Which branch of mathematics takes its name from the Latin for 'pebble'?
"Functional (mathematics) In mathematics, the term functional (as a noun) has at least two meanings. This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations. The first concept, which is more modern and abstract, is discussed in detail in a separate article, under the name linear form. Commonly, the space formula_3 is a space of functions; thus the functional takes a function for its input argument, then it is sometimes considered a ""function of a function"" (a higher-order function). Its use originates in the calculus of variations,"
"Calculus Calculus (from Latin ""calculus"", literally 'small pebble', used for counting and calculations, as on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of"
"also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To ""calculate"" means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer using logic, reason or common sense. The English word derives from the Latin ""calculus"", which originally meant a small stone in the gall-bladder (from Latin ""calx""). It also meant a pebble used for calculating, or a small stone used as a counter in an abacus (Latin ""abacus"", Greek ""abax""). The abacus was an instrument used by Greeks and Romans for arithmetic"
"Algebra Algebra (from Arabic """"al-jabr"""", literally meaning ""reunion of broken parts"") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to"
"Isopsephy Isopsephy (; ""isos"" meaning ""equal"" and ""psephos"" meaning ""pebble"") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to other words evaluating the equal number, which satisfies ""isos"" or ""equal"" in the term. The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, which corresponds to ""psephos"" or ""pebble"" and ""counting"" in the term. Isopsephy is related to gematria—the same practice using the Hebrew alphabet and, later, also the English alphabet—and the ancient"
"Pebble A pebble is a clast of rock with a particle size of 2 to 64 millimetres based on the Krumbein phi scale of sedimentology. Pebbles are generally considered larger than granules (2 to 4 millimetres diameter) and smaller than cobbles (64 to 256 millimetres diameter). A rock made predominantly of pebbles is termed a conglomerate. Pebble tools are among the earliest known man-made artifacts, dating from the Palaeolithic period of human history. A beach composed chiefly of surface pebbles is commonly termed a shingle beach. This type of beach has armoring characteristics with respect to wave erosion, as well"
"Mathetics Mathetics is the science of learning. The term was coined by John Amos Comenius (1592–1670) in his work ""Spicilegium didacticum"", published in 1680. He understood ""Mathetics"" as the opposite of ""Didactics"", the science of teaching. Mathetics considers and uses findings of current interest from pedagogical psychology, neurophysiology and information technology. In 1962, The University of Alabama's Mathetics Foundation began publication of ""The Journal of Mathetics"". However, only two issues were ever printed, the first in January and the second in April. The contents of the first issue included: Seymour Papert, MIT mathematician, educator, and author, explains the rationale behind"
"was ankle- to hip-deep. Pebble A pebble is a clast of rock with a particle size of 2 to 64 millimetres based on the Krumbein phi scale of sedimentology. Pebbles are generally considered larger than granules (2 to 4 millimetres diameter) and smaller than cobbles (64 to 256 millimetres diameter). A rock made predominantly of pebbles is termed a conglomerate. Pebble tools are among the earliest known man-made artifacts, dating from the Palaeolithic period of human history. A beach composed chiefly of surface pebbles is commonly termed a shingle beach. This type of beach has armoring characteristics with respect to"
"make calculations is illustrated down to modern times by the fact that ""calx"" is ""pebble"" in Latin, which is the ethymology for the word ""calculation"". The board contains the letters M (= 10.000), Ψ (Boetian for 1.000), H (= 100), Δ (= 10) and (=5, or possibly the unit symbol for the Drachma). White pebbles are added next to each letter in order to give the number of each quantity unit. Next to them appear the former symbols used to represent the Greek coins: Obol (Boetian symbol O, 1/6 of a Drachma), half an Obol (С) and a quarter of"
"Arithmetic Arithmetic (from the Greek ἀριθμός ""arithmos"", ""number"" and τική [τέχνη], ""tiké [téchne]"", ""art"") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms ""arithmetic"" and ""higher arithmetic"" were used until the beginning of the 20th century as synonyms for ""number theory"" and are sometimes still used to refer to a wider part of"
"Princeton University Department of Mathematics The Princeton University Department of Mathematics is an academic department at Princeton University. Founded in 1760, the department has trained some of the world's most renowned and internationally recognized scholars of mathematics. Notable individuals affiliated with the department include John Nash, Senior Research Mathematician and winner of the 1994 Nobel Prize; Alan Turing, who received his doctorates from the department; and Albert Einstein who frequently gave lectures at Princeton and had an office in the building. Since 2012, the chair of the department has been David Gabai, who was awarded the Oswald Veblen Prize in"
