Other than Ralph, who are two other characters that lose their innocence in the novel Lord of the Flies, and what are some examples to prove it?

Aside from Ralph, the characters of Maurice and Roger also lose their innocence throughout the novel Lord of the Flies. At the beginning of the novel Maurice is portrayed as a funny, helpful boy. In Chapter 2, Maurice helps the boys gather driftwood for the fire, and in Chapter 5 he makes the boys laugh to cheer them up towards the end of a depressing meeting. Roger is also viewed as a helpful, positive character at the beginning of the novel. In Chapter 1, Roger is the first to suggest that the boys choose their leader via a vote, and in Chapter 2 he also partakes in gathering driftwood for the signal fire. The boys' behavior is innocent because they are acting civilly and have not yet partaken in savage acts.

There are several critical moments throughout the novel that depict Maurice and Roger's decent into savagery and loss of innocence. In Chapter 4, Maurice and Roger are walking past the littluns building sandcastles on the beach, when Roger begins destroying the sandcastles. Maurice follows along and begins kicking down the sandcastles. Maurice "felt the unease at his wrongdoing" because in his old life he would have been chastised for ruining the boys' sandcastles. (Golding 60) Later on in Chapter 4, Roger begins to throw stones at Henry, but purposely misses. Roger purposely missing is significant because it depicts the remnants of civility still left in his memory, and his remaining innocence, which is waning.  

After joining Jack's savage group of hunters, Maurice becomes so involved that he suggest the boys use a drum for ceremoniously slaughtering pigs. In Chapter 10, Maurice has completely descended into barbarism, and he accompanies Jack and Roger to steal Piggy's glasses. Roger turns into a sadist by the end of the novel, and there are several scenes that portray his brutal behavior. In Chapter 8, Roger viciously stabs the pig up its rear and laughs about it, and in Chapter 11 Roger rolls a boulder, killing Piggy. Maurice and Roger's participation in savage acts and support for Jack's tyrannical leadership prove they have completely lost their innocence.

Am I going against God's creation for enjoying Surrealism so much?

The Surrealism movement began in Paris in the 1920s and continued through the 1960s, although people still use the word "surreal" frequently to describe artistic work that embodies the principles these artists followed. Andre Breton (who also created Dada, a literary art form employing random collections of words) founded the movement in 1924 when he wrote "The Surrealist Manifesto," but the term "surrealism" was first used by Guillaume Apollinaire, in the review of a ballet created by Pablo Picasso, Leonide Massine, Jean Cocteau, and Erik Satie. These artists, as well as Salvador Dali, Joan Miro, Marcel Duchamp, Rene Magritte, Marc Chagall, and Max Ernst were a few of the artists whose work came to be associated with this movement.

Psychoanalysis was being more widely known and read about at this time, and the Freudian concepts of repression and unconscious desire were important to the Surrealists, who believed that people are often encouraged to repress their inner thoughts and feelings out of fear or guilt. There are contemporary artists who are considered modern Surrealists, such as Jacek Yerka, Mark Ryden and Vladimir Kush.

I think your question has to do with Surrealism's representation of unusual beings (chimeras, or creatures who combine parts of different animals) and strange portrayals of humans who do not conform to the so-called "normal" ways we view such things. Interestingly, such creatures are now potentially possible through the wonders of gene-splicing and genetic engineering!

There is a great deal of religious art that has been produced throughout history, and one way of looking at Surrealism is to appreciate the artists' attempts to explore the intimate recesses of the human mind, much as science is a way of exploring human potential of knowledge of the known universe. If your belief system dictates that God created Man in his own image, then the existence of intelligent and creative beings can be seen as something that God is in favor of. Then again, humans do a lot of things that do not seem to agree with what God had in mind...

I think if you enjoy this art and find it stimulating, you can view it as a celebration of the human spirit, an appreciation of human endeavor, and the joy and wonder that creativity can bring to us all.

Where is the symbolism in To Kill a Mockingbird?

