Framework of the Study This study requires the interplay of some Abstract Algebra (particularly group theory) and Graph Theory concepts. Abstract Algebra, occasionally called Modern Algebra, deals with the study of monoids, groups, rings, fields and other algebraic structures and their properties. The concept of group is fundamental to Abstract Algebra because other structures, such as rings and fields can all be regarded as groups endowed with additional operations and axioms. Group involves a set that is defined by and closed under a binary operation. It satisfies three conditions: associativity, existence of identity element and an inverse of every element in that set. Groups are categorized into five classifications: Abelian, cyclic, dihedral, symmetric and alternating groups (Carter, 2009). Abelian groups, named after Niels Henrik Abel (1802 – 1829), are those groups that exhibit the commutative property. A group is considered cyclic if it has an element that can generated every other element in the group. This element is termed as generator. A dihedral group …show more content…
Price (2014) stated that understanding the geometry of a graph may tell something about the underlying group. Commutative property of Abelian groups, for instance, can be seen visually in their Cayley digraphs. Carter (2009) and Willis (2001) both wrote that commutativity of a group can be checked by starting with a certain element/vertex in the digraph then walk through two arrows of different colors/types then restarting with the same vertex but traversing the arrows in the inverse order of colors/types. When this technique is done for every vertex in the digraph and the two walkthroughs of reverse orders from each vertex terminate on the same vertex, then one can say that the group is an Abelian group. Figure 1ab (on page 5) and Figure 3 (on page 7) show a non-commutative and commutative groups,
Math is everywhere when most people first think of math or the word “Algebra,” they don’t get too excited. Many people say “Math sucks” or , “When are we ever going to use it in our lives.” The fact is math will be used in our lives quite frequently. For example, if we go watch a softball game all it is, is one giant math problem. Softball math can be used in many
In this level, we are switching from individual behavior to group behavior. A group is define as two or more individual, interacting and interdependent who are initially coming together to achieve particular objectives (Stephen P.Robbins, Timothy A.Judge, 2014). There are two types of group which are formal group and informal group (Stephen P.Robbins, Timothy A.Judge, 2014). Group can bring a lot of advantages to all the group members. For instance, work as a group is able to generate positive synergy through coordinated effort that allows organization to increase performance.
* The definition of graphs, it is possible for the edge group to be empty though the graphs have some vertices. Such graphs wi...
The influence that the behaviors of groups have is one of the most important factors that help shape and contribute to a functional society. With their works, William Edward Burghardt
Just as members of an ingroup categorize themselves, in the intergroup theory we categorize outgroup members. Identities are created primarily from physical characteristics and first impressions. This is a classification created for one group about the other group.
Categorized within each group alphabetically.
Chapter Fourteen, Algebraic Thinking, Equations, and Functions, begins with defining the big ideas of algebraic and functional thinking. Each big idea is taught by combining objects and mathematical situations and the connection between the two. Algebraic and Functional thinking are taught as early as Kindergarten, where the teacher connects the mathematical situations to real world problems. Algebra is a broad concept; however, if we look at the number system, patterns, and the mathematical model we can make it explicit and connect it to arithmetic. This chapter highlights three major ways to incorporate arithmetic and algebra in the classroom: number combinations, place-value relationships, and algorithms. In each category, there are subcategories that feature properties. It continues to spotlight how to understand, apply, and use the properties presented. Furthermore, the chapter discussed the variety of patterns and functions. Student who make observations are able to understand patterns. Repeating and Growing patterns are the types of patterns seen in a classroom during mathematics. In addition, within these patterns you’ll see are recursive patterns,
Group processes and structure focuses on studying small group differences and their relationships to social structure. Researchers who follow this framework tend to do empirical studies as experimental research. There are three theories within the Group process structure.
This is when two or more people who interact with each other share a common interest, goals, experiences and needs. One group would be the the anti- purge group, they all had the common interest of stopping anyone participating in the purge. Another example would be Leo, Charlie Roan, Joe, Laney and Marco’s they share the common interest of stopping the purge but to do that , Leo has to make sure Roan stays alive so she can run for president. The reason they share this interest is because they know what it is like to lose someone in the purge and they don't want anyone killed anymore based on their wealth status. Another group would be the wealthy people, the Senator running against Roan and the New Founding Fathers of America they are considered groups because they all have the same interest of continuing the purge. The reason they want to do this is because they do not know what it is like to be poor, so they have an advantage of bringing poor people into their house to kill them so they do not have to go out on to the un-safe streets they can just kill people in their
Groups were assigned by professor and consisted of diverse students with various backgrounds. Our first task was writing group contract which involved participation of all group members and required closer contact among students. Tuckman’s Group Development Stages model can be used to show how our group worked together, as our ‘4U’ team had gone through each stage. Example of the forming stage was the first meeting when all group members tried to be polite and asked questions, such as ‘what is major?’, ‘what is your GPA?’, we tried to be kind to each other and be cautious to avoid misunderstandings in the beginning of our work. However, everything changed when we received the task to write contract and our group entered second stage of the Tuckman’s model. We experimented and tried to analyze who is doing better at brainstorming, writing, proofreading, and managing tasks. Therefore, some secondary tension occurred as all group members argued about topic, goals and norms we should establish. Our group consisted of four members which made it difficult to pass to third stage of Tuckman’s model. There was a conflict about topic; we had two ideas involving water quality problem and meal-plan issue. Both topics were interesting and challenging, there was an equal distribution of voices among these topics and group members openly disagreed, competed for a status and tried to persuade that their ideas are more important. There was not norming stage as separate, as conflicts occurred all the time, statuses of group members were also constantly changing. Group norms were continually adjusted and changing from the forming to performing stage. For instance, one of the explicit norms was that everyone should be prepared to the meeting (establi...
Groups can be defined as, any number of people with whom interact with each other, are psychologically aware of one an other and perceive themselves as a group. Effective groups are important as they endeavour to take care of each group member, get tasks done and strive to achieve their goals, whilst being stimulating, enjoyable and rewarding (Schein (1998), as cited in Fowler, Gudmundsson, & Whicker, 2011, p.16). Groups
Algebra is the only subject in school and in math that uses letters and numbers to find the answer of a problem. Algebra shows the relationship of how one solution or problem changes the other solution or problem. Algebra helps teach student’s minds to be always looking for a solution for the problem that they are faced with. Not only are student’s minds looking for solutions, but algebra encourages their minds to develop reasoning skills. Students can find that algebra is involved in their other classes and algebra helps them to think critically in these classes.
In order to analyze the differing beliefs concerning mathematics, an agreed-upon definition – or rather, description – of mathematics must be established. Merriam-Webster defines math as “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and [the science] of space configurations and their structure, measurement, transformations, and generalizations.” This definition certainly includes what most people think about when they consider what math is – complex concepts that they hope never to have to
Mathematics is the science of numbers and their operations, interrelations, combinations, generalizations, abstractions and of space configurations and their structure, measurement, transformation, and generalizations (Merriam-Webster, 2016). Mathematics is inextricably linked to science in that it plays a pivotal role in the unification, verification and exploration in science.
-People form groups seeking need satisfaction. They bring goals, values and even hopes to the group process and endeavour to find a situation in which, for the most part, they can achieve what they want. Schein has an excellent treatment of the steps of group formation and growth. The group formation and maintenance depend on shared norms, values, and so on as the glue that holds members together so they constantly seek to find and preserve commonality.