Orthogonality and Characters

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

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

Covers the construction of R and equivalence relations in sequences and linear recurrences.

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

Introduces the basics of group theory, defining groups, categories, and groupoids.

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

Covers the properties and sets related to linear algebra, emphasizing the importance of understanding these concepts.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

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

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