67 résultats pour "mathematics"

Brandenburg Technical University Cottbus
Department 1, Institute of Mathematics
Chair for Numerical Mathematics an Scientific Computing
Prof.
) 1 = 1 ; 2= 3 = 2i Eigenvectors: 0 @ 1 1 1 0 1 5 0 1 1 1 A ~x= ~ 0 1 = 1: 0 @ 0 1 1 0 0 5 0 1 2 1 A ; ~x =t(1 ;0 ;0) T 1 = 2 i: 0 @ 1 2i 1 1 0 1 2i 5 0 1 1 2i 1 A ~x= ~ 0 0 @ 1 2i 1 1 0 1 1 2i 0 0 0 1 A ~x= ~ 0 ; ~x = 2i 1 2i; 1 2i; 1 T 1 = 2i: 0 @ 1 + 2 i 1 1 0 1 + 2 i5 0 1 1 + 2 i1 A ~x= ~ 0 0 @ 1 + 2 i1 1 0 1 1 + 2 i 0 0 0 1 A ~x= ~ 0 ; ~x = 2i 1 + 2 i; 1 + 2 i;1 T H 13.3: det(A E ) = det 1 1 1 3 = (1 )(3 ) 1 = 2 4 + 2 : Eigenvalues: 1= 2 = 2 p 2 E...

Brandenburg Technical University Cottbus
Department 1, Institute of Mathematics
Chair for Numerical Mathematics an Scientific Computing
Prof.
) 1 = 1 ; 2= 3 = 2i Eigenvectors: 0 @ 1 1 1 0 1 5 0 1 1 1 A ~x= ~ 0 1 = 1: 0 @ 0 1 1 0 0 5 0 1 2 1 A ; ~x =t(1 ;0 ;0) T 1 = 2 i: 0 @ 1 2i 1 1 0 1 2i 5 0 1 1 2i 1 A ~x= ~ 0 0 @ 1 2i 1 1 0 1 1 2i 0 0 0 1 A ~x= ~ 0 ; ~x = 2i 1 2i; 1 2i; 1 T 1 = 2i: 0 @ 1 + 2 i 1 1 0 1 + 2 i5 0 1 1 + 2 i1 A ~x= ~ 0 0 @ 1 + 2 i1 1 0 1 1 + 2 i 0 0 0 1 A ~x= ~ 0 ; ~x = 2i 1 + 2 i; 1 + 2 i;1 T H 13.3: det(A E ) = det 1 1 1 3 = (1 )(3 ) 1 = 2 4 + 2 : Eigenvalues: 1= 2 = 2 p 2 E...

Algebra
I
INTRODUCTION
Algebra, branch of mathematics in which symbols (usually letters) represent unknown numbers in mathematical equations.
B Order of Operations and Grouping Algebra relies on an established sequence for performing arithmetic operations. This ensures that everyone who executes a string of operations arrives at the sameanswer. Multiplication is performed first, then division, followed by addition, then subtraction. For example: 1 + 2 · 3 equals 7 because 2 and 3 are multiplied first and then added to 1. Exponents and roots have even higher priority than multiplication: 3 · 2 2 = 3 · 4 = 12 Grouping symbols override...

Algebra
I
INTRODUCTION
Algebra, branch of mathematics in which symbols (usually letters) represent unknown numbers in mathematical equations.
B Order of Operations and Grouping Algebra relies on an established sequence for performing arithmetic operations. This ensures that everyone who executes a string of operations arrives at the sameanswer. Multiplication is performed first, then division, followed by addition, then subtraction. For example: 1 + 2 · 3 equals 7 because 2 and 3 are multiplied first and then added to 1. Exponents and roots have even higher priority than multiplication: 3 · 2 2 = 3 · 4 = 12 Grouping symbols override...
 Area (mathematics).
 e (mathematics).
 Number (mathematics) I INTRODUCTION Number (mathematics), word or symbol used to designate quantities or entities that behave like quantities.

Trigonometry
I
INTRODUCTION
Trigonometry, branch of mathematics that deals with the relationships between the sides and angles of triangles and with the properties and applications of the
trigonometric functions of angles.
If point P, in the definition of the general trigonometric function, is on the yaxis, x is 0; therefore, because division by zero is inadmissible in mathematics, the tangent and secant of such angles as 90°, 270°, and 270° do not exist. If P is on the xaxis, y is 0; in this case, the cotangent and cosecant of such angles as 0°, 180°, and  180° do not exist. All angles have sines and cosines, because r is never equal to 0. Since r is greater than or equal to x or y, the values of si...


Trigonometry
I
INTRODUCTION
Trigonometry, branch of mathematics that deals with the relationships between the sides and angles of triangles and with the properties and applications of the
trigonometric functions of angles.
If point P, in the definition of the general trigonometric function, is on the yaxis, x is 0; therefore, because division by zero is inadmissible in mathematics, the tangent and secant of such angles as 90°, 270°, and 270° do not exist. If P is on the xaxis, y is 0; in this case, the cotangent and cosecant of such angles as 0°, 180°, and  180° do not exist. All angles have sines and cosines, because r is never equal to 0. Since r is greater than or equal to x or y, the values of si...

Matrix Theory and Linear Algebra
I
INTRODUCTION
Matrix Theory and Linear Algebra, interconnected branches of mathematics that serve as fundamental tools in pure and applied mathematics and are becoming
increasingly important in the physical, biological, and social sciences.
vectors and V is called a vector space of dimension m. Two and threedimensional Euclidean spaces are vector spaces when their points are regarded as specified by ordered pairs or triples of real numbers. Matrices may be used to describe linear changes from one vector space into another. Contributed By:James Singer Reviewed By:J. Lennart BerggrenMicrosoft ® Encarta ® 2009. © 19932008 Microsoft Corporation. All rights reserved.
 Absolute Value (mathematics).
 Transform (mathematics).
 Base (mathematics).
 Simplify (mathematics).
 Mean (mathematics).
 Mode (mathematics).

