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Mathematics

Mathematics

Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. The remarkable fact that the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics." Today, the natural sciences, engineering, economics, and medicine depend heavily on new mathematical discoveries. The word "mathematics" comes from the Greek μάθημα (máthema) meaning "science, knowledge, or learning" and μαθηματικός (mathematikós) meaning "fond of learning". It is often abbreviated maths in Commonwealth English and math in North American English.

History

:Main article: History of mathematics The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g. addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry. Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse. Historically, the major disciplines within mathematics arose, from the start of recorded history, out of the need to do calculations on taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change. Mathematics since has been much extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today.

Inspiration, pure and applied mathematics, and aesthetics

Mathematics arises wherever there are difficult problems that involve quantity, structure, space, or change. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. Newton invented infinitesimal calculus and Feynman his Feynman path integral using a combination of reasoning and physical insight, and today's string theory also inspires new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Within applied mathematics, two major areas have split off and become disciplines in their own right, statistics and computer science. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty also in a clever proof, such as Euclid's proof that there are infinitely many prime numbers, and in a numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in "A Mathematicians Apology" expressed the belief that these esthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. Main article: Mathematical beauty.

Notation, language, and rigor

Mathematical writing is not easily accessible to the layperson. A Brief History of Time, Stephen Hawking's 1988 bestseller, contained a single mathematical equation. This was the author's compromise with the publisher's advice, that each equation would halve the sales. The reasons for the inaccessibility even of carefully-expressed mathematics can be partially explained. Contemporary mathematicians strive to be as clear as possible in the things they say and especially in the things they write (this they have in common with lawyers). They refer to rigor. To accomplish rigor, mathematicians have extended natural language. There is precisely-defined vocabulary for referring to mathematical objects, and stating certain common relations. There is an accompanying mathematical notation which, like musical notation, has a definite content and also has a strict grammar (under the influence of computer science, more often now called syntax). Some of the terms used in mathematics are also common outside mathematics, such as ring, group and category; but are not such that one can infer the meanings. Some are specific to mathematics, such as homotopy and Hilbert space. It was said that Henri Poincaré was only elected to the Académie Française so that he could tell them how to define automorphe in their dictionary. Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow mechanically from axioms by means of formal axiomatic reasoning. This is to avoid mistaken 'theorems', based on fallible intuitions; of which plenty of examples have occurred in the history of the subject (for example, in mathematical analysis). Axioms in traditional thought were 'self-evident truths', but that conception turns out not to be workable in pushing the mathematical boundaries. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (strong enough) axiom system has undecidable formulas; and so a final axiomatization of mathematics is unavailable. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.

Is mathematics a science?

Carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. The mathematician-physicist Leon M. Lederman has quipped: "The physicists defer only to mathematicians, and the mathematicians defer only to God (though you may be hard pressed to find a mathematician that modest)." If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics. [http://info.med.yale.edu/therarad/summers/ziman.htm] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.

Overview of fields of mathematics

As noted above, the major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations) and to the empirical mathematics of the various sciences (applied mathematics). The study of quantity starts with numbers, first the familiar natural numbers and integers and their arithmetical operations, which are characterized in arithmetic. The deeper properties of whole numbers are studied in number theory. The study of structure began with investigations of Pythagorean triples. Neolithic monuments on the British Isles are constructed using Pythagorean triples. Eventually, this led to the invention of more abstract numbers, such as the square root of two. The deeper structural properties of numbers are studied in abstract algebra and the investigation of groups, rings, fields and other abstract number systems. Included is the important concept of vectors, generalized to vector spaces and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics, quantity, structure, and space. The study of space originates with geometry, beginning with Euclidean geometry. Trigonometry combines space and number. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles, calculus on manifolds. Within algebraic geometry is the description of geometric objects as solution sets of polynomal equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may be the greatest growth area in 20th century mathematics. Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a most useful tool. The central concept used to describe a changing quantity is that of a function. Many problems lead quite naturally to relations between a quantity and its rate of change, and the methods of differential equations. The numbers used to represent continuous quantities are the real numbers, and the detailed study of their properties and the properties of real-valued functions is known as real analysis. These have been generalized, with the inclusion of the square root of negative one, to the complex numbers, which are studied in complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior. Beyond quantity, structure, space, and change are areas of pure mathematics that can be approached only by deductive reasoning. In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic, which divides into recursion theory, model theory, and proof theory, is now closely linked to computer science. When electronic computers were first conceived, several essential theoretical concepts in computer science were shaped by mathematicians, leading to the fields of computability theory, computational complexity theory, and information theory. Many of those topics are now investigated in theoretical computer science. Discrete mathematics is the common name for the fields of mathematics most generally useful in computer science. An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis, and prediction of phenomena where chance plays a part. It is used in all the sciences. Numerical analysis investigates methods for using computers to efficiently solve a broad range of mathematical problems that are typically beyond human capacity, and taking rounding errors or other sources of error into account to obtain credible answers.

Major themes in mathematics

An alphabetical and subclassified list of mathematical topics is available. The following list of themes and links gives just one possible view. For a fuller treatment, see Areas of mathematics or the list of lists of mathematical topics.

Quantity

This starts from explicit measurements of sizes of numbers or sets, or ways to find such measurements. : :Number – Natural number – Integers – Rational numbers – Real numbers – Complex numbers – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base

Structure

:Pinning down ideas of size, symmetry, and mathematical structure. : :Abstract algebra – Number theory – Algebraic geometry – Group theory – Monoids – Analysis – Topology – Linear algebra – Graph theory – Universal algebra – Category theory – Order theory – Measure theory

Space

:A more visual approach to mathematics. : :Topology – Geometry – Trigonometry – Algebraic geometry – Differential geometry – Differential topology – Algebraic topology – Linear algebra – Fractal geometry

Change

:Ways to express and handle change in mathematical functions, and changes between numbers. : :Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems – Chaos theory – List of functions

Foundations and methods

:Approaches to understanding the nature of mathematics. :philosophy of mathematics – mathematical intuitionism – mathematical constructivism – foundations of mathematics – set theory – symbolic logic – model theory – category theory – Logic – reverse mathematics – table of mathematical symbols

Discrete mathematics

:Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values. : :Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory

Applied mathematics

:Applied mathematics uses the full knowledge of mathematics to solve real-world problems. :Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Mathematical economics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory

Important theorems

:These theorems have interested mathematicians and non-mathematicians alike. :See list of theorems for more :Pythagorean theorem – Fermat's last theorem – Gödel's incompleteness theorems – Fundamental theorem of arithmetic – Fundamental theorem of algebra – Fundamental theorem of calculus – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – classification theorems of surfaces – Gauss-Bonnet theorem – Quadratic reciprocity – Riemann-Roch theorem.

