Lecture topics and Jupyter notebook files

Thur May 9: lec_0509.ipynb, HTML version viewable in browser

• Degree sequence of random graph vs Poisson; Graph connectedness using Depth First Search

Tue May 7: lec_0507.ipynb, HTML version viewable in browser

• Random walk on graph; random graphs (fixed num of edges); degree sequence vs Poisson

Thur May 2: lec_0502.ipynb, HTML version viewable in browser

• Graphs in the real world and in math; random walk on graph

Tue April 30: lec_0430.ipynb, HTML version viewable in browser

• Generating samples from actual Poisson, standard Normal distributions; Intro to Graphs/networks

Thur April 25: lec_0425.ipynb, HTML version viewable in browser

• Poisson distribution

Tue April 23: lec_0423.ipynb, HTML version viewable in browser

• Discrete vs Continuous Random Variables; Probability Mass Function (pmf); Probability Density Function (pdf); Normal Distribution

Thur April 18: lec_0418.ipynb, HTML version viewable in browser

• Law of Large Numbers; Central Limit Theorem; demonstration with histograms

Tue April 16: lec_0416.ipynb, HTML version viewable in browser

• Random walk; Brownian motion as limit of random walk

Thur April 11: lec_0411.ipynb, HTML version viewable in browser

• Review of Mandblebrot set; Fixed and periodic points; attracting fixed points and multiplier test; drawing orbits

Tue April 9: lec_0409.ipynb, HTML version viewable in browser

• Mandblebrot set; Zooming in near Feigenbaum point

Thur April 4: lec_0404.ipynb, HTML version viewable in browser (Corrected)

• Julia sets for linear polynomials az+b; Zoom in on Julia set; Colored Julia set

Tue April 2: lec_0402.ipynb, HTML version viewable in browser (Corrected)

• Finish up Apollonian gasket (see last class notebook); Julia sets for polynomials, code for Julia set of quadratic polynomial

Thur March 28: lec_0328.ipynb, HTML version viewable in browser

• Drawing the Apollonian gasket: Descartes circle theorem, classes, ap_circle, ap_gasket

Tue March 26: lec_0326.ipynb, HTML version viewable in browser

• Sierpinski triangle: area, dimension, drawing with Sage; Intro to Apollonian gasket

Thu March 14: tree.py turtle graphics

• Length of Koch snowflake; fractal dimension; Drawing a fractal tree with turtle

Tue March 12: snowflake.py turtle graphics

• Intro to fractals: tour of different fractals, Koch snowflake using turtle graphics

Thur March 7: lec_0307.ipynb, HTML version viewable in browser

• Digital signatures with RSA; SHA hash function; Survey of cryptography-related protocols: commitment, public key, infrastructure

Tue March 5: lec_0305.ipynb, HTML version viewable in browser

• RSA public key cryptosystem, message padding

Thu Feb 28: lec_0228.ipynb, HTML version viewable in browser

• Prime number theorem, finding large primes, discrete logarithm, Diffie-Helmann key exchange algorithm

Tue Feb 26: lec_0226.ipynb, HTML version viewable in browser

• Modular exponentiation, fast algorithm for modular exponentiation using repeated doubling and binary expansion, Fermat's little theorem, Euler's theorem

Tue Feb 19: lec_0219.ipynb, HTML version viewable in browser

• Extended gcd algorithm; computing modular inverses; logarithmic vs linear vs quadratic vs exponential growth; Complexity of addition, multiplication, gcd; Debugging tips

Thu Feb 14: lec_0214.ipynb, HTML version viewable in browser

• Symmetric key vs asymmetric key cryptography, modular multiplication cipher, greatest common divisor (gcd), Euclidean algorithm for gcd

Thu Feb 07: lec_0207.ipynb, HTML version viewable in browser

• Shift cipher again more verbosely, Vigenere cipher, one-time pad, modular arithmetic

Tue Feb 05: lec_0205.ipynb, HTML version viewable in browser

• Start Cryptography Unit: .find, substitution cipher, shift (Caesar) cipher

Thu Jan 31: lec_0131.ipynb, HTML version viewable in browser

• Basics of programming in Sage/Python: lists, print, if, else, for, while, functions, recursion

Tue Jan 29: lec_0129.ipynb, HTML version viewable in browser

• Opening Sage, using Jupyter notebook, basic arithmetic, plot, plot3d, parametric_plot, polynomials, factor, lists