What if I asked you to solve for x in the following example:

2 + 4 x = 5

You subtract 2 from both sides to get the term involving x by itself

4 x = 3

and then divide by 4 to get just x

x = 3/4 = (5 - 2) / 4

Your problem is identical to this one, except with 5654, 188, and 52800 instead of 2, 4, and 5.

Edit: I don't know if you already do this, but solving these problems is a lot cleaner if you don't convert all the pi's into decimals right away. Just let them sit there in the equation and do one conversion at the end. That way you don't have to scratch your head and wonder if 1800*pi is the same as the 5654 you have in your equation.

i took a game theory class, was maybe best class i've ever had.

Concepts and Constructs
Every society creates its social terrain by the people who inhabit its spaces. These spaces in turn inform how those people perceive and receive the undulations (the barriers and obstructions) of the social contour. How those people negotiate the social contour is dependent upon several factors such as cultural imagery, economic resources, and linguistic utilization. These factors, a lot of times, are invisible due to their institutionalization when they are implemented as policies, statutes, and rules and regulations. The process of institutionalization is deemed to be a “natural” part of society and becomes a commonsensical part of everyday living. Despite their manufactured construction, they are promoted, implicitly and at times explicitly, as society’s necessity that reifies how things are the way they are (i.e. status quo).

Hegemony: The dominant group/culture/class is able to exercise domination over subordinate classes or groups through this process. It refers to the maintenance of domination not by the sheer exercise of force but primarily through consensual social practices, social forms, and social structures produced in specific sites such as the church, the state, the school, the mass media, the political system, and the family. By social practices, I refer to what people say or do. Of course, social practices may be accomplished through words, gestures, personally appropriated signs and rituals, or a combination of these. Social forms refer to the principles that provide and give legitimacy to specific social practices. Social structures can be defined as those constraints that limit individual life and appear to be beyond the individual’s control, having their sources in the power relations that govern society.

Hegemony is a struggle in which the powerful wins the consent of those who are oppressed, with the oppressed unknowingly participating in their own oppression.

Hegemony is a cultural encasement of meanings, a prison-house of language and ideas that is “freely” entered into by both dominators and dominated. Both rulers and ruled derive psychological and material rewards in the course of confirming and reconfirming their inequality. The hegemonic sense of the world seeps into popular “common sense” and gets reproduced there; it may appear to be generated by that common sense.

The dominant class need not impose force for the manufacturing of hegemony since the subordinate class actively subscribes to many of the values and objectives of the dominant class without being aware of the source of those values or interests which inform them.

Ideology: Hegemony could not do its work without the support of ideology. Ideology permeates all of social life and does not simply refer to the political ideologies of communism, socialism, capitalism, existentialism, and anarchism. It refers to the production and representation of ideas, values, and beliefs and the manner in which they are expressed and lived out by both individuals and groups. Simply put, ideology refers to the production of sense and meaning. It can be described as a way of viewing the world, a complex of ideas, various types of social practices, rituals, and representations that we tend to accept as natural and as common sense.
Discourse: Discourse is a family of concepts. It is a body of anonymous, historical rules, always determined in the time and space that have defined a given period, and for a given social economic, geographical, or linguistic area, the conditions of operation of the enunciative function. Discourses are made up of discursive practices. Discursive practices refer to the rules by which discourses are formed, rules that govern what can be said and what must remain unsaid, and who can speak with authority and who must listen. Thus, we can have dominant discourses, and they are seen as regimes of truth, as general economies of power/knowledge, or as multiple forms of constraint.

Truth: Truth such as educational truth, scientific truth, religious truth, legal truth etc. must not be understood as a set of discovered laws that exist outside of power/knowledge relations and which somehow correspond with the “real.” We cannot know truth except through its effects. Truth is not relative (in the sense that truth proclaimed by various individuals and societies are all equal in their effects) but is relational (statements that are considered true are dependent upon history, cultural context, and relations of power operative in a given society, discipline, institution etc.). The crucial question here is that if truth is relational and not absolute, what criteria can we use to guide our actions in the world?

Truth of a theory can only be defined by its ability to intervene into, to give us a different and perhaps better ability to come to grips with, the relations that constitute its context. If neither history nor texts speak its own truth, truth has to be won; and it is, consequently, inseparable from relations of power.

