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Shor's algorithm: factoring integers
Covers the basics of Shor's algorithm for factoring integers and the steps involved in the quantum algorithm.
Elementary Algebra: Numeric Sets
Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.
Integers and Rings
Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.
Complexity & Induction: Algorithms & Proofs
Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.
Hermite Normal Form: Computation & Properties
Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.
Mathematical Parenthesis on Groups and Lagrange Theorem
Explores cosets in commutative groups, Lagrange theorem, and integer factorization.
Cartesian Product and Induction
Introduces Cartesian product and induction for proofs using integers and sets.
Discrete Log Problem: Pollard's Rho Method
Introduces Pollard's rho method for the discrete log problem and finding collisions efficiently in a cyclic group.
Mathematical Induction: Basics and Applications
Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.
Number Theory: GCD and LCM
Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.