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Mariah S.
Double major in Mathematics and Political Science at the University of Toronto
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Writing
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Question:

In the beginning of Thucydides’ History, the Spartan King Archidamus offers an explanation of courage that emphasizes shame and self-control (see pp. 25-28 of the Woodruff translation, i.e. sections 1.80-85).  First, analyze Archidamus’ conception of courage, by explaining the relation of his conception of courage to other Spartan ideals that Archidamus discusses, such as shame, self-control, good judgment, and moderation.  Then compare and contrast Archidamus’ ideals with the ideals embodied in Socrates’ education of the future guardians in Republic Books 2-3, with specific attention to Socrates’ desire to cultivate self-control, a proper sense of shame, and moderation in his guardians.  Do the citizens produced by Socratic education, as described in Books 2-3 of the Republic, seem likely to resemble the idealized Spartans described by King Archidamus? If so, then specify why and in which ways; if not, then explain why not. Be sure to support your views with specific examples and quotations from the texts.

Mariah S.

Calculus
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Question:

If the integral from 1 to k of (dx/(x*sqrt(x^5-1))) equals the integral from k to infinity of (dx/(x*sqrt(x^5-1))), find the value of k.

Mariah S.

This problem is relatively straightforward once you solve for the indefinite integral. You will need to use system of equations and u-substitution for this problem. First, let u = (x^5-2)^1/2; du = 5x^4/(2(x^5-2)^1/2)dx Thus, the new form of the integral becomes the integral of (2(x^5-1)^1/2/5x^4(x^5-1)^1/2) = 2/5*integral of (1/x^5) = 2/5*integral of (1/(u^2+1)) =2/5 arctan(u) =2/5arctan(sqrt(x^5-1)) + C From there, you just solve for system of equations to arrive at a numerical answer. The hard part is solving for the integral!

English
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Question:

Compare Machiavelli's understanding of virtù as explained in The Prince in comparison to Aristotle's understanding of virtue and concern for the human good.

Mariah S.

The main difference to be found between Machiavelli's and Aristotle's understanding of virtue derives from the key assumptions about how the authors believe society ought to be structured. Machiavelli's understanding of virtue aligns with his view that the many are simply tools for the ruling class, or the prince, to manipulate to further their own power. With this mentality, Machiavelli realizes that life is far from ideal and it is necessary to realize that there are instances in which utilizing vices may guarantee the safety and security of power while virtue may at times lead to one's demise. Further, Machiavelli sees virtue as a way to manipulate the many into submission. For example, Machiavelli advocates that one ought to appear Christian in values towards his subjects but not actually practice Christian virtues as they are not practical for the maintenance and acquisition of power. With this, it is clear that Machiavelli does not believe that there is an objective good or effectual truth -- one must take actions to further one's power. However, Aristotle believes in this notion of the "objective good" and believes that each citizen's end is to promote goodness and the best quality of life within the city. Aristotle holds virtue as he explains in Politics in such high regard that he believes that the virtue of the individual is more important than law. He explains laws are only guidelines and cannot prevent crime -- even if a law exists, a citizen can still break it. Thus, Aristotle argues that citizens should obey laws because of their desire to promote inner goodness and a violation of a law is net detrimental to society. In a similar light, Aristotle argues that laws should not be obeyed out of fear of punishment but out of the desire to promote the common good within society. When evaluating Machiavelli and Aristotle, it is imperative to realize that their different understandings of virtue may not necessarily be tied to their own moral standings of the realization of virtue but is actually a result of their understandings of society. Aristotle believes that the only way to establish true political order is to create a basis of goodness within political life and society whereas Machiavelli sees society as an opportunity for the elite to grab for the augmentation of their power. With this, Machiavelli sees virtue as a tool whereas Aristotle sees virtue as a foundation for modern political life.

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