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Commutative algebra is a branch of algebra that studies commutative rings, their ideals, and modules over such rings. It provides the algebraic foundation for algebraic geometry and number theory. Topics Covered Ring Polynomial Ring Affine Algebraic Varieties Modules Tensor Product Localization Noetherian and Artinian Rings Continue reading
Posted in Commutative Algebra
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How to instantiate a typeclass? Take CoeOut as an example : Continue reading
Posted in Formal Verification
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Notes from learning Lean and the Mathlib library. Mathematics in Lean Chapter 8: Basics Chapter 9: Groups and Rings Chapter 10: Linear Algebra Continue reading
Posted in Formal Verification
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This section will collect learning notes on cryptographic primitives, protocols, and the mathematics behind their security. Planned topics Complexity of Lattice Problems Continue reading
Posted in Cryptography
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Complexity of Lattice Problems Planned topics (notes not yet published): Continue reading
Structures
Invariant Subspaces Definition 5.1 – Invariant Subspace Let $T \in \mathcal{L}(V)$ be a (linear) operator on vector space $V$. When we restrict $T$ to a subspace $U \subseteq V$, we are not sure the corresponding vectors will still lie in $U$. If they do, we say that $U$ is an… Continue reading
Posted in Linear Algebra
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