StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...
Nobody downloaded yet

Lie Groups - Assignment Example

Comments (0) Cite this document
Summary
In the paper “Lie Groups” the author discusses the work of Norwegian mathematician Sophus Lie in the mid-nineteenth century, who has provided means of solving all kinds of differential equations. He found that symmetries of differential equations could be found and used systematically. …
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER93.8% of users find it useful
Lie Groups
Read TextPreview

Extract of sample "Lie Groups"

Download file to see previous pages During this period he gave lectures in mathematics to the students union. He displayed a fine talent in explaining the geometry of the heavens. To provide a means of living, while he decided on his future, he took to lecturing in mathematics. His readings of works in geometry evoked an interest in the subject and he did some original research on the real representation of imaginary quantities in projective geometry. This experience led to the decision to devote his efforts to research in geometry and life as a mathematics researcher. Five years later in 1873, he took the momentous decision of creating a theory of continuous transformation groups, which meant a deviation from his original choice of working in geometry. This research was to occupy the rest of his creative work in mathematics. This creative work of Sophus Lie was to provide mathematics with the Lie theory, Lie groups and symmetries in the solutions of ordinary differential equations (ODEs). (2)
Lie theory has evolved considerably since the days of Sophus Lie, but its basic shape stabilized for the most part upon the publication in 1946 of the pioneering book of Claude Chevalley. A short book by Cartan, which is equally pioneering, had paved the way. If we are willing to ignore a number of details, the subject has two ingredients and three correspondences. The two ingredients are Lie groups and Lie algebras.
A Lie group is a group, wherein it is possible to continuously parameterize its elements by real numbers, like rotation group, which can be parameterized by Euler angles. The significance of Lie groups is in their application to mathematical analysis, physics, and geometry. (3)
There has been sufficient study into the specific classes of infinite-dimensional Lie groups, examples of which are, groups of operators, gauge. ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
  • CHICAGO
(Lie Groups Assignment Example | Topics and Well Written Essays - 1750 words, n.d.)
Lie Groups Assignment Example | Topics and Well Written Essays - 1750 words. https://studentshare.org/mathematics/1703763-lie-group
(Lie Groups Assignment Example | Topics and Well Written Essays - 1750 Words)
Lie Groups Assignment Example | Topics and Well Written Essays - 1750 Words. https://studentshare.org/mathematics/1703763-lie-group.
“Lie Groups Assignment Example | Topics and Well Written Essays - 1750 Words”. https://studentshare.org/mathematics/1703763-lie-group.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Lie Groups

Interest groups

... The interest groups within the United s are drawn up in such a way that there is immense learning which can be attained. This paper takes a keen look at the issues which have marred America and how the same have called for devising pathways that would lead to the launch of the interest groups – the groups and bodies that essentially dictate how well related people would be looked after, especially in the event of a disaster or catastrophe. This paper studies how the roles of the interest groups within the modern day American politics has shaped up, and how these roles are translated to bring out a true message for the Americans. What is even more significant here is the fact that this study aims to find which strategies are made use...
40 Pages(10000 words)Dissertation

Strategic Groups

...?Strategic Groups Introduction Strategic groups may be defined as a group of companies or corporations that employs similarities in their various processes of production (Hunt, 1972). The company’s performance and behavior in the market are similar hence the term strategic groups. This paper aims at discussing the rivalry that strategic groups face and how they aim at neutralizing the competition. The paper discusses the rivalry between Google Incorporation and other rivalry groups that offer similar services and products. Google and Microsoft have been on market command wars while Samsung and Apple have also been battling it on the mobile phone productions. Google in particular has several strategic advantages that have enabled...
6 Pages(1500 words)Essay

How to lie in Statistics

... percent (14). For example, the best way to have a 100 percent assurance that there are 47 percent male students staying in a dormitory is to count all the all males living in the dormitory (15). The sample results normally represent the average characteristics of the entire population. In statistical parlance, the mean is also known as the average figure or choice of the entire population. In layman’s terms, any person would act in the average manner in the same given situation. However, there are people who prefer to violate the normal or average action or reaction of the group or community (51). These are exemptions to the general rule or average findings of the population. Based on the above discussion, I theorized the lie should...
4 Pages(1000 words)Essay

