Algorithms & Theory

This course is a foundational introduction to computational complexity theory, covering Turing machines, decidability, complexity classes (P, NP, PSPACE), and the P vs. NP problem, defining the core of the subfield.

Demaine's work on algorithmic lower bounds and hardness of approximation directly addresses fundamental questions within computational complexity theory.

O'Donnell's research on analysis of Boolean functions and hardness of approximation directly contributes to the theoretical foundations of computational complexity.

Arithmetic geometry provides the deep mathematical foundations for modern cryptography, particularly elliptic curve cryptography, by leveraging properties of algebraic varieties over finite fields for secure key exchange and digital signatures.

SICP's rigorous approach to program construction and reasoning, particularly its emphasis on referential transparency and formal semantics, naturally bridges to formal methods and type theory for program correctness.

This lecture explores alternative foundational approaches to mathematics, specifically multiset theory, which offers a different perspective on cardinality and arithmetic compared to traditional set theory and category theory.