Portal:Cryptography. Cryptography Portal Cryptography (from Greek κρύπτω, "to hide, to conceal, to obscure", and γράφω, "to etch, to inscribe, to write down") is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. Cryptography is often used to replace or in combination with steganography. In the past, cryptography helped ensure secrecy in important communications, such as those of spies, military leaders, and diplomats. In recent decades, the field of cryptography has expanded its remit in two ways. Firstly, it provides mechanisms for more than just keeping secrets: schemes like digital signatures and digital cash, for example. Selected article Selected picture Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger presented the first key-recovery attacks on full AES. [1] Mathematics-related portals.
Portal:Statistics. Portal:Analysis. Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Ibn al-Haytham, Descartes (Discourse on the Method), Galileo, and Newton, as a practical method of physical discovery. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.[1].
Portal:Topology. From Wikipedia, the free encyclopedia Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry. Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds on set theory, considering both sets of points and families of sets.
When the discipline was first properly founded, toward the end of the 19th century, it was called geometria situs (Latin geometry of place) and analysis situs (Latin analysis of place). Informally speaking, a graph is a set of objects called points, nodes, or vertices connected by links called lines or edges. Purge server cache. Portal:Category theory. Portal:Number theory.
From Wikipedia, the free encyclopedia Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. (See the list of number theory topics.) The term "arithmetic" is also used to refer to number theory. This is a somewhat older term, which is no longer as popular as it once was. Number theory used to be called the higher arithmetic, but this too is dropping out of use. Nevertheless, it still shows up in the names of mathematical fields (arithmetic functions, arithmetic of elliptic curves, arithmetic geometry). In number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1.
Purge server cache. Portal:Discrete mathematics. From Wikipedia, the free encyclopedia Discrete mathematics has become popular in recent decades because of its applications to computer science. Discrete mathematics is the mathematical language of computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are tremendously significant in applying ideas from discrete mathematics to real-world applications, such as in operations research. The set of objects studied in discrete mathematics can be finite or infinite. Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects.
Topics in Discrete mathematics Purge server cache. Portal:Algebra. Portal:Geometry. From Wikipedia, the free encyclopedia Geometry arose as the field of knowledge dealing with spatial relationships. Geometry is one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have been extended. They sometimes show a high level of abstraction and complexity. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry. (See areas of mathematics.) A geometer is one who works or is specified in geometry. The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by ancient Greek, Indian and Arab mathematicians. Euclid of Alexandria The above shows an example of doubly ruled surface – the hyperboloid of one sheet.
Purge server cache. Portal:Mathematics. Portal:Contents/Mathematics and logic. Portal:Logic. From Wikipedia, the free encyclopedia As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. [1] The history of logic is the study of the development of the science of valid inference (logic).
While many cultures have employed intricate systems of reasoning, and logical methods are evident in all human thought, an explicit analysis of the principles of reasoning was developed only in three traditions: those of China, India, and Greece. Logic was known as 'dialectic' or 'analytic' in Ancient Greece. Jump up ^ J. Purge server cache. Portal:Epistemology. According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief.
The term "epistemology" is based on the Greek words "επιστήμη or episteme" (knowledge or science) and "λόγος or logos" (account/explanation). It was introduced into English by the Scottish philosopher James Frederick Ferrier (1808-1864).[1] Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims. In other words, epistemology primarily addresses the following questions: "What is knowledge?
" In epistemology and in its modern sense, rationalism is "any view appealing to reason as a source of knowledge or justification" (Lacey 286). Portal:Philosophy of science. Portal:History of science. Edit The History of Science Portal The content of science, as well as the meaning of the very idea of science, has continually evolved since the rise of modern science and before.
The history of science is concerned with the paths that led to our present knowledge as well as those that were abandoned (and thus overlaps with the history of ideas, history of philosophy and intellectual history), and seeks to explain past beliefs—even those now considered erroneous—in their social, cultural and intellectual contexts.
It also forms the foundation of the philosophy of science and the sociology of science, as well as the interdisciplinary field of science, technology, and society, and is closely related to the history of technology. The study of science and technology includes both processes and bodies of knowledge. Scientific processes are the ways scientists investigate and communicate about the natural world. Darwin's first sketch of an evolutionary tree ...Archive edit Selected anniversaries.