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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
What is the difference between abstract algebra and linear algebra?
Linear algebra concerns vector spaces whether finite- or infinite-dimensional. Abstract algebra, or modern algebra, includes linear algebra, along with many other kinds of objects, such as groups, rings, fields, lattices, and so on. In part, it was an attempt to put mathematics on a more rigorous footing.
Please see the links.
Are bounded domain functions periodic?
No. You can always "cheat" to prove this by simply giving the function's domain a bound.
Ex: f: [0,1] --> R
I simply defined the function to have a bounded domain from 0 to 1 mapping to the codomain of the set of real numbers. The function itself can be almost anything, periodic or not.
Another way to "cheat" is to simply recognize that all functions having a domain of R are bounded functions, by definition, in the complex plane, C.
(Technically, you would say a non-compact Hermitian symmetric space has a bounded domain in a complex vector space.) Obviously, those functions include non-periodic functions as well.
What is the difference between an axiom and a theorem?
An axiom is a self-evident statement that is assumed to be true. A theorem is proved to be true.
Was the matrix destroyed in transformers 2?
yes but it later fix at the end of transformers 2 revenge of the fallen
It does indeed seem like there should be a rule for adding radicals. There are rules for adding, subtracting, multiplying, and dividing whole numbers, and there are rules for multiplying and dividing radicals. However, there is no "rule" for adding radicals. For example, sqrt(2)+sqrt(3) does NOT equal sqrt(5), sqrt(6), or any other "radical" you could think of. In a professional research paper (and on any exam you may take) an answer of sqrt(2)+sqrt(3) would be a proper answer (assuming it is correct). However, a number like sqrt(4)+sqrt(1) can be simplified. This is simply 3.
Essentially, if a radical has no "nice square root" it cannot be simplified.
It is important to note, however, that an expression like sqrt(2)+sqrt(8) can be simplified. Since sqrt(8)=sqrt(4)sqrt(2)=2sqrt(2), the desired quantity could be simplified to 3sqrt(2).
I hope this was quite informative, and in time to help!
What is axioms of real number?
The real number system is a mathematical field. To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first. And finally, a Field is a Ring over which division - by non-zero numbers - is defined. The algebraic structures (Group, Ring, Field) are more than a term's worth of studying. There are also several mathematical terms above which have been left undefined to keep the answer to a manageable size. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!
What is the value of a 30-40 krag?
As of 2014 the 30-40 Krag gun is valued around 1300.00. A guns value is determined by the market demand, rarity, and its condition.
Prove A plus Ab equals A using boolean algebra theorem?
A+A*b does not mean A plus Ab
the operation signified by "+" is called "or"
the operation signified by "*" is called "and"
there are four possible outcomes of a+a*b
if a=1 and b=1 the result is 1
if a=1 and b=0 the result is 1
if a=0 and b=1 the result is 0
if a=0 and b=0 the result is 0
a+a*b is 1 if a is 1 and a+a*b is 0 if a is 0 regardless of the value of b
thus a+a*b=a
Q.E.D.
What illness do you get from overeating math worksheet?
(Tongue in cheek response): Numberitis (pronounced with a silent 'b' as 'numerititis', as if mumbled instead of numBered) is a painful inflammation having to do with numbers. It can be uni-focal (one area) or multi-focal (many areas). Additionally, the uni- or multi- prefixes can refer to just select numbers or all numbers that precipitate or aggravate the inflammation.
Scientists think Numberitis only affects certain areas of the brain, but other scientists argue that while numberitis primarily involves the upper neurons of the Central Nervous System, numberitis must certainly involve lower neurons and the peripheral nervous system as well. The second group of scientists point to the fact that sufferers of Numberitis have difficulty thinking about numbers, mathematical concepts and theories, as well as writing numbers, formulas, or the dreaded "showing your work" for each step of a math problem. However, the first group of scientists state that the inability to write (the mechanical doings involved with math using the muscles and nerves of the dominant hand) may just be a PTSD-like complex in which the numberitis sufferer has an avoidance psychological problem. Since the two groups of scientists cannot agree on the precise physical or mental locus of difficulty, numberitis remains in both the ICD and the DSM which are the diagnostic code books physicians and psychologists use to label disorders and conditions.
