MAT 331 - Computer-Assisted Mathematical Problem Solving - Fall 2023
TuTh 4:00PM - 5:20PM at Math Tower S-235S (computer lab in basement)
MAT 331 - Computer-Assisted Mathematical Problem Solving - Fall 2023
TuTh 4:00PM - 5:20PM at Math Tower S-235S (computer lab in basement)
For the first few weeks we will be following Learning MATLAB by Tobin Driscoll. Link to SIAM site to purchase a hard copy.
A link to the virtual SINC site.
Scripts and functions should be saved in your MySBFiles directory; other dirctories on the SINC site machines are erased after 48 hours. These MySBFiles can be accessed directly from any machine with an internet connection at MySBFiles.
The university has a WRTD writing requirement that can be fulfilled by submitting two of the projects from this class. If you intend to fulfill the requirement this way, let me know you want to use your MAT 331 projects for this requirement, and register for the zero-credit course MAT 459. I will post possible projects here as the semester proceeds and we will discuss a few in class.
Grades will be based on:
(1) In class quizzes (25%). I will provide a sample practice quiz to do at home beforehand.
(2) Homework (25%). Like a mini-project. This will involve writing a short report stating the problem, describing how to solve it, the MATLAB code you used, and a table of pictures that illustrate your solution.
(3) Projects (50%). Longer than a homework and usually involving a little outside reading. You must do two out of a selection of projects. There will be a third optional project to improve your grade.
Some topics we will explore if time permits include:
Prime numbers
Graph theory, random graphs
Random walks, harmonic measure
DLA (Diffusion Limited Aggregation)
Percolation
Root finding, Newton's method
Polynomial Iteration
The Mandelbrot set & Julia sets
Shift codes, Substitution codes
Letter frequency, digrams
One time pads, Venona
RSA
Class Projects:
Due November 9th
The giant component of a random graph based on "The evolution of random graphs" by Bela Bollobas
The box-counting dimension of the Weierstrass function; see this video for an introduction to fractals and dimension
Points of increase in random walk based on "Point of increase for random walks" by Yuval Peres
Due November 30th (choose 1)
Distinguishing authors; narrative.txt, cask.txt, usher.txt, sawyer.txt, finn.txt, innocents.txt, roughing.txt
Solving a random shift code; rs.m; mystery.txt.rs
Primality testing; see this video for an introduction
Matlab can be opened either through the virtual sinc site itself or through the "virtual sinc site desktop" on the virtual sinc site.
With MATLAB open, by default there is a path that looks like:
C:\Program Files\MATLAB\R2022a\bin
Change this by clicking the arrow to the left of C: to X:. This will allow you to save files in MySBFiles
You will need to mount MySBFiles. Open "MATE terminal" (this is different from the regular terminal). It will prompt you for your NETID password. Now, in MATLAB you can change your current directory to MySBFiles to see, save, and load your files.
How to write projects/ homework
Write the homework and projects through the matlab editor. To access this, type: edit
Give a title and separate each problem with a section by use of %%. Type any comments with %. Each problem should have comments explaining the problem and your solution, as well as possibly any code to go along with it, and the final output. Remember you can supress any unneeded output with the use of a semicolon ; at the end of a line.
Homeworks/ Projects should then be published to pdf using the "Publish" button. They will by default be saved in a folder called "html".
Do not forget to explain what you are doing clearly! This counts just as much as getting the correct answers for the homeworks and projects.
August 29 Introduction; course admin, class webpage, how to download and open MATLAB/ virtual SINC site, open documentation, format long, pi, arithmatic, digits, vpa, sqrt, sin, exp, char, strfind
August 31 vectors and matrices, colon operator, sum, MySBSFiles, creating a directory, subdirectories, save, load; Practice quiz 1; Scripts
September 5 plot, scatter, scatter 3, figure, hist, hold on, grid on, title, legend, linspace, find, logical indexing; Quiz 1 (last 30 mins of class). Scripts. Plotting didn't work well today. To fix this enter opengl('save','software') upon opening matlab. You may need to reopen matlab for it to take effect.
September 7 Editor; publish; Sample homework; Sample homework Tex; Script; Sample Solution.
September 12 Polynomials; tic toc, anonymous functions, fzero, bisection; Scripts
September 14 More on polynomials and Newtons method; Homework 1 due; Practice quiz 2; Scripts
September 19 rand and some probability; Quiz 2 (last 30 mins of class); Scripts
September 21 Area of disks; Scripts
September 26 More probability; Scripts
September 28; Graphs; Homework 2 due (volumes of n-balls); Scripts
October 3 Graphs; Scripts
October 5 Random graphs, the giant component; Practice Quiz 3; graphs.mat; Scripts
October 10 (Fall Break: No Classes in Session)
October 12 Random graphs; Quiz 3 (last 30 mins of class); Scripts
October 17 Hall's marriage problem; Tutte's perfect matching criteria; Scripts
October 19 Cryptography; Practice quiz 4; Scripts
October 24 Cryptography; Homework 3 due; genealogy.mat; Scripts
October 26 Cryptography; Quiz 4 (last 30 mins of class)
October 31 Cryptography
November 2 Questions about projects
November 7 RSA
November 9 Project 1 due
November 14 von Koch snowflake; Real Iteration; Scripts
November 16 Complex iteration
November 21 Complex iteration (Lesson recorded) Password: @%d0R8gJ ; Scripts
November 23 (Thanksgiving break: No Classes in Session)
November 28 Mandelbrot set; Newton's method revisited; Scripts; Two notes on Julia sets and the Mandelbrot set
November 30; Random walks Project 2 due; Scripts
December 5; harmonic measure and DLA
December 7; harmonic measure and DLA (Last Day of Class); Homework 4; Scripts
December 19, 5:00 PM: Last chance to turn in optional third project. NO FINAL EXAM.
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