Elliptic curves are a class of cubic curves (defined by a cubic polynomial in two variables) with deeply surprising and beautiful properties. The most surprising fact about elliptic curves is that their points naturally form a group structure under some geometric operation. Elliptic curves show up everywhere in mathematics from tori defined over the complex numbers to generating abelian extensions of number fields. Elliptic curves also feature prominently in the Birch and Swinnerton-Dyer conjecture, one of the millenium prize problems, and Andrew Wiles' proof of Fermat's last theorem. In this class we will develop the fundamental results about elliptic curves such as the Mordell-Weil theorem and Weierstrass function theory before diving head-first into some more advanced territory mentioned above. This class will be a meandering relentless rollercoaster through some of the most beautiful connections in modern mathematics rather than a reasonably-paced, well-structured, and rigorous development of a topic. Expect proofs to be "sketched", definitions to be hand waved, and lots of inane terminology to be used. That said, expect to come away with an broader awareness of open problems in mathematics, a much richer appreciation of the interplay between geometry and algebra, and a healthy respect for cubic polynomials in two variables.

To meme or not to meme, that is the question: Whether ‘tis nobler in the Sub to repost The gifs and jokes of yester year Or to create OC against the sea of reposts And in downvoting end them. To OC–to post; To post perchance to meme–ay there’s the sub, For in that post of OC what memes may come, When we have shuffled off this bottom text, Must give us pause–But that the dread of spici’r OC, That undiscover’d board, for whose born no memelord returns, puzzles the will, And makes us rather post the memes we have Than create others we not of? Thus Four Chan doth make normies of us all.

We will begin a fantastical journey into some of the most beautiful and useful geometric objects in modern mathematics, Lie groups, by asking the simple question: how do we represent rotations in 3D space. This question will lead us to define a strange algebraic object, the quaternions, investigate the mysterious topology of spheres living in four (and more) dimensions, marvel at a beautiful images of a sphere in dimension four decomposed into tori by the Hopf fibration, and finally discuss how these higher-dimensional geometric objects are, in fact, physically realized by spin in the strange world of quantum mechanics.

The meaning of term "Mathematical Logic" is fairly non-trivial. Mathematical logic is, on the one hand, the study of the logic of mathematics rigorizing the notions of "proof" and "example" in the framework of formal logic. But Mathematical logic is also the application of mathematical methods to logic using tools such as induction and set theory to proof meta-theorems about logic. It is even the application of logic to solving (somewhat) concrete math problems. In this course we will discuss all these flavors of mathematical logic as we introduce the basic concepts of completeness, consistency, satisfiability, and categoricity, discuss foundational results linking model theory (the study of examples) to proof theory (the study of formal proofs), then investigate the limitations of first-order logic, and finally prove Godel's momentous incompleteness theorem of first-order arithmetic. On the way, we will naturally develop foundational ideas about the theory of computation and how decidability and incompleteness are intricately linked. Time permitting, we will discuss applications of mathematical logic to problems in algebraic geometry such as the Ax-Grothendieck theorem and Lefschetz principle.

On the 17 of January, 1779, the sails of The Resolution peaked above the eastern horizon of Kealakekua bay, Hawaii. At her helm was James Cook, an industrious British explorer searching for the western route to Asia. At the time of Cook’s arrival, the Polynesian natives of Kealakekua were joyously assembled on the beach–in the midst of celebrating their annual Makahiki festival honoring the sea god Lono. When Cook landed, he was celebrated by the natives as the god Lono: he was draped in fine red fabrics (the color of Polynesian divinity); prostrated to and given sacrifices of fruit and roast pigs; and paraded around the island while the Hawaiians chanted “Lono, Lono, Lono!” …Or at least, that’s how the story goes. In his book, The Apotheosis of Captain Cook, Gananath Obeyesekere rejected the position held by “every biographer and historian of Cook” that the Englishman was interpreted as a Polynesian God. Obeyesekere argued that the sources supporting the apotheosis are weak at best, and are entangled with gossip and myth. Obeyesekere’s skepticism of apotheosis sources is not unfounded; in a 1982 lecture at Princeton University, Polynesian Historian Marshall Salhins declared that the Hawaiian king was so distraught at the departure of Cook that: “By all accounts, British as well as Hawaiian, they told him such sad stories as the death of kings as to force him to sit upon the ground” (so that Cook could leave). Obeyesekere notes that these “accounts” are a blatant plagiarism of Shakespeare’s Richard II, and therefore cannot be legitimate: “For god’s sake, let us sit upon the ground/ And tell sad stories of the death of kings (Richard II, act III scene II).” This course will examine the historiographic debate surrounding the Apotheosis of Captain cook. The main historiographic raised by the ‘Apotheosis question’ is how to elucidate the beliefs of native peoples in the absence of a substantial source archive. The Polynesians left no written records from 1779; discerning whether they actually understood Captain Cook as Lono presents a serious problem for Polynesian historians. By analyzing the discourse surrounding the ‘Apotheosis question,’ we can make larger statements about historical methodology, epistemological frameworks, and interpretation of an incomplete source record.

