Algebra System Experience Transfer

September 26, 2011, convened a meeting of students to discuss the recent study tasks. (1) Mathematics Category: Category theory, applied Mathematics (set theory, group, ring, domain), cellular automata (CA), etc. (2) Method class: Engineering Innovation Methodology, (3) Open title Report: What are the problems? What problem do you want to solve? Modeling methods, what techniques are used, and how are the effects validated?

Here is a little bit of learning about algebraic systems.

1. Set is the basis of algebra

The relationship between the observer and the observed R:R is a subset of the set a{me, not me}x b{present, non-present} (the product set of A and B).

2. One of the sources of modern algebra

During the Renaissance, the radical solutions of 3 and 4 equations (groups) were studied mainly in elementary algebra. After more than 200 years, people tried to find the radical solution of the 5-time equation, but there was no gain. In 1832, the French mathematician Galois (1811-1832) used the idea of "group" to solve the problem of solving the algebraic equations with radicals completely. He was the first mathematician to put forward the idea of "group", which was generally referred to as the founder of modern algebra.

Abel The Norwegian mathematician has proved that there are no root formulas for the 5 or more equations; Galois found that the root formula of the equation is related to the symmetry of the root. If the Galois group solvable the equation can be solved.

3. The second source of modern algebra

The four-dollar number (Quaternions) was a mathematical concept discovered by Hamilton (Hamilton, 1805-1865) in 1843. It is shaped like ai+bj+ck+d number, A, B, C, D is real, i^2=j^2=k^2=-1,ij=k ji=-k jk=i kj=-i ki=j ik=-j. The multiplication of four-dollar numbers does not conform to the commutative law (commutative).

4. Three sources of modern algebra

Fermat 1637 studied the general solution of X^2+y^2=z^2 is: x=2mn,y=m^2-n^2,z=m^2+n^2, where M,n (m>n) is any positive integer "." There can be no positive integer solution for X^n+y^n=z^n (N>2). "This is the famous Fermat conjecture. June 23, 1993, Wiles Andrew, a 40-year-old math department at Princeton University, quietly declared, "I proved Fermat conjecture."

5. Is the algebraic system very dangling?

actually otherwise Algebraic systems are---operations that give algebraic structures to a set. Arithmetic is the reaction of things, such as 1+2=3. Some things are not simply expressed in numbers, in order to express the connection of such things, we should study the special arithmetic = algebraic structure. A particular algebraic structure is an algebraic system.

6. Boolean algebra system

With such a picture, that is, the establishment of a Boolean algebra system is the concept of God horse framework, you can guarantee to learn the digital circuit and high score? @ Electric Doll

7. Algebra in life (algebraic systems)

The elements of the mathematical discussion extend from numbers and algebra to the collection of things, and the operations extend from +-*/to more general structures (relationships).

Given the specific combination of the population system, the relationship between marriage and friends has been created.

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Algebra System Experience Transfer