Important conjectures

See list of conjectures for more :These are some of the major unsolved problems in mathematics. :Goldbach's conjecture – Twin Prime Conjecture – Riemann hypothesis – Poincaré conjecture – Collatz conjecture – P=NP? – open Hilbert problems.

History and the world of mathematicians

See also list of mathematics history topics :History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues

Mathematics and other fields

:Mathematics and architecture – Mathematics and education – Mathematics of musical scales

Common misconceptions

Mathematics is not a closed intellectual system, in which everything has already been worked out. There is no shortage of open problems. Pseudomathematics is a form of mathematics-like activity undertaken outside academia, and occasionally by mathematicians themselves. It often consists of determined attacks on famous questions, consisting of proof-attempts made in an isolated way (that is, long papers not supported by previously published theory). The relationship to generally-accepted mathematics is similar to that between pseudoscience and real science. The misconceptions involved are normally based on:
- misunderstanding of the implications of mathematical rigour;
- attempts to circumvent the usual criteria for publication of mathematical papers in a learned journal after peer review, with assumptions of bias;
- lack of familiarity with, and therefore underestimation of, the existing literature. The case of Kurt Heegner's work shows that the mathematical establishment is neither infallible, nor unwilling to admit error in assessing 'amateur' work. And like astronomy, mathematics owes much to amateur contributors such as Fermat and Mersenne. Mathematics is not accountancy. Although arithmetic computation is crucial to accountants, their main concern is to verify that computations are correct through a system of doublechecks. Advances in abstract mathematics are mostly irrelevant to the efficiency of concrete bookkeeping, but the use of computers clearly does matter. Mathematics is not numerology. Numerology uses modular arithmetic to reduce names and dates down to numbers, but assigns emotions or traits to these numbers intuitively or on the basis of traditions. Mathematical concepts and theorems need not correspond to anything in the physical world. In the case of geometry, for example, it is not relevant to mathematics to know whether points and lines exist in any physical sense, as geometry starts from axioms and postulates about abstract entities called "points" and "lines" that we feed into the system. While these axioms are derived from our perceptions and experience, they are not dependent on them. And yet, mathematics is extremely useful for solving real-world problems. It is this fact that led Eugene Wigner to write an essay on The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Mathematics is not about unrestricted theorem proving, any more than literature is about the construction of grammatically correct sentences. However, theorems are elements of formal theories, and in some cases computers can generate proofs of these theorems more or less automatically, by means of automated theorem provers. These techniques have proven useful in formal verification of programs and hardware designs. However, they are unlikely to generate (in the near term, at least) mathematics with any widely recognized aesthetic value.

See also


- Mathematical game
- Mathematical problem
- Mathematical puzzle
- Puzzle

Bibliography


- Benson, Donald C., The Moment Of Proof: Mathematical Epiphanies (1999).
- Courant, R. and H. Robbins, What Is Mathematics? (1941);
- Davis, Philip J. and Hersh, Reuben, The Mathematical Experience. Birkhäuser, Boston, Mass., 1980. A gentle introduction to the world of mathematics.
- Boyer, Carl B., History of Mathematics, Wiley, 2nd edition 1998 available, 1st edition 1968 . A concise history of mathematics from the Concept of Number to contemporary Mathematics.
- Gullberg, Jan, Mathematics--From the Birth of Numbers. W.W. Norton, 1996. An encyclopedic overview of mathematics presented in clear, simple language.
- Hazewinkel, Michiel (ed.), Encyclopaedia of Mathematics. Kluwer Academic Publishers 2000. A translated and expanded version of a Soviet math encyclopedia, in ten (expensive) volumes, the most complete and authoritative work available. Also in paperback and on CD-ROM.
- Kline, M., Mathematical Thought from Ancient to Modern Times (1973).
- Pappas, Theoni, The Joy Of Mathematics (1989).

External links


- [http://www.cut-the-knot.org/ Interactive Mathematics Miscellany and Puzzles] — A collection of articles on various math topics, with interactive Java illustrations at cut-the-knot
- Rusin, Dave: [http://www.math-atlas.org/ The Mathematical Atlas]. A guided tour through the various branches of modern mathematics.
- Stefanov, Alexandre: [http://us.geocities.com/alex_stef/mylist.html Textbooks in Mathematics]. A list of free online textbooks and lecture notes in mathematics.
- Weisstein, Eric et al.: [http://www.mathworld.com/ MathWorld: World of Mathematics]. An online encyclopedia of mathematics.
- Polyanin, Andrei: [http://eqworld.ipmnet.ru/ EqWorld: The World of Mathematical Equations]. An online resource focusing on algebraic, ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations.
- A mathematical thesaurus maintained by the [http://nrich.maths.org/ NRICH] project at the University of Cambridge (UK), [http://thesaurus.maths.org/ Connecting Mathematics]
- [http://planetmath.org/ Planet Math]. An online math encyclopedia under construction, focusing on modern mathematics. Uses the GFDL, allowing article exchange with Wikipedia. Uses TeX markup.
- [http://www.mathforge.net/ Mathforge]. A news-blog with topics ranging from popular mathematics to popular physics to computer science and education.
- [http://www.youngmath.net/concerns Young Mathematicians Network (YMN)]. A math-blog "Serving the Community of Young Mathematicians". Topics include: Math News, Grad and Undergrad Life, Job Search, Career, Work & Family, Teaching, Research, Misc...
- [http://metamath.org/ Metamath]. A site and a language, that formalize math from its foundations.
- [http://world.std.com/~reinhold/dir/mathmovies.html Math in the Movies]. A guide to major motion pictures with scenes of real mathematics
- [http://math.cofc.edu/faculty/kasman/MATHFICT/default.html Mathematics in fiction]. Links to works of fiction that refer to mathematics or mathematicians.
- [http://www.mathhelpforum.com/math-help Math Help Forum]. A forum, for math help, math discussion and debate.
- [http://www.sosmath.com/CBB S.O.S. Mathematics Cyberboard] a math help forum which incorporates a LaTeX extension, making it easier for members to write and display math formulae.
- [http://www-history.mcs.st-and.ac.uk/~history/ Mathematician Bibliography]. Extensive history and quotes from all famous mathematicians.
- [http://www.physicsmathforums.com/ Physics Math Forums]
- Category:School subjects fiu-vro:Matõmaatiga zh-min-nan:Sò·-ha̍k ko:수학 ms:Matematik ja:数学 simple:Mathematics th:คณิตศาสตร์

