2011 Concordia Math May Seminar
 2011 Student Photo Journal
 When we were hiking in the Swiss Alps, I was also struck by the thought that many mathematicians came here to gain perspective. And I can see why, it was absolutely gorgeous! Mathematics is a process that involves thinking outside the box. The Swiss Alps offer a relaxing setting for the brain to rejuvenate. It is a place away from the usual busyness of life, and the different scenery sparks new ideas. Michelangelo took a stone that other artists rejected and turned it into the "perfect" sculpture of David, admired by all. Archimedes was in the bath when the idea of density and displacement came. Brunelleschi was the first to have the idea to make the dome of the Duomo like making an egg stand up. I learned firsthand from taking Modern Algebra that sometimes taking a break or attacking a proof in a completely different way can lead to a breakthrough. Morris Kline even states that "Mathematics employs a high order of intuition and imagination." This month long trip really was a great way to jump start the imagination and really appreciate the ideas and work behind all the mathematical proofs and structures and artwork we viewed.
 Throughout the PreMay Seminar and the May Seminar trip, I have come to realize that math is so much more than the disjoint academic subject I thought it was, separate from all others. Instead, it is interconnected to many areas of life and has had a significant influence on people's ideas. Mathematics is not simply a list of formulas to memorize or problems to complete, but a discipline that has impacted multiple forms of art, elicited controversial changes to longheld beliefs, risen above the boundary of being used for practical needs, and even interconnected diverse cultures through the use of mathematical language.
 Math is an underappreciated art. Math is just so hard to define, describe, and comprehend that many people don't even try to understand it. Many more do try to understand it but give up. Then there are those who keep looking for the answers, some making great discoveries, some with nothing to show for it. But in the end they all discover that there is always more to discover than has already been found.
 Mathematics is hidden in the world around us, but is used all the time without us recognizing it being used. For example, telling time, predicting the weather, storing hundreds of photos as jpegs on tiny cards, dealing with currencies, and keeping planes on schedule all involve math and are connected or used by everyone every day.
 Math is the essential foundation of the world, and yet it never really gets the glory. Art, literature, science, business, and basically every academic area rely on and use math. If one listens through the clanging of our fastpaced world and sorts through the tangles of history, one will be sure to stumble upon math. It show up in modern life, many historical sites, and the application of science and business. Math is all around us. If we focus on it and seek it out, it will lead us to many of the greatest discoveries throughout the world.
 I will be honest, since I'm not a math major I have never really thought about math. I always knew it was important, but I just assumed math meant only working on complex problems that no one has ever heard of in some small dark office. I realize now that is completely not the reality of math now and in the past. Many things throughout the semester and May seminar have worked to change that.
 Maybe part of the reason people cannot bring themselves to live a life devoted to math is because math is such a taxing thing. As was seen in books we read, like Logicomix, and in other stories about great mathematicians, that devotion to mathematics does not always pay off. You may find your life's work unraveled by some new proof or some flaw in an old proof. You could also just go mad!
 On our trip we have used and seen many connections to math. Some like converting currency or splitting bills are obvious. Others were explained to us in museums and lectures. But we have also had encounters with math on a grander yet subtle way. Both in the preMay seminar and throughout our May seminar trip we have followed the history of math and the history of the major empires of the western world.
 So while I learned some of the history, culture, and mechanics behind the math, I've honestly taken away more in my philosophical view of math than anything else. I love math, I've always loved math, but I have always been and shall remain only a dabbler. Some people feel the allure of the mysterious realm of mathematics, but most of us are content with our elementary school knowledge that people pieced together for us thousands of years ago. The ignorance of the masses is not a good thing, but throughout the ages the mathematician has always been there to light the way with new ideas. And the ideas will continue to help us for millennia to come.
 On this trip and in the preMay sem class we have seen and used math in many aspects of our daily lives. For me I discovered a new appreciation for math because of its connection to science and society. Before this class I knew I used math often but I thought of it as a tool. I didn't realize its connection with society and thus its importance in history and in today's world. This trip and class have shown me that math is all around us and impacts the course of history.