We don’t speak truth and falsehood but create domains where they are practiced!
Michel Foucault

Power: Power is not a possession but is an exercised force. Power is ubiquitous and comes in many forms. Put another way, power is multifaceted and is everywhere (tied to the creation of truth). Its meaning is linked to its effects when it is applied with intention. Power can exist in covert and overt forms. Its use can reside in provinces of passive/indirect resistance or dominant/direct oppression. Power in and of itself is not good or bad. Its determination is judged by its effects.

Truth and power: Truth is verified through praxis (informed actions) guided by phronesis (the disposition to act truly and rightly) and power, and is given meaning by application and intention.
Knowledges: Knowledges are multiplicitous. That is, there are multiple forms of knowledges and they are poly-layered and sedimentary (i.e. cyclical chronology). In this way, knowledges are not ahistorical nor are they apolitical.

Knowledges, as opposed to information, are disruptive, discomforting, and problematizing.

Knowledges are informed by, and in turn, form insights, identities, practices, and beliefs and values. Knowledges do not conform to the commonsensical understandings and deconstruct the taken-for-granted conceptions of what is or the status quo.

Knowledge construction is always problematic but is manufactured to be fluid and non-problematic.

Paradigm: A paradigm refers to the shared images, assumptions, and practices that characterize a community of people, practitioners, and scholars in a geographical area, institution, and academic field, respectively. In any specific field, one can find different paradigms; thus, it is reasonable to conclude that any field of study is usually marked by competing intellectual and normative perspectives. A paradigm governs not a subject matter but a group of people, practitioners, and scholars (Kuhn, 1970).
Paradigm, as a concept, is important not merely because it guides people, practitioners, and scholars in their work, it also illustrates that paradigms are related to the nexus of social and political values in the larger society. That is, the genesis or creation, development, and effects of a given paradigm have to be measured against wider social and cultural commitments. In other words, a paradigm might be viewed as in opposition to or in support of the dominant ideology, but it cannot be judged independently of it.
Educational, cultural, workers (i.e. teachers) are not only born into a specific historical context, they embody its history in varying ways, both as a state of consciousness and as sedimented experience, as a felt reality. Thus, educational workers can be viewed as not only products of history but as producers of history as well
Giroux, 1997

Technology and Control
..in the contemporary period, the technological controls appear to be the very embodiment of Reason for the benefit of all social groups and interests- to such an extent that all contradiction seems irrational and all counteraction impossible.

The social controls have been introjected to the point where even individual protest is affected at its roots. The intellectual and emotional refusal "to go along" appears neurotic and impotent. But the term "introjection" perhaps no longer describes the way in which the individual by [herself]/himself reproduces and perpetuates the external controls exercised by [her]/his society. Introjection suggests a variety of relatively spontaneous processes by which a Self (Ego) transposes the "outer" into the "inner." Thus introjection implies the existence of an inner dimension distinguished from and even antagonistic to the external exigencies-an individual consciousness and an individual unconscious apart from public opinion and behavior. The idea of "inner freedom" here has its reality: it designates the private space in which [woman]/man may become and remain [herself]/himself (Marcuse, 1964).

Mimesis
Today this private space has been invaded and whittled down by technological reality. Mass production and mass distribution claim the entire individual, and industrial psychology has long since ceased to be confined to the factory. The manifold processes of introjection seem to be ossified in almost mechanical reactions. The result is, not adjustment but mimesis: an immediate identification of the individual with [her]/his society and, through it, with the society as a whole.
In this process, the "inner" dimension of the mind in which opposition to the status quo can take root is whittled down. The loss of this dimension, in which the power of negative thinking-the critical power of Reason-is at home, is the ideological counterpart to the very material process in which advanced industrial society silences and reconciles the opposition. The impact of progress turns Reason into submission to the facts of life, and to too dynamic capability of producing more and bigger facts of the same sort of life. The efficiency of the system blunts too individuals' recognition that it contains no facts which do not communicate the repressive power of the whole. If the individuals find themselves in the things which shape their life, they do so, not by giving, but by accepting the law of things--not the law of physics but the law of their society.
The achievements of progress defy ideological indictment as well as justification; before their tribunal, the "false consciousness of their rationality becomes the true consciousness.”
Marcuse, 1964

Prejudice: Prejudice is a prejudgment of something or someone that/who possesses unknown qualities or characteristics. Prejudgment usually takes a negative assessment of those unknown qualities or characteristics and is attributed to that thing or person AND to the group to which that thing or person belongs, in totality. Prejudgment presupposes an institutional and social position of power or authority where a decision that is opinion-based is seen and deemed to be factual.