Quantity

:For the use in linguistics, see length (phonetics). Quantity is a general term used to refer to any type of quantitative property or attribute, such as mass, length, or time. A particular quantity is a magnitude of a scalar or vector quantity. The term quantity is also often used to refer to denumerable (countable) collections of objects. A given quantity is usually represented either as a number of units, together with the type of those units, or a number of objects with a referent defining the type of object. Thus, scalar quantities such as mass, and vector quantities such as force, are continuous quantities and are usually represented as a multiple of a real number and a unit of continuous quantity, such as a gram or newton. A count of a denumerable collection of entities is represented as an integer and the type of object or entity, such as an apple or a set. A number, including a particular measurement, is not by itself a quantity. Examples are
- 1.76 litres (liters) of milk, which is continuous quantity
- 2 \pi r metres, where r is the length of a radius of a circle expressed in metres (or meters)
- one apple, two apples, three apples, where the number is an integer representing the count of a denumerable collection of objects (apples)
- 500 people (also involving a count) Where the count is one then the indefinite article may be used (for example, a car) and similar alternatives exist for other particular counts (for example, a brace of pheasant, a dozen eggs). Quantification in its very simplest sense can be found in statements such as "A is greater than B". In the example cited, an expression is made that A has a greater quantity of something (such as volume or charisma) than B; and that if A and B were placed in an ordered set, then A would come after B if the order is arranged on an increasing (rather than decreasing) scale.

See also:


- physical quantity Category:Elementary mathematics Category:Measurement ko:양 (크기) ja:量 simple:Quantity

Space

:This article is about space — the scientific and philosophical concepts. For other uses of space, see space (disambiguation). Attempting to understand the nature of space has always been a prime occupation for philosophers and scientists. Perhaps as a result of this considerable discussion, it is difficult to provide an uncontroversial and clear definition of the nature of space, except its physical definition (see below). This article looks at the way space is dealt with variously by physicists, mathematicians and philosophers, and at the relation between space and the mind.

Physics and Space

Space is one of the few fundamental quantities in physics meaning it can't be defined via other quantities because there is nothing more fundamental known at present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined via measurement. Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of 1/299 792 458 of a second (exact). In classical physics, space is a three-dimensional Euclidean space where any position can be described using three coordinates. Relativistic physics examines spacetime rather than space; spacetime is modeled as a four-dimensional manifold, and currently, there are theories that can support even eleven-dimensional spaces. Before Einstein's work on relativistic physics, time and space were seen as independent dimensions. Einstein's work unified the two into spacetime. In spacetime, measurements of space and time are held to be relative to velocity.

Measurement

The measurement of physical space has long been important. Geometry, the name given to the branch of mathematics which measures spatial relations, was popularised by the ancient Greeks, although earlier societies had developed measuring systems. The International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used within science. Geography is the branch of science concerned with identifying and describing the Earth, utilising spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualisation purposes and to act as a locational device. Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

Astronomy and space

In astronomy, space refers collectively to the relatively empty parts of the universe. Any area outside the atmospheres of any celestial body can be considered 'space'. Although space is certainly spacious, it is now known to be far from empty, and filled with a tenuous plasma. In particular, the boundary between space and Earth's atmosphere is conventionally set at the Karman line.

Mathematics and space

In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space. In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space. As far as the concept of dimension is defined, this need not be 3: it can also be 0 (a point), 1 (a line), 2 (a plane), more than 3, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions. Kinds of mathematical spaces include:
- Banach space
- Euclidean space
- Hilbert space
- Metric space
- Probability space
- Projective space
- Topological space
- Vector space

The philosophy of space

Space has a range of definitions.
- One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move.
- A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework (together with time and number) within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. In this view space does not refer to any kind of entity that is a "container" that objects "move through". These opposing views are relevant also to definitions of time. Space is typically described as having three dimensions, and that three numbers are needed to specify the size of any object and/or its location with respect to another location. Modern physics does not treat space and time as independent dimensions, but treats both as features of spacetime – a conception that challenges intuitive notions of distance and time. An issue of philosophical debate is whether space is an ontological entity itself, or simply a conceptual framework we need to think (and talk) about the world. Another way to frame this is to ask, "Can space itself be measured, or is space part of the measurement system?" The same debate applies also to time, and an important formulation in both areas was given by Immanuel Kant. In his Critique of Pure Reason, Kant described space as an a priori notion that (together with other a priori notions such as time) allows us to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur. Similar philosophical questions concerning space include: Is space absolute or purely relational? Does space have one correct geometry, or is the geometry of space just a convention? Historical positions in these debates have been taken by Isaac Newton (space is absolute), Gottfried Leibniz (space is relational), and Henri Poincaré (spatial geometry is a convention). Two important thought-experiments connected with these questions are: Newton's bucket argument and Poincaré's sphere-world.

The psychology of space

The way in which space is perceived is an area which psychologists first began to study in the middle of the 19th century, and it is now thought by those concerned with such studies to be a distinct branch within psychology. Psychologists analysing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived. Other, more specialised topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation. "Veridical perception" is the term used to describe the processing of the information provided by the sensory organs to an extent whereby it allows interaction with the actuality of that perceived. It is worth noting that the way we perceive space may not necessarily be representative of the actuality of space.

Anxiety and space

Space can also cause anxiety in people, with agoraphobia manifesting itself in some people as a fear of open spaces, and claustrophobia being the fear of enclosed spaces. Astrophobia is the fear of celestial space, Kenophobia is the fear of empty spaces and spacephobia is the fear of outer space.

Personal space

The term personal space refers to the amount of space a person likes to maintain between their own person and that of other people.

Use of space

The definition of physical space in relation to ownership, in which space is seen as property, has long been an important issue. Whilst some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behaviour, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming. Ownership of space is not restricted to land. Ownership of Airspace and of waters is decided internationally. Public space is a term used to define areas of land which are open to all, whilst private property is that area of land owned by an individual or company, for their own use and pleasure.

