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WASH SUMMER RESEARCH INSTITUTE 2025

The Wash Summer Research Institute is a 6-week-long virtual program, completely free of cost, designed for curious and motivated students in grades 6–11. Meeting once a week from June 22 to July 27, this program offers an engaging and accessible way to explore advanced topics in STEM.

💡 Course Offerings:

🔢 Introduction to Number Theory – Dive into the world of primes, modular arithmetic, and cryptography.
🧠 Computational Neuroscience – Explore how we can model the brain using Python and data science.
🤖 Demystifying Deep Learning – Unravel the magic behind neural networks and artificial intelligence

No prior experience is required—just curiosity and a willingness to learn! 🚀 Apply now to expand your knowledge and connect with like-minded peers.

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DEADLINE to apply: May 21st, 2025 11:59 PM

COURSE OUTLINES

🔢 Course 1: Introduction to Number Theory

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Week 1: Foundations of Number Theory

  • Introduction to number theory & its real-world applications

  • Divisibility, prime numbers, greatest common divisor (GCD)

  • Activity: Implement the Euclidean Algorithm by hand

Week 2: Modular Arithmetic & Congruences

  • Understanding modular arithmetic (clock math)

  • Solving modular equations

  • Activity: Crack a basic modular arithmetic puzzle

Week 3: Prime Numbers & Factorization

  • Sieve of Eratosthenes (prime number generation)

  • Euler’s Totient Function

  • Activity: Write a simple Python program to generate primes

Week 4: Cryptography & Number Theory

  • RSA encryption & public-key cryptography

  • Computing modular inverses

  • Activity: Encrypt and decrypt a message using RSA

Week 5: Quadratic Residues & Advanced Topics

  • Quadratic residues & Legendre symbol

  • Pell’s Equation and integer solutions

  • Activity: Solve a real-world Pell’s equation problem

Week 6: Open Problems in Number Theory

  • Goldbach’s Conjecture, Twin Prime Conjecture

  • Introduction to continued fractions

  • Activity: Explore an open problem and discuss its implications

🔹 Capstone Project: “The Mathematics of Secrets” – Students design and implement a simple encryption scheme using modular arithmetic and prime factorization, then test it by encrypting/decrypting messages.

🧠 Course 2: Computational Neuroscience

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Week 1: Introduction to Neuroscience & Python Basics

  • Overview of neurons, synapses, and networks

  • Introduction to Python for neuroscience (NumPy, Matplotlib)

  • Activity: Simulate a simple neuron firing in Python

Week 2: Modeling Neurons with Code

  • Hodgkin-Huxley & Leaky Integrate-and-Fire models

  • Simulating neuron dynamics

  • Activity: Implement a basic spiking neuron model

Week 3: Neural Networks & Learning Mechanisms

  • Hebbian learning & synaptic plasticity

  • Modeling neural adaptation

  • Activity: Code a Hebbian learning rule in Python

Week 4: Neural Data Analysis & Visualization

  • Introduction to EEG and fMRI

  • Analyzing real neural datasets

  • Activity: Visualize EEG data with Python

Week 5: Brain-Machine Interfaces & AI Connections

  • How BMIs work & real-world applications

  • AI models inspired by neuroscience

  • Activity: Explore neural networks and compare to biological neurons

Week 6: The Future of Neuroscience & Ethical Considerations

  • Neuroethics & emerging research

  • Open discussions on brain augmentation & AI

  • Activity: Debate the ethics of brain-enhancing technology

🔹 Capstone Project: “Simulating a Digital Brain” – Students create a basic computational model of a neural circuit (e.g., visual processing or decision-making) and analyze how it behaves under different conditions.

🤖 Course 3: Demystifying Deep Learning

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Week 1: Introduction to Neural Networks

  • What is deep learning? How does it mimic the brain?

  • Basics of perceptrons and activation functions

  • Activity: Build a simple perceptron in Python

Week 2: Training a Neural Network

  • Gradient descent & backpropagation

  • Training a model with TensorFlow/PyTorch

  • Activity: Train a neural network to recognize handwritten digits

Week 3: Convolutional Neural Networks (CNNs) & Image Recognition

  • How CNNs process images

  • Feature extraction & filter visualization

  • Activity: Implement a CNN to classify images

Week 4: Recurrent Neural Networks (RNNs) & Time-Series Data

  • How RNNs handle sequential data

  • Applications in text and speech recognition

  • Activity: Train an RNN to generate simple text predictions

Week 5: AI Ethics & Bias in Deep Learning

  • Where AI fails & why it can be biased

  • Ethical concerns with large-scale AI models

  • Activity: Analyze bias in an AI model

Week 6: Future of Deep Learning & AI Applications

  • AI in neuroscience, medicine, and sustainability

  • Open-source AI models and ongoing research

  • Activity: Brainstorm ethical AI applications

🔹 Capstone Project: “Training an AI for Good” – Students design and train a deep learning model for a meaningful application (e.g., classifying handwritten numbers, detecting environmental changes, or analyzing simple text patterns).

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