Welcome to Covariance
...whenever new abstract objects are constructed in a specified way out of given ones, it is advisable to regard the construction of the corresponding induced mappings on these objects as an integral part of their definition.
Recently updated notes
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🗺️ Map of Content - Algebra Qual | 2:47 PM - April 02, 2025 |
The Algebra Qual | 9:51 AM - April 02, 2025 |
Syllabus | 9:51 AM - April 02, 2025 |
Knowledge
Mathematics
Algebra theory
Not to be confused with the general concept of algebra (abstract or otherwise), an algebra is an algebraic structure similar to a module, only with two internal binary operations.
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Algebras | 7:21 AM - March 31, 2025 |
Exterior algebras | 7:22 AM - March 31, 2025 |
Symmetric algebras | 7:23 AM - March 31, 2025 |
Symmetric and alternating tensors | 7:23 AM - March 31, 2025 |
Tensor algebras | 7:23 AM - March 31, 2025 |
Algebraic geometry
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Examples of classical conic duality | 7:24 AM - March 31, 2025 |
Category theory
Field theory
Group theory
Module theory
Ring theory
Tropical algebraic geometry
Software
Blender
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Houdini
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Systems of equations |