projects

https://people.sc.fsu.edu/~jburkardt/classes/python_2025/projects/projects.html

projects lists the end-of-semester projects available for students in the class:
MATH 2604: Advanced Scientific Computing 4,
"Mathematical Programming with Python,"
University of Pittsburgh,
Monday/Wednesday/Friday, 1:00-1:50pm,
Instructor: John Burkardt,
Spring Semester 2025.

Each student may design a project based on their own ideas and interests, or select one from the following list.

• Calendar, a calendar is a device for naming and indexing days. Because calendars include information about the day of the week, the month, the season, the year, it becomes difficult to answer simple questions like what day of the week was I born, how many days have I lived, what is today's date in the Chinese calendar, and so on. In this project, you will try to write programs that answer some of these questions.
• Cats, a common machine learning task is to ``classify'' data, that is, to make a judgment about what class it belongs to. An especially difficult classification problem involves images. A special kind of technique for this problem is known as a convolutional neural network, which is able to identify specific features that show up in related images. This project involves running a keras program that tries to determine whether a picture is a cat or a dog. Your task would be to explain how the program works, and what special features of a convolutional neural network make it possible to sort the images.
  Student G.Z. has taken this project.
• Flow Optimization, based on an article by Reinhard Sellmair, which considers the problem of a directed network which includes source and sink nodes, whose links have limited capacity. It is desired to plan the movement of some objects from the source nodes to the sink nodes, minimizing an associated cost. The article points to a Python implementation. You could start by trying to get this code and run it. Then you might try to explain some of what is going on, or come up with some new examples to test the code on.
• HJB PDEs, This project involves Principal Agent problems, which can be formulated as a Hamilton-Jacobi-Bellman PDE. It is interesting to study how the initial condition affects the resulting solution.
  Student C.D. has suggested and reserved this project.
• Keras, using the keras program to analyze a set of 50,000 movie reviews from the Internet Movie Database, which have already been labeled "positive" or "negative" reviews. By looking at the word choice in each review, try to predict the positive or negative rating.
  Student I.Z. has reserved this project.
• Life, this project asks you to implement a Python version of John Conway's Game of Life. This is a simulation studying the changes in a grid of cells, some of which are living and some dead. Deaths and births occur according to a set of rules.
  Student T.Y. has reserved this project.
• Maze, decide how to represent a maze as a rectangular logical array; generate a random maze; try several algorithms that seek a path from a starting point to an end point. Discuss why some algorithms fail.
  Student M.S. has reserved this project.
• Minecraft, an ice farm can be established on an n by n grid of cells. Some cells can be initialized to be permanently occupied by water. A miner can collect the cells that have turned to ice. Afterwards, emptied cells with appropriate neighbors may refill up water, which may then turn to ice. The goal is to generate appropriate choices of the fixed water cells which guarantee a rapid restoration of the ice field.
  Student E.H. has suggested and reserved this project.
• Polygon, for an arbitrary polygon, determine if it is convex or regular (not self-intersecting). Compute the area and centroid. Triangulate a convex polygon (not hard) or a regular polygon (hard, I can give you a code to do this). Compute random samples of a polygon, and estimate integrals. Is a point in the polygon? Do two polygons intersect?
• Primality, finding new prime numbers is useful, because they are part of many encryption systems. Fermat and Mersenne both considered special classes of numbers that seemed to contain many large primes. Checking the primality of a very large number is a difficult task. One tool is the Lucas-Lehmer test. In this project, you will look at using implementing this tool in Python and applying it to several candidates that might be prime.
• Scattering, an important problem in geometry is how to evenly distribute a set of points inside a given shape, which might be a square or circle, a polygon, an ellipse, or an irregular shape such as the outline of a body. A good method for doing this mainly requires the ability to produce as many random sample points from the region as we need. In this project, you will start with a bad arrangement of points inside a circle, and try to transform them into a neat pattern.
• Solar Cycle, based on an article posted on "Towards Data Science", which considers historical data about the sun, including sunspots and solar intensity, and seeks to identify and display patterns in the data.
  Student C.M. has reserved this project.
  Student E.N. has reserved this project.
• StarBattle, an online puzzle game in which you are given a grid subdivided into regions. The player must place a star in each region. However, there must never be two stars in the same row or column.
  Student G.R. has suggested and reserved this project.
• Triangle, compare several methods for generating random points in a triangle. Some of them will not do a good job. Use each method to plot 1000 points and see which plots seem uniform. For the acceptance/rejection approach, you will need to work out a method that decides whether each point you generate is inside the triangle.
• Wator, a simulation of the competition between fish and sharks. It takes place over a 2D grid. Fish swim peacefully, and gradually reproduce, but can get eaten if they run into a shark. Sharks swim around looking for fish, and increase their population if they run into (and eat) a fish. Depending on the simulation parameters, the populations can crash or explode, or evolve into a steady cycle. This is based on a short article by A K Dewdney in Scientific American.
  Student R.C. has reserved this project.