 Power (mathematics).
 Inequality (mathematics).
 Variable (mathematics).
 Variable (mathematics).
 Median (mathematics).
 Root (mathematics).
 Infinity (mathematics).
 Factor (mathematics).


Geometry
I
INTRODUCTION
Geometry, branch of mathematics that deals with shapes and sizes.
Conic sections, a commonly studied topic of geometry, are twodimensional curves created by slicing a plane through a threedimensional hollow cone. A Euclid’s Postulates Euclid, who lived about 300 BC, realized that only a small number of postulates underlay the various geometric theorems known at the time. He determined that these theorems could be deduced from just five postulates. 1. A straight line may be drawn through any two given points. 2. A straight line may be drawn infinitely or be...
 Principia Mathematica  filosofia.
 Transitive Property (mathematics).

Calculus (mathematics)
I
INTRODUCTION
Limits
This graph, which charts the function f(x)=1x, shows that the value of the function approaches zero as x becomes larger
and larger.
DerivativesThe derivative of a function at a given point is equal to the slope of the line that is tangent to the function at that givenpoint. In this example, the derivative of f(x) at x0 is defined as the slope of AB in the limit of h going to zero. As hbecomes increasingly smaller, B moves along the curve towards A, and AB increasingly approximates T, the tangent to thecurve at x0.© Microsoft Corporation. All Rights Reserved. Let the dependent variable y be a function of the independent vari...
 Associative Property (mathematics).
 Commutative Property (mathematics).
 Distributive Property (mathematics).
 Coordinate System (mathematics).


Arithmetic
I
INTRODUCTION
Arithmetic, branch of mathematics that arises from counting, the most basic mathematical operation.
Subtract the units: 6  3 = 3. Then subtract the tens column: 6 – 2 = 4. The results of these two singledigit subtractions, written side by side, provide the answer: Subtraction is a bit more complicated if we need to subtract a larger digit from a smaller one. For example, when subtracting 47 from 92, the units value (7) of 47 isgreater than the units value (2) of 92. We can handle this situation using a procedure called borrowing, which is like carrying in reverse. Ten units can be borrowe...

Complex Numbers
I
INTRODUCTION
Complex Numbers, in mathematics, the sum of a real number and an imaginary number.
sometimes referred to as an Argand diagram. If a complex number in the plane is thought of as a vector joining the origin to that point, then addition of complexnumbers corresponds to standard vector addition. Figure 1 shows the complex number 3 + 2 i obtained by adding the vectors 1 + 4 i and 2  2 i. Figure 1: Complex Plane in Cartesian CoordinatesThis graph illustrates the addition of two complex numbers by using vectors in the complex plane with cartesiancoordinates. The parallelogram shows...
 Principia Mathematica [Bertrand Russell et Alfred North Whitehead]  fiche de lecture.
 Topology I INTRODUCTION Topology, branch of mathematics that explores certain properties of geometrical figures.
 Mathematical Symbols I INTRODUCTION Mathematical Symbols Mathematics employs many symbols to describe numerical operations and relationships.
 Mathematical Symbols I INTRODUCTION Mathematical Symbols Mathematics employs many symbols to describe numerical operations and relationships.
 Number Theory I INTRODUCTION Number Theory, branch of mathematics that deals with the properties and relationships of numbers (see Number).

Statistics
I
INTRODUCTION
Statistics, branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision
making.
frequency, column (d), is the ratio of the frequency of an interval to the total count; the relative frequency is multiplied by 100 to obtain the percent relative frequency.The cumulative frequency, column (e), represents the number of students receiving grades equal to or less than the range in each succeeding interval; thus, thenumber of students with grades of 30 or less is obtained by adding the frequencies in column (c) for the first three intervals, which total 53. The cumulative relativef...


Statistics
I
INTRODUCTION
Statistics, branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision
making.
Professional pollsters typically conduct their surveys among sample populations of 1,000 people. Statistical measurementsshow that reductions in the margin of error flatten out considerably after the sample size reaches 1,000.© Microsoft Corporation. All Rights Reserved. The raw materials of statistics are sets of numbers obtained from enumerations or measurements. In collecting statistical data, adequate precautions must be taken tosecure complete and accurate information. The first problem of...

Isaac Newton.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the t...

Isaac Newton
I
INTRODUCTION
Isaac Newton (16421727), English physicist, mathematician, and natural philosopher, considered one of the most important scientists of all time.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the t...

Isaac Newton.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the t...

Isaac Newton.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the t...

Condorcet, MarieJeanAntoineNicolas Caritat de
years he also came under the influence of Euler, Fontaine, the Bernouillis and, above all, of the distinguished mathematician and academician, Jean Le Rond D'Alembert , who became his patron. He was elected Perpetual Secretary of the Academy of Sciences in 1773, and in 1782 became a member of the French Academy. An enthusiastic supporter and theorist of the Revolution, he played an important role in the drafting of the Déclaration des droits in 1789. Suspected later of being a Girondin, he w...
 PRINCIPIA MATHEMATICA (PRINCIPES MATHÉMATIQUES), Bertrand Russel et Alfred North Whitehead
 Pi. Pi, Greek letter (p) used in mathematics as the symbol


Math is Fun
of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."[15] Albert Einstein (1879–1955) 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."[16] French mathematician Claire Vois...
 Number Systems I INTRODUCTION Number Systems, in mathematics, various notational systems that have been or are being used to represent the abstract quantities called numbers.