We define the notion of a module and show how essentially, it is just a way of expressing solutions to matrix equations.
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Weil's insight: A Lefschetz fixed point formula for varieties?
Zeta functions for varieties over finite fields
What are the Weil conjectures about?
Galois cohomology and descent data
Central simple algebras as twisted forms of matrix algebras
Descent data and twisted forms
Grothendieck topologies
Fibre products and Galois covers
Etale cover - open cover analogy
Difference Operator
The simply connected or universal covering space
Partitions
Fundamental Group of Circle and the Fundamental Theorem of Algebra
Linear Ordinary Differential Equations
ExponentialGenerating Functions
Counting and bijections
Catalan numbers
Counting monomials
Taylors theorem
Analytic Power Series
Ratio test for convergence
Cauchy products and absolutely convergent series
Cauchy Completeness and existence of limits.
Lifting properties of covers and deck transformations