18.781 | Spring 2012 | Undergraduate

Theory of Numbers

Lecture Notes

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756 kB
Cyclotomic Polynomials, Primes Congruent to 1 mod n, Lecture 12 Notes
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292 kB
Introduction, Lecture 1 Notes
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734 kB
Euclidean Algorithm, Primes, Lecture 2 Notes
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753 kB
Binomial Coefficients, Congruences, Lecture 3 Notes
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326 kB
Fermat, Euler, Wilson, Linear Congruences, Lecture 4 Notes
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802 kB
Linear Congruences, Chinese Remainder Theorem, Algorithms, Lecture 5 Notes
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763 kB
Primality, Factoring, RSA, Hensel's Lemma, Lecture 6 Notes
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812 kB
Congruences mod Primes, Order, Primitive Roots, Lecture 7 Notes
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765 kB
Primitive Roots (Prime Powers), Index Calculus, Lecture 8 Notes
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765 kB
Quadratic Residues, Quadratic Reciprocity, Lecture 9 Notes
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694 kB
Jacobi Symbol, Computation, Zolotareff's Definition, Lecture 10 Notes
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768 kB
Square Roots, Tonelli's Algorithm, Number of Consecutive Pairs of Squares mod p, Lecture 11 Notes
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312 kB
Arithmetic Functions, Lecture 13 Notes
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764 kB
Mobius Inversion Formula, Zeta Functions, Lecture 14 Notes
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764 kB
Linear Recurrences, Lecture 15 Notes
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725 kB
Generating Functions, Lecture 16 Notes
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312 kB
More on Generating Functions, Two Squares Theorem, Lecture 17 Notes
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751 kB
Continued Fractions I, Lecture 18 Notes
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759 kB
Continued Fractions II: Inequalities, Lecture 19 Notes
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746 kB
Periodic Continued Fractions, Quadratic Irrationalities, Lecture 20 Notes
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771 kB
Brahmagupta-Pell Equation, Lecture 21 Notes
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752 kB
Four Squares Theorem, Lecture 22 Notes
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742 kB
Pythagorean Triples, Fermat Descent, Lecture 23 Notes
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741 kB
Rational Points on Conics, Lecture 24 Notes

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Spring 2012
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Undergraduate
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