Mathematics is the study of quantity Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things, structure Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly, space Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines ', and change Calculus is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,. Mathematicians A mathematician is a person whose primary area of study and/or research is the field of mathematics. The most notable mathematicians are generally thought to be Sir Isaac Newton, Johann Carl Friedrich Gauss and Archimedes of Syracuse seek out patterns A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created have enough in common for the underlying,[2][3] formulate new conjectures A conjecture is a proposition which is presumed to be real, true, or genuine, mostly based on inconclusive grounds. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds. In mathematics, a conjecture is an unproven, and establish truth by rigorous Rigour or rigor has a number of meanings in relation to intellectual life and discourse. These are separate from public and political applications with their suggestion of laws enforced to the letter, or political absolutism. A religion, too, may be worn lightly, or applied with rigour deduction Deductive reasoning, sometimes called deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is said to be deductive when the truth of the conclusion is purported to follow necessarily or be a logical consequence of the premises and its corresponding conditional is a necessary truth. Deductive from appropriately chosen axioms In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other truths and definitions A definition is a formal passage describing the meaning of a term . The term to be defined is the definiendum (plural definienda). A term may have many subtly different senses or meanings. For each such sense, a definiens (plural definientia) is a cluster of words that defines that specific sense of the term.[4]
There is debate over whether mathematical objects such as numbers A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels , and points exist naturally or are human creations. The mathematician Benjamin Peirce After graduating from Harvard, he remained as a tutor , and was subsequently appointed professor of mathematics in 1831. He added astronomy to his portfolio in 1842, and remained as Harvard professor until his death. In addition, he was instrumental in the development of Harvard's science curriculum, served as the college librarian, and was called mathematics "the science that draws necessary conclusions".[5] Albert Einstein Albert Einstein (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ; 14 March 1879–18 April 1955) was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Through the use of abstraction Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalising it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena and logical Logic, from the Greek λογική is the art and science of reasoning. There are many different conceptions of what the field of logic comprises. How these notions relate to each other can sometimes be controversial. Logic is considered by some to be the study of the general features, or form, of arguments, as is studied in the sub-disciplines of reasoning Reasoning is the cognitive process of looking for reasons for beliefs, conclusions, actions or feelings, mathematics evolved from counting Counting is the mathematical action of continually adding one at a time, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with an injective function from the remaining objects to the natural numbers starting from two), or for well-ordered objects, to, calculation The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people, measurement In science, measurement is the process of obtaining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a meter or a kilogram. The term can also be used to refer to the result obtained after performing the process, and the systematic study of the shapes The shape of an object located in some space is the part of that space occupied by the object, as determined by its external boundary – abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties (position and orientation in space; size) and motions In physics, motion means a change in the location of a body. Change in motion is the result of applied force. Motion is typically described in terms of velocity, acceleration, displacement, and time. An object's velocity cannot change unless it is acted upon by a force, as described by Newton's first law also known as Inertia. An object's momentum of physical objects. Practical mathematics has been a human activity for as far back as written records The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past exist. Rigorous arguments Logic, from the Greek λογική is the art and science of reasoning. There are many different conceptions of what the field of logic comprises. How these notions relate to each other can sometimes be controversial. Logic is considered by some to be the study of the general features, or form, of arguments, as is studied in the sub-disciplines of first appeared in Greek mathematics Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. The word "mathematics" itself derives from the ancient Greek μάθημα , meaning "subject of instruction".. The study of, most notably in Euclid Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the "Father of Geometry." He was active in Hellenistic Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is the most successful textbook and one of the most influential works in the history of mathematics,'s Elements Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry. Mathematics continued to develop, in fitful bursts, until the Renaissance The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Florence in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historic era, but since the changes of the Renaissance were not uniform across Europe, this is a general use of the, when mathematical innovations interacted with new scientific discoveries The timeline below shows the date of publication of major scientific theories and discoveries, along with the discoverer. In many cases, the discovery spanned several years, leading to an acceleration in research that continues to the present day.[7]
Today, mathematics is used throughout the world as an essential tool in many fields, including natural science In Science, the term natural science refers to a naturalistic approach to the study of the universe, which is understood as obeying rules or laws of natural origin. Overall, natural science is the core of all sciences, engineering Engineering is the discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions, medicine Medicine is the art and science of healing. It encompasses a range of health care practices evolved to maintain and restore health by the prevention and treatment of illness, and the social sciences The social sciences are the fields of scientific knowledge and academic scholarship that study social groups and, more generally, human society. The social sciences initially were constituted of five fields: Jurisprudence and Amendment of the Law; Education; Health; Economy and Trade; Art. The contemporary field of science comprise academic. Applied mathematics Historically, applied mathematics consisted principally of applied analysis, most notably differential equations, approximation theory , and applied probability. These areas of mathematics were intimately tied to the development of Newtonian Physics, and in fact the distinction between mathematicians and physicists was not sharply drawn before the, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction, and beauty. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.[8]
Contents |
WEAU-TV 13
Provide instruction to students in the area of mathematics (including calculus and possibly physics). Assist in the design, writing and implementation of ...
and more »
Department of Mathematics, Stony Brook University
hu, 05 Nov 2009 23:29:08 GM
Stony Brook University's Department of . Mathematics. expects to have positions available with a starting date of September 2010. We anticipate appointing tenured and/or tenure-track faculty members and three Simons Instructors (a ...
Q. I have to write an essay on "how to convince a friend that mathematics is interesting". I need 3 reasons, and support of each of the reasons. Having a hard time since I cannot stand math!
Asked by Gianni - Mon Sep 7 12:58:36 2009 - - 5 Answers - 0 Comments
A. If it is just to convince your friend, then try to find out the things that interest this friend and then relate mathematics to his interests. I guessing relating should be relatively easy since most items (or least this is true to me) are related to mathematics. Hope this will help you.
Answered by LW - Wed Sep 9 06:18:54 2009