Though they agree that numberitis is not technically an "illness"-- because it is not self-limiting like a viral cold or flu-- they do not agree on whether numberitis is a disorder or a condition. (Illness, disorder, and condition each have specific but separate definitions in the medical-psychiatric fields.)
Causation: Doctors do not yet fully understand numberitis. There have been links to various possible causes, but no scientific proof. Several small studies have shown that some sufferers reported "overeating math work sheets" but other studies showed that other students had "overrated the difficulty of problems on their math work sheets". This "over-rating" usually had to do with students thinking the problems were "harder" than what they were, in reality. Non-sufferers rated most of the math problems as "easy" or "medium" but only "if I studied and paid attention in class". Comparisons of "overeaters of math worksheets" and those who never ate a math work sheet were inconclusive, except the non-eaters said "WHY would anyone EAT a math worksheet?!" This group shuddered and grimaced with just the thought of doing this act. The study had to be terminated.
Duration: Though numberitis can persist for some sufferers, doctors have found that the inflammation eases when students practice solving math problems. In addition to solving problems, a small group improved when they also ate a peanut butter sandwich just before working on their math homework. Those with peanut allergies substituted with a meat sandwich, protein being equal to that in peanut butter. Some peanut allergy sufferers tried an old treat their grandmothers enjoyed: banana sandwiches, and found equal relief of numberitis.
Parental Caution: Physicians and Psychiatrists agree that parents should not permit their children to eat (let alone overeat) their nightly homework. Eating paper has many known health damages, including getting stuck in the intestines, making a wad of paper, so the child cannot have a bowel movement! The inability to 'go' can severely affect the improvement of numberitis, since attention is taken away from math and becomes centered on 'going' to the bathroom. Physicians and Psychiatrists also caution that parents should never give in to numberitis! Students need to work with numbers to "cure" the numberitis inflammation. Parents should never do math homework for their child! You will never create a Math Wiz if numberitis persists!
Genetics: There is NO evidence of any genetic factor in numberitis. There is NO evidence of Pica (eating paper is one example) or any "number difficulty" in the parents, grandparents, or great-grandparents of children who develop numberitis after overeating their math worksheets. No testing has been done about the type of paper or ink, but studies ruled out any connection to parents who have tattoos.
Medications: Numberitis is best treated through working number problems. NO medication has shown the drastic improvement gotten from "doing math". There is no vaccine. But a student who does not improve the numberitis may be given very painful "F" shots in both arms and buttocks. The "F" shot is best given at the time of Report Cards, so the student has many weeks thereafter to work math problems and cure the numberitis. The "F" shots have been shown, through over 200 years of use, to correct the numberitis condition very effectively when all other means have proven less effective. The "F" shots, via studies, have been shown to be safe enough to be repeated every 9 weeks or so-- indefinitely or until "cured".
Numberitis Support Groups: Support for numberitis has never been so widely available as it is today! Sufferers can band together to achieve a group cure! Tutors can give extra aid if needed. Parents can restrict Internet and Cell Phone use, as part of their support for their children! Support, Math Practice, eating better, and a no-nonsense approach will help even the most troubled overeaters of math worksheets! CURE IS YOURS, if you practice and make numbers FUN!
Mathematics and Imagination: Working math problems needs a good mind, an imaginative mind. When you see a number, 'picture it' in your mind. Make it dance with other numbers, changing partners. Pretend the number is climbing up a wall, or coming down a flight of stairs. Picture what the number 'does' when it meets other numbers.
How to avoid Numberitis: Simple! Do your math homework!
Is Numberitis contagious -- No.
Is Numberitis a virus -- No.
Is Numberitis a bacteria -- No.
Will Numberitis go away-- YES! Just stop overeating your math worksheets and instead do the math!
Note: This is a Tongue in cheek response. Numberitis is not a real condition.
Value of 1947 Remington model 550-1 22 caliber?
Gun Traders Guide lists a value of from $87 for "good" to $242 "new in the box", but that's not what they sell for in the real world. I have 34 of the 550 series and have paid as little as $25 through $500. On average a nice model 550-1 (most any year) will sell for around $250.00............
