Search results
Results from the WOW.Com Content Network
The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned in the list of arguments that the function ...
Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...
The diagram accompanies Book II, Proposition 5. [ 1 ] A mathematical proof is a deductive argument for a mathematical statement , showing that the stated assumptions logically guarantee the conclusion.
The argument principle is also applied in control theory. In modern books on feedback control theory, it is commonly used as the theoretical foundation for the Nyquist stability criterion. Moreover, a more generalized form of the argument principle can be employed to derive Bode's sensitivity integral and other related integral relationships. [1]
Cantor's diagonal argument (among various similar names [note 1]) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers.
The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery.But its first chapter is Lakatos's own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–4 in the British Journal for the Philosophy of Science.
A Mathematician's Lament, often referred to informally as Lockhart's Lament, is a short book on mathematics education by Paul Lockhart, originally a research mathematician at Brown University and U.C. Santa Cruz, and subsequently a math teacher at Saint Ann's School in Brooklyn, New York City for many years.
The 1998 book Proofs from THE BOOK, inspired by Erdős, is a collection of particularly succinct and revelatory mathematical arguments. Some examples of particularly elegant results included are Euclid's proof that there are infinitely many prime numbers and the fast Fourier transform for harmonic analysis .