Lectures related to Algebraic Structures: Groups and Rings

Covers vector spaces in R2 and R3, including planes and lines.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explains orthogonality and characters in group representations, including equivalence classes and vector space dimensions.

Covers the definitions and properties of vector spaces, including axioms and examples.