What are the five continents that Jared Diamond refers to in Guns, Germs, and Steel and what were the settlement patterns of each?

The five continents to which Jared Diamond refers in Guns, Germs, and Steel are Eurasia, Australia, Africa, North America, and South America. The settlement patterns include humans first appearing in Africa, then expanding to the other continents. Humans went from Africa to Eurasia and Australia, and then to North and South America.
The settlement by humans of the continents resulted in the societies that we now have. Diamond argues in Guns, Germs, and Steel that these geographic trends resulted in variations in terms of which societies proved more technologically advanced than others. For example, he argues that European terrain favored the development of writing and agriculture.

Most books that set out to recount world history concentrate on histories of literate Eurasian and North African societies. Native societies of other parts of the world—sub-Saharan Africa, the Americas, Island Southeast Asia, Australia, New Guinea, the Pacific Islands—receive only brief treatment, namely as concerns what happened to them very late in their history, after they were discovered and subjugated by western Europeans.

The main thrust of Guns, Germs, and Steel is the argument that geography, rather than inherent human traits such as intelligence, determined why European and Asian societies conquered other societies, such as those of Africa. According to this argument, factors outside of humans, such as infectious germs, can take more responsibility for social outcomes than humans themselves.

When analyzing the settlement patterns of human populations, Diamond references the continents of Eurasia, Africa, Australia/Oceania, North America, and South America. Diamond concludes that there are clear factors which determined why humans migrated and settled in some environments more than others, mainly the availability of resources/materials (such as water, minerals, land, plants, and animals) and conditions (such as weather, geographic positioning, location relative to other lands, and threat potentials). Favorable conditions allowed for larger states and greater technology to develop.
Diamond explains that the shape, size, and location of continents affected the migration and sustainability of human groups. He claims that isolation thwarts innovation and modernization, limiting settlement; therefore, the settlement of Australia/Oceania took longer due to the isolation of the continent. He also argues that the continent of Eurasia allowed for greater success in settling, due to east–west, travel than the continents of North and South America, where people faced north–south travel with drastic climate changes. Human groups situated along the same latitudinal axis shared similar seasons and climates and, thus, easier travel; this allowed for the exchange of more ideas, trade, resources, and technology. Settlements and cultures thrive in sustainable, advantageous conditions. Thus, cultural diffusion occurred more readily throughout Eurasia and into the northern coast of Africa, due to close proximity.

Diamond‘s five continents are the ones with human life: North and South America, Africa, Australia, and Eurasia. Antartica is not discussed since it has never independently supported human life. Diamond’s thesis is deceptively simple: human civilization developed and spread according to the geographic orientation of land masses. That is, civilization spread most easily from east to west (or west to east); this is because climate tends to stay the same on similar latitudes. It was easier for domesticated grains to spread to areas with similar climates and growing seasons than to spread to places that were much colder or hotter. In this way, agriculture could easily spread from the Fertile Crescent west toward the the Mediterranean but not as easily north to Northern Europe. Another factor that influenced the spread of technology and agriculture, according to Diamond, was geographic isolation; Australia, for example, was never able to develop agriculture on its own, despite being ahead of other regions in other ways (for instance, in the development of water craft).

Most geographers assume that the world can be divided into six continents, corresponding to the six major landmasses of Africa, Antarctica, Eurasia, Australia/Oceania, North America, and South America. Diamond discusses five of these. The single exception is Antarctica, as it has no indigenous human life and is therefore not relevant to his work.
In terms of settlement patterns, Diamond emphasizes that the land mass of Eurasia is laid out to make east-west trade and travel relatively easy, so that civilizations could exchange resources and ideas, something that facilitated the development of advanced civilizations. Africa and the Americas, by contrast, are laid out primarily on north-south axes, with many barriers to trade. Australia and Oceania are surrounded by oceans, limiting cultural cross-fertilization. 
Diamond also discusses how favorable conditions for agriculture led to early dense settlements in Eurasia, something that also fostered the development of advanced civilizations.

