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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 do you convert clothe size to sq ft?
It depends upon the type of clothing and style, so there's no one formula. For any one type of clothing, I suppose you could measure the square footage of each size and do a linear regression to obtain an equation.
How do you find the dimensions of an 84 inch traffic sign?
One dimension is 84 inches.
For the others, you would need to measure the sign.
Is 0.016 the same this as 160 percent?
To turn a decimal into a percent, multiply by 100. 0.016*100 = 1.6, so 0.016 is 1.6 percent.
What would the world be like without pi?
The Physical world does not depend on Humans or the sciences to exist. Without the understanding of sciences (or mathematics) the infrastructure that Humans have built would not exist as it does today. If we had not grasped the "Concept" of Pi, then anything built utilizing a Circle or part of a circle (Arc) would have to be constructed via trial and error. All Circle related things would be very difficult to predict or understand...such as planetary orbits, etc.
Value of 1953 browning serial 393040 worht?
Check the auction sites. To many variables that you don't address, like gauge/caliber, overall condition, accessories, box, manual, number of rounds fired, etc..
What are the origins of algebra?
While the word "algebra" comes from Arabic word (al-jabr, الجبر literally, restoration), its origins can be traced to the ancient Babylonians,[1] who developed an advanced arithmetical system with which they were able to do calculations in an algorithmic fashion. The Babylonians developed formulas to calculate solutions for problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. By contrast, most Egyptians of this era, and most Indian, Greek and Chinese mathematicians in the first millennium BC, usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Sulba Sutras, Euclid's Elements, and The Nine Chapters on the Mathematical Art. The geometric work of the Greeks, typified in the Elements, provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations, though this would not be realized until the medieval Muslim mathematicians.
The Hellenistic mathematicians Hero of Alexandria and Diophantus [2] as well as Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brahmasphutasiddhanta are on a higher level.[3] Later, Arab and Muslim mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khowarazmi was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable.
The word "algebra" is named after the Arabic word "al-jabr , الجبر" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala , الكتاب المختصر في حساب الجبر والمقابلة, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by the Islamic Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī (considered the "father of algebra"), in 820. The word Al-Jabr means "reunion"[4]. The Hellenistic mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is much debate over whether al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.[5] Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[6] Those who support Al-Khwarizmi point to the fact that he introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to,[7] and that he gave an exhaustive explanation of solving quadratic equations,[8] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[9] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."[10]
The Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. Another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various cases of cubic equations.[11] He also developed the concept of a function.[12] The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji,[13] and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations using numerical methods. In 1637 Rene Descartes published La Géométrie, inventing analytic geometry and introducing modern algebraic notation.
Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Abstract algebra was developed in the 19th century, initially focusing on what is now called Galois theory, and on constructibility issues.
What is meant by an anholonomic space and an idempotent vector?
An anholonomic space, more commonly referred to as a nonholonomic space, is simply a path-dependent space.
For example, if I went to the kitchen to get a snack, I know that, regardless of what path I take to get back to my room, I will get back to my room. I could have gone outside, on the roof, to a liquor store, or wherever, but the ultimate result from adding up all those paths is that I'll be back in my room. That is because I'm in a holonomic space, or a path-independentspace. Now, if after traveling to all those locations I came back to what I thought should be my room, but instead found myself at, say, the beach, I would be in an anholonomic space, where my destination changes depending on my path taken, ie. my destination is path-dependent.
An idempotent vector doesn't really have any meaning since the concept of idempotence applies to operations. The term idempotence basically just means something that can be applied to something else over and over again without changing it, like adding zero to a real number or multiplying that number by one. That's why a vector, in and of itself, can't be idempotent. However, multiplyinga unit basis vector, ie. one that wouldn't change the magnitude or direction of another vector, to another vector would be an idemtopic operation in a vector space.
What is the value of a 1967 Mercedes 250 sel?
Depends on the condition of the vehicle and it's mileage.
When your date asks you how much you think she weighs.
well if you use the substitution 1/y = x the formula becomes
1/y sin(y) or sin(y)/y. Now near where y = 0 (x->infinity)
sin(y)/y is approximately 1. So does that help? I'm not sure what
the hausdorff distance is. It's been a very long time since I've taken
a math course.
Why is it that 45 cannot be used as a power in math?
45 can be used as a power, or exponent, in math.
The word derives from the arabic word "al-gabr", which was in use for many years before it was used in the title of a book written in 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī. The book was entitled Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, and was the first compilation of algebraic processes.
How do you write 0.955 as a percentage?
0.955 written as a percentage is 95.5%. Whenever you turn a decimal into a percentage, move the decimal over two times to the right.
Putting a question mark at the end of a sequence of a few numbers does not make it a sensible question.