Perhaps the most important symbol to discuss in To Kill A Mockingbird is the symbolism behind the mockingbird. The title is more than just a title but is a symbol for what is to come in the story. The mockingbird symbolizes innocence, so the title means that innocence is being killed or destroyed. Throughout the book, there are several characters who can be viewed as mockingbirds, such as Jem, Tom Robinson, Dill, and Boo Radley. This means that they are innocents who are damaged or destroyed by evil. After Tom Robinson is shot, Mr. Underwood even compares his death to the act of killing a songbird. Additionally, the fact that Jem, Scout, and Atticus have the last name Finch, which is a type of bird, may portray that they are vulnerable in the racist town of Maycomb.

Another symbol in To Kill a Mockingbird is Boo Radley. Boo Radley is used within the story as a means to show how Jem and Scout mature and grow throughout the story. In the beginning, Boo is a town superstition that frightens the children. This shows how innocent Jem and Scout are and that their beliefs are not based on their own, real experiences, but they are based on the beliefs of those around them. As the story continues, and Boo leaves presents for the children and mends Jem's pants, the children begin to see Boo as an intriguing and real human being, not just the town spook. In the end, they realize that he is a kind and understanding person, a mockingbird in his own right, a child damaged by a ruthless father. The changing relationship between the children and Boo Radley serves to reveal Jem and Scout's growing maturity and moral awareness.

What's Roger's role in chapter 11 of Lord Of The Flies?

Roger acted as a sentinel at the Castle Rock where Jack and his tribe had set up a fort. It was his job to sound the alarm when Ralph or any of the others approached. His duty was made clear when Jack at one point asked him why he wasn't on watch. He explained that he had just come down, but did not complete his sentence.

Roger was one of the older boys and Jack's right hand. He therefore could be deemed second in command. He was one of the choirboys and was a member of Jack's hunters. Throughout the novel, he is painted as a dangerous character, one with an almost instinctive leaning towards evil. He was secretive and seemed not to like attention as illustrated in the following extract:

There was a slight, furtive boy whom no one knew, who kept to himself with an inner intensity of avoidance and secrecy. He muttered that his name was Roger and was silent again.

Golding consistently paints him as a sinister character who is quite cynical as in the following examples:

The dark boy, Roger, stirred at last and spoke up.

Roger took the conch and looked round at them gloomily. “I’ve been watching the sea. There hasn’t been the trace of a ship. Perhaps we’ll never be rescued.”

Roger is also deliberately destructive and seems to enjoy scaring and even hurting others. He intentionally destroys the littluns castles and later throws stones at Henry whilst hiding from view.

He was not noticeably darker than when he had dropped in, but the shock of black hair, down his nape and low on his forehead, seemed to suit his gloomy face and what had seemed at first an unsociable remoteness into something forbidding.

When he and Jack capture a pig, it is Roger who seems to relish the idea of inflicting pain on the helpless creature:

Roger found a lodgment for his point and began to push till he was leaning with his whole weight. The spear moved forward inch by inch and the terrified squealing became a high pitched scream.

It is therefore hardly surprising that he is responsible for Piggy's horrific death. Roger had intentionally pushed on a lever to dislodge a large rock which bounded down, first shattering the conch and then knocking Piggy over the ledge, hurtling him forty feet down to his demise. 

Write out a table of indices modulo 23. Express all the other primitive roots of 23 as powers of 5.

Modular arithmetic has a lot of weird properties we don't find in conventional arithmetic. The idea that you can get any number mod 23 by raising powers of 5 is pretty strange, but it's true.

Let's first review what we mean by "primitive roots of 23". A primitive root modulo n is a number g such that every number a coprime to n is equal to some power of g, mod n; that is,

`forall a exists k : g^k equiv a mod n`

The value of k, the power you have to raise to, is the index.

Since 23 is prime, this is really all a (other than 0), whereas for a composite base (such as mod 8 or mod 10) we'd have to exclude factors of the base.

So what we're looking for is the numbers g that satisfy this, as well as the values of k that make it work.

I think the simplest way to start is just to write out a table of values and their powers, mod 23. (I think this is what your teacher means by an "index table", though that can also mean a couple of other things.) Most of the powers will eventually end up with an infinite series of 1s at the end.

