## Posts in: Block 1

## Introduction to Art History: A Lineage of Historic Interpretation and Beauty

*Woman of Willendorf*and cave paintings hidden deeply within the Lascaux Caves in France, all the while exploring what these representations could’ve meant in a pre-historic age (an age before written history). Next we travelled into the humble beginnings of modern civilization by examining objects such as

*the Stele of Naram-sin,*which memorializes an Akkadian general’s victory over his mortal enemies in ancient Mesopotamia. Afterwards, we travelled to Egypt where the striking mastaba-inspired and originally white limestone-covered great Pyramids of Giza still sit as the enormous tombs of Pharaohs Khufu, Khafre, and Menkaure. Finally, we were swept to the Aegean Sea to witness the beautifully painted fresco of a male figure flipping himself over a bull while abstract, almost floating, female figures witness this feat from both sides. We also studied the gorgeous ruins of the city of Knossos on the island of Crete, which revealed a structure so large and incredibly designed that the historian Arthur Evans first defined it as a “palace” which he thought belonged to the mythical King Minos.

## Real Analysis: Week 2 (and doing things with real numbers)

Since learning about some of the basic properties of the real numbers, about how they form a line that is completely continuous, we’ve begun to talk about what those properties allow us to *do* with the real numbers. When we think about and talk about math, we tend to think and talk about manipulating numbers, not simply admiring their existence. The idea that “proving calculus” is important rests on the fact that our society requires (and our minds enjoy) this kind of numerical manipulation, and that we want the results of these endeavors to have some real meaning.

The first type of active manipulation of numbers that we talked about was the act of arranging real numbers into a sequence. A sequence of numbers is a subset of real numbers which are arranged in a particular order. Further, each element of the sequence can be constructed from some formula; that is, if you want to find the fifth term in the sequence, you can plug “5” into a given formula and acquire that term. For example, we can create a sequence of all numbers of the form {1/n} where each “n” that we plug in is a natural number (the kind of number that you can count on your hands). In the sequence, the first element is 1, the second element is 1/2, the third element is 1/3, and so on.

This sequence, like all sequences, contains an infinity number of terms. This is because there are an infinite number of natural numbers, and therefore an infinite number of “n”s to plug into the given formula. An infinitely long list of numbers all sharing a common formula is a pretty astounding, but it turns out that many sequences have an even more incredible property. This property is called *convergence*, and it means that after a certain term in the sequence, there are an infinite number of terms which are all practically equal to each other.

The sequence {1/n} is a sequence with this property. Eventually, as the natural numbers which we plug into the formula get very large, the term as a whole gets very small. And when n gets extremely large, when we start dividing 1 by numbers like 1,000,000,000, the elements of our sequence get very close to each other and to zero. Because of this, we say that the sequence {1/n} converges to zero. Interestingly, the terms are never actually equal to zero, and never actually equal to each other. 1/1,000,000,000 is a different number than 1/1,000,000,001, although they are very, very close together in value.

There are actually a lot of sequences that converge, and which converge to a variety of real numbers. This property of convergence is deeply tied to the structure of the real numbers- that line which we learned about at the very beginning of class. Since that line contains every possible number, it is possible for it to contain an infinite number of numbers which are as close together as we could want, without those numbers ever actually being equal. This allows for convergence: if the real line were missing values, there would be gaps in the line which inhibited the closeness of terms in a given sequence.

Sequences, while fascinating, might seem on the surface to not actually “do” much in terms of manipulating numbers. They hold a lot of power, however. They allow us to not only order information, but a potentially infinite amount of it. We can add terms of these sequences together to get new sequences, or to get sums of numbers that approximate complicated functions. These are all things we’re going to talk about in the next few days of class, as we keep looking at what the line of real numbers allows us to do.

~Anna

## Week 2: The Essay

After a relaxing weekend filled with reading, coloring, exploring the arts, and taking a stroll with nature, our class piled into the room. With our refreshed minds we prepared for our next assignment.

