The vector

* What is a vector?

** Vectors are functions

** Representation of vectors using Python dictionaries

*** Sparsity

** What can we represent with a vector?

* Vector addition

** Vector addition: The zero vector

** Vector addition: Vector addition is associative and commutative

** Vector addition: Vectors as arrows

* Scalar-vector multiplication

** Scalar-vector multiplication: Scaling arrows

** Scalar-vector multiplication: Associativity of scalar-vector multiplication

** Scalar-vector multiplication: Line segments through the origin

** Scalar-vector multiplication: Lines through the origin

* Combining vector addition and scalar multiplication

** Combining vector addition and scalar multiplication: Distributive laws

** Combining vector addition and scalar multiplication: First look at convex combinations

** Combining vector addition and scalar multiplication: First look at affine combinations

* Vectors over GF(2)

** Vectors over GF(2): Perfect secrecy

** Vectors over GF(2): All-or-nothing secret-sharing using GF(2)

** Vectors over GF(2): Lights Out

* Dot-product

** Dot-product: Total cost or benefit

** Dot-product: Linear equations

** Dot-product: Measuring similarity: Comparing voting records

** Dot-product: Vectors over GF(2)

*** Dot-product: Simple authentication scheme

*** Dot-product: Attacking simple authentication scheme

* Dictionary-based representations of vectors

** Dictionary-based representations of vectors: Setter and getter

** Vec class

** Using Vec

*** Assertions in Vec

*** Testing Vec with doctests

*** list2vec

*** The vecutil module

* Solving a triangular system of linear equations

** Solving a triangular system of linear equations: Backward substitution

* 
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