We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions. There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions. There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions. There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
We will begin this course by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions. There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions. There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
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