Kategoriarkiv: Algebra

Gauss påskformel

Glad påsk alla trogna läsare!  Påskdagen infaller, enligt ett beslut på kyrkomötet i Nicea år  325 AD den första söndagen efter första fullmåne efter  Vårdagjämningen.  Carl friedrich Gauss utvecklade en formel för att beräkna när denna dag infaller ett godtyckligt … Läs mer

Publicerat i Algebra, matematik 1c, Uncategorized | Lämna en kommentar

Partialbråksuppdelning.

Partialbråksuppdelning går ut på att man skriver om ett rationellt uttryck som summan av ratioenlla uttryck av lägre gradtal Partialbråksuppdelning ger ansatsen Handpåläggning ger och . Sätter vi nu får vi eller dvs . Detta är användbart bl.a. vid integrationer … Läs mer

Publicerat i Algebra | Märkt | Lämna en kommentar

Matrices

A matrix is a square or retangular array of numbers or function of numbers that obeys certain laws. The numbers are distinguished by two subscripts ij. The first indicating the row and the second indicating the column (vertical). in which … Läs mer

Publicerat i Algebra, matematik 5 | Märkt , | Lämna en kommentar

Eulers polyederformula

Definition: A graph is called planar if can be drawn in one plane without any arcs crossing each other. Definintion: The graph G = (V,E) is called bipartite if the nodes can be divided into two disjunct parts V = … Läs mer

Publicerat i Algebra, Gymnasiematematik(high school math), matematik 5 | Märkt , | 2 kommentarer

More Graphtheory

More graph-terminology: The distance between two nodes is the shortest distance between the two nodes. A graph that starts and ends in the same node is called a cycle or a closed circuit. A simple path trespasses every node only … Läs mer

Publicerat i Algebra, Gymnasiematematik(high school math), Uncategorized | Lämna en kommentar

Peculiar functions with descriptions

The cycloid describes the motion of a point on the perimeter of a wheel. The tractoria  (or tractrix) is a curve where the length of the tangent from the tangentialpoint to the x-axis has a constant length a. Its evolute is the … Läs mer

Publicerat i Algebra, matematik 1c | Märkt | Lämna en kommentar

Solving polynomial equations, descartes theorem

A large part of the algebra courses at upper secondary-school level are devoted to solving equations or factorization of polynomials. This is often the same thing. Some terminology. All of these are the same: Solving a polynomial equation. Finding roots … Läs mer

Publicerat i Algebra, Gymnasiematematik(high school math), matematik 2c | Märkt , , , , | Lämna en kommentar

Modular arithmetic & the Chinese Rest Theorem

modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers ”wrap around” upon reaching a certain value—the modulus. An example of this is the clock which starts repeating itself when it has reached 12. Therefore it … Läs mer

Publicerat i Algebra, Gymnasiematematik(high school math) | Lämna en kommentar

Diophantine equations

A Diophantine equation is an equation in which only integers are allowed as coefficients. Also the solutions must be integers. This can be written as ax + by = c. This is a linear diophantine equation. For non-linar diophantine equations … Läs mer

Publicerat i Algebra, Gymnasiematematik(high school math), matematik 1c, Uncategorized | Märkt | Lämna en kommentar

Dimensions and different coordinate sytems

The number of figures necessary for specifying the position of a point is called the dimension of the space. For a two dimensional space it is sufficient to use two numbers (x, y) : one specifying the position on a … Läs mer

Publicerat i Algebra, Geometri, matematik 1c, Uncategorized | Märkt , | 1 kommentar