 Another realization I made about mathematics throughout the course of the semester was that while mathematics has so many diverse practical utilities that is not necessarily the purpose of all mathematics. All throughout history, different cultures utilized mathematics in different ways. The Egyptians seemed to solely use math for practical purposes, whether it was in trading or determining possible results of the flooding of the Nile. The Greeks, on the other hand, were true theorists. I noticed this tension between practicality and theory in the mathrelated museums we went to, as well. For example, it seemed to me that the Galileo Museum as almost entirely focused on the practical uses of mathematics, while the math exhibit in the British Science Museum was the complete opposite.
 Over the course of our trip, I found myself constantly asking the question, "Where is the math in all of this?" Caught up in all the excitement of being in a new place with such storied history, the true purpose of seeing mathematics in different light eluded me for a portion of the trip. But now sitting down and reflecting on our awesome trip, I realize math was deeply embedded in basically everything we did.
 One exhibit at the Galileo Museum in Florence that stood out to me was the ramp Galileo created to illustrate acceleration. A ball was placed at the top, and began to roll while being timed by a pendulum. As the ball rolled, it hit the bells that were placed farther and farther apart. Although farther apart, the ball still hit each bell at the same time, hence depicting acceleration.
 As math has progressed we use what we know and then improved upon it. Things that once puzzled the greatest mathematical minds are now common knowledge for any elementary school student. It was quite inconvenient, for example, before the concept of zero came about. There was no way to represent a lack of value or of place values in larger numbers. Before I took the Mathematics in Another Light class I had never thought too much about the work done to come up with concepts as simple as standardized symbols, numerals, zero, and negative numbers. Until you think about the simple concepts you can't appreciate the very nature of math.
 I came to realize a really interesting aspect of mathematicsthat it is not strictly confined to practical uses. In my opinion it is cool to think o f math as something that transcends the reality I know.
 Before I took this class and before I went on this trip, I must admit that I had a comparatively narrow view of the field of mathematics: to me, it was little more than a tool that drove my primary field of study, which is physics. Through a careful application of certain specific result from mathematics, it was physics that allowed mankind to discover, create, and solve. However, after taking this class and participating in this trip, as well as spending some time in both my math& physics senior seminar classes, I have come to realize that this restricted viewpoint of mathematics was inadequate, even almost ridiculous in some respects. I have discovered that mathematics has far more used than I'd initially imagined, and that these uses have stretched much further back in time that I had realized.
 Many people, including myself, might have trouble connecting mathematics to this trip, if they were only given a brief itinerary of this last month. But after taking the class and actually going on the tri, my perspective has totally changed. Mathematics was present in everything we did and saw. From the simple everyday tasks like using money and telling time, to the different styles of architecture, art, and museum exhibits we saw, mathematics can be found everywhere.
 Math 300 is a great way to explore and learn about mathematics in another light. Sometimes math is taken for granted and not always appreciated on the level it should be; however, this class and excursion through Europe helped me develop a new kind of appreciation and love for math. On this trip I have seen math on an everyday level, used for scientific and other developments, and honored at many important monuments.
 In the preMay sem class I found it very interesting to learn about the development of technical mathematics that I take for granted. For example, the development of notation by early civilizations, the discovery of negative numbers, solving quadratic equations, Liouville's proof of nonalgebraic numbers, etc. However, while on the trip I was surprised by the amazing and advanced applications of mathematics by different people throughout history.
 When growing up, I always disliked, struggled with, and didn't understand what math could possibly be used for beyond the simple basics of it. Then in middle school, I finally started to appreciate math more but still couldn't figure out what more it could be used for. During this class and the preMay seminar, I have started to recognize math in a lot more areas of life. Now I realize that math plays a large role in art, architecture, and in travel. Also, math seems to have a lot more to it than meets the eye.
 When I originally registered for the preMay seminar course, I was mainly just looking forward to seeing a bunch of different countries and enjoying a month abroad. I have always loved math, but I had never before learned about its roots or theories in any detail. Going on the May seminar trip and taking the preMay seminar class has really helped to open my eyes to a world completely surrounded in math. Even the most ancient cultures have deep mathematical roots and absolutely amazing advances in the history of math. My traveling and education has shown me how to truly appreciate math and its impacts across the globe.
 Seeing mathematics in another light. Before this trip, and the preMay seminar, mathematics for me consisted of going to math class, learning about new formulas, techniques, problemsolving skills, and doing homework and earning a good grade. Mathematics was a daily task which was a means to an enda potential career. It would be safe to say that this trip, and class prior to it, will forever change my view on mathematics.