"example, 241 is represented as σμα (200 + 40 + 1). Isopsephy Isopsephy (; ""isos"" meaning ""equal"" and ""psephos"" meaning ""pebble"") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to other words evaluating the equal number, which satisfies ""isos"" or ""equal"" in the term. The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, which corresponds to ""psephos"" or ""pebble"" and ""counting"" in the term. Isopsephy is related to gematria—the same practice using"
"divisions geometry, arithmetic, and algebra. The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Bertrand Russell wrote this famous tongue-in-cheek definition, describing the way all terms in mathematics are ultimately defined by reference to undefined terms: The subject in which we never know what we are talking about, nor whether what we are saying is true. Many other attempts to characterize mathematics have led to humor or poetic prose: A mathematician"
"been invented by graduate students at the University of Washington in 1952. After Isbell's paper, other mathematicians have published papers using the name ""Rainwater"" and have acknowledged ""Rainwater's assistance"" in articles. Isbell published other articles using two additional pseudonyms, M. G. Stanley and H. C. Enos, publishing two under each. Many of his works involved topology and category theory: In abstract algebra, Isbell found a rigorous formulation for the Pierce–Birkhoff conjecture on piecewise-polynomial functions. He also made important contributions to the theory of median algebras. In geometric graph theory, Isbell was the first to prove the bound χ ≤ 7"
"Mathematics Mathematics (from Greek μάθημα ""máthēma"", ""knowledge, study, learning"") includes the study of such topics as quantity, structure, space, and change. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proofs. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist."
"1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the ""Millennium Prize Problems"", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a $1 million reward. Mathematics Mathematics (from Greek μάθημα ""máthēma"", ""knowledge, study, learning"") includes the study of such topics as quantity, structure, space, and change. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity"
"be published in his ""Method of Fluxions""), but Leibniz published his ""Nova Methodus pro Maximis et Minimis"" first. Newton claimed Leibniz stole ideas from his unpublished notes, which Newton had shared with a few members of the Royal Society. This controversy divided English-speaking mathematicians from continental European mathematicians for many years, to the detriment of English mathematics. A careful examination of the papers of Leibniz and Newton shows that they arrived at their results independently, with Leibniz starting first with integration and Newton with differentiation. It is Leibniz, however, who gave the new discipline its name. Newton called his calculus"
"the other two sides. The ancient mathematical texts are available with the prior mentioned Ancient Egyptians notation and with Plimpton 322 (Babylonian mathematics c. 1900 BC). The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term ""mathematics"" from the ancient Greek ""μάθημα"" (""mathema""), meaning ""subject of instruction"". Plato's influence has been especially strong in mathematics and the sciences. He helped to distinguish between pure and applied mathematics by widening the gap between ""arithmetic"", now called number theory and ""logistic"", now called arithmetic. Greek mathematics greatly refined"
"Greek mathematics Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word ""mathematics"" itself derives from the , meaning ""subject of instruction"". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key"
"at the turn of the century, but after 1711 both of them became personally involved, accusing each other of plagiarism. The priority dispute had an effect of separating English-speaking mathematicians from those in the continental Europe for many years. Only in the 1820s, due to the efforts of the Analytical Society, did Leibnizian analytical calculus become accepted in England. Today, both Newton and Leibniz are given credit for independently developing the basics of calculus. It is Leibniz, however, who is credited with giving the new discipline the name it is known by today: ""calculus"". Newton's name for it was ""the"
"probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field. Enumerative combinatorics is the most classical area of combinatorics and concentrates on counting the number of certain combinatorial objects. Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. Fibonacci numbers is the basic example of a problem in enumerative combinatorics. The twelvefold way provides"
"which has developed the online learning system also called Lemma (https://www.lem.ma). Lemma combines high-quality lectures on subjects ranging from Linear Algebra to Tensor Calculus with a rich variety of practice problems that are designed to provide the students with immediate feedback. The systems also includes a real-time messaging service that allows educators and students to connect in informal, yet informative sessions. Pavel Grinfeld Pavel Grinfeld (also known as Greenfield) is a mathematician and associate professor of Applied Mathematics at Drexel University working on problems in moving surfaces in applied mathematics (particularly calculus of variations), geometry, physics, and engineering. Grinfeld received"