Instruction Groups

...Instructional Groups The placement into groups is an effective strategy in the teaching and learning process. This paper discusses situations in which whole group instruction, within-class grouping and flexible grouping can be combined within the classroom. Whole group instruction refers to the presentation of material to all the students at the same time. Students are not separated into different groups for instruction. The teaching method, resources, and time of delivery are the same for each student. Within-class grouping involves the categorization of students into groups based on their ability or performance level. Thus, the teacher may have a number of high achievers in one group and low achievers in another. Students enter...
4 Pages(1000 words)Essay

Noble Lie and Platos Republic

... Noble Lie and Plato’s Republic Noble lie is a myth or not a true thing that is clearly in religious nature. In Plato’s republic, this lie is told by elite or the ruling class to the ruled or the common man to maintain social harmony. In this paper there will be discussion both in favor and against the noble lie. In the context of imaginary challenge of Meletus to Socrates regarding Noble lie, the conclusion and analysis after the discussion will be that lying is against the enquiry of nature according to Socrates or by scientific procedure that ensures revealing of facts and truth. The noble lie, though it is told for the sake of social harmony, it develops ignorance in common man and suppresses his opposition or nature of enquiry in his...
8 Pages(2000 words)Essay

How to Lie with Statistics

... Group Review of ‘How to lie with statistics’ by Darrell Huff. The book simply talks about how precise a collection of can be. In addition, it gives the insight of what statistics and estimations are all about. In fact, the book shows vividly that statistics can lie and the estimations made are not fully reliable because the data collected simply represent a few numbers of real values and neglects the larger number. Statistical Lie. A class is made up of thirty students. Five have A’s, 7 have B’s and the rest have failed. A person decides to run a survey on class performance and samples only ten students. He falls only on the failed students and samples them. He later concludes the all the students in class have failed. Therefore...
1 Pages(250 words)Essay

How to Lie with Statistics

If the bottom of a line or bar chart is truncated, the difference can seem larger than real and can prove useful to the illustrator of the project.
The book suggests that the choice of the proportion of x and y-axis can change the perspective as well it is simple to do with modern software available now. He also shows how two or three-dimensional objects can be used to change the perception of the viewer. The writer provided many examples of how biased examples can give way to inaccurate results. He says drawing average to depict statistics can give wrong inference to common people and it is essential to know the range and median for correct information reflection. For example, average salary alone cannot give complete informat...
4 Pages(1000 words)Essay

Diversified groups

...Diversified Groups Different groups working on a plant floor exhibit different levels of performance, with some performing better than others. The extent to which a group performs well depends upon a range of factors that include but are not limited to synergy and harmony among the group members, clarity of goals, strategic planning directed at achievement of goals, leadership and management of the group. The performance of a group depends upon the performance of the members it is composed of; “The energy and talent on teams comes from individuals” (March, 1991). When the members in a group are talented and skilled, are clear about the goals they want to achieve and their individualistic and collective responsibilities in that, and deem...
1 Pages(250 words)Coursework

The Ways We Lie

... Institute Lying, it has become a part of human lives since they do it from the moment we wake up, move around the house, get on the bus, or train to our workstations until the moment we get back to our houses again to rest. We all do have our reasons to tell a lies or a series of lies, some of which is right, while others will consider it wrong on every angle (Ariely, 2008). According to three philosophers, St. Augustine, Immanuel Kant, and St. Thomas Aquinas, there is no ethical reason to prompt you to lie. What is a lie? From various definitions, we get to understand what a lie or what lying is. It has different definitions: 1. To give false information intentionally.-Wiktionary 2. The act of conveying a false intention or image...
7 Pages(1750 words)Research Paper

Interest Groups

...Interest groups Interest groups promote specific issues or positions, which enable them to take a non-partisan approach to politics. Political parties on the other hand, must have a generally unified view on politics even though all its members may not agree on details. Political parties field candidates that are drawn from their party for elective posts. Interest groups support any political party or candidate that favors or promotes their issue or position as far as legislature or governance is concerned. Interest groups serve as an important check and balance to political power as they serve as a representative of public opinion. Politicians are well aware of the popularity of interest groups and their ability to sway public opinion...
1 Pages(250 words)Essay
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.

Let us find you another Assignment on topic Lie Groups for FREE!

Contact Us