Is pre-algebra or algebra harder?
The Latin prefix pre- means "before" so Pre-Algebra means "Before Algebra". Pre Algebra gives you the bottom bricks or the foundation of your math building. This is the most important mathematics year of your life so try not to mess it up
algebra is harder.
What is the value of a nimm 1977 coin?
Could you please explain what you mean by "nimm"? What is the coin's denomination? If it is foreign, do you know what country it came from? What image(s) and/or inscription(s) are on the coin?
When do you use a semicolon in algebra?
Well, according to what I learned when I was in Algebra I, you should never have to use a semicolon.
What is the value of a Colt 45's 1962 program?
A 1962 Houston Colt 45's program/Scorecard is worth about $15.-$25. in excellent - near/mint condition. As with all collectibles, condition is the most important factor of all providing that the item is authentic. With programs/scorecards the slightest flaws will bring the price down significantly. An exceptional mint condition scorecard could sell for more.
Common flaws would be staining, foxing (yellowing), fading, stains, creases, rips, loose pages, cracked binding, and writing on the cover. Un-scored programs will generally sell at a higher price than a scored program but sometimes it doesn't effect value. The over all condition, and how well the cover displays will.
The value on a "scored" program as opposed to a un-scored program can vary depending on the game, and collectors preference. In general I would say an un-scored program will sell at a higher price. Some collectors do not mind scored programs, or might prefer it scored. A game in note that might sell at a higher price "scored" would be Don Larsens perfect game in the World Series. I will leave a link below for more information on scorecards, and publications.
What is the US M8A1 scabbard value?
You can obtain these for about 30-60 dollars depending on who produced the scabbard.
Algebra is using variables such as x to solve a problem. One example is x+3=8 in which x equals 5.
What is difference between linear syntax and relational algebra?
They are not alternative solutions so that we can compare them.
Relational database (which is based on relational algebra) demands (atleast the founder of relational database Codd suggests) that the query language follow linear syntax. The linear syntax languages don't rely up on newline characters as terminators of expressions or statements -- instead they rely on other tokens such as semicolon or comma and so on.
What is the value of a 1964 Commemorative with serial 14?
Which commemorative? Wyoming Diamond Jubilee? What condition? sales@countrygunsmith.net
How do you do matrix multiplication in c using structure?
You took an example of The Product AB is determined as the dot products of the ith row in A and the jth column in B,placed in ith row and jth column of the resulting m x p matrix C.
so: this may help you.
#include <stdio.h>
#include <stdlib.h>
// function prototypes
void Matrix_Mult( int a1[][3], int a2[][4], int a3[][4] );
void Matrix_MultAlt( int a1[][3], int a2[][4], int a3[][4] );
int dot3(const int a1[][3], const int a2[][4], int row, int col);
void PrnNx4 (int ar[][4], int n);
//---------------------------------------------------------------------------------
// Function: main(void)
// Description:
// demonstration of Matrix Multiplication
//
// Programmer: Paul Bladek
//
// Date: 10/31/2001
//
// Version: 1.0
//
// Environment: Hardware:IBM Pentium 4
// Software: Microsoft XP with .NET framework for execution;
// Compiles under Microsoft Visual C++.Net 2005
//
// Calls: Matrix_Mult(int a1[][3], int a2[][4], int a3[][4])
// Matrix_MultAlt(int a1[][3], int a2[][4], int a3[][4])
// PrnNx4(int ar[][4]
//
//
// Parameters: int a1[][3] -- left matrix
// int a2[][4] -- right matrix
// int a3[][4] -- answer matrix
//
// Returns: EXIT_SUCCESS
// ------------------------------------------------------------------------------
int main(void)
{
int A[2][3] = {{1, 3, 4},
