Ergodic Theory
This book builds up ergodic theory from the ground up, starting with measure theory, based on classes I taught at Euler Circle.
Books
Books I have written.
Transition to Proofs
This book helps students transition from numerical-answer problems to proof-based mathematics, while also teaching interesting mathematics, focusing on number theory, combinatorics, and analysis. It is intended for students who already have significant problem-solving background, based on a yearlong sequence I have taught many times at Euler Circle.
Algebraic Topology
This book builds up to algebraic topology starting by introducing point-set topology and group theory. It covers the classification of compact surfaces, fundamental groups, and the basics of homology. This is based on a class we taught at SUMaC for many years.
Cryptography
This book begins with classical ciphers such as the substitution and Vigenère ciphers. Then it shifts to modern cryptography, including Diffie-Hellman, RSA, and elliptic curve cryptography. It concludes with some more specialized topics such as zero-knowledge proofs, secret sharing, cryptographic voting, and quantum computing. This is based on classes I taught at EPGY and Euler Circle.