The Balkan Wars of 1912-1913 were a series of conflicts between the Ottoman Empire and its former European territories which triggered brutal violence against Balkan Muslim civilians. Of the 2.3 million Muslims living in the Balkans prior to the wars, approximately 27% died in under six years as a result of attrition, famine, and disease outbreaks, and another 35% fled as refugees to Anatolia and Eastern Thrace. This tragedy represented a defining moment in Turkish national history. Before 1912 most Ottoman Muslims had associated with numerous linguistic, cultural, and ethnic backgrounds; however, the traumatic expulsion of 813,000 Balkan Muslims to Anatolia catalyzed a surge in the popularity of ethnic ‘Turkish’ nationalism among the geographically-consolidated Ottoman-Muslim polity. I argue that this defining moment in Turkish history has continued to impact the modern population, not only through historical memory, but through heritable biochemical memory. This course will question whether the psychophysical stress of Balkan Muslim refugees sustained during the Balkan Wars of 1912-1913 left an epigenetic mark on their living descendants. This course will serve as an introduction to the field of intergenerational psychoepigenetics, a discipline which spans biochemistry, psychology, and history. I will provide an overview of the biochemical research project I am planning to perform in Turkey the year after I graduate college in 2020 (I am working towards a dual degree in Biochemistry and Ottoman History). We will perform a literature review of existing intergenerational psychoepigenetic studies, learn the basics of what epigenetics is as a biochemical phenomenon, and parse out common misperseptions about what this discipline can and cannot tell us; specifically, we will be interested in the intergenerational epigenetic impact of trauma. Next we will situate ourselves within the historical context of the Balkan Wars, and their relevance to the modern country of Turkey. Last we will talk about how my proposed biochemical project would be conducted, which living people in the modern population would be best to include in the present study, and methods of biochemical analysis.

Nuclear Magnetic Resonance (NMR) is one of the most imporant tools in organic chemistry for identifying the composition and detailed electronic structure of compounds. NMR is a quantum mechanical effect of the interaction of the nucleus of an atom (or generally each nucleus comprising a complex molecule) with a strong applied magnetic field. Specifically, the effect is due to the strange nature of quantum spin, intrinsic angular momentum carried by the nucleus and how spin couples to external magnetic fieds. Furthermore, this interaction effect is senstive to the nearby nucleli and electronic envioronment so that each nucleus will have a distinct NRM resonance figerprint associated to its position in the molecular structure alowing NRM spectroscopy to ID the molecule. In this course we will discuss the physics of quantum mechanical spins in magnetic fields and the process by which they absorb radiation at specific resonance frequencies. We will then shiow how NRM spectroscopy is used in practice and the process by which compounds may be identified. Finally, if time permits we will discuss other chemical and medical applications of NMR phenomena.

I have a chapter of my senior thesis due Monday I am grinding on, so I will submit the course abstract columbus day weekend.

In this class we will be studying the fundamental building block of life: carbon. From the 118 elements on the periodic table, life on earth has continually utilized carbon to form the foundation of its cellular membranes, catalytic molecules, and genetic material. Indeed, close to 20% of human body mass is entirely carbon. To understand the ubiquity of the carbon atom, we will begin by analyzing its unique and durable bonding properties. Next, we will study carbon’s versatile geometry through an analysis of atomic orbital hybridization. We will then take a step back to look at how carbon’s properties allow it to form the bedrock of larger organic molecules comprising the other building blocks of life: Oxygen, Hydrogen, Nitrogen, and Phosphorus. In the second half of the class we study the relative stability and reactivity of organic molecules. In this vein, will discuss partial charges/electron distribution, molecular resonance theory (delocalized pi orbitals) and steric strain. We will finish the class with an analysis of functional groups: the atom(s) with which make organic chemical reactions possible.

In this second installment of my organic chemistry series, we will be studying how small carbon-based molecules react with one another to form novel chemical products. We will build off topics of partial charges, molecular resonance, and steric strain (discussed in my “Fundamentals of Organic Chemistry” class) to understand what motivates certain molecules to react with one another and not with others. We will begin our study by studying the simplest molecular reaction: the acid/base reaction (exchange of a proton). Next we will look at simple nucleophile/electrophile reactions, including SN1 and SN2 reactions. We will also analyze what makes a good nucleophile (electron donor), and use this knowledge to predict which molecules might interact with one another. Much of this part of the course will be focused on transition and intermediate states–the series of momentary stages molecules go through as they are converted to products. Our knowledge of transition states will allow us to understand the conditions under which certain reactions can occur or be inhibited, as well as how those reactions can be catalyzed by enzymes. To end our class, we will analyze the most versatile functional group in organic chemistry: the carbonyl (carbon double bonded to an oxygen). The carbonyl group enables a plethora of chemical reactions, and is indispensable to the creation of large biomolecules in cells.

