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Deterministic Algorithms Probabilistic algorithms - Fermat Test > If n is a prime then $a^{n-1} \textrm{mod} n=1$ for all $1 If $a^{n-1} \textrm{mod} n \neq 1$ for some a, $1

Primes Asymmetric-key cryptography uses primes extensively. The topic of primes is a large part or any book on number theory. This section discusses only a few concepts and facts to pave the way for Chapter 10. Definition - A primeis divisible only by itself and 1. