Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
Martin Gardner was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was also a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century. He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
Ian Nicholas Stewart is a British mathematician and a popular-science and science-fiction writer. He is Emeritus Professor of Mathematics at the University of Warwick, England.
Morris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Leonard Eugene Dickson was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, History of the Theory of Numbers.
Popular mathematics is mathematical presentation aimed at a general audience. Sometimes this is in the form of books which require no mathematical background and in other cases it is in the form of expository articles written by professional mathematicians to reach out to others working in different areas.
The Collapse of Chaos: Discovering Simplicity in a Complex World (1994) is a book about complexity theory and the nature of scientific explanation written by biologist Jack Cohen and mathematician Ian Stewart.
Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
Infinity represents something that is boundless or endless, or else something that is larger than any real or natural number. It is often denoted by the infinity symbol ∞.
The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press (ISBN 978-0-691-11880-2). It provides an extensive overview of mathematics, and is noted for the high caliber of the contributors. The book was a 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".
Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All proposed definitions are controversial in their own ways.
Does God Play Dice: The New Mathematics of Chaos is a non-fiction book about chaos theory written by British mathematician Ian Stewart. The book was initially published by Blackwell Publishing in 1989.
Julius Wilhelm Richard Dedekind was a German mathematician who made important contributions to abstract algebra , axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.
Walter Warwick Sawyer (1911–2008) was a mathematician, mathematics educator and author, who taught on several continents.
Ian Robertson Porteous was a Scottish mathematician at the University of Liverpool and an educator on Merseyside. He is best known for three books on geometry and modern algebra. In Liverpool he and Peter Giblin are known for their registered charity Mathematical Education on Merseyside which promotes enthusiasm for mathematics through sponsorship of an annual competition.
Robert Edmund Edwards (1926–2000), usually cited simply as R. E. Edwards, was a British-born Australian mathematician who specialized in functional analysis. He is the author of several volumes in Springer's Graduate Texts in Mathematics.
