Mathematics

Bolzano–Weierstrass Theorem; Cauchy Sequences; Series

Limsup and Liminf; Power Series; Continuous Functions; Exponential Function

Error-Correcting Codes: Hamming Codes

Review for 18.100B Real Analysis Midterm

Duality in Linear Programming

Generative AI: Text-to-Image Models

Deep Learning for Natural Language: Transformers, Self-Supervised Learning

Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space

Lecture 20: Pointwise Convergence; Uniform Convergence

Lecture 6: Cauchy Convergence Theorem

Introduction to Linear Programming

Tropical Geometry for the One-Loop Cosmological Collider

Singularities in Mixed Characteristic

The Pila-Zannier Strategy for Drinfeld Modules

Edge Modes on String Horizons

Frobenius Structures on Quantum Connections of Calabi-Yau 3-Folds

Bounded Arithmetic Meets Probability, and Applications in Cryptography

Hodge Theory and Representations of Real Groups

Automorphism in Gauge Theory and Clifford-Hierarchy Stabilizer Codes

Combinatorics and Geometry of Fundamental Physics and Cosmology

Constrained Floer Homology

On Dimension and Absolute Continuity of Self-Similar Measures

Beyond Translation-Invariance in Arithmetic Harmonic Analysis

Lattice Packing of Spheres in High Dimensions Using a Stochastically Evolving Ellipsoid