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Why 4,000 Mathematicians Came to Seoul

By Ryan Lee, VI Form

 

CrowdThis summer, the International Congress of Mathematicians (ICM) was held in Seoul, Korea. Lasting ten days, ICM 2014 started on August 13th. Over four thousand mathematicians from around the world came to Seoul to share information on research studies on mathematics and congratulate the mathematicians getting the Fields Medal. (Fields Medal is an award for mathematicians that is similar to the prestige of the Nobel Prize; it is awarded to four people not over the age of forty.) The Seoul ICM consisted of hundreds of lectures as well as numerous booths. The lectures ranged from some well-known fields such as number theory, combinatorics, geometry, and algebra to less familiar topics such as lie theory and topology. Many famous academic publishers such as the (more…)

An Extension of the Arithmetic Derivative

By Seung Jae Lee V Form, Alex Padron VI Form, and Luya Wang VI Form

Instructor:  Mr. Rick Umiker, Mathematics Faculty

Abstract:  In this paper, we examine the product rule and the arithmetic derivative. We first find a closed-form formula for the arithmetic derivative over positive integers. We then extend the argument to negative numbers, rational numbers, power roots, and complex numbers. Throughout our research, we also use Mathematica graphics to help visualize the behavior of the arithmetic derivative over different domains and explore boundary conditions and intermediate lines. Finally, we discuss the continuity of arithmetic derivative and give a continuous form that satisfies the product rule. (more…)

Crystallographic Restriction Theorem and Molecular Symmetry

By Julie Geng, V Form

Author’s Note: 

As many of my peers and teachers know, I am a big chemistry “nerd”. While I am engrossed in organic synthesis, I aim to broaden my perspective by making the connections between chemistry and other STEM subjects. Interdisciplinary studies are indispensable nowadays, as many scientific breakthroughs are results of the collective efforts of specialists in various interrelated fields.

Introduction

As exemplified by the copious examples in “Linear Algebra: A Modern Introduction” by David Poole, linear (more…)

Creating High School Students’ Dispositions for Lifelong Learning Through Open Online Courses

By Lauren Riva, Director of the St. Mark’s Mathematics Institute

People are members of an ever-changing world, a world in which change occurs more and more rapidly. These swift changes give rise to major problems for the workforce because workers (especially those involved in design, production, maintenance, sales, and planning) are constantly faced with the need to learn how new systems work (Dubinsky, 2000; Van Dam, 2012). Becoming and remaining a productive member of the workforce requires more than simply being well versed in present day systems; an individual must also be able to adapt their knowledge and skills to new situations. (more…)

Double Inverted Pendulum in 2D and 3D Space

by Ryan Lee, V Form

modelopdobleThis summer, I went to Mathematica Summer Camp. Mathematica is computer software made by Wolfram Research. This tool is commonly used by mathematicians and scientists. In the camp, each student completes a project through Mathematica.

During the first week, we met our mentors and chose what we would create during the camp. At that time, I was particularly interested in Chaos Theory, a field of study in mathematics that focuses on “chaotic” behaviors that are sensitive to initial conditions, one example of which is the butterfly effect. When I was learning about Chaos Theory, the double inverted pendulum and Swinging Atwood’s Machine interested me. There were a few videos on the internet recording this type of (more…)