While prejudice is not elevated to the same legal and theoretical level of discrimination, it is a prerequisite for discrimination.
Discrimination: Discrimination is the denial of rights, opportunities, and privileges that comes with being a member of a group, institution, and society. That is, members/citizens of a nation, country, or society are guaranteed social pathways that can lead to the attainment of goals of economic, political, and cultural success and cannot and should not be denied equal access AND treatment to the legal protection that promotes the realization of those goals.

Discrimination works most perniciously and efficiently at the societal level and between groups of people. It works actively, as opposed to passively, in a particular direction and is implicated in using political authority, social influences and economic resources to achieve its goal(s). Discrimination works because we believe in its mythology. It works from the top down, not from the bottom up, thus the impoverished/poor cannot discriminate against the wealthy/rich which means there cannot be reverse discrimination.

Types of discrimination: Discrimination takes on different meanings and hues when certain social characteristics are used to define the rationale for the denial of rights, opportunities, and privileges of a group of people. If discrimination is based on racial characteristics, it is racism; if on gender, it is sexism; if on sexual preferences, it is homophobia; if on age, it is agism; if on hearing, it is audism (not autism) etc.

Stages of Social Cognitive Processing: Information that is new, unrevealed, goes through many stages of processing by the recipient. Often, the receiver of the information can choose to cease, regress, or facilitate the process at any given stage of the information acquisition dependent on the severity of the challenge of the new information to the old or acquired information and the necessity of personal liberation, respectively. The choice to stop, go backward, or move forward is based not on an individualized motive, but is based on the familial, social, moral, intellectual, cultural, and economic imperatives.

The processing of the unrevealed and challenging information a lot of times does not transition smoothly from one stage to the next and does, almost always, overlaps one another and may even regress to the previous stage.
The difficulty of transitioning from one stage to the next is based largely upon the identity association with the old information and how that information plays out in the social and cultural circumstances of the recipient. In most cases, the recipients will choose to ensconce themselves in zones of social comfort where little disruptions to their social reality can take place.

The stages of Social Cognitive Processing are:
1. Disbelief
2. Denial
3. Acknowledgement
4. Reconciliation
5. Liberation
6. Transformative action
Where are you?

Hidden curriculum: HC refers to the unintended outcomes of the schooling and societal processes. It deals with the tacit ways in which knowledge and behavior get constructed, outside the usual course materials and formally scheduled lessons. For example, classroom and employment sexism as a function of the hidden curriculum results in the unwitting and unintended granting of power and privilege of males over females and accounts for the following outcome:
• Girls start school ahead of boys in reading and basic computation, by the time they graduate from high school, boys have higher SAT scores in both areas.
• Females are matriculating more than males in colleges and universities in numbers but still make between 68 to 72 cents for every dollar doing the same jobs.
• African Americans constitute about 13% of the population in the US, 6% of which are African American males who represent more than 40% of the prison population.
• Asian Americans composed of around 2-3% of the US population. They represent more than 6-8% of the university population but less than 1% of the work force. Yet, they are seen as the “model minority” where gang violence in large urban centers is often ignored.
• Native Americans are the original settlers on the North American continent. They have the casinos.
• Welfare mothers possess a stereotypical image of an African American female with 4+ children running rampant with no value or control. Yet, a majority of welfare mothers are European American women.
• Males have more social fluidity and are assigned less social responsibilities to familial obligations. When females engage in those activities, they are seen in a different light.
• Poor people steal, rich people creatively acquire.
• Poor people commit crime, rich people make mistakes.
The 384 wealthiest families in the world own more than 40% of the wealth and more than 60% of the resources out of 6+ billion people.
What do these statements and statistics mean to you?


Questions:
1. Mimesis is a social construct that describes how we have learned to capitulated to external stimuli for the purpose of adaptation to the demands of society. It is a procedure where we give legitimacy to messages for introjection and adoption in socially ossifying structural dictates as truth.
a. What is introjection?
b. What is social ossification?
c. What is mimesis?
d. If this is how we have learned in the process of truth making, how do we unlearn it?
e. In your opinion, once we have unlearned a former truth or a falsehood, how do we go about constructing a new truth?

ow my eyes

Any thoughts? Trying to write a very good paper for this final but I feel like I am only getting half the picture on some of the questions. 10 pages so far but he said we should hit 30+ easily.