A few of them will have every single number somewhere in their list; those are the primitive roots of 23.

original value | powers
0 | 0, 0, 0, ...
1 | 1, 1, 1, ...
2 | 2, 4, 8, 16, 9, 18, 13, 3, 6, 12, 1, 1, 1, ...
3 | 3, 9, 4, 12, 13, 16, 2, 6, 18, 8, 1, 1, 1, ...
4 | 4, 16, 18, 3, 12, 2, 8, 9, 13, 6, 1, 1, 1, ...
5 | 5, 2, 10, 4, 20, 8, 17, 16, 11, 9, 22, 18, 21, 13, 19, 3, 15, 6, 7, 12, 14, 1, 1, 1, ...
6 | 6, 13, 9, 8, 2, 12, 3, 18, 16, 4, 1, 1, 1, ...
7 | 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20, 2, 14, 6, 19, 18, 11, 8, 10, 1, 1, 1, ...

And so on; so I'm not doing all your work for you, I'm going to leave you the rest of the table to finish.

If you have access to a programming language, here's a nice little script (in Python, but easily translatable to other languages) that will print out the powers of g mod n for you (just plug in for g and n; you could even run a for loop over them):

x = g
while (x > 1):
    print(x)
    x = (x*g)%n

Or you can do it by hand of course. It's tedious, but not complicated.

Instead, I'm going to focus on the part that comes after you finish the table.

Notice how every number from 1 to 22 is somewhere in the table for powers of 5. That means 5 is a primitive root of 23.

The same is true of the powers of 7; so 7 is also a primitive root of 23.

Since you can get any number as a power of any primitive root, that means you can also get any other primitive root as a power of any primitive root.

We picked 5 as our favorite primitive root, so we want to express 7 as a power of 5. Read through the table, and you'll find that 7 = 5^19 mod 23.

You could just as well have chosen 7 as your favorite and found that 5 = 7^7 mod 23; but we were told to make 5 our favorite.

Hopefully you can take it from here. Complete the table; any rows that contain all numbers from 1 to 22 are primitive roots. Go back to the row for powers of 5 and find the column equal to that number; then you can express the new primitive root g as some power of 5.

What are the five types of organizations? I have normative, coercive, and utilitarian, but the chart asks for five?

Normative, coercive, and utilitarian and the three formal organizational structures.

When five structures are involved, we are commonly talking about Mintzberg's Five Types of Organizational Structure.

• 
  Entrepreneurial - A generally loose organizational structure driven by creativity, yet often featuring low discipline. A tech startup managed by its founders is one example.


• 
  Professional - Featuring a moderate level of bureaucracy and driven by professional and competent workers, often with highly specialized skills.


• 
  Machine - Characterized by a high level of bureaucracy. Feature high structure and are often long-lived, but have limited openness to new ideas. Government agencies are examples.


• 
  Divisional - Typical of large corporation which divide themselves into more focused business unit, each responsible for a distinct set of product lines.


• 
  Innovative - A structure designed to allow for brand new leadership styles focused on decentralized decision making. Often seen in emergent industries.

How did Jem get even with Scout for contradicting him about "Hot Steams"?

In Chapter 4, Dill tells Scout that he has the ability to smell death and that she will die in three days. Jem tells them to hush and says, "you act like you believe in Hot Steams." (Lee 48) Scout responds by saying, "You act like you don't." (Lee 49) Jem explains that a "Hot Steam" is a lonely soul that cannot get into heaven and wallows around on lonesome roads at night. The consequence of walking through a "Hot Steam" is that you will become one when you die. Jem tells Dill that you have to say, "Angel-bright, life-in-death; get off the road, don't suck my breath" to avoid from being wrapped by one. (Lee 49) Following the conversation about "Hot Steams," the children decide to roll the tire. Jem is still upset that Scout contradicted him during the discussion on "Hot Steams" and pushes the tire with all his might once she gets into it. Scout ends up crashing into the Radley's front porch on accident and leaves the tire behind. Jem is forced to run into the Radley yard to retrieve the tire.