I'm writing an analysis essay on James Hogg's The Brownie of Bodsbeck. I've received feedback suggesting I connect how the nationalistic and ideological struggles coincide with the fight for gender equality through Nanny. It has also been suggested that I show that Hogg’s depiction of Nanny’s nationalistic pride directly fuels her fervor for feminine agency. How can I show this? "Through his depiction of Nanny and Katherine, Hogg shows that the fight for ideological freedom and the fight for gender equality need not be mutually exclusive." What does this mean?

From the information given in this question, it sounds as if your editor would like to see a further demonstration in your essay of the two female characters and how their struggles mirror the larger national issues in the story. The Brownie of Bodsbeck is known for Hogg's unconventional female characters, who do not conform to stereotypical female roles. Katherine's importance to the nation, despite the fact that she is unmarried and denies courtship with the "Highland hero," gives Scotland a new kind of heroine that is set apart from earlier symbolic Scottish figures. Other characters are male but are lower-class in Scottish standards, yet play a vital part in helping their country. Hogg is showing how two non-traditional types of national hero are nonetheless hugely important to their nation. Many characters deny Katharine's usefulness and are even frightened of her, but Nanny is one of the few that can see through the former "ideals" to the new revolution that is coming true in reality. The feedback from your instructor implies that he/she would like you to juxtapose these two characters and their femininity with the larger picture of Scottish politics and freedom.

How does Virginia's goodness win over Simon's evilness?

I don't know if I would go so far as to say that Sir Simon is evil. I'd describe his ghostly activities more as "naughty;" however, in life, he did kill his wife for being too plain. That is quite evil. If a reader views this story as a battle of good versus evil, then Sir Simon is the story's evil bad guy, and the Otis family would be the heroic good guys. Virginia is the member that ultimately vanquishes evil from the Canterville Chase. The key difference from a typical good versus evil battle, though, is that Virginia's goodness doesn't defeat Sir Simon's evilness in any kind of pitched battle. She accidentally comes across the ghost late in the story, and she kindly asks him to stop pestering her family.

"I am so sorry for you," she said, "but my brothers are going back to Eton to-morrow, and then, if you behave yourself, no one will annoy you."

From this point forward, Virginia and Sir Simon have a cordial conversation with each other, and she learns what happened in his past and why he is haunting the house. As the conversation continues, Virginia learns that Sir Simon is actually quite tired of the haunting. He wants it all to be over.

"Please don't go, Miss Virginia," he cried; "I am so lonely and so unhappy, and I really don't know what to do. I want to go to sleep and I cannot."

He cannot enter his eternal rest unless he has Virginia's help. She must escort him to the Garden of Death. He will be granted access because he is with the pure and innocent Virginia. She agrees to do this, and Sir Simon is released from his haunting. Virginia's purity, innocence, and goodness is ultimately what allows Sir Simon to finally move on. Her goodness doesn't so much as overcome his evilness as it does guide him to eternal rest.

Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 12

Suppose that $\displaystyle f(x) = \frac{x^2}{x^2 + 3}$

a.) Determine the intervals on which $f$ is increasing or decreasing.

If $\displaystyle f(x) = \frac{x^2}{x^2 + 3}$, then

By using Quotient Rule,


$
\begin{equation}
\begin{aligned}

f'(x) =& \frac{(x^2 + 3)(2x) - x^2 (2x)}{(x^2 + 3)^2}
\\
\\
f'(x) =& \frac{6x}{(x^2 + 3)^2}

\end{aligned}
\end{equation}
$


Again, by using Quotient Rule


$
\begin{equation}
\begin{aligned}

f''(x) =& \frac{(x^2 + 3)^2 (6) - 6x (2 (x + 3) (2x))}{((x^2 + 3)^2)}
\\
\\
f''(x) =& \frac{6 (x^2 + 3) [(x^2 + 3) - 4x^2]}{(x^2 + 3)^4}
\\
\\
f''(x) =& \frac{6x^2 + 18 - 24x^2}{(x^2 + 3)^3}
\\
\\
f''(x) =& \frac{-18x^2 + 18}{(x^2 + 3)^3}

\end{aligned}
\end{equation}
$


To find the critical numbers, we set $f'(x)$, so..


