Math 480 - Homework 6
Due ...

As usual, write in your diary as you do the following exercises. TeX submission required.

  1. If you did the last homework you have installed mathematica. Now install sage.

  2. Choose half a dozen varied interesting exercises from math courses you've taken or are taking and figure out how to do them with mathematica or with sage. Some should be from calculus, but I'd love to see examples from linear algebra, differential equations, discrete math ...

    In the previous paragraph, read the "or" the way mathematicians do. It's inclusive. I'd really like you to do some of the problems with both, and compare the process. (I assume the answers will be the same.)

    Note: this is not a programming question. Choose exercises that are essentially computations (some symbolic, some numerical), not proofs.

    Sample question: http://math.stackexchange.com/questions/1247252/how-to-integrate-frac1x2-4x63-2-with-respect-to-x">

    Can you do this in Mathematica? Can you get Mathematica to tell you how you could have done it yourself?

  3. Here are seven text files to decode. I've permuted just the alphabet, leaving white space, punctuation and numbers as in the original. No serious encryption would do that.

    Find the orginal plaintext for each file. Document your steps and thought process in your TeX solution. You should probably begin with letter frequencies, perhaps digraphs. Use your scramble.py to do partial replacements as you experiment.

    The word structure will help. At some point you might be able to begin to make guesses based on content. The file names might help. (Matt should be able to decode his without doing any work at all.)

    When you've solved a puzzle, find the source of the plain text.