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
Lecture 3: Fundamental Questions
Lecture 4: Importance of Equivalence
Lecture 5: Reduction of Forms
Lecture 6: Reduced Forms Are Representatives of Equivalence Classes
Lecture 7: Genus Theory


Course II Introduction to Abstract Algebra with Applications to Social Systems
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