$
\begin{equation}
\begin{aligned}

0 =& \frac{6x}{(x^2 + 3)^2}
\\
\\
0 =& 6x

\end{aligned}
\end{equation}
$


The critical number is $x = 0$

Hence, we can divide the interval by

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f'(x) & f \\
\hline\\
x < 0 & - & \text{decreasing on} (- \infty, 0) \\
\hline\\
x > 0 & + & \text{increasing on} (0, \infty)\\
\hline
\end{array}
$

These values are obtained by evaluating $f''(x)$ within the specified
interval. The concavity is upward when the sign of $f''(x)$ is positive. On the
other hand, the concavity is downward when the sign of $f''(x)$ is negative.

b.) Find the local maximum and minimum values of $f$.

We will use the Second Derivative Test to evaluate $f''(x)$ with the critical number:

So when $x = 0$,


$
\begin{equation}
\begin{aligned}

f''(0) =& \frac{-18(0)^2 + 18}{(0^2 + 3)^3}
\\
\\
f''(0) =& \frac{2}{3}

\end{aligned}
\end{equation}
$



Since $f'(0)$ and $f''(0) > 0, f(0) = 0$ is a local minimum.

c.) Find the intervals of concavity and the inflection points.

We set $f''(x) = 0$ to determine the point of inflection, so..


$
\begin{equation}
\begin{aligned}

f''(x) = 0 =& \frac{-18x^2 + 18}{(x^2 + 3)^3}
\\
\\
0 =& -18x^2 + 18
\\
\\
18x^2 =& 18

\end{aligned}
\end{equation}
$


The points of inflection are $x \pm 1$

Let's divide the interval to determine the concavity

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity} \\
\hline\\
x < -1 & - & \text{Downward} \\
\hline\\
-1 < x < 1 & + & \text{Upward} \\
\hline\\
x > 1 & - & \text{Downward}\\
\hline
\end{array}
$

These data obtained by substituting any values of $x$ to $f'(x)$ within the specified interval. Check its sign, if it's positive, it means that the curve is increasing on that interval. On the other hand, if the sign is negative, it means that the curve is decreasing on that interval.

Explicate the poem "Names" by Robert Hayden.

This poem by Robert Hayden partly describes his own life and the realization that the name he was raised with is not the name of his birth parents. However, some African American readers have also taken this poem as representative of their own feelings upon realizing that the names used by their families are, ultimately, names taken from slave owners, not their original names. This feeling has been famously expressed by Malcolm X.
At the beginning of the poem, the speaker is a bookish child who is called names such as "Four Eyes" because he wears glasses. This causes him to retreat into books, "Tom Swift and Kubla Khan."
When he reaches his "fourth decade," the speaker discovers that the name he had always believed was his own—as opposed to the false names people called him—was, in fact, a false name too. This makes him feel disoriented, but he ultimately realizes that it does not matter—those who lied to him "are dead," "like the life my mother fled." Whatever has happened to him in the past does not really matter, and yet, he cannot help pausing to consider what might have been, "the life I might have led." Knowing how he has been lied to, the speaker cannot help but feel that he is in some way "a ghost, an alter ego" of the self he perhaps should have been.

"Names" is a semi-autobiographical poem. The first stanza details the taunting that Hayden endured as a child due to his "extreme nearsightedness":

Once they were sticks and stones I feared would break my bones: Four Eyes. And worse. Old Four Eyes fled to safety in the danger zones Tom Swift and Kubla Khan traversed

The "safety" appears to be the young Hayden's retreat into fiction ("Tom Swift") and poetry ("Kubla Khan"). For Hayden, whose home life was also a place of anger and violence, the books may have offered the only safety that he could find.
The second stanza seems to address his newly discovered knowledge of the fact that he had been raised by "foster parents" after his birth parents left him:

When my fourth decade came, I learned my name was not my name. I felt deserted, mocked. Why had the old ones lied? No matter. They were dead.

The "old ones" refer to the foster parents who raised him. Now, his real name—the one he thought was "real" due to blood ties—becomes another source of mockery, another indirect way of being made to feel inadequate and unwanted.
In the third stanza, "the name on the books" has a possible double meaning. It could refer to the names of the authors or historical figures that Hayden read in his youth or his legal name, which has no standing because he is not "on the books." His loss of a name leads him to question his overall identity. Who is he, if not Robert Hayden? Does he really exist, or is he existing as a version of another self he will never know?
https://www.poetryfoundation.org/poets/robert-hayden

What different attitudes do the two waiters express about the old man?

