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
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
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
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 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
Building a Foundation in Mathematics
Building a Foundation in
Learn fundamental mathematical concepts using real-world, on-the-job scenarios that electricians face every day. Building a Foundation in Mathematics uses a building block approach by beginning with very basic concepts like whole numbers and fractions, and building upon this knowledge to get to more complex material like Boolean algebra. Each concept is covered deliberately and thoroughly before moving on to the next, guaranteeing a strong working knowledge of each area. This clear, straightforward approach, coupled with practical examples that engage readers and provide a context for learning, make 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: 1418006327
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 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
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...
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...
⚫️ Foundations of Mathematics Final Exam Review: Part 1 [fbt] (MATH 0309 - Developmental Math II)
This Fort Bend Tutoring [fbt] Live Stream is part 1 of 2 final exam review videos for the developmental mathematics college course foundations of mathematics (Developmental Mathematics II). Math concepts, from the course MATH 0308/MATH 0409/MATH 0309, covered are solving linear equations, factori...