Program

We begin by learning how mathematical models describe real‑world systems and how small changes in inputs can affect outcomes. Students also get comfortable with Python, the programming language used throughout the camp.

Highlights:

• The modeling cycle

• Linear and proportional models

• Working with data

• Introductory optimization

• Python basics: variables, arrays, plotting, and simple scripts

Students discover how vectors and matrices represent data, transformations, and systems of equations — essential tools for modern modeling and computation.

Highlights:

• Vectors and matrices

• Matrix multiplication

• Systems of linear equations

• Using Python (NumPy) to compute and visualize transformations

We explore how repeated processes evolve over time and how eigenvalues help us understand long‑term behavior in models such as population dynamics and Markov chains.

Highlights:

• Iterative processes

• Eigenvalues and eigenvectors (intuitive approach)

• Applications to population models and Markov chains

• Computing eigenvalues and simulations in Python

Students learn how to make optimal decisions under constraints — a core idea in operations research, economics, and engineering.

Highlights:

• Linear constraints and feasible regions

• Objective functions

• Real‑world optimization problems

• Solving linear programs in Python and visualizing solutions

We study how graphs model connections, routes, and relationships — from transportation networks to communication systems.

Highlights:

• Nodes, edges, and weighted graphs

• Shortest‑path problems

• Applications to routing and logistics

• Building and analyzing networks in Python (NetworkX)

Students learn how randomness influences real‑world systems and how simulations help us understand uncertainty.

Highlights:

• Probability models

• Discrete distributions

• Monte‑Carlo simulation

• Random processes and simple stochastic models in Python

Students split into two small groups and begin a guided modeling project. Each group chooses a theme such as optimization, networks, Markov chains, or simulation.

Highlights:

• Choosing a project topic

• Defining assumptions and goals

• Building the mathematical model

• Beginning the Python implementation

Students complete their projects, prepare visualizations, and present their findings to the group.

Highlights:

• Final computations and analysis

• Creating plots and interpreting results

• Short group presentations

• Certificates and wrap‑up