Lectures related to Arithmetic

Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.

Explores the implementation of digital filters, emphasizing memory cells, circular buffers, and real-time processing challenges.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Introduces floating point number representation, round-off errors, and their impact on numerical computations.

Covers Barrett reduction, Montgomery form of integers, and efficient Montgomery product computation.

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.