The Essay is our last big assignment that is supposed to encompass our lives. The first day we described our golden memory, which is the memory that really stood out to us. For some, like myself, it was a very emotional and spiritual experience. Finding that golden moment and highlighting some of the key moments was probably one of my favorite parts of the class, because I was able to find that special moment and other moments leading up to it. After we all found our golden moments, we shared with our class. I don’t know about you, but there is something wonderful about sharing something special to you from a composition notebook.

In order to make our golden moment stand out from our essay, we were also asked to write about memories that go with the same theme as the golden one. In addition to that, we had to read essays that embodied voice, imagery, and characterization. The next day we came up with our own list of what these writing techniques meant to us and what it means to evoke that in our pieces. And each day we would share our writing pieces and give each other feedback on how to enhance and further grow our essay. We had a writing day on Friday, to start typing up our pieces and arranging them to our liking. The first draft of our essay is what we will be in Workshop for Third week. I would tell you more about that, but I will save that for another time. Until next time!

## Week 1: The Ask Album

The first day of Creative Nonfiction Writing started by climbing 3 flights of stairs in Armstrong and into a packed classroom. Our professor, Felicia Chavez, set the tone waited till everyone got settled. There were 25 students in class room, 9 of them were wait-listed. We all wanted to be in the class. We all wanted to be a part of what was bound to be a spiritual experience. Professor Chavez passed out the syllabus and what was expected of us. She wanted to make it very clear that this class was very different from other creative writing classes, let alone English class, and if this wasn’t the class for us, then we should leave. Nobody left. Professor Chavez continued to talk about the course and then took a 3 minute break so that people could leave if they wanted to. Nobody left. Those who were wait-listed were asked to leave and told they were more than welcome to take her other blocks. The 16 of remaining sat in a circle and learned about the first assignment.

The Ask Album is the big question that you don’t know the answer to. Its the big red door with the brass know in your head that is filled with possibilities but not answers. Our task was to physically make our album revolving around the big question by first Friday. It was a pretty daunting project in my eyes. It seemed less daunting but still imminent when she said that we would be working on our Ask Album all week. Each day, she would give us writing prompts as homework to figure out that question. We would write for at least 30 minutes and then edit for no more than 30 minutes. When we would share our pieces, some of the most beautiful sentences came out. Some were moved to tears, some to laughter, but in the end we were all here for each other.

Friday came and we all piled in quite unsure if our project made the cut. Professor Chavez was so happy to see everyone and our Ask Albums. When we all presented our Albums, I felt closer to my class. It was like we were this little family sharing our feelings every day. We were all emotionally and physically exhausted but all extremely proud of each others work. Professor Chavez gave us our assignment for the weekend and I think a few of us groaned before actually reading it. Our homework was a Play-List of relaxing and pleasurable things we get to do over the weekend. I thoroughly enjoyed all of it by the end and was ready for week two to star

## Real Analysis: Week 1 (and one really important line)

One week ago, I didn’t know what Real Analysis even was. I knew it must be important (it’s a requirement for the major, after all), and that it was probably a theory based course (since we’re “analyzing” how numbers work, rather than learning the methods that these workings allow). Going into the first day that way was exciting- after a summer spent mostly at home, it felt like I was throwing myself into some far off corner of the universe and waiting to find out what it looked like.

As it turns out, Real Analysis is a little bit more like *every* corner of the universe. Our professor, Molly, introduced the class as a course that would allow us to begin “proving calculus.” And calculus- that’s huge. Calculus may be only one branch of mathematics, but it’s the branch that most of math education in the US most naturally leads to. That makes sense, too, since calculus has so many applications in so many important fields. Proving the validity of calculus implicitly assures the validity of fields in economics, physics, chemistry, and pretty much any natural or social science which uses complicated statistics to understand a data set. Real Analysis, then, seemed like some pretty powerful stuff.

