Two Tracks, One Exploration

Choose your path through AI and Mathematics.
Six weeks of independent exploration, deep learning, hands-on projects, and exposure to frontier topics.

Weeks 1-2

Shared Foundations

Weeks 3-4

Track Specialization

Weeks 5-6

Advanced Topics & Projects

All Students AI Mathematics Data Science Natural Language Processing Number Theory Algebraic Geometry Group Theory Other Topics Final AI Projects Final Math Projects

Choose Your Track

Both tracks emphasize deep understanding through exploration. Choose what excites you the most — you'll have opportunities to explore and see connections.

AI Track

Build intelligent systems from the ground up

You'll Learn To

  • Write Python code for data analysis and modeling
  • Build and train machine learning models
  • Understand how neural networks learn
  • Work with modern NLP and language models
  • Think critically about AI capabilities and limitations
Frontier Exposure

Large language models, transformer architectures, AI agents, and the mathematics behind deep learning.

Mathematics Track

Explore the deep structures of mathematics

You'll Learn To

  • Think rigorously about proofs and mathematical structure
  • Explore number theory and its applications
  • See geometry through an algebraic lens
  • Understand abstract algebra and group theory
  • Connect different areas of mathematics
Frontier Exposure

Elliptic curves, modular forms, the classification of finite simple groups, and connections to modern cryptography.

Prerequisites by Track

AI Track

  • Some programming experience (Python preferred)
  • Comfort with algebra and graphing
  • Familiarity with systems of linear equations and matrices
  • Geometry helpful but not required

Mathematics Track

  • Comfort with algebra and polynomial equations
  • Basic geometry
  • Graphing fundamentals
  • Programming helpful but not required

Exposure to precalculus is helpful but not required for either track. Enthusiasm to explore and experiment is essential! We'll send preparation materials to all admitted students.

Your Six-Week Journey

Weeks 1-2

Shared Foundations

All students explore both AI and Mathematics together, building a common foundation and discovering where their interests lie.

AI Track Math Track attends

Introduction to AI & Python

Get hands-on with the tools and concepts of modern AI.

  • What is AI?
  • Introduction to Python
  • Working with Jupyter Notebooks
  • Introduction to Data
  • Introduction to Modeling
  • Vibe Coding & Making Models
Math Track AI Track attends

Mathematical Foundations

Build rigorous mathematical thinking from the ground up.

  • What is Mathematics?
  • Axioms and Arithmetic
  • Properties of Arithmetic
  • Solving Linear Equations
  • Solving Quadratic Equations
  • Plane Geometry, Lines & Conics
Weeks 3-4

Deep Exploration

Choose your path and go deeper. Select specialized courses within your track based on your interests.

AI Track – 2 options

Data Science

  • Linear & Polynomial Regression
  • Regularization Techniques
  • Binary Classification
  • Hyperplane Classification
  • Decision Trees & Random Forests

Natural Language Processing

  • Classification Models
  • Hidden Markov Models
  • Cryptography & Linguistic Statistics
  • Probability and Statistics
  • Sentiment Analysis & Tokenization
Math Track – 3 options

Number Theory

  • Modular Arithmetic
  • Prime Numbers & Factoring
  • Chinese Remainder Theorem
  • Quadratic Reciprocity

Algebraic Geometry

  • Intersecting Lines & Conics
  • Relating Shapes and Equations
  • Counting Intersections
  • Projective Space

Group Theory

  • What is a Group?
  • Subgroups and Cosets
  • Product and Quotient Groups
  • Finite Groups and Abelian Groups
Weeks 5-6

Make It Your Own

The final stretch is yours to shape. Pursue an independent project, or dive deeper into advanced frontier topics.

AI Advanced Topics

Neural Networks & Deep Learning

  • Neural Network Models
  • Training Neural Networks
  • Convolutional Neural Networks
  • Transformer Models
  • Word2Vec & Vector Embeddings

Large Language Models

  • BERT Models & Machine Translation
  • Transformer Architectures
  • AutoEncoders
  • PyTorch & Training LLMs
  • LLM Tooling, MCPs, and Agents
Math Advanced Topics

Number Theory Frontiers

  • Hilbert Symbols
  • Rational Points on Conics
  • Gauss Sums
  • Cyclotomic Fields

Algebraic Geometry Frontiers

  • Divisors on Curves
  • Genus 1 Curves & Elliptic Curves
  • Plane Embeddings
  • Moduli and Modular Curves

Group Theory Frontiers

  • Solving the Rubik's Cube
  • Simple Groups & Classification
  • Sporadic and Exceptional Groups
  • Lie Groups & Root Systems

Ready to Explore?

Whether you're drawn to AI, mathematics, or both — we'd love to have you join us for six weeks of discovery.

Start Your Application

Commitment to Nondiscrimination

The AIMS Summer School does not discriminate on the basis of race, color, national origin, ancestry, sex, gender, gender identity, gender expression, sexual orientation, age, religion, disability, marital status, veteran status, genetic information, or any other characteristic protected by applicable federal, state, or local law in its admissions, educational programming, financial aid, employment practices, or other activities.

We recognize the existing gender and racial disparities within the mathematics community. In our commitment to fostering a diverse and inclusive environment, we highly encourage applications from individuals of underrepresented backgrounds.