Lectures related to Untitled | EPFL Graph Search

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Principal Ideal Domains: Structure and Homomorphisms

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

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Quotients of Groups by Relations of Equivalence

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

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Group Theory Basics

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Cardinality and Group Theory

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Linear Algebra: Surjections

Explores surjections in linear algebra, demonstrating their importance in mapping elements between sets.

Isometries and Group Homomorphisms

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.