We started our first class with some of that powerful stuff, right away, talking about what the set of “real numbers” even is. It’s hard to wrap my head around it, to be honest, because here’s what the real numbers are- they’re the line of every possible number that exists in either the positive or negative direction of zero, with not a single gap in them. The numbers we deal with most frequently in our day to day life are “natural numbers,” the kinds of numbers you can count on your fingers. They’re every number you can get by starting with 1 and adding 1 to itself as many times as you could possibly want. It’s an infinite number of numbers, but compared to the real numbers, the natural numbers are missing a lot. To get to the real numbers from the natural numbers, you first step through the integers. The integers include the natural numbers, every negative version of a natural number, and zero. But we’re still not even close to the real numbers. Next we step through the rational numbers- these are every number you can get by taking a ratio of two integers. So numbers like 13/167, or 2/9, those are rational numbers. And as you can probably imagine, that’s also a really big set of numbers.

But it turns out that, for as many rational numbers as there are, there are far more numbers that can never be expressed as a ratio of two integers. So if we were to lay all of the rational numbers out in a line, there would be spaces, empty spots of numbers which we couldn’t express using that set. The real numbers, though, fix that problem. They include every rational and *irrational* number. Essentially, any number that you could find out in the world, only the set of real numbers is guaranteed to include it.

So the real numbers are pretty special. We learned that in the first fifteen minutes of class. And it turns out that because the real numbers are so special, mathematical systems that use the real numbers have some cool properties. We’ve been exploring those kinds of properties since them. For example, any interval of numbers (like the interval from 0 to 1, written as (0,1)) is guaranteed to have a single largest element, one unique number bounding the entire set below it. But if you don’t use the real numbers, you can’t guarantee such a thing. That’s just one example, but the essential thing I’ve learned so far is this: the simple fact that the real numbers exist allows for and dictates the behavior of entire fields like calculus . The rules of most math that I’ve ever seen in my life are themselves governed by a line.

For only the start of a class, that’s a pretty amazing thing to have already learned, and I can’t wait to see where in the universe we end up in the next few days.

~Anna

- » Read more «
- 4th September 2016 -
- Posted by Anna in Block 1, MA375, Mathematics & Computer Science

## HY233 U.S History from 1943-73 post1

In HY233, a central paradox lies at the heart of all the readings and discussions with which we have engaged. On the one hand, the era following World War II represented the prime of, as Tom Brokaw dubbed it, “our greatest generation.” But on the other, the same era marked the brief high point of a social and political system soon to be challenged by the tumult of the ’60s.

By 1945, we had defeated the Axis Powers and their accompanying evils, pulled ourselves out of the Great Depression and built a massive military industrial complex. By 1947, the Truman doctrine declared, with regard to the Soviet Union, that once again America would stand against totalitarian regimes that, “reach their full growth when the hope of a people for a better life has died.” Following in his footsteps, Eisenhower continued a cold-war policy of containment abroad and Keynesianism and social planning at home. Reducing the defense budget from 50 billion to 40 billion, keeping inflation at 1.5% annually, ensuring open access to oil and other precious commodities, and maintaining tranquility within the home front all seemed like good ideas. The liberal consensus was widely agreed upon in Congress. Unlike today, elected congressmen from both parties actually collaborated in a successful effort to do their jobs: pass legislation.

But beneath a veneer of peaceableness and prosperity, rumblings of a different America and a different world grew louder.

Such sounds were most theatrically and poignantly expressed by the likes of such rock stars as Mick Jagger, Bob Dylan, and Otis Redding. “Come mothers and fathers/ throughout the land/ and don’t criticize/what you can’t understand/your sons and your daughters/are beyond your command/your old road is rapidly agin,'” sung Dylan in “The Times They Are a Changin’.” Many American youth saw the world differently than their parents and proudly espoused a new set of progressive beliefs.

Both the Feminist and The Black Civil Rights Movements reared their heads and would become of increasing national importance. The patriarchal breadwinner complex and institutionalized racism would be challenged like never before. The post-war tranquility many Americans had become accustomed to would also be shaken by the events of the Cold War. With Kennedy’s aggressive cold-war rhetoric and increase in armaments, the Cuban Missile Crisis should have been all but expected. Narrowly avoiding a world-wide nuclear melt-down, Americans had for the first time been forced to confront the scary realities of nuclear war.

