Lectures related to Differential graded algebra

Lie Groups: Representations and Transformations

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

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Integration: more examples and rational functions

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Complement: Monotone Class Theorem

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

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.

Course Evaluation and Algebra

Covers the course evaluation results and an algebraic explanation of employment rate growth.

Graded Ring Structure on Cohomology

Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.

Long Exact Sequence of Ext-Modules

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Optimization Problems: Algebra and Trinomial Equations

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

Analytical Study of Space

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Number of Solutions in Linear Systems

Explores the number of solutions in linear systems of equations and the conditions for no solution, a unique solution, or an infinite number of solutions.