Recent Comments
Category Archives: Mathematics
Index
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
Leave a comment
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
Leave a comment
Summary
Fundamentals Basic Logic Inference $P \to Q, P \implies Q$ $P \to Q, \neg Q \implies \neg P$ $P \lor Q, \neg P \implies Q$ $P (\text{or } Q) \implies P \lor Q$ $P, Q \implies P \land Q$ $P \land Q \implies P (\text{or } Q)$ $P \lor Q… Continue reading
Posted in Math of Proof
Leave a comment
Index
Notes on the basic language, strategies, and recurring patterns used in proofs. Parts summary-math-of-proof Continue reading
Posted in Math of Proof
Leave a comment