A Mathematical Prelude to the Philosophy of Mathematics

A Mathematical Prelude to the Philosophy of Mathematics
Author :
Publisher : Springer
Total Pages : 206
Release :
ISBN-10 : 9783319058160
ISBN-13 : 3319058169
Rating : 4/5 (60 Downloads)

Synopsis A Mathematical Prelude to the Philosophy of Mathematics by : Stephen Pollard

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

Prelude to Mathematics

Prelude to Mathematics
Author :
Publisher : Courier Corporation
Total Pages : 228
Release :
ISBN-10 : 9780486152776
ISBN-13 : 0486152774
Rating : 4/5 (76 Downloads)

Synopsis Prelude to Mathematics by : W. W. Sawyer

This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.

Explorations in Ancient and Modern Philosophy

Explorations in Ancient and Modern Philosophy
Author :
Publisher : Cambridge University Press
Total Pages : 393
Release :
ISBN-10 : 9780521750721
ISBN-13 : 0521750725
Rating : 4/5 (21 Downloads)

Synopsis Explorations in Ancient and Modern Philosophy by : M. F. Burnyeat

The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.

Philosophical Dimensions in Mathematics Education

Philosophical Dimensions in Mathematics Education
Author :
Publisher : Springer Science & Business Media
Total Pages : 235
Release :
ISBN-10 : 9780387715759
ISBN-13 : 0387715754
Rating : 4/5 (59 Downloads)

Synopsis Philosophical Dimensions in Mathematics Education by : Karen Francois

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory
Author :
Publisher : Courier Dover Publications
Total Pages : 196
Release :
ISBN-10 : 9780486797144
ISBN-13 : 0486797147
Rating : 4/5 (44 Downloads)

Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Mathematics and Logic

Mathematics and Logic
Author :
Publisher : Courier Corporation
Total Pages : 189
Release :
ISBN-10 : 9780486670850
ISBN-13 : 0486670856
Rating : 4/5 (50 Downloads)

Synopsis Mathematics and Logic by : Mark Kac

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Mathematics and Computation

Mathematics and Computation
Author :
Publisher : Princeton University Press
Total Pages : 434
Release :
ISBN-10 : 9780691189130
ISBN-13 : 0691189137
Rating : 4/5 (30 Downloads)

Synopsis Mathematics and Computation by : Avi Wigderson

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Introduction to Mathematical Thinking

Introduction to Mathematical Thinking
Author :
Publisher : Courier Corporation
Total Pages : 292
Release :
ISBN-10 : 9780486167428
ISBN-13 : 0486167429
Rating : 4/5 (28 Downloads)

Synopsis Introduction to Mathematical Thinking by : Friedrich Waismann

Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.

Philosophy of Mathematics

Philosophy of Mathematics
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 514
Release :
ISBN-10 : 9783110470772
ISBN-13 : 3110470772
Rating : 4/5 (72 Downloads)

Synopsis Philosophy of Mathematics by : Thomas Bedürftig

The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection

Naming Infinity

Naming Infinity
Author :
Publisher : Harvard University Press
Total Pages : 252
Release :
ISBN-10 : 9780674032934
ISBN-13 : 0674032934
Rating : 4/5 (34 Downloads)

Synopsis Naming Infinity by : Loren Graham

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.