Fundamental Concepts of Geometry

Author: Bruce E. Meserve

Publisher: Courier Corporation

ISBN: 048615226X

Category: Mathematics

Page: 336

View: 3467

Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 3144

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 8843

This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

Mathematical Foundations of Computer Science

Author: G. Shankar Rao

Publisher: I. K. International Pvt Ltd

ISBN: 8188237493

Category: Computer science

Page: 472

View: 6091

Explains the fundamental concepts in mathematics. It can be used by the students in computer science as an introduction to the underlying ideas of mathematics for computer science. It explains topics like mathematical logic, predicates, relations, functions, combinatorics, algebraic structures and graph theory. It would be useful for the students of B.Tech, BCA, & MCA. Key Features: * Comprehensive discussion on logic, function, algebraic systems, recurrence relations and graph theory * Wide variety of exercises at all levels * Several worked out examples

Outline Course of Pure Mathematics

Author: A. F. Horadam

Publisher: Elsevier

ISBN: 1483147908

Category: Mathematics

Page: 594

View: 7975

Outline Course of Pure Mathematics presents a unified treatment of the algebra, geometry, and calculus that are considered fundamental for the foundation of undergraduate mathematics. This book discusses several topics, including elementary treatments of the real number system, simple harmonic motion, Hooke's law, parabolic motion under gravity, sequences and series, polynomials, binomial theorem, and theory of probability. Organized into 23 chapters, this book begins with an overview of the fundamental concepts of differential and integral calculus, which are complementary processes for solving problems of the physical world. This text then explains the concept of the inverse of a function that is a natural complement of the function concept and introduces a convenient notation. Other chapters illustrate the concepts of continuity and discontinuity at the origin. This book discusses as well the significance of logarithm and exponential functions in scientific and technological contexts. This book is a valuable resource for undergraduates and advanced secondary school students.

Epistemological Foundations of Mathematical Experience

Author: Leslie P. Steffe

Publisher: Springer Science & Business Media

ISBN: 1461231787

Category: Psychology

Page: 312

View: 6927

On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.

Abstract Algebra

Author: W. E. Deskins

Publisher: Courier Corporation

ISBN: 0486158462

Category: Mathematics

Page: 656

View: 7064

Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.

Mathematical Foundations of Quantum Statistics

Author: Aleksandr Iakovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486400259

Category: Science

Page: 232

View: 3207

A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

Foundations of Mathematical Analysis

Author: Saminathan Ponnusamy

Publisher: Springer Science & Business Media

ISBN: 0817682929

Category: Mathematics

Page: 570

View: 2150

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

The Foundations of Mathematics

Author: Ian Stewart,David Tall

Publisher: OUP Oxford

ISBN: 0191016489

Category: Mathematics

Page: 432

View: 4013

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 approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

Was ist Mathematik?

Author: Richard Courant,Herbert Robbins

Publisher: Springer-Verlag

ISBN: 3642137016

Category: Mathematics

Page: 400

View: 8832

"Was ist Mathematik?" lädt jeden ein, das Reich der Mathematik zu betreten, der neugierig genug ist, sich auf ein Abenteuer einzulassen. Das Buch richtet sich an Leser jeden Alters und jeder Vorbildung. Gymnasiallehrer erhalten eine Fülle von Beispielen, Studenten bietet es Orientierung, und Dozenten werden sich an den Feinheiten der Darstellung zweier Meister ihres Faches erfreuen.