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Octahedral tangle of four trefoil knots by Carlo H. Séquin at UC Berkeley

Pure Math Python

Number Theory, Knot Theory, and Optimization

Number Theory

 

Articles about interesting, and sometimes surprising, relationships in number theory, for example:  For large n, Euler’s constant e is equal to the factorial of n divided by the number of derangements in the set of permutations of n.   I use Python for symbolic and numeric experiments that demonstrate the concepts, identities, and theorems.

The target audience is undergraduate Mathematics majors and Mathematics graduate students.

 

Knot Theory 

 

Python code that explores two ways to derive the Alexander polynomial for a knot:  the first using the knot’s braid and the second using the knot's quandles.

 

The target audience is undergraduate Mathematics majors and Mathematics graduate students.

 

Optimization

 

An introduction to symbolic programming in Python using Sympy, together with Python-oriented explanations of selected topics in optimization theory and optimization algorithms.

 

The target audience is undergraduate Mathematics and Economics majors.