Course outline
July 6, 2022
Course outline #
Lecture 1: Sets, bags, lists #
Mathematical structures as data structures (5 min) #
- sets, bags, lists, tuples
Multiplicity functions (10 min) #
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Representing data structures as oracles that answer questions about themselves
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Example of a traditional duality
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Union, intersection, chaining, in terms of multiplicity
Lifting functions (15min) #
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functions as uniform relations, relations as pixelated images
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lifting functions: multi-images and multi-pre-images
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multi-functions as images
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multi-images as counting pixels in rows and columns
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multiple arguments
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application of lifting: pairing (5 min)
Lecture 2: Groups, graphs, and paths #
Graphs (10 min) #
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kinds of graph
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labeled graphs
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graph homomorphisms
Groups (10 min) #
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Cyclic, Dihedral
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how groups generate labeled graphs
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subgroups
Paths (10 min) #
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Groupoid structure of paths
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Path maps as groupoid homomorphisms
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Kinds of path homomorphism
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Application: Coverings