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Infinity : a very short introduction
In this 'Very Short Introduction', Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.
Book
On radicals over strict partial order sets
In this paper we deal with strict linear orders and find a poset Un such that any radical over Un coincides with the congruent closure of a system S which defines a poset of a height at most n.
Journal Article
Figuring it out : entertaining encounters with everyday math
\"This is a book of mathematical stories--funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand.\"--Jacket.
Book
On direct product of algebraic sets over groups
We study systems of group equations of the form S = S1 (X) U S2 (Y), where X, Y are disjoint sets of variables. The central problem is the description of the radical Rad(S) in terms of the systems Si. We prove that Rad(S) may contain equations which are not derived from equations from Rad(Si). Systems of equations are considered in the following classes of groups: abelian, free and 2-step nilpotent groups.
Journal Article
Quite right : the story of mathematics, measurement, and money
\"My aim is to explain how mathematical ideas evolved in response to the growing levels of organization in human societies, from pre-historic times to the present day\"-- Preface.
Book
Fixed Point Theorems Concerning Hausdorff F-PGA Contraction in Complete Metric Space
Harandi Amini-Harandi [2012], in 2012 established the existence of a fixed point by using the concept of set-valued contraction. In the present paper, authors have generalized this concept by considering Hausdorff F-PGA contraction and assured the existence of a fixed point. Hence, it is interesting to note that in a complete Hausdorff metric space, the fixed point exists with a lighter contraction map.
Journal Article
Discussion on the application of Lagrange mean value theorem
The Lagrange mean value theorem has been widely used in the following aspects; ( 1 )Prove equation; ( 2 )Proof inequality; ( 3 ) Study the properties of derivatives and functions; (4) Prove the conclusion of the mean value theorem; (5) Determine the existence and uniqueness of the roots of the equation; (6 ) Use the mean value theorem to find the limit.
Journal Article
Ptolemy's philosophy : mathematics as a way of life
The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy's general philosophical system--including his metaphysics, epistemology, and ethics-- and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy's technical studies in the physical and mathematical science. She show how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy' unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy's Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy--theoretical and practical--and advanced the mathematical way of life as the true path to human perfection.
Book
On the linear complexity of new generalized cyclotomic binary sequences of period pnqm
Sequences with high linear complexity are of importance in different applications. These sequences can be derived from generalized cyclotomic classes. In this paper, we construct new families of binary sequences of period pnqm using new generalized cyclotomic classes, as well as study the linear complexity of these sequences. We obtain the estimate of the linear complexity of new sequences and show that they have high linear complexity for m + n > 2.
Journal Article