In the final installment of my organic chemistry series, we will use our knowledge of molecular reactions to plan the synthesis of carbon-based molecules of our own choosing. “Synthesis” entails a series of tightly controlled chemical reactions which enable us to create and alter a small molecule; the efficient synthesis of such molecules has wide reaching applications in fields stretching from industry to pharmacology, This course will provide an overview of synthesis techniques: when to add nucleophiles to expand the size of a molecule, how to convert one functional group to another, and how to eliminate extemporaneous parts of a molecule to attain to a final product. We will center our study around the carbonyl group and its derivatives, as these groups provide the centerpiece of most synthesis strategies. This course, while far from comprehensive, should provide you with an understanding of how an organic chemist sees and shapes the molecular world. I hope you leave this course with an appreciation of the beauty of the molecular world and the laws which govern it.

The Parthenon in Athens is perhaps the most iconic structure in the western world. It is seen by many westerners as a monument to democracy, education, and civilization. The Parthenon was once adorned with the finest marble statues of the classical world, depicting the adventures of the mighty Greek gods and goddesses: Zeus, Poseidon, Hermes, and of course–Athena. Yet today, the Parthenon has been stripped of its marbles, it stands on the acropolis, bare and unornamented. How could this have happened to the greatest architectural masterpiece of the western world? In this class we will learn about the incredible life story of the Parthenon marbles. We will meet a fascinating early archeologist named Lord Elgen, who won an entire war in Egypt so he could controversially strip the marbles in the early 1800s. We will uncover how Greece responded to Elgen, how the debate over the true ownership of the marbles is still raging, and where the marbles are today. This class will illustrate how controversial archeology can be–once the hatchet has been unearthed, it is not easily buried.

History is a fascinating discipline that allows us to study the rise and fall of empires, the accomplishments of great individuals, and change of societies over time. We study history to gain insights into the present political/societal moment–and so we don’t repeat the mistakes of the past. But what exactly is history? Carl Becker answers this question: “History is what the present chooses to remember about the past.” Becker’s point is very problematic if we want to discover what actually happened in the past; if history is an incomplete recollection of the past, then how do we discover what actually happened so we can learn from it? How do we get to the truth? In this class, we will be trying to answer the above questions. To do so, we will be introduced to the field of “Historiography,” the study of historical theory and methods. We will look at a couple historical case studies, and have time for discussion at the end. I would highly recommend anyone interested in history to take this introduction to historiography; an understanding how to study human experiences in the past–and the historical events which connect them– is indispensable to the modern historian.

The Republic of Turkey is the most diverse country in the modern Middle East. Its over 80 million citizens hail from across eastern Europe, the Balkans, Asia Minor, and the Arabian world. Turkey’s diversity is attributable to its unique geopolitical position: it sits at the crossroads of Europe and west Asia, and has historically been an intersection of innumerable peoples, cultures, religions and ideas. Due to this incredible diversity, Turkey has been continually faced with the deceptively simple question “Who is a Turk?” over its 80 year history. This question is highly political, as it relates to how Turks understand themselves in the broader context of the world. Are all Turks Muslim? Are they European? Are they Western or eastern? Can they be all these identities or do they have to choose one? In this class, we will be looking at how Turkish politicians have defined what it means to be a “Turk” and how this has related to their broader political agendas. We will be focusing on two Turkish politicians specifically: Mustafa Kemal Ataturk (the founder of Turkey and its first president) and Racep Erdogan (Turkey’s current president). Understanding the struggle for national identity in Turkey has never been more urgent than today, as Turkey is undergoing rapid political change and shifts in collective consciousness.

Cancer is an inevitable part of Human life. This phenomenon occurs because the human genome mutates innumerable times a day, and eventually these mutations will lead to uncontrolled cell growth (i.e. cancer). Despite significant pharmacological efforts over the past seventy years to treat various forms of cancer, most treatments are still insufficient, and many types of cancer are still considered “un-drugable”. But today, we are on the brink of a pharmaceutical revolution that will change how we think about treating cancer. In this class, I will be talking about my own lab research on combating mutated genes that lead to cancer, and how this research is into the larger field of experimental pharmacology. For those interested, I work on identifying potential allosteric sites on oncogenic proteins that can be targeted by small organic molecules as a means to inhibit constitutive activation. (All big science words, I know. I don’t expect you to know any of them, just come ready to learn and ask questions!)

To meme or not to meme, that is the question: Whether ‘tis nobler in the Sub to repost The gifs and jokes of yester year Or to create OC against the sea of reposts And in downvoting end them. To OC–to post; To post perchance to meme–ay there’s the sub, For in that post of OC what memes may come, When we have shuffled off this bottom text, Must give us pause–But that the dread of spici’r OC, That undiscover’d board, for whose born no memelord returns, puzzles the will, And makes us rather post the memes we have Than create others we not of? Thus Four Chan doth make normies of us all.