Reference

[http://search.eb.com/eb/article?tocId=46639 Space perception]. Encyclopædia Britannica from Encyclopædia Britannica Online. Accessed June 12, 2005. Category: Topology Category:Environments ko:공간 ja:空間 simple:Space

Deductive reasoning

In traditional Aristotelian logic, deductive reasoning is inference in which the conclusion is of lesser or equal generality than the premises, as opposed to inductive reasoning, where the conclusion is of greater generality than the premises. Other theories of logic define deductive reasoning as inference in which the conclusion is just as certain as the premises, as opposed to inductive reasoning, where the conclusion can have less certainty than the premises. In both approaches, the conclusion of a deductive inference is necessitated by the premises: the premises can't be true while the conclusion is false. (In Aristotelian logic, the premises in inductive reasoning can also be related in this way to the conclusion.) inductive reasoning

Examples

Valid: :All men are mortal. :Socrates is a man. :Therefore Socrates is mortal. :The picture is above the desk. :The desk is above the floor. :Therefore the picture is above the floor. Invalid: :Every criminal opposes the government. :Everyone in the opposition party opposes the government. :Therefore everyone in the opposition party is a criminal. This is invalid because the premises fail to establish commonality between membership in the opposition party and being a criminal. This is the famous fallacy of undistributed middle.

Axiomatization

More formally, a deduction is a sequence of statements such that every statement can be derived from those before it. Naturally, this leaves open the question of how we prove the first sentence (since it cannot follow from anything). Axiomatic propositional logic solves this by requiring the following conditions for a proof to be met: A proof of α from an ensemble Σ of wffs is a finite sequence of wffs: :β1,...,βi,...,βn where :βn = α and for each βi (1 ≤ i ≤ n), either :
- βi ∈ Σ or :
- βi is an axiom, or :
- βi is the output of Modus Ponens for two previous wffs, βi-g and βi-h. Different versions of axiomatic propositional logics contain a few axioms, usually three or more than three, in addition to one or more inference rules. For instance Gottlob Frege's axiomatization of propositional logic, which is also the first instance of such an attempt, has six propositional axioms and two rules. Bertrand Russell and Alfred North Whitehead also suggested a system with five axioms. For instance a version of axiomatic propositional logic due to Jan Lukasiewicz (1878-1956) has a set A of axioms adopted as follows: :
- [PL1] p → (q → p) :
- [PL2] (p → (q → r)) → ((p → q) → (p → r)) :
- [PL3] (¬p → ¬q) → (q → p) and it has the set R of Rules of inference with one rule in it that is Modu Ponendo Ponens as follows: :
- [MP] from α and α → β, infer β. The inference rule(s) allows us to derive the statements following the axioms or given wffs of the ensemble Σ.

Natural Deductive Logic

In one version of natural deductive logic presented by E.J. Lemmon that we should refer to it as system L, we do not have any axiom to begin with. We only have nine primitive rules that govern the syntax of a proof. The nine primitive rules of system L are: #The Rule of Assumption (A) #Modus Ponendo Ponens (MPP) #The Rule of Double Negation (DN) #The Rule of Conditional Proof (CP) #The Rule of ∧-introduction (∧I) #The Rule of ∧-elimination (∧E) #The Rule of ∨-introduction (∨I) #The Rule of ∨-elimination (∨E) #Reductio Ad Absurdum (RAA) In system L, a proof has a definition with the following conditions: #has a finite sequence of wffs (well-formed-formula) #each line of it is justified by a rule of the system L #the last line of the proof is what is intended (Q.E.D, quod erat demonstrandum, is a Latin expression that means: which was the thing to be proved), and this last line of the proof uses the only premise(s) that is given; or no premise if nothing is given. Then if no premise is given, the sequent is called theorem. Therefore, the definitions of a theorem in system L is:
- a theorem is a sequent that can be proved in system L, using an empty set of assumption. or in other words:
- a theorem is a sequent that can be proved from an empty set of assumptions in system L An example of the proof of a sequent (Modus Tollendo Tollense in this case): An example of the proof of a sequent (a theorem in this case): Each rule of system L has its own requirements for the type of input(s) or entry(es) that it can accept and has its own way of treating and calculating the assumptions used by its inputs.

References


- Jennings, R. E., Continuing Logic, the course book of 'Axiomatic Logic' in Simon Fraser University, Vancouver, Canada
- Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002

See also


- Correspondence theory of truth
- Defeasible reasoning
- Inductive reasoning
- Hypothetico-deductive method
- Propositional calculus
- Soundness
- Retroductive reasoning
- Validity Category:Logic ko:연역법 ja:演繹



Accounting

Accountancy (British English) or accounting (American English) is the measurement, disclosure or provision of assurance about information that helps managers and other decision makers make resource allocation decisions. Financial accounting is one branch of accounting and historically has involved processes by which financial information about a business is recorded, classified, summarized, interpreted, and communicated. Auditing, a related but separate discipline, is the process whereby an independent auditor examines an organization's financial statements in order to express an opinion -- that conveys reasonable but not absolute assurance -- as to the fairness and adherence to generally accepted accounting principles, in all material respects. Practitioners of accountancy are known as accountants. Officially licensed accountants are recognized by titles such as Chartered Accountant (UK, Canada), Certified Public Accountant (US), Certified Management Accountant (Canada). or Certified General Accountant (Canada). The majority of "public" accountants in Canada are Chartered Accountants; however, Certified General Accountants are also authorized by legislations to practise public accounting and auditing in all Canadian provinces, except Quebec as of 2005. Accountancy attempts to create accurate financial reports that are useful to managers, regulators, and other stakeholders such as shareholders, creditors, or owners. The day-to-day record-keeping involved in this process is known as bookkeeping. At the heart of modern financial accounting is the double-entry book-keeping system. This system involves making at least two entries for every transaction: a debit in one account, and a corresponding credit in another account. The sum of all debits should always equal the sum of all credits. This provides an easy way to check for errors. This system was first used in medieval Europe, although claims have been made that the system dates back to Ancient Greece. According to critics of standard accounting practices, it has changed little since. Accounting reform measures of some kind have been taken in each generation to attempt to keep bookkeeping relevant to capital assets or production capacity. However, these have not changed the basic principles, which are supposed to be independent of economics as such.

