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.