Even though the two waiters understand that the old man is lonely and has recently attempted suicide, the younger waiter remains unsympathetic. He himself, he says, would not want to be that old; an old man "is a nasty thing," he says, even though the older waiter points out how clean the old man is. The younger waiter is impatient because the old man is the last customer and is keeping him from going home to his wife.
The older waiter, on the other hand, is more understanding of the old man's loneliness. As he says to the younger waiter,

I am of those who like to stay late at the café . . . With all those who do not want to go to bed. With all those who need a light for the night.

Unlike the younger waiter, who has "youth, confidence, and a job," the older waiter understands the nothingness the old man faces— the sense of uselessness or used-upness that perhaps led him to attempt suicide and that causes him to stay late at the café . The older waiter understands the appeal of a "clean and pleasant" place with good light and no music.
It's not clear what the root cause of the old man's troubles might be, but the specifics of his situation are unimportant. What matters is that the older waiter is sensitive to the same sort of emotional void the old man feels. At the end of the story, for lack of a better term, the older waiter labels that void as "insomnia."

The younger waiter finds the old man burdensome, and he is unsympathetic about his suicide attempt, saying to the deaf man, "you should have killed yourself last week." He acknowledges to the other waiter that he knows the old man is lonely, but he still wants him to leave so that they can close the cafe and go home. He tells the other waiter that he wouldn't want to be old like the man, asserting "an old man is a nasty thing."
The "unhurried," older waiter seems to know more about the old man, such as that his niece was the one who cut him down during his suicide attempt by hanging. He defends the old man, telling the other waiter that the old man needs a "clean and pleasant" "well-lighted" cafe in which to drink at night. He does not see the old man as a burden and believes that staying open another hour will be a kindness that the old man deserves. The older waiter expresses empathy for the old man, while the younger waiter expresses only impatience.

What is the theme of freedom and loss of innocence in Lord of the Flies?

The book is about a group of boys who end up stranded on a deserted island in the middle of a war when their plane crashes.  They have no adults, since the only adults die in the plane crash and no one knows where they are.  The theme of freedom and loss of innocence is explored by the boys’ reaction to their situation. 
The boys have to set up a little society on their island.  They begin by electing a leader.  They choose Ralph because he found a conch shell and blew it, bringing them all together.  This symbolic leadership is all they have.  

They obeyed the summons of the conch, partly because Ralph blew it, and he was big enough to be a link with the adult world of authority; and partly because they enjoyed the entertainment of the assemblies. But otherwise they seldom bothered with the biguns and their passionately emotional and corporate life was their own. (Ch. 4) 

Ralph has trouble keeping everyone in line. He can’t get things accomplished.  He wants to get a signal fire going and tended.  He wants to get shelters built.  He wants to keep the boys together and organized.  Unfortunately, it is sort of like herding cats.  The older ones are uncooperative and the younger ones are ditzy. 
The other complication in the boys’ efforts to enjoy their freedom, and directly related to their loss of innocence, is the contrasting personalities of Jack and Ralph.  Ralph wants order and democracy.  Jack wants adventure and control.  Ralph tries to placate him by assigning him the leader of the hunters, but this is the beginning of the end for the boys. 
The descent into anarchy and loss of innocence the boys experience is a direct result of their inability to compromise.  Jack and Ralph cannot agree, and Ralph has no leadership skills to speak of.  The hunts for the pig become more and more violent.  The boys begin celebrating with pig dances.

Then Maurice pretended to be the pig and ran squealing into the center, and the hunters, circling still, pretended to beat him. As they danced, they sang.
“Kill the pig. Cut her throat. Bash her in.”
Ralph watched them, envious and resentful. (Ch. 4) 

Especially as war paint gets involved, the pig hunts become symbolic of the lifestyle the boys are turning to.  It is less about democracy and maintaining order, and more about the fun of the hunt, the taste of the meat, and the pull of the savagery.  The first time the dance gets out of hand, the boys kill Simon imagining he is the Beastie.
After the death of Simon, the schism is complete and Ralph knows he has lost.  Any connection to the civilized world, and the innocent nature of the boys' past, is gone.  By the time Piggy is killed, it is not much of a shock to the reader.