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Course Criteria
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0.00 - 4.00 Credits
Khovanov homology (a continuation from Fall 2010)
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0.00 - 4.00 Credits
Starting at the very beginning, we will develop the foundations of the theory. We will explore how the existence of a foliation gives rise to topological understanding of the underlying manifold. For example, Reeb's stability theorem that a closed orientable 3-manifold with a S2 leaf is 2-fold covered by S2xS1 and Novikov's theorem that a closed 3-manifold without compact leaves must have infinite fundamental group. Finally, we will study various properties and characterizations of taut foliations. This includes their relation with the Thurston norm on 2-dimensional homology as well as various existence and non existence results.
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0.00 - 4.00 Credits
Various topics in modern statistical mechanics and related areas of mathematical physics are discussed, including condensed matter theory, field theory, and quantum mechanics of atoms and molecules. Guest speakers are invited to report on their current research.
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0.00 - 4.00 Credits
Symplectic geometry and the theory of dynamical systems have a nontrivial common core around Hamiltonian dynamics. It seems natural to try to bring ideas from these seemingly different fields together. A good starting point are questions concerned with the dynamics of area-preserving disk maps. A basic tool, which will be developed, is the theory of pseudoholomorphic curves. The study of area-preserving disk maps will be accomplished by studying suitable almost complex four manifolds. This graduate course should lead up to some interesting PhD topics, just in time with the program on "Symplectic Dynamics" at the IAS in 2011/2012.
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0.00 - 4.00 Credits
A general introduction to the theory of induced subgraphs (a continuation from Fall 2010).
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0.00 - 4.00 Credits
An introduction to medieval culture in Western Europe from the end of the classical world to ca. 1400. The course focuses on themes such as the medieval concepts of self, humanity, and God; nation-building, conquest and crusade; relations among Christians, Jews, and Moslems; literacy, heresy, and the rise of vernacular literature; gender, chivalry, and the medieval court. Material approached through various cultural forms and media; some lectures by invited guest lecturers. Two lectures per week with discussion following.
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0.00 - 4.00 Credits
This lecture and laboratory course will acquaint non-biology majors with the theory and practice of modern molecular biology, with a focus on biological topics of current public interest. Topics include: structure of DNA, RNA, proteins, genomes and an overview of state-of-the-art technologies including cloning, recombinant DNA and PCR. The course will address how recent scientific advances affect issues relevant to human biology including forensics, stem cells, molecular evolution and the genetic basis of human traits and behaviors such as obesity and aggression.
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0.00 - 4.00 Credits
What should students know about their genes and genomics? Today, the field of Human Genetics is explored and debated like no other. To understand the medical applications and ethical implications of Human Genetics, one must grasp its scientific foundations. We will approach these topics using: lectures, textbook, journal and newspaper readings, precept discussions, and patient interviews. We will consider the following subjects: gene structure and function; the genetics and genomics of populations and of selected human disorders (cancer, mental illness, metabolic diseases); and clinical genetics (inheritance patterns, diagnosis, treatment).
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0.00 - 4.00 Credits
Important concepts and elements of molecular biology, biochemistry, genetics, and cell biology, are examined in an experimental context. During the second half of the semester, topics-based sections will be taught by different faculty members in the following areas: cell biology, virology, neuroscience, microbiology and development. This course fulfills the requirement for students majoring in the biological sciences and satisfies the biology requirement for entrance into medical school.
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