Lectures related to Abstract Concepts: Semi-Ring

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.

Covers the basics of formal languages, including alphabets, words, and languages, as well as operations like concatenation and reversal.

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

Explains the definition and properties of integer multiplication in various scenarios.

Covers the properties of rings, examples of rings, and polynomials.

Covers the addition of fractions and properties of rational numbers, emphasizing associativity and summing fractions with the same denominator.

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Explores properties of matrices, endomorphisms, and linear applications in vector spaces.

Covers the concept of convolution and its properties in signal processing.

Explains how systems are composed in parallel or series.

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Covers set identities and different approaches to prove them, including set builder notation and membership tables.

Covers the fundamental concepts of formal languages, including alphabets, words, languages, and word equality.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Introduces matrix algebra operations and their properties, including commutativity and distributivity.

Covers the concept of natural numbers, including properties like commutativity and associativity.

Explores polynomial operations, properties, and subspaces in vector spaces.

Introduces the basics of group theory, including operations, properties, and Lie groups.

Covers matrix multiplication, properties, and the identity matrix in algebraic operations.

Explains the cup and cap product in algebraic topology and their relation to homology groups.