Lecture topics and Jupyter notebook files

I will be posting the Jupyter notebooks that I make during each of the two lectures. If you just want to view the notebooks or copy and paste from them, use the HTML version. If you want to run them on your computer, you will need the ipynb version (see comment at bottom). Notebooks from the two lectures be quite similar, but one or the other may have more comments, so it may be helpful to look at both.

Thur May 7: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Poisson distribution, Binomial distribution

Tue May 5: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Connectedness of graphs, Depth First Search

Thur April 30: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Random walk on a graph, Random graph with fixed number of vertices and edges

Tue April 28: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Normal distribution, probability density function, Graphs/Networks, drawing graphs with networkx

Thur April 23: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

More Law of Large Numbers, Variance of a random variable, Central Limit Theorem

Tue April 21: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Random variables, Averages of random variables, Law of Large Numbers

Thur April 16: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Brownian motion fractal curve as the limit of random walks, finding the appropriate scaling for random walk

Tue April 14: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Mandlebrot set, Fixed/periodic points

Thur April 9: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Zooming in on Julia sets, Orbits, Colored Julia sets

Tue April 7: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Review of Julia sets, sage function to draw Julia sets for f(z)=z^2+c

Thur April 2: Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Review of complex numbers, complex valued functions, Julia sets

Tue Mar 31: (See Blackboard->Zoom for recording) Lecture 1 ipynb, Lecture 1 HTML, Lecture 1 Whiteboard | Lecture 2 ipynb, Lecture 2 HTML , Lecture 2 Whiteboard

Sierpinski triangle, drawing it with Sage, area and dimension of Sierpinski triangle

Thur Mar 12: tree_turtles.py

Length of Koch snowflake, fractal dimension of Koch snowflake, fractal binary tree drawn with python turtle graphics

Tue Mar 10: snowflake_turtles.py, Fractal gallery

Intro to fractals, drawing a Koch snowflake using python turtle graphics (doesn't work with Jupyter; see Useful resources for instructions on using turtle graphics).

Thur Mar 5: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Euler's totient theorem, RSA public-key cryptosystem

Tue Mar 3: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Sage builtin functions for number theory (is_prime, next_prime, rand_int, power_mod), Diffie-Helmann key-exchange, Fermat's little theorem

Thur Feb 27: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Modular exponentiation: fast algorithm using repeated squaring and binary expansion, different bases (binary, decimal, hexadecimal)

Tue Feb 25: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Using Extended Euclidean algorithm to compute modular inverses, modular exponentiation, modular exponentiation using repeated squaring when exponent is power of two

Thur Feb 20: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Debugging strategies, greatest common divisor (gcd) using Euclidean algorithm

Tue Feb 18: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Modular multiplication cipher, recursion (use to compute factorial, Fibonacci sequence)

Thur Feb 13: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Vigenere cipher, one-time pad

Tue Feb 11: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Lists (accessing elements, last element, length), strings, Fibonacci sequence, list of squares of integers, Cryptography, keyboard cipher, shift (Caesar) cipher

Tue Feb 4: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

More for loops, using for loop to compute sum and product, test for even/odd using mod %, while loop, defining functions

Thur Jan 30: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Opening ipynb with Jupyter/Sage, variables, = vs ==, comparison, logical connectors (and,or), if statements, for loops

Tue Jan 28: Lecture 1 ipynb, Lecture 1 HTML, Lecture 2 ipynb, Lecture 2 HTML

Opening Sage, using Jupyter notebook, basic arithmetic, plot, polynomials, factor, lists

Running the ipynb notebooks: Make sure the name of the file you get ends with .ipynb rather than .txt. To ensure this, right-click the link, and select the appropriate menu option. Alternatively, if you get a .txt file, manually rename it to remove the .txt at the end. Once downloaded in proper form, open sage/juptyer and find the file on the dashboard, and open it from there.