introduction to the foundations of mathematics 2nd edition

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Introduction To The Foundations Of Mathematics

Author : Raymond L. Wilder
ISBN : 9780486488202
Genre : Mathematics
File Size : 57. 11 MB
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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.

The Foundations Of Mathematics

Author : Ian Stewart
ISBN : 9780198706434
Genre : Mathematics
File Size : 47. 98 MB
Format : PDF, ePub
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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.

Mathematical Physics

Author : Sadri Hassani
ISBN : 0387985794
Genre : Science
File Size : 41. 20 MB
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This modern introduction to mathematical physics is ideal for physicists interested in the mathematics they use and for mathematicians interested in seeing how the ideas of their discipline find realization in an applied setting. The presentation balances formalism and application and the abstract and concrete.

Introduction To Mathematical Structures And Proofs

Author : Larry J. Gerstein
ISBN : 9781461442653
Genre : Mathematics
File Size : 53. 76 MB
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As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.

Exploring Education

Author : Alan R. Sadovnik
ISBN : 0415808618
Genre : Education
File Size : 51. 93 MB
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This much-anticipated fourth edition of Exploring Education offers an alternative to traditional foundations texts by combining a point-of-view analysis with primary source readings. Pre- and in-service teachers will find a solid introduction to the foundations disciplines -- history, philosophy, politics, and sociology of education -- and their application to educational issues, including school organization and teaching, curriculum and pedagogic practices, education and inequality, and school reform and improvement. This edition features substantive updates, including the addition of discussion on the neo-liberal educational policy and recent debates about teacher evaluation, updated data and research, and new readings by leading researchers, such as Diane Ravitch, Robert Dreeben, and Helen F. Ladd. At a time when foundations of education are marginalized in many teacher education programs and teacher education reform pushes scripted approaches to curriculum and instruction, Exploring Education helps teachers to think critically about the "what" and "why" behind the most pressing issues in contemporary education.

Principia Mathematica

Author : Alfred North Whitehead
ISBN : 052106791X
Genre : Logic, Symbolic and mathematical
File Size : 64. 12 MB
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A Friendly Introduction To Mathematical Logic

Author : Christopher C. Leary
ISBN : 9781942341079
Genre :
File Size : 52. 9 MB
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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Godel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises."

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