Lectures related to Poincare Inequality: Young the Quality on the Night

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Covers the concept of limits of sequences, including definitions, examples, boundedness, and more.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Complement: Monotone Class Theorem

Explains the independence of events and sets in an algebraic context.

Linear Algebra: Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Introduction to Physics: Observations, Mathematics, and Natural Phenomena

Introduces the basics of physics, emphasizing curiosity, observation, and mathematical description of natural phenomena.

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Group Theory Basics

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Monster Group Construction

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

Quadratic Spaces and Quaternion Algebra

Explores quadratic spaces, norms, and quaternion algebra over fields.

Ring of Polynomials: Coefficients and Multiplication

Covers the ring of polynomials, focusing on coefficients and multiplication.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Modular Arithmetic: Foundations and Applications

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

Complex Numbers: Roots and Polynomials

Covers the properties of complex numbers, including finding roots and factorizing polynomials.

Approximations in Engineering: Leading Digits and Dominant Balance

Explores the significance of leading digits and dominant balance in engineering approximations, showcasing historical methods like slide rules and their relevance in solving challenging problems.

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.