{2, 0, 1}},
B[3][4] = {{1, 2, 3, 1},
{2, 2, 2, 2},
{3, 2, 1, 4}},
C[2][4] = {{0, 0, 0, 0},
{0, 0, 0, 0}};
Matrix_Mult(A, B, C);
PrnNx4(C, 2);
Matrix_MultAlt(A, B, C); // alternate form that calls dot3
PrnNx4(C, 2);
return EXIT_SUCCESS;
}
//---------------------------------------------------------------------------------
// Function: Matrix_Mult(int a1[][3], int a2[][4], int a3[][4])
// Description:
// multiplies a 2X3 matrix by a 3X4 matrix
//
// Programmer: Paul Bladek
//
// Date: 10/31/2001
//
// Version: 1.0
//
// Environment: Hardware:IBM Pentium 4
// Software: Microsoft XP with .NET framework for execution;
// Compiles under Microsoft Visual C++.Net 2005
//
// Calls: None
//
// Called By: main()
//
// Parameters: int a1[][3] -- left matrix
// int a2[][3] -- right matrix
// int a3[][3] -- answer matrix
// ------------------------------------------------------------------------------
void Matrix_Mult(int a1[][3], int a2[][4], int a3[][4])
{
int i = 0;
int j = 0;
int k = 0;
for(i = 0; i < 2; i++)
for( j = 0; j < 4; j++)
for( k = 0; k < 3; k++)
a3[i][j] += a1[i][k] * a2[k][j];
}
//---------------------------------------------------------------------------------
// Function: Matrix_MultAlt(int a1[][3], int a2[][4], int a3[][4])
// Description:
// multiplies a 2X3 matrix by a 3X4 matrix -- Alternate Form
//
// Programmer: Paul Bladek
//
// Date: 10/31/2001
//
// Version: 1.0
//
// Environment: Hardware:IBM Pentium 4
// Software: Microsoft XP with .NET framework for execution;
// Compiles under Microsoft Visual C++.Net 2005
//
// Calls: dot3(const int a1[][3], const int a2[][4], int row, int col)
//
// Called By: main()
//
// Parameters: int a1[][3] -- left matrix
// int a2[][3] -- right matrix
// int a3[][3] -- answer matrix
// ------------------------------------------------------------------------------
void Matrix_MultAlt(int a1[][3], int a2[][4], int a3[][4])
{
int i = 0;
int j = 0;
for( i = 0; i < 2; i++)
for( j = 0; j < 4; j++)
a3[i][j] = dot3(a1, a2, i, j);
}
//---------------------------------------------------------------------------------
// Function: dot3(const int a1[][3], const int a2[][4], int row, int col)
// Description:
// dot product of a1 row and a2 col
//
// Programmer: Paul Bladek
//
// Date: 10/31/2001
//
// Version: 1.0
//
// Environment: Hardware:IBM Pentium 4
// Software: Microsoft XP with .NET framework for execution;
// Compiles under Microsoft Visual C++.Net 2005
//
// Calls: None
//
// Called By: Matrix_MultAlt(int a1[][3], int a2[][4], int a3[][4])
//
// Parameters: int a1[][3] -- left matrix
// int a2[][3] -- right matrix
// int row -- the row number
// int col -- the column number
//
// Returns: the dot product
// ------------------------------------------------------------------------------
int dot3(const int a1[][3], const int a2[][4], int row, int col)
{
int k = 0;
int sum = 0;
for( k = 0; k < 3; k++)
sum += a1[row][k] * a2[k][col];
return sum;
}
//---------------------------------------------------------------------------------
// Function: PrnNx4(int ar[][4], int n)
// Description:
// prints out an NX4 matrix
//
// Programmer: Paul Bladek
//
// Date: 10/31/2001
//
// Version: 1.0
//
// Environment: Hardware:IBM Pentium 4
// Software: Microsoft XP with .NET framework for execution;
// Compiles under Microsoft Visual C++.Net 2005
//
// Called By: main()
//
// Parameters: int ar[][4] -- matrix to print
// int n -- number of elements
// ------------------------------------------------------------------------------
void PrnNx4 (int ar[][4], int n)
{
int i = 0;
int j = 0;
for(i = 0; i < n; i++)
{
for( j = 0; j < 4; j++)
printf("%4d", ar[i][j]);
putchar('\n');
}
}
Does every matrix have a determinate?
No, since there is no such thing as a determinate.
And, in any case you were wondering about improving your spelling so as to make you questions more answerable, a non-square matrix does not have a determinant.
What is the value of a 1917 Newfoundland .25 coin?
Retail values range from $1 in very worn condition up to about $8 if only slight wear shows.