Paragraphs, do it.

Done.

I've thought about taking a Game Theory class. I've only heard good things about it.

What exactly is it about? Things like Prisoner's Dilemma? Tip-for-Tap? Granted I only took an intro Econ, so would that hinder me?

~BD

Edit: Also, if anyone can explain to me how to use the Clebsch-Gordon Table in layman's terms that would be wonderful. Its a Quantum Mechanics table, but most sites describing it brush over the details since it is just so "clearly" "obvious" how to use

Wrapped up my paper so please do not bother with reading that monster unless you just want to for kicks. Hoping he will grade for content but we shall see.

it looks like they are just tables of solutions. you find the value of m you want for the values of j1 and j2 you need and follow the chart for the values you need for m1,m2, and j, and it spits out the sum of the angular momentum.

just from breezing over this

http://en.wikipedia.org/wiki/Table_of_C ... efficients

I was actually able to work out the table, it just took a couple of practice problems to really set me in the right direction, thanks though Simon.

Hopefully anilv still checks this out, because I have some analysis questions, yet again xD. Heres the 3 that are giving me the most trouble. I just have trouble wrapping my head around these sets of continuous functions. Anywho, here they are:

1.) (a) The Arzela-Ascoli theorem asserts that if A ⊂ Rn is compact, then

B ⊂ C(A, Rm ) is compact ⇐⇒ B is closed, bounded, and equicontinuous.

Prove the forward part of the implication, i.e. that B is compact =⇒ B is closed, bounded and
equicontinuous.

(b) Let D = {f ∈ C([0, 1], R)| ||f || ≤ 1}. Show, using Arzela-Ascoli, that although D is closed and
bounded it is not compact. (This is the same set as in the previous problem, but approached
through a different argument.)

2.) Let k(x, y) be a continuous real-valued function on the square U = {(x, y)|0 ≤ x ≤ 1, 0 ≤ y ≤ 1} and
assume that |k(x, y)| < 1 for each (x, y) ∈ U . Let A : [0, 1] → R be continuous. Prove that there is a
unique continuous real-valued function f (x) on [0, 1] such that

f (x) = A(x) + ∫k(x, y)f (y) dy. (Integral is from 0 to 1)

3.) Let A ⊂ Rm be compact and let B ⊂ C(A, Rm ) be compact. Prove that B is equicontinuous as follows:

(a) Prove that the map E : C(A, Rm ) × A → Rm defined by (f, x) → f (x) is continuous.

(b) Use uniform continuity of E restricted to B × A to deduce the result.

Again, much thanks for any help, either nudging me in the right direction or showing me the light, either way Im always pleased with any help

~BD

1.
a) B compact implies that B is closed and bounded. It's closed because otherwise there's a Cauchy sequence in B with no limit point in B, and it's bounded because otherwise you can construction a sequence that grows without bound, and therefore has no convergent subsequence. Therefore, we need B compact => B equicontinuous. We're going to use the fact that every f in B is continuous. Fix x_0 in A and epsilon > 0. By definition there exists delta > 0 such that || x - x_0 || < delta implies || f(x) - f(x_0) || < epsilon. Denote delta_f to denote the dependence. Now define a new function g: B -> R by g(f) = delta_f. Since B is compact, if g is continuous then it achieves its maximum so there is some delta that works for all f in B, implying that B is equicontinuous. Let me leave to you the proof that g is continuous (since i haven't worked it out yet ).

b) By Arzela-Ascoli, it suffices to show that D is not equicontinuous in order to prove that D is not compact. Consider the set of functions f_n : [0,1] -> R defined by f_n(x) = min{nx, 1}. Set epsilon = 1 and observe that | f_n(x) - f_n(0) | < 1 only where | x - 0 | < 1/n. Therefore, there is no uniform bound on the delta value, so D is not equicontinuous.

2. Ack, I remember having this as a homework problem at one point. I don't remember how to do it, sadly. Bug me about it again later if you still can't find anyone else to help.

3. I find it odd that this question seems to imply #1.
a) If find it easier to formulate this in terms of the topological definition of continuity. It's equivalent to the epsilon-delta definition you are familiar with, and we can discuss why if you want. Anyway, the topological definition is that g: A to B is continuous if for every open set U of B, the inverse image of U under g is open in A. Sounds weird I know, but it really is just the epsilon-delta definition.

