In abstract mathematics, a very large topic is the concept of a group. This is studied in Group Theory, which at a mathematical level is the study of symmetry in a very abstract way (groups usually manifest themselves in nature in forms of symmetry) [5]. Recently, there have been various breakthroughs in group theory, such as the Classification of Finite Simple Groups (the longest mathematical proof) [7], and the three-hundred page proof that all odd-ordered groups are solvable, which won the Abel prize [6].

A group is a set of objects, called elements, that, when paired with an operation , satisfy three axioms: closure (for all elements a and b in the set, ab is also in the set), associativity (for all three elements a, b, and c, a(bc)=(ab) c), existence of an identity (there exists an element e such that for all elements a, ea=ae=a) and existence of inverses (for all elements a, there exists an element a-1 such that aa-1=e). From these axioms, a few simple consequences arise, and group theory is the study of these consequences [5].

Here is an example of a group (this group is known as the dihedral group). If we take a triangle, we can create a group with three elements. If we set the element e as the element that does nothing to the triangle, e would be the identity. We can then say that α is the element that turns the triangle 120° clockwise and α2 turns the triangle 240° clockwise. This set {e, α, α2} is associative, has closure, has an identity, and has inverses. One thing that should be mentioned, because it will be useful in the future, is the idea of a generator. If we say that e=α0, then we can say that all elements in the group can be represented as a power of α. This means that α is a generator of the group. The more complex groups can have many generators [8].

The last axiom, the existence of inverses, has caused problems in groups, because in some groups the inverse is not immediately obvious. One good example of such a group is the Rubiks...

...Please consult your syllabus and study guide for detail step-by-step group project guidelines.
Here is a reminder on your group project submission requirements for Part 1:
1. Submit team document in Microsoft Word. Submit your writing as a narrative, a list of tips or a combination. The length of paper will vary depending on number of team members and format chosen by team.
2. Include sources in APA format. All references must be cited in paper....

...Stages of group development
Group development is a process of forming a therapeutic group. There are lot of challenges and experiences that you can go through in this step. There are many stages involved in forming a group and in this essay this will be demonstrated through self and experiences being a part of a group member. There will also be examples and therapeutic suggestions that will be useful to assist with...

...Social Exchange Theory
Definition
Social exchange theory: is a social psychological and
sociological perspective that explains social change and
stability as a process of negotiated exchanges between
parties. Social exchange theory posits that human
relationships are formed by the use of a subjective costbenefit analysis and the comparison of alternatives. The
theory has roots in economics, psychology and
sociology. Social exchange...

...When Professor Saumya Pant set us this assignment she told us that we could choose any topic at all that she has touched upon in class and we have to note our response to it. It does not need to be a theory only. I read the theories and had initially thought that I would like to comment on how men are forced to conform to certain stereotypes and at times have to bottle up their emotions to ensure they are accepted by the people around them. However, 2 days before...

...
SHAASTRA CUBE OPEN - ALGORITHM MANUAL
Step 1 - The Cross
The first thing you have to do is to create a cross on the first layer, like so:
Step 2 - The Corners
The next step is to put the corners in, like this:
The corners will most likely be on the bottom layer. It is important to first put the cubie you wish to move underneath where it needs to go. That is, the white-blue-red cubie should be underneath the white-blue-red corner.
There is an algorithm for...

...colorful cubical form we know as a Rubik’scube!
However, Rubik did not give the cube his name—he called it the “Magic Cube.” It was renamed the Rubik'sCube by the Ideal Toy Corporation in 1980.
Little did Rubik know that his cube would become a sensation around the world with the first world championship held in his native, Budapest, in 1982, with a sixteen year old Vietnamese girl winning...

...IFRS 5
IFRS 5 is about non-current assets held for sale and discontinued operations, which state that the aims of disclosed discontinued operations and non-current asset disposal is to helped group of users of the financial statement to assess the financial effects. The definition of discontinued operation in IFRS may differ from other accounting standard, IFRS has defined discontinued operation is an asset or component of a company that either has been disposed or is regarded...

...CM32OX: Topics in Mathematics
Game Theory
Andrew Pressley
At first sight. the Theorv of Games’ might appear to be
a trivial pursuit. However.
game theory aims to model any situation involving conflic
t where each party (or
‘player’) has only partial control over the outcome. This
includes not only games in
the usual sense (e.g. chess, bridge, poker), but also many
situations in economics.
politics, business and management. In fact, game theory
was...

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