Reading notes for Graduate Operating Systems at UCSD. The notes are based on the readings and discussions from the course.
Notes
Personal final notes for CSE 105 Theory of Computability. Not comprehensive – only like a final exam cheat sheet. Regular Expression Precedence: \((R)\) → \(R^{*}\) → \(R_{1} R_{2}\) → \(R_{1} \cup R_{2}\) \(\emptyset\) represents empty set; \(\epsilon\) represents empty string; \(R^+ \equiv RR^*\) Proving closure Given: What does it mean for L to be in class? e.g. \(L\)* a regular language, so given a DFA/NFA* \(M_L\) WTS: The result of applying the operation to \(L\) is still in this class.
Differential Equations Classification Ordinary/Partial involving only ordinary derivatives with respect to a single independent variable is called an ordinary differential equation. involving partial derivatives with respect to more than one independent variable is a partial differential equation. Linear/Non-linear Linear: One in which the dependent variable \(y\) and its derivatives appear in additive combinations of their first powers. May be written in the form \[ a_{n}(x) \frac{d^{n} y}{d x^{n}}+a_{n-1}(x) \frac{d^{n-1} y}{d x^{n-1}}+\ldots+a_{1}(x) \frac{d y}{d x}+a_{0}(x) y=F(x) \]
Personal notes for CSE20 - Discrete Mathematics for Computer Science. Taken Fall 2020, with professor Shachar Lovett. See Course Homepage Sets Recursive definition of sets Basis step: Specify finitely many elements of \(S\) Recursive step: Give a rule for creating a new element of \(S\) from known values existing in \(S\), and potentially other values. String The set \(\Sigma^*\)of strings over the alphabet \(\Sigma\) is defined recursively by Basis step: \(\lambda \in \Sigma^*\) (where \(\lambda\) is the empty string containing no symbols)