Anyway, fix y in Rm and fix epsilon > 0. We have an open ball U of radius epsilon centered at y, that is U = { z in Rm : || y - z || < epsilon}. We must show that the inverse image V of U under E is open (in the product space C(A, Rm) x A). It suffices to show that every element in V has a little open ball around it that lies completely in V.

Let (f, x) in V. By definition, || y - f(x) || < epsilon. Since f is continuous, there's an open set W in A around x such that f sends the entire open set into U (perturbing x doesn't make you land outside U). Define delta = (epsilon - || y - f(x) ||) / 2. Then the open set Z in C(A, Rm) defined by {g : || f - g || < delta} has the property that || y - g(x) || < || y - f(x) || + delta < epsilon. Therefore, we have an open set Z x W in the product space C(A, Rm) x A, containing the point (f,x) and lying completely inside V, the inverse image of U under E.

b) Since B x A is compact and E is continuous, it's uniformly continuous on the restriction.

Those are all really helpful, I think we were on the right track in some of them, but you definitely pointed us in the right direction!

As for 2, we are still having a little trouble where to even begin, but Im going to look around on the internet and see if I cant find a hint on it somewhere..

Theres 3 more that I was struggling with, but beyond that I was able to get the other 14, so I'd say that is an improvement

Heres the others:

4.) Let V be a normed vector space with norm || · ||, and define a function d : V × V → R+ by
d(x, y) = {0, x=y
{1 + ||x − y||, x =/= y

(a) Prove that d is a metric on V .

(b) Is (V, d) a complete metric space?

(c) Characterize the open sets of (V, d) (justify your answer carefully). What is another metric on V
that has the same system of open sets?

5.) (a) Prove that a sequence xn (of real numbers) converges if and only if corresponding to an arbitrary
positive number ϵ there exists a positive integer N such that for all positive integers p,

|xN +p − xN | < ϵ.

(b) Prove that the condition limn→+∞ (xn+p − xn ) = 0 for every positive integer p is necessary but
not sufficient for the convergence of the sequence xn . Hint: Consider a sequence suggested by the terms 1, 2, 2*1/2 , 3, 3*(1/3) , 3* 2/3, 4, 4 *1/4 , 4* 2/4, 4*3/4 , 5, 5*1/5 , · ·

6.) Let Cb (R, R) be the set of bounded continuous functions from R to R. Let

B = {f ∈ Cb (R, R)| ||f || ≤ 1}

where ||.|| is the supremum norm on Cb . Is B a compact subset of Cb (R, R)? Prove your claim.

Oh, there was also one more that I think I was able to answer, but I just wanted to see if my answer was right:

7.) Find a countable collection of open sets covering B = {f ∈ C([0, 1], R) | ||f || ≤ 1} that does not admit
a finite subcover.

My answer was that we take the sets (0, n/(n+1)) where n in N. Is this correct, considering that we are now dealing with continuous functions?

~BD

4.
a)
Reflexivity: d(x,x) = 0 and d(x,y) > 0 for all x≠y.
Symmetry: d(x,y) = d(y,x)
Triangle Inequality: d(x,z) ≤ d(x,y) + d(y,z)

These follow from the properties of the Euclidean norm and simple geometry.

b) For (V,d) to be complete, we need that every Cauchy sequence converges. The only Cauchy sequences of (V,d), however, are ones that terminate at some value and keep that value forever. This is because any two distinct points can never be arbitrarily close under this metric. So yes, (V,d) is complete.

c) Every individual point x is an open set since it satisfies the property of being the only point that is less than some epsilon > 0 distance away from x. Therefore, every subset of V is open, since the arbitrary union of open sets is open. This is the same as the discrete topology, induced by the metric d(x,x) = 0, d(x,y) = 1 for all x≠y.

5.
a) This is essentially asking you to prove that the reals are complete. I'm not sure what you are allowed to use since this fact is well known.

b) The previous condition obviously implies the limit condition, but not vice versa as exhibited by the counterexample.

6. We proved in 1(b) of the previous set that a very similar set of functions was not equicontinuous, and so by Arzela-Ascoli was not compact. The same argument applies here.

7. Something's not right. You are supposed to find open subsets of B, not of the real line. The counterexample I provided in the previous question deals with the fact that you can get a sequence of functions whose slope at a point approaches infinity. Maybe the cover you want is the open set of all functions whose slope is everywhere strictly less than n.

Does anyone happen to know if one can acquire something like a stat struct using an inode number rather than a filename?