Notes in ACME Volume 2

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Status	Last Update	Fields
Published	09/06/2023	Temporal Complexity
Published	11/09/2023	Spatial Complexity
Published	11/09/2023	Big O: [$]f(x) \in O(g(x))[/$] as [$]x \to \infty[/$]
Published	11/09/2023	Little o: [$]f(x) \in o(g(x))[/$]
Published	11/09/2023	Logarithmic Time
Published	11/09/2023	Sublinear Time
Published	11/09/2023	Linear Time
Published	11/09/2023	Quadratic Time
Published	11/09/2023	Cubic Time
Published	11/09/2023	Polynomial Time
Published	11/09/2023	Exponential Time
Published	11/09/2023	Asymptotically Equivalent: [$]f \sim g[/$] as [$]n \to \infty[/$]
Published	11/09/2023	Fundamental Theorem of Finite Calculus
Published	11/09/2023	Difference Operator
Published	11/09/2023	Reindexing
Published	11/09/2023	Size of Cartesian Product
Published	11/09/2023	Number of permutations of $S$
Published	11/09/2023	Permutations of r objects from set with n elements
Published	11/09/2023	Unordered choice: r elements from set of n
Published	11/09/2023	Binomial Theorem
Published	11/09/2023	Pascal's Rule
Published	11/09/2023	Total Order (4 rules)
Published	11/09/2023	Well Ordered
Published	11/09/2023	Archimedean Property
Published	11/09/2023	Division Theorem
Published	11/09/2023	GCD(a,b)
Published	11/09/2023	Euclidean Algorithm
Published	11/09/2023	$a \equiv b \pmod n$
Published	11/09/2023	$\mathbb{Z_n}$
Published	11/09/2023	Substitution rule (modular arithmetic)
Published	11/09/2023	Fermat's Little Theorem
Published	11/09/2023	Master TheoremComplexity of recursive function is{{c4::$T(n) = a \cdot T\left(\frac{n}{b}\right) + f(n)$}}{{c5::$f \in O(n^d)$}}Complexity:{{c6::\…
Published	11/09/2023	Gamma Function
Published	11/09/2023	Stirling's Approximation
Published	11/09/2023	Simple Graph
Published	11/09/2023	Closed Walk
Published	11/09/2023	Path
Published	11/09/2023	Cycle
Published	11/09/2023	Connected Graph
Published	11/09/2023	Tree
Published	11/09/2023	Forest
Published	11/09/2023	Stack
Published	11/09/2023	Queue
Published	11/09/2023	Directed Rooted Tree (4 things)
Published	11/09/2023	Height of tree
Published	11/09/2023	Balance of a node in BST
Published	11/09/2023	AVL Tree
Published	11/09/2023	Priority Queue
Published	11/09/2023	Binary Heap: Binary Tree with 3 properties{{c3::Every level is full, except maybe the lowest}}{{c2::Parent <= children}}{{c1::Leaves as far left as…
Published	11/09/2023	Dynamic Programming
Published	11/09/2023	Bellman's Optimality Principle
Published	11/09/2023	Depth-first Search Advantages
Published	11/09/2023	Breadth-first Search Advantages
Published	11/09/2023	Orthonormal Set
Published	11/09/2023	Spanning Tree
Published	11/09/2023	Minimum Spanning Tree (MST)
Published	11/09/2023	Prim's Algorithm
Published	11/09/2023	Encoding Scheme
Published	11/09/2023	Instantaneous Decoding
Published	11/09/2023	Information Scheme
Published	11/09/2023	Average Word Length
Published	11/09/2023	Binary Code
Published	11/09/2023	Class P
Published	11/09/2023	NP Problems
Published	11/09/2023	NP-hard Problems
Published	11/09/2023	NP-Complete Problems
Published	11/09/2023	Knapsack Problems
Published	11/09/2023	Pseudopolynomial Problems
Published	11/09/2023	Hamiltonian Cycle
Published	11/09/2023	Discrete Probability
Published	11/09/2023	Continuous Probability
Published	11/09/2023	Event (discrete)
Published	11/09/2023	Mutually Exclusive