Thus, while wide agreement in the government allowed for an efficient political system, the “liberal consensus” of the 50’s would soon have to face up to the problems of basing a society on two incorrect assumptions. First, Americans were wrong to overestimate the threat of the Soviet Union. Truman’s polarizing language was a direct product of his desire to send foreign aid to Greece. Had he considered the implications of such rhetoric we probably wouldn’t have had to deal with the absurdity of McCarthyism. Nor would later officials have had strong ground on which to argue that billions of dollars were better spent developing the capacity to blow up the Soviets 10 times over than to be used to address domestic concerns. Second, Americans were wrong in believing that capitalism could eliminate class distinctions at home. The Civil Rights movement was a product of distinctions based on race and class. Blacks and other disenfranchised groups still had no seat at the table, and they insisted that it was time that white America recognized it.

America was changing quickly. To learn how it continued to change, be sure to check back for the next post on the issues covered in my class, HY233, taught by Doug Monroy.

## Class Length

Another huge concern I had coming in to my class was the length of time I would spend in class each day. In high school, I had never had a three hour class, and I was worried that the professor would not be able to fill that time and keep our interests.

As it turns out, this has not been a problem at all! We start class everyday at 9:15 am in Palmer Hall. We spend the first half of class engaging in discussion about the reading material from the homework. We have class for about 1 hour and 15 minutes, and then we take a break. Susan is usually great about seeing when we need a break, and giving us time to collect our thoughts before the second half of class. Breaks usually last about 15 minutes. We can spend the break however we’d like. Many of us stand in the hallway and talk, catch up on our phone messages, eat a snack, or even take a quick nap in the breakout room adjacent to our classroom. Then, after break, it’s right back to business. If Susan is lecturing that day, she’ll take the second half of class to do that. The second half is usually also reserved for quizzes or worksheets.

We end class anywhere between 11:45 and 12:15 depending on the day. While it can seem daunting to be in class for so long, it hasn’t ever felt like it was dragging. The small break after the first half of class allows us to catch our breath and clear our heads before jumping back into a discussion or class work.

When class ends, it’s only about noon and you have the rest of the day to do as you please.

So far, I am loving the block plan and it’s intense study, and I can’t wait to continue in my FYE second block.

I’ll write again soon!

-Nila

## Safety First!

All geared up for lab!

## HY 104- Homework Load

As an incoming freshman, I was very worried at the start of the year that I would not be able to keep up academically in college. Colorado College has such an amazing academic reputation, and I was wrought with fear that it would be too much to handle. Coming from a large public high school, I was accustomed to honors and AP classes, but I just did not know how I would fare. Today, I hope to assuage your fears, and give you the details on the homework load for this “West In Time” requirement-fulfilling FYE.

HY 104 is definitely a reading-heavy course. On average, every night I have about 2-4 hours of reading. The weekends have brought about six hours of homework total. The readings for this class have been a mix of literature, non-fiction research papers, scientific articles, historical accounts, primary sources, and even plays. The wide variety of reading material is great! I have found that if one reading assignment is not especially exciting to me, the next night’s material is.

While reading, I usually take detailed notes in a separate notebook. Many of my classmates have chosen to write in the textbooks, but I prefer to keep my thoughts and the actual text separate. I have found it helpful to include chapter plot summaries, thick questions, notes on character motivation, and bullet points of main ideas in my notebook about the material. Keeping notes on each reading has helped me sort out my thoughts, and also aids in remembering discussion topics in class.

So far, we have only had one essay. It was five pages and analyzed Greek conceptions of human power. We just got our essays back, and I plan on doing a separate post about our first college essay. For your own reference, it took me about ten hours to write the essay from start to finish. This time included the help that I received from Susan during her office hours, and a trip to the Writing Center.

We have nine books that we each had to purchase (which cost me about $140 total by the way), and Susan tells us that we will use them all over the course of this class. We have also used many online articles and documents. So far, we have read through three of our books almost in their entirety. While that may seem like a lot, it has been very manageable for me. It is also nice that we do not have to worry about another class. The Block Plan has been working out nicely for me in that way.

In conclusion, I have found that the homework load has been very manageable in this course. I will most likely do an update/final thoughts post on this topic towards the end of Block 2.

Thank you so much for reading, and I will write again soon.

-Nila