History

The art of accountancy on a scientific principle must certainly have been understood in Italy before 1495, when Luca Pacioli (1445 - 1517), also known as Friar Luca dal Borgo, published at Venice his treatise on book-keeping. The first known English book on the science was published in London by John Gouge or Gough in 1543. It is described as A Profitable Treatyce called the Instrument or Boke to learn to knowe the good order of the kepyng of the famouse reconynge, called in Latin, Dare and Habere, and, in English, Debitor and Creditor. A short book of instructions were also published in 1588 by John Mellis of Southwark, in which he says, "I am but the renuer and reviver of an ancient old copie printed here in London the 14 of August 1543: collected, published, made, and set forth by one Hugh Oldcastle, Scholemaster, who, as appeareth by his treatise, then taught Arithmetics, and this booke in Saint Ollaves parish in Marko Lane." John Mellis refers to the fact that the principle of accounts he explains (which is a simple system of double entry) is "after the forme of Venice". The very interesting and able book described as The Merchants Mirrour, or directions for the perfect ordering and keeping of his accounts formed by way of Debitor and Creditor, after the (so termed) Italian manner, by Richard Dafforne, accountant, published in 1635, contains many references to early books on the science of accountancy. In a chapter in this book, headed "Opinion of Book-keeping's Antiquity," the author states, on the authority of another writer, that the form of book-keeping referred to had then been in use in Italy about two hundred years, "but that the same, or one in many parts very like this, was used in the time of Julius Caesar, and in Rome long before." He gives quotations of Latin book-keeping terms in use in ancient times, and refers to "ex Oratione Ciceronis pro Roscio Comaedo"; and he adds: :"That the one side of their booke was used for Debitor, the other for Creditor, is manifest in a certain place, Naturalis Historiae Plinii, lib. 2, cap. 7, where hee, speaking of Fortune, saith thus: : Huic Omnia Expensa. : Huic Omnia Feruntur accepta et in tota Ratione mortalium sola : Utramque Paginam facit." An early Dutch writer appears to have suggested that double-entry book-keeping was even in existence among the Greeks, pointing to scientific accountancy having been invented in remote times. There were several editions of Richard Dafforne's book printed---the second edition having been published in 1636, the third in 1656, and another was issued in 1684. The book is a very complete treatise on scientific accountancy, it was beautifully prepared and contains elaborate explanations; the numerous editions tend to prove that the science was highly appreciated in the 17th century. From this time there has been a continuous supply of literature on the subject, many of the authors styling themselves accountants and teachers of the art, and thus proving that the professional accountant was then known and employed. Very early in the 18th century, the services of an accountant practising in the city of London were made use of in the course of an investigation into the transactions of a director of the South Sea Company, who had been dealing in the company's stock. During this investigation the accountant appears to have examined the books of at least two firms of merchants. His report is described Observations made upon examining the books of Sawbridge and Company, by Charles Snell, Writing Master and Accountant in Foster Lane, London. The United States owes the concept of the Certified Public Accountant designation to England which had coined the Chartered Accountant designation in the 19th century.

Accountancy qualifications and regulation

The requirements for entry in the profession of accounting vary from country to country.

British Commonwealth

In the United Kingdom, Canada, Australia and several other Commonwealth countries, the equivalents of Certified Public Accountant (CPA) include Chartered Accountant (CA - in UK, British Commonwealth and former British states), Chartered Certified Accountant (ACCA - United Kingdom), International Accountant (AIA - United Kingdom), Certified Public Accountant (CPA - Ireland and CPA - Hong Kong), Certified General Accountant (CGA - Canada), and Certified Practising Accountant (CPA - Australia). Please refer to the latest statutory auditing rights of above accounting bodies in individual jurisdictions and distinction from non-audit bodies for various consumers. In UK, only 3 chartered accountants (England & Wales, Scottish and Irish)and their equivalents (AIA and ACCA) are "Registered Auditors" under Companies Act. ACA is the best known and most respected qualification in the UK, equivalent of a CA but handled by a different board ICAEW.

Canada

In Canada, there are three recognized accounting bodies: the Canadian Institute of Chartered Accountants (CA), the Certified General Accountants Association of Canada (CGA), and the Society of Management Accountants of Canada (CMA). CA and CGA were created by Acts of Parliament in 1902 and 1913 respectively and CMA was established in 1920. The CA program focuses in public accounting and candidates must obtain auditing experience from public accounting firms; the CGA program takes a general approach allowing candidates to focus in their own financial career choices; the CMA program focuses in management accounting. All three programs require a candidate to obtain a degree and practical accounting experience before certification. Auditing and Public Accounting are regulated by the provinces. Historically, only CAs can perform audits in Ontario. After the corporate accounting scandals including the Enron scandal, the provincial government of Ontario passed a new Public Accounting Act allowing qualified CAs, CGAs and CMAs to audit. In Quebec, CAs still have monopoly in the audit of public companies; In British Columbia and Prince Edward Island, CAs and CGAs have equal status regarding public accounting and auditing; In the rest of Canada, CAs, CGAs, and CMAs are considered equivalents pursuant to provincial and territorial legislations. A recent attempt between the CAs and CMAs (in 2005) to join forces to form a new unified body failed as the respective organisations could not reach consensus on a number of important issues. This failure represented a factual indicator of the continued and strong resentment of the infringement of other accounting designations' influence and opinion upon others, as well as a possible measure of the degree of pride that still remained within each of Canada's three recognised accounting bodies. The recent measure (2004) of opening Ontario's public practice to all three bodies may actually have exacerbated the competition between these organisations, especially in light of the historic monopoly conferred to the CA association.