Published	11/09/2023	Collectively Exhaustive
Published	11/09/2023	Discrete Probability Measure (2 things)
Published	11/09/2023	$P(E \cup F)$
Published	11/09/2023	Binary Search complexity
Published	11/09/2023	Merge Sort Complexity
Published	11/09/2023	Dijkstra's Complexity
Published	11/09/2023	Prim's Algorithm Complexity
Published	11/09/2023	Huffman Encoding Complexity
Published	11/09/2023	Linked List Complexities
Published	11/09/2023	Stack/Queue Complexities
Published	11/09/2023	BST Complexities
Published	11/09/2023	AVL Tree Complexities
Published	11/09/2023	Kruskal's Algorithm Complexity
Published	11/09/2023	Heap Complexity
Published	11/09/2023	Heapify Algorithm Complexity
Published	11/09/2023	left-left imbalance (AVL)
Published	11/09/2023	left-right imbalance (AVL)
Published	11/09/2023	right-right imbalance (AVL)
Published	11/09/2023	right-left imbalance (AVL)
Published	11/09/2023	$\sum_{k=1}^n k^2$
Published	11/09/2023	$P(E\|F)$
Published	11/09/2023	Probability Chain Rule
Published	11/09/2023	Law of Total Probability
Published	11/09/2023	Bayes' Rule
Published	11/09/2023	Baye's Rule on Mutually Exclusive + Collectively Exhaustive Subset
Published	11/09/2023	Probability Independence
Published	11/09/2023	Collection of Independent Events
Published	11/09/2023	Discrete Random Variable
Published	11/09/2023	Event $X=a$
Published	11/09/2023	Probability Mass Function of X
Published	11/09/2023	Expectation/Mean of Random Variable
Published	11/09/2023	Law of the Unconscious Statistician
Published	11/09/2023	Random Variables Independent
Published	11/09/2023	Variance of X
Published	11/09/2023	Support of Distribution
Published	11/09/2023	Bernoulli Distribution
Published	11/09/2023	Indicator Random Variable
Published	11/09/2023	Binomial Distribution
Published	11/09/2023	Binomail Distribution Function
Published	11/09/2023	Bernoulli Expectation
Published	11/09/2023	Bernoulli Variance
Published	11/09/2023	Binomial Expectation
Published	11/09/2023	Binomial Variance
Published	11/09/2023	Poisson Distribution
Published	11/09/2023	Poisson Expectation
Published	11/09/2023	Cumulative Distribution Function
Published	11/09/2023	Continuous Distribution
Published	11/09/2023	Probability Density Function
Published	11/09/2023	Continuous Expectation
Published	11/09/2023	Continuous Uniform Distribution
Published	11/09/2023	Normal Distribution PDF
Published	11/09/2023	Gamma Dsitribution
Published	11/09/2023	Poisson Continuous PDF
Published	11/09/2023	Multivariate Random Variable
Published	11/09/2023	Bivariate
Published	11/09/2023	Univariate
Published	11/09/2023	Marginal PMF at a
Published	11/09/2023	Marginal PDF $f_i$
Published	11/09/2023	Continuous Random Variables Independent
Published	11/09/2023	Multivariate Expected Value
Published	11/09/2023	Covariance
Published	11/09/2023	Covariance Matrix
Published	11/09/2023	Covariance (Expectation Definition)
Published	11/09/2023	Multinomial Distribution
Published	11/09/2023	Statistic
Published	11/09/2023	Estimator
Published	11/09/2023	Sample Mean Estimator
Published	11/09/2023	Biased Sample Variance estimator
Published	11/09/2023	Bias of $\hat{\theta}$
Published	11/09/2023	Unbiased Sample Variance
Published	11/09/2023	Likelihood of $\theta$
Published	11/09/2023	Maximum Likelihood Estimate
Published	11/09/2023	Markov's Inequality
Published	11/09/2023	Chebyshev's Inequality
Published	11/09/2023	Weak Law of Large Numbers
Status	Last Update	Fields