Author : F. William Lawvere
Publisher : Cambridge University Press
Page : 280 pages
File Size : 37,71 MB
Release : 2003-01-27
Category : Mathematics
ISBN : 9780521010603
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Author : A. G. Hamilton
Publisher : Cambridge University Press
Page : 272 pages
File Size : 16,18 MB
Release : 1982
Category : Mathematics
ISBN : 9780521287616
Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 16,23 MB
Release : 2000
Category : Mathematics
ISBN : 9780521770347
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
Author : Katherine Loop
Publisher : Master Books
Page : 0 pages
File Size : 36,46 MB
Release : 2016-09-02
Category :
ISBN : 9780890519141
Katherine Loop has done the remarkable! She has written a solid math course with a truly Biblical worldview. This course goes way beyond the same old Christian math course that teaches math with a few Scriptures sprinkled in and maybe some church-based word problems. This course truly transforms the way we see math. Katherine makes the argument that math is not a neutral subject as most have come to believe. She carefully lays the foundation of how math points to our Creator, the God of the Bible. The nature of God, His Creation, and even the Gospel itself is seen through the study of math. Katherine does a marvelous job of revealing His Glory in this one-of-a-kind math course. Katherine Loop's Principles of Mathematics Biblical Worldview Curriculum is a first of its kind. It takes math to a whole new level students and parents are going to love. It is a guaranteed faith grower!
Author : Joseph Breuer
Publisher : Courier Corporation
Page : 130 pages
File Size : 34,27 MB
Release : 2012-08-09
Category : Mathematics
ISBN : 0486154874
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 39,69 MB
Release : 2020-01-23
Category : History
ISBN : 1108497829
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 17,35 MB
Release : 2014-07-23
Category : Mathematics
ISBN : 0486497089
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author : Karel Hrbacek
Publisher :
Page : 272 pages
File Size : 46,35 MB
Release : 1984
Category : Mathematics
ISBN :
Author : Ian Anderson
Publisher : Courier Corporation
Page : 276 pages
File Size : 33,88 MB
Release : 2002-01-01
Category : Mathematics
ISBN : 9780486422572
Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
Author : Steven R. Lay
Publisher : Courier Corporation
Page : 260 pages
File Size : 36,85 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 0486458032
Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity. It leads students to open questions and unsolved problems, and it highlights diverse applications. Author Steven R. Lay, Professor of Mathematics at Lee University in Tennessee, reinforces his teachings with numerous examples, plus exercises with hints and answers. The first three chapters form the foundation for all that follows, starting with a review of the fundamentals of linear algebra and topology. They also survey the development and applications of relationships between hyperplanes and convex sets. Subsequent chapters are relatively self-contained, each focusing on a particular aspect or application of convex sets. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Hints, solutions, and references for the exercises appear at the back of the book.