"""μάθημα"" (""mathema""), meaning ""subject of instruction"". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today"
"combinatorics, a field of mathematics that developed independently in modern mathematics. Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources (see ""Babylonian astronomical diaries""). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically. Except for Timocharis and Aristillus, he was the first Greek known to divide the circle in 360 degrees of 60 arc minutes (Eratosthenes before him used a simpler sexagesimal system dividing a circle into 60 parts). He also used"
"some early work in this area by Hellenistic geometers, notably Pappus (c. 340). The greatest flowering of the field occurred with Jean-Victor Poncelet (1788–1867). In the late 17th century, calculus was developed independently and almost simultaneously by Isaac Newton (1642–1727) and Gottfried Wilhelm Leibniz (1646–1716). This was the beginning of a new field of mathematics now called analysis. Though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable: finding tangent lines to odd curves, and finding areas enclosed by those curves. The methods of calculus"
"such as George Peacock (1791–1858). Systematic mathematical treatments of logic came with the British mathematician George Boole (1847) who devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1 and logical combinations (conjunction, disjunction, implication and negation) are operations similar to the addition and multiplication of integers. Additionally, De Morgan published his laws in 1847. Logic thus became a branch of mathematics. Boolean algebra is the starting point of mathematical logic and has important applications in computer science. Charles Sanders Peirce built upon the work of Boole to"
"similarly used pebbles (in Latin: ""calculi"" ""little stones"", whence English ""calculate""). Addition is straightforward, and relatively efficient algorithms for multiplication and division were known. As Arabic numerals and the zero came into use, ""pen reckoning"" gradually displaced ""counter casting"" as the common accounting method. Jetons for calculation were commonly used in Europe from about 1200 to 1400, and remained in occasional use into the early nineteenth century. From the late 13th century to the end of the 14th century, purpose-made jetons were produced in England, similar in design to contemporary Edwardian pennies. Although they were made of brass they were"
"and vector analysis. Peano played a key role in the axiomatization of mathematics and was a leading pioneer in the development of mathematical logic. Peano had by this stage become heavily involved with the ""Formulario"" project and his teaching began to suffer. In fact, he became so determined to teach his new mathematical symbols that the calculus in his course was neglected. As a result, he was dismissed from the Royal Military Academy but retained his post at Turin University. In 1903 Peano announced his work on an international auxiliary language called ""Latino sine flexione"" (""Latin without inflexion,"" later called"
"scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire, when it is thought to have been exported to other countries. The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Also Demosthenes (384 BC–322 BC) talked of the need to use pebbles for calculations too difficult for your head. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the"
"in physics, engineering, and many other areas. The earliest known work on conic sections was by Menaechmus in the fourth century BC. He discovered a way to solve the problem of doubling the cube using parabolas. (The solution, however, does not meet the requirements of compass-and-straightedge construction.) The area enclosed by a parabola and a line segment, the so-called ""parabola segment"", was computed by Archimedes via the method of exhaustion in the third century BC, in his ""The Quadrature of the Parabola"". The name ""parabola"" is due to Apollonius who discovered many properties of conic sections. It means ""application"", referring"
"Del Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), it may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it"
"Enumerative geometry In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory. The problem of Apollonius is one of the earliest examples of enumerative geometry. This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. In general, the problem for three given circles has eight solutions, which can be seen as 2, each tangency condition imposing a quadratic condition on the space of circles. However, for special arrangements of the given circles, the number of"
"Cobble (geology) A cobble (sometimes a cobblestone) is a clast of rock defined on the Udden–Wentworth scale as having a particle size of , larger than a pebble and smaller than a boulder. Other scales define a cobble's size in slightly different terms. A rock made predominantly of cobbles is termed a conglomerate. Cobblestone is a building material based on cobbles. Cobbles, also called cobblestones, derive their name from the word cob, meaning a rounded lump. The term is further related to the German """", meaning ""head"". Chester Wentworth referred to cobbles as ""cobble bowlders"" in his 1922 paper that"