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Course Outline
(PS, PDF, DVI)
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Course Syllabus
(PS, PDF, DVI)
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Brief Project Descriptions
(PS,
PDF,
DVI)
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Detailed Project Descriptions
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Primes in Arithmetic Progressions
(PS,
PDF,
DVI)
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The Prime Number Theorem
(PS,
PDF,
DVI)
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Dirichlet's class number formula
(PS,
PDF,
DVI)
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Class numbers and Binary Quadratic Forms
(PS,
PDF,
DVI)
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Pell's Equation and the Continued
Fraction of Sqrt(D)
(PS,
PDF,
DVI)
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Geometry and Sums of 4 squares
(Minkowski's theorem)
(PS,
PDF,
DVI)
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Arithmetic and Sums of 4 squares
(Quaternion Algbras)
(PS, PDF, DVI)
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Algebra and Sums of 4 squares
(Local-global principle and Class numbers)
(PS,
PDF,
DVI)
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Analysis and Sums of 4 squares
(Siegel's theorem)
(PS,
PDF,
DVI)
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Local-Global principle for rational points
on conics and p-adic numbers
(PS, PDF, DVI)
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Algebra and analysis in the p-adic numbers
(PS, PDF, DVI)
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Public Key Cryptography
(PS,
PDF,
DVI)
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Factoring and Primality testing
(PS,
PDF,
DVI)
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Elliptic Curve Cryptography
(PS,
PDF,
DVI)
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The group law on ellitic curves, and finding
rational and integral points
(PS,
PDF,
DVI)
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Congrence and Hasse-Weil Zeta functions
(PS,
PDF,
DVI)
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Solving x^3 + y^3 = z^3 and x^4 + y^4 = z^4
(PS,
PDF,
DVI)
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Cubic and Biquadratic Reciprocity
(PS,
PDF,
DVI)
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Cyclotomic numbers and Fermat's Last Theorem
(PS,
PDF,
DVI)
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Special values of zeta(s)
(PS, PDF, DVI)
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Constructibility of Regular Polygons
(PS, PDF, DVI)
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...
(PS, PDF, DVI)
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Homeworks
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HW #1
(PS,
PDF,
DVI)
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HW #2
(PS,
PDF,
DVI)
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HW #3
(PS,
PDF,
DVI)
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HW #4
(PS,
PDF,
DVI)
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HW #4.5
(PS,
PDF,
DVI)
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HW #5
(PS,
PDF,
DVI)
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HW #5.5
(PS,
PDF,
DVI)
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