United States of America

In the United States, practicing accountants include Certified Public Accountants (CPAs), Certified Internal Auditors (CIAs), Certified Management Accountants (CMAs) and Accredited Business Accountants (ABAs). The difference between these certifications is primarily the types of services provided, although individuals may earn more than one certification. Additionally, much accounting work is performed by uncertified individuals, who may be working under the supervision of a certified accountant. A CPA is licensed by the state of his/her residence to provide auditing services to the public, although most CPA firms also offer accounting, tax, litigation support, and other financial advisory services. The requirements for receiving the CPA license varies from state to state, although the passage of the Uniform Certified Public Accountant examination is required by all states. This examination is designed and graded by the American Institute of Certified Public Accountants. A CIA is granted a certificate from the Institute of Internal Auditors (IIA), provided that the candidate passed a rigorous examination of four parts. A CIA mostly provides his/her services directly to their employers rather than the public. A CMA is granted a certificate from the Institute of Management Accountants (IMA), provided that the candidate passed a rigorous examination of four parts and meet the practical experience requirement from the IMA. A CMA mostly provides his/her services directly to his/her employers rather than the public. A CMA can also provide his services to the public, but to an extent much lesser than that of a CPA. An ABA is granted accreditation from the Accreditation Council for Accountancy and Taxation (ACAT), provided that the candidate passed the eight-hour Comprehensive Examination for Accreditation in Accounting which tests proficiency in financial accounting, reporting, statement preparation, taxation, business consulting services, business law, and ethics. An ABA specializes in the needs of small-to-mid-size businesses and in financial services to individuals and families. In states where use of the word "accountant” is not permitted, the practitioner may use Accredited Business Advisor. The United States Department of Labor's Bureau of Labor Statistics estimates that there are about one million persons [http://www.bls.gov/oes/current/oes132011.htm] employed as accountants and auditors in the U.S. U.S. tax law grants accountants a limited form of accountant-client privilege.

Accounting scholarship

Refer Accounting scholarship for professorship.

The "Big Four" accountancy firms

The "Big Four auditors" are the largest multinational accountancy firms.
- PricewaterhouseCoopers
- Deloitte Touche Tohmatsu
- Ernst & Young
- KPMG The Big 4 accountancy firms can all trace their history back to firms in Europe, from which they have descended through a long line of mergers. Many of the originating firms were from the United Kingdom. As British trade interests expanded, correspondent firms were established throughout the world by the organisations. These firms are associations of the partnerships in each country rather than having the classical structure of holding company and subsidiaries, but each has an international 'umbrella' organisation for co-ordination. However, due to the dominant size of the United States' economy, the offices of the Big 4 accountancy firms based in the United States have always generated more revenue than the rest of the Big 4 accountancy firms' offices in the world combined. Before the Enron and other accounting scandals, there were five large firms and were called the Big Five. Since Arthur Andersen's assurance practice split, with a plurality joining KPMG in the US and Deloitte & Touche outside of the US, Arthur Andersen left from the group. Previous to this there were also groupings referred to as the "Big Six" and the "Big Eight". Enron turned out to be only the first of a series of accounting scandals that enveloped the accounting industry in 2002. This is likely to have far-reaching consequences for the U.S. accounting industry. Application of International Accounting Standards originating in International Accounting Standards Board headquartered in London and bearing more resemblance to UK than current US practices is often advocated by those who note the relative stability of the U.K. accounting system (which reformed itself after scandals in the late 1980s and early 1990s). Accounting reform of a far more comprehensive sort is advocated by those who see issues with capitalism or economics, and seek ecological or social accountability.

Topics in accounting

See list of accounting topics for complete listing.

Auditing


- Assurance services
- Audit
- Information technology audit

Types of accountancy


- Cost accounting
- Cash-basis and accrual-basis
- Financial accountancy
- internal and external accountancy
- Management accounting
- Project accounting
- Positive accounting
- Environmental accounting

Accountancy Principles

Accounting principles, rules of conduct and action are described by various terms such as concepts, conventions, tenets, assumption, axioms, postulates.

Accounting concepts


- Entity concept
- Dual aspect concept
- Going concern concept
- Accounting period concept
- Money measurement concept
- Historical Cost concept
- Periodic matching of cost and revenue concept
- Verifiable objective evidence concept
- Realization concept
- Accrual concept

Accounting conventions


- convention of disclosure
- convention of materiality
- convention of consistency
- convention of conservatism

Use of computers in accountancy


- Accounting software
- Databases
- spreadsheet programs

Accounting standards


- United States generally accepted accounting principles
- United Kingdom generally accepted accounting principles
- International Accounting Standards

Agencies


- United States
  - Federal Reserve (for banks)
  - U.S. Securities and Exchange Commission (for public companies)
- European Union
  - European Central Bank

Accounting standard-setting bodies


- United States
  - American Institute of Certified Public Accountants
  - Financial Accounting Standards Board
  - Governmental Accounting Standards Board
  - Federal Accounting Standards Advisory Board
  - U.S. Securities and Exchange Commission
- United Kingdom
  - Institute of Chartered Accountants in England & Wales (ICAEW)
  - Institute of Chartered Accountants of Scotland (ICAS)
  - Association of Chartered Certified Accountants (ACCA)
  - Chartered Institute of Management Accountants (CIMA)
  - Chartered Institute of Public Finance Accountants (CIPFA)
  - Association of International Accountants (AIA), a UK Registered Auditor is being consulted for Standard setting.
  - Association of Accounting Technicians (AAT)
- Republic of Ireland
  - Institute of Chartered Accountants in Ireland
- Canada
  - Accounting Standards Board "AcSB"
- International
  - International Accounting Standards Board

Auditing standards-setting bodies


- United States
  - Public Company Accounting Oversight Board - public companies
  - American Institute of Certified Public Accountants - general
  - Government Accountability Office - recipients of federal grants

See also


- Accounting reform
- Banking
- Cultural references to accountants
- Economics
- Finance
- Fiscal year
- Luca Pacioli
- Standard accounting practices
- Tax
- Critical accounting policy

Finding related topics


- List of accounting topics
- List of finance topics
- List of management topics
- List of human resource management topics
- List of marketing topics
- List of economics topics
- List of production topics
- List of information technology management topics
- List of business law topics
- List of business ethics, political economy, and philosophy of business topics
- List of business theorists
- List of economists
- List of corporate leaders
- List of companies

