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Abstract Algebra
Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.
1,849 Questions
How many seconds are there in 100 years?
3,217,760,000 seconds GUESS WHAT!!?? I DIDN'T USE A CALCULATOR!!! I SMRT!!!!!!!!!! ~A 12 yr. old girl :)
What is the value of a 1930 helvetia Swiss 20 franc?
Today they can be had for between $165 and $299 depending upon condition.
Find the difference between place values of the two 9s in 79520986?
The first 9 is in the Millions place, the second is in the Hundreds. The difference is 4 orders of magnitude.
What is the use of matrices in engineering?
Matrices are a vital mathematical tool for calculating forces, vectors, tensions, masses, loads and a myriad of other factors that must be accounted for in engineering to ensure a safe and resource-efficient structure.
What is the value of a Ruger 45-70 number 3?
The Ruger No. 3 carbine was produced from 1972 to 1987. It is booked at $500 for 100% condition (new in box), $300 at 90%, $250 at 80%, and $200 at 70%.
A complex number has an imaginary component and is of the form a + bi. (And i is the square root of -1 in this application.)
A matrix is a table of numbers. For example, we might give the current (x,y,z) coordinates of a dozen asteroids using a 12 * 3 matrix.
A complex matrix is a matrix of complex numbers.
this is used in trigonometry. its means angle side angle
others include ssa (side side angle), saa (side angle angle), ssa (side side angle), sas (side angle side), sss (side side side), aaa (angle angle angle)
What is an example of a group that has used comparative advertising?
This advertising technique is very common and is used by nearly every major industry, including airlines and automobile manufacturers.
What are the different types of numbers And where did they originate from?
From the simplest to more complicated, there are:
- N, the set of Natural or counting numbers [0], 1, 2, 3, ...
- Z, the set of all integers, ..., -3, -2, -1, 0, 1, 2, 3, ...
- Q, the set of all rational numbers (Q for quotient). These are numbers of the form p/q where p and q are integers and q is not 0.
- Irrational numbers, such as sqrt(2), e, cuberoot(171/2) and so on. These cannot be expressed in the form of a ratio and so are not rational.
- Transcendental numbers are a special type of irrational numbers. Most well known irrational numbers arise as solutions to [non-constant] polynomials with rational coefficients. However, there are numbers such as pi and e (extremely important to mathematics) which are transcendental.
- R, the set of Real numbers are made up of the rational and irratoinal numbers.
- C, the set of complex numbers. These have a part that is real (as above) and a part that is iaginary - related to the square root of -1.
What is the value of 1 peseta?
It is 1 peso! And if you wanted to know its value in some other currency then you need to specify which country's peseta you are talking about and also in which country's currency you want its value.
What is the definition of algebra?
Algebra is: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic
2 : any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations often analogous to those of arithmetic
Algebra is adding, subtracting, multipling, and dividing with variable and numbers!
there is a easier way to know what it is just think of the letter as something like a for apple here is a e.g
a=5 and p=6
a=apple and p = pear
2a+2p=22
this means 2xa which is 2x5 and 2xp which is 2x6
the answer of 2a and 2p you add together which would be 10+12 which answer 22 and that is your answer
If d divides the order of a group does the group has a subgroup of order d?
The general answer is no. Consider A4={(1),(12)(34),(13)(24),(14)(23),(123),(124),(132),(134),(142),(143),(234),(243)}. The subgroups of A4 are: A4, <(12)(34)>, <(13)(24)>, <(14)(23)>, <(123)>=<(132)>, <(124)>=<(142)>, <(134)>=<(143)>, <(234)>=<(243)>, {(1),(12)(34),(13)(24),(14)(23)}, {(1)}. The order of A4 is 12, the order of <(12)(34)>, <(13)(24)> and <(14)(23)> is 2, the order of <(123)>=<(132)>, <(124)>=<(142)>, <(134)>=<(143)> and <(234)>=<(243)> is 3, the order of {(1),(12)(34),(13)(24),(14)(23)} is 4, and the order of <(1)> is 1. Clearly there are no subgroups of order 6, but 6 definitely divides the order of A4. The statement is true for all finite abelian groups, and when d is a power of a prime (i.e., when d=pk for a prime p and a non-negative integer k).
There are 86,400 seconds in one day; simply multiply that by the number of days and you have your answer.
4daysX24hours/day=96hours 96hoursx3600(seconds/hour)=345,600 seconds
Why there are no power values for negative bases?
There are so the question is irrelevant. (-3)^4 = 81.
algebra the branch of mathematics dealing with the properties and relations of numbers; the generalized and extension of arithmetic. - algebraic
What is associative property of addition?
The associative property of addition means that the order in which you add terms doesn't matter.
(1 + 2) + 3 = (2 + 3) + 1 = (1 + 3) + 2
* * * * *
NO! The above answer is conflating the associative and commutative properties.
The associative property for addition states that
(a + b) + c = a + (b + c)
The order in which the operations are carried out does not matter. And, as a result, either can be written, without ambiguity, as a + b + c
The associative property DOES NOT state that a + b = b + a. The order of the terms DOES matter. For that you need the operation to be commutative.
There are mathematical operations that are associative but not commutative (matrix multiplication, for example).
When elements are grouped without change of order, as:
(a+b)+c=a+(b+c)
How many verticals does a cylinder have?
As a cylinder has 0 corners, the answer to that question will be 0 A cylinder does not have any vertices. The faces are circular and do not have any points where the edges meet each other.
For solid geometric shapes, a vertex (singular form of vertices) is a point where three or more edges meet. Since a cylinder has only two edges meeting each other (the circle and the rectangle), it has 0 vertices.
On March 1, 2009 at 12:00:01 AM, there will be 306 remaining days until January 1, 2010, which equals 7344 hours or 440,640 minutes, or 26,438,400 seconds. For any period before or after March 1, 2009, add or subtract about 600,000 seconds per week.
