Fields of Mathematics

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 or magnitude 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.

roman religion sales price per square foot sapphire science museums scifi and literature

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.

sequence of gothic styles small appliances small appliances sound recording start of the renaissance

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 and calculus on manifolds. Within algebraic geometry is the description of geometric objects as solution sets of polynomial 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.

streamline moderne structural evolution of byzantine architecture supply and demand synthetic and artificial gemstones taxes and public finance

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.

technicalization technique tempered glass the antecedents of human sacrifice in the aztec culture the internet

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 role. It is used in all the sciences. (Many statisticians, however, do not consider themselves to be mathematicians, but rather part of an allied group.) Numerical analysis investigates computational methods for efficiently solving a broad range of mathematical problems that are typically much too large for a human's capacity; it includes the study of rounding errors or other sources of error in computation.

Nofeerentals.com
Apartment rental NY NYC, Rental apartments in New York city Nofeerentals.com has rental apartments and provides no fee apartment rental in downtown Manhattan New York City near New York University and all Manhattan
http://www.nofeerentals.com/index.asp

lansend.com: Microsoft Certified Computer consultants in New York, NY
Microsoft Certified Computer consultants providing computer and network consulting services in New York ,NY Manhattan Queens, Lan Wan Networking VPN.
http://www.lansend.com

NotasInc.com
Colombian crafts, handmade handicraft, unique gifts
Unique gifts & handmade handicrafts handcrafted by Colombian artisans. Stained glass paintings, embossed ceramic paintings, jute handicrafts, leather sculptures, hand embroidered cloth & tapestry
http://www.notasinc.com/index.htm

Quiktea
Authentic Indian Tea, Very tastea , Very Indian- Instant Chai
QuikFoods currently has QuikTea - an Instant Chai, QuikCafe - Instant Coffee & Chicory Blend with Milk, and Diets. We've also put our top flavors in single serving foil and are available in 3 pouch box, 20 pouch box, and 1KG foil bags - Great for vending services
http://www.quiktea.com/index.cfm

precious topaz

Mathematics

History of Social sciences

Mathematical beauty

Mathematical notation

Fields of Mathematics

Mathematics lists

Mathematics is a science

Common misconceptions