External links


-
- [http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Pacioli.html Luca Pacioli]
- [http://accounting.rutgers.edu/raw/rtest1.html List of accounting sites]
- [http://www.theaccounting.org/ Accounting]
- [http://www.icaew.co.uk/library/index.cfm?AUB=TB2I_7258 Accounting history links]
- [http://www.acaus.org/history/hs_pac.html Accounting, a Virtual History]
- [http://www.responsive.co.nz/theory.html Accounting Theory]
- [http://www.responsive.co.nz/tutorial.html Accounting Tutorial]
- [http://www.duncanwil.co.uk Duncan Williamson's Accounting Site]
- [http://www.maap.co.uk/checklist.php?choice=checklist MAAP's UK Accountancy Checklist The Next Year]
- [http://www.quickmanagement.com/a/account-management.asp Accounting Management] — Brief view on accounting.
- [http://www.buzzbusiness.com/directory/accounting/ Accounting Directory] — A listing of accounting sites.
- [http://www.trinity.edu/rjensen Bob Jensen's Accounting Site]
- [http://www.columbia.edu/~kky2001/pubs.html Accounting and Valuation Research page]
- [http://www.HavenWorks.com/accounting Accounting News]
- [http://www.greekshares.com/account12.asp The Basics of Accounting]
- [http://www.insidesarbanesoxley.com inside Sarbanes Oxley] - Resources for accountants
- [http://www.insidesarbanesoxley.com inside Sarbanes Oxley] - Resources for accountants concerning the Sarbanes-Oxley Act of 2002, including Sarbanes Oxley books, articles, and discussion
- [http://www.becompta.be/ Accounting in french]
- [http://business.fullerton.edu/centers/ccrg The Center for Corporate Reporting & Governance at California State University, Fullerton]
- [http://www.hkicpa.org.hk Hong Kong Institute of Certified Public Accountants (formerly Hong Kong Society of Accountants)]
- [http://www.bookkeeping-course.com free bookkeeping course]
- [http://www.tgiltd.com Free Accounting Software Selection Assistance] Category:Accounting Accountant ja:会計

Astronomical

:This article is about the science branch. For information about the magazine, see Astronomy (magazine). Astronomy (magazine) as they circled the Moon in 1969. Located near the center of the far side of Earth's Moon, its diameter is about 58 miles (93 km).]] Astronomy (Greek: αστρονομία = άστρον + νόμος, astronomia = astron + nomos, literally, "law of the stars") is the science of celestial objects and phenomena that originate outside the Earth's atmosphere, such as stars, planets, comets, galaxies, and the cosmic background radiation. It is concerned with the formation and development of the universe, the evolution and physical and chemical properties of celestial objects and the calculation of their motions. Astronomical observations are not only relevant for astronomy as such, but provide essential information for the verification of fundamental theories in physics, such as general relativity theory. Complementary to observational astronomy, theoretical astrophysics seeks to explain astronomical phenomena. Astronomy is one of the oldest sciences, with a scientific methodology existing at the time of Ancient Greece and advanced observation techniques possibly much earlier (see archaeoastronomy). Historically, amateurs have contributed to many important astronomical discoveries, and astronomy is one of the few sciences where amateurs can still play an active role, especially in the discovery and observation of transient phenomena. Astronomy is not to be confused with astrology, which assumes that people's destiny and human affairs in general are correlated to the apparent positions of astronomical objects in the sky -- although the two fields share a common origin, they are quite different; astronomers embrace the scientific method, while astrologers do not. In other words, there is no proof that the stars predict our future, but there is proof that our planet is 93 million miles from the sun.

Divisions

In ancient Greece and other early civilizations, astronomy consisted largely of astrometry, measuring positions of stars and planets in the sky. Later, the work of Kepler and Newton, whose work led to the development of celestial mechanics, mathematically predicting the motions of celestial bodies interacting under gravity, and solar system objects in particular. Much of the effort in these two areas, once done largely by hand, is highly automated nowadays, to the extent that they are rarely considered as independent disciplines anymore. Motions and positions of objects are now more easily determined, and modern astronomy is more concerned with observing and understanding the actual physical nature of celestial objects. Since the twentieth century, the field of professional astronomy has split into observational astronomy and theoretical astrophysics. Although most astronomers incorporate elements of both into their research, because of the different skills involved, most professional astronomers tend to specialize in one or the other. Observational astronomy is concerned mostly with acquiring data, which involves building and maintaining instruments and processing the results; this branch is at times referred to as "astrometry" or simply as "astronomy". Theoretical astrophysics is concerned mainly with ascertaining the observational implications of different models, and involves working with computer or analytic models. The fields of study can also be categorized in other ways. Categorization by the region of space under study (for example, Galactic astronomy, Planetary Sciences); by subject, such as star formation or cosmology; or by the method used for obtaining information.

By subject or problem addressed

theoretical astrophysics. Photographed by Mars Global Surveyor, the long dark streak is formed by a moving swirling column of Martian atmosphere (with similarities to a terrestrial tornado). The dust devil itself (the black spot) is climbing the crater wall. The streaks on the right are sand dunes on the crater floor.]]
- Astrometry: the study of the position of objects in the sky and their changes of position. Defines the system of coordinates used and the kinematics of objects in our galaxy.
- Astrophysics: the study of physics of the universe, including the physical properties (luminosity, density, temperature, chemical composition) of astronomical objects.
- Cosmology: the study of the origin of the universe and its evolution. The study of cosmology is theoretical astrophysics at its largest scale.
- Galaxy formation and evolution: the study of the formation of the galaxies, and their evolution.
- Galactic astronomy: the study of the structure and components of our galaxy and of other galaxies.
- Extragalactic astronomy: the study of objects (mainly galaxies) outside our galaxy.
- Stellar astronomy: the study of the stars.
- Stellar evolution: the study of the evolution of stars from their formation to their end as a stellar remnant.
- Star formation: the study of the condition and processes that led to the formation of stars in the interior of gas clouds, and the process of formation itself.
- Planetary Sciences: the study of the planets of the Solar System.
- Astrobiology: the study of the advent and evolution of biological systems in the Universe. Other disciplines that may be considered part of astronomy:
- Archaeoastronomy
- Astrochemistry
- Astrosociobiology
- Astrophilosophy See the list of astronomical topics for a more exhaustive list of astronomy-related pages.

