ideas).
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege. Thank you to Professor Joel David Hamkins for your help with this video. Hi! I'm Jade. Subscribe to Up and Atom for physics, math and computer s...