Program/Course Material
SWIM 2010
Here below you can find additional program/course material.
| Course I | An Introduction to Number Theory and Diophantine Equations |
| Bibliography | My Numbers, My Friends; Intro to Number Theory; An Intro to the Theory of Numbers; Queen of Mathematics; A Pathway Into Number Theory; Disquisitiones Arithmeticae |
| The Definition of Genera | The Definition of Genera |
| Lecture Summaries | Lecture 1: Famous Diophantine Equations |
Lecture 2: A First Look at Binary Quadratic Forms |
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Lecture 3: Fundamental Questions |
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Lecture 4: Importance of Equivalence |
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Lecture 5: Reduction of Forms |
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Lecture 6: Reduced Forms Are Representatives of Equivalence Classes |
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Lecture 7: Genus Theory |
| Course II | Introduction to Abstract Algebra with Applications to Social Systems |
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| Lecture Notes 1 of 7 | Course Outline, Introduction, Sociometric Matrices, The Rise of the Medici, Markov Chains, The DeGroot Model, Primitive Societies, Family Tree Diagrams, Primitive Marriage Rules, and Additional Topics - Southern Women, Southern Women Data |
| Lecture Notes 2 of 7 | Course Reference, Sociometric Matrices, Degree Distributions, Matrix Algebra Review, Communication Networks, and Power |
| Lecture Notes 3 of 7 | Communication Networks, Power, and Markov Chains |
| Lecture Notes 4 of 7 | Markov Chains and The DeGroot Model |
| Lecture Notes 5 of 7 | The DeGroot Model, Symmetries of the Square, Groups, Properties of Groups, Primitive Societies, Primitive Marriage Rules, Family Tree Diagrams |
| Lecture Notes 6 of 7 | Course Resource, Group, Symmetries of the Square, Properties of Group, Subgroup Tests, Primitive Marriage Rules, Permutation Groups, Functions, Multiple Network Relations, Local Network Structure, Sothern Women Data |
| Lecture Notes 7 of 7 | Southern Women, Southern Women Data, Graph Partitioning |