Ways of obtaining information

list of astronomical topics :Main article: Observational astronomy. In astronomy, information is mainly received from the detection and analysis of light and other forms of electromagnetic radiation. Other cosmic rays are also observed, and several experiments are designed to detect gravitational waves in the near future. A traditional division of astronomy is given by the region of the electromagnetic spectrum observed:
- Optical astronomy is the part of astronomy that uses optical components (mirrors, lenses, CCD detectors and photographic films) to observe light from near infrared to near ultraviolet wavelengths. Visible light astronomy (using wavelengths that can be detected with the eyes, about 400 - 700 nm) falls in the middle of this range. The most common tool is the telescope, with electronic imagers and spectrographs.
- Infrared astronomy deals with the detection and analysis of infrared radiation (wavelengths longer than red light). The most common tool is the telescope but using a detector which is sensitive to the infrared. Space telescopes are also used to avoid atmospheric thermal emission, atmospheric opacity, and the effects of astronomical seeing at infrared and other wavelengths.
- Radio astronomy detects radiation of millimetre to dekametre wavelength. The receivers are similar to those used in radio broadcast transmission but much more sensitive. See also Radio telescopes.
- High-energy astronomy includes X-ray astronomy, gamma-ray astronomy, and extreme UV (ultraviolet) astronomy, as well as studies of neutrinos and cosmic rays. Optical and radio astronomy can be performed with ground-based observatories, because the atmosphere is transparent at the wavelengths being detected. Infrared light is heavily absorbed by water vapor, so infrared observatories have to be located in high, dry places or in space. The atmosphere is opaque at the wavelengths of X-ray astronomy, gamma-ray astronomy, UV astronomy and (except for a few wavelength "windows") Far infrared astronomy, so observations must be carried out mostly from balloons or space observatories. Powerful gamma rays can, however be detected by the large air showers they produce, and the study of cosmic rays can also be regarded as a branch of astronomy.

History of astronomy

cosmic ray :Main article: History of astronomy. In early times, astronomy only comprised the observation and predictions of the motions of the naked-eye objects. Aristotle said that the Earth was the center of the Universe and everything rotated around it in orbits that were perfect circles. Aristotle had to be right because people thought that Earth had to be in the center with everything rotating around it because the wind would not scatter leaves, and birds would only fly in one direction. For a long time, people thought that Aristotle was right, but it is probable that Aristotle accidentally did more to hinder our knowledge than help it. The Rigveda refers to the 27 constellations associated with the motions of the sun and also the 12 zodiacal divisions of the sky. The ancient Greeks made important contributions to astronomy, among them the definition of the magnitude system. The Bible contains a number of statements on the position of the earth in the universe and the nature of the stars and planets, most of which are poetic rather than literal; see Biblical cosmology. In 500 AD, Aryabhata presented a mathematical system that described the earth as spinning on its axis and considered the motions of the planets with respect to the sun. Observational astronomy was mostly stagnant in medieval Europe, but flourished in the Iranian world and other parts of Islamic realm. The late 9th century Persian astronomer al-Farghani wrote extensively on the motion of celestial bodies. His work was translated into Latin in the 12th century. In the late 10th century, a huge observatory was built near Tehran, Persia (now Iran), by the Persian astronomer al-Khujandi, who observed a series of meridian transits of the Sun, which allowed him to calculate the obliquity of the ecliptic. Also in Persia, Omar Khayyám performed a reformation of the calendar that was more accurate than the Julian and came close to the Gregorian. Abraham Zacuto was responsible in the 15th century for the adaptations of astronomical theory for the practical needs of Portuguese caravel expeditions. During the Renaissance, Copernicus proposed a heliocentric model of the Solar System. His work was defended, expanded upon, and corrected by Galileo Galilei and Johannes Kepler. Galileo added the innovation of using telescopes to enhance his observations. Kepler was the first to devise a system that described correctly the details of the motion of the planets with the Sun at the center. However, Kepler did not succeed in formulating a theory behind the laws he wrote down. It was left to Newton's invention of celestial dynamics and his law of gravitation to finally explain the motions of the planets. Newton also developed the reflecting telescope. Stars were found to be faraway objects. With the advent of spectroscopy it was proved that they were similar to our own sun, but with a wide range of temperatures, masses, and sizes. The existence of our galaxy, the Milky Way, as a separate group of stars was only proven in the 20th century, along with the existence of "external" galaxies, and soon after, the expansion of the universe, seen in the recession of most galaxies from us. Modern astronomy has also discovered many exotic objects such as quasars, pulsars, blazars and radio galaxies, and has used these observations to develop physical theories which describe some of these objects in terms of equally exotic objects such as black holes and neutron stars. Physical cosmology made huge advances during the 20th century, with the model of the Big Bang heavily supported by the evidence provided by astronomy and physics, such as the cosmic microwave background radiation, Hubble's Law, and cosmological abundances of elements.

Timelines in astronomy

cosmological abundances of elements
- Artificial satellites and space probes
- Astronomical maps, catalogs, and surveys
- Big Bang
- Black hole physics
- Cosmic microwave background astronomy
- Cosmology
- Galaxies, clusters of galaxies, and large scale structure
- Interstellar medium and intergalactic medium
- Natural satellites
- Other background radiation fields
- Solar astronomy
- Solar system astronomy
- Stellar astronomy
- Telescopes, observatories, and observing technology
- White dwarfs, neutron stars, and supernovae

See also


- List of astronomical topics
- Astronomers and Astrophysicists
- Astronomical cycles
- Astronomical naming conventions
- Astronomical object
- Astronomical observatories
- Astronomy organizations
- Astronomical symbols
- Space science
- Celestial navigation

Astronomy tools


- Binoculars
- Telescope
- Computers
- Calculator
- Observatory
- Space observatory
- Maksutov telescope

External Links


- [http://www.space.com/ Space.com]
- [http://www.Astronomy.com/ Astronomy.com]
- [http://www.AbsoluteAstronomy.com/ AbsoluteAstronomy.com]
- [http://www.badastronomy.com/ Bad Astronomy]
- [http://www.nasa.gov/ Nasa]
- [http://www.run4space.com Run4Space Forum]
- [http://antwrp.gsfc.nasa.gov/apod/astropix.html/ Astronomy Picture of the Day] ko:천문학 ms:Astronomi ja:天文学 simple:Astronomy th:ดาราศาสตร์

Eugene Wigner

Eugene Paul Wigner (Hungarian Wigner Pál Jenő) (November 17, 1902 – January 1, 1995) was a Hungarian physicist and mathematician who received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". Within the world of physics, Wigner was referred to as "the Silent Genius" as he was thought of by his contemporaries as the intellectual equal to Einstein, without the notoriety. He was one of a generation of physicists of the 1920s who remade the world of physics. This generation was a collection of people from Berlin to London to Zürich to Pisa, though not quite yet to New York or Chicago, Illinois. The first physicists in this new generation — Werner Heisenberg, Erwin Schrödinger, and Paul Dirac, to name three — created quantum mechanics. Quantum mechanics was a dazzling new world, which threw open dozens of fundamental physical questions. A new set of men (and a few women) c