Lectures related to Binary Operations: Addition and Multiplication

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Modular Arithmetic: Understanding RSA Cryptosystem

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Prime Numbers: Deterministic Approaches

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Number Theory: Modular Arithmetic

Explores modular arithmetic, congruence, and number manipulation in a mathematical context, showcasing the power of modular reduction and the tricks of casting out nines.

Number Theory: Integer Representation

Covers the representation of integers using different bases and algorithms for base expansion.

Prime Numbers and Algorithms

Covers prime numbers, primality testing algorithms, modular arithmetic, and efficient exponentiation methods.

Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Binary Numbers and Bit Fields

Introduces binary numbers, modular arithmetic, signed numbers, and character encoding in C.

Algorithms Exam Preparation

Offers a recap before the Algorithms exam, covering problem-solving strategies and algorithm implementation with sample problems.

Exponentiation: Time Complexity

Covers the fast exponentiation algorithm and its time complexity, prime number properties, and the El-Gamal encryption scheme.

Algorithms in Computer Science: Search and Sort Techniques

Provides an overview of essential search and sort algorithms in computer science.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Integer Representations: Magnitude & Complement

Explores integer representations, focusing on sign-and-magnitude, one's complement, two's complement, Excess-N, overflow, underflow, and binary multiplication.

Rudiments of Number Theory

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

Algorithms: Final Exam Review

Provides a detailed review of the 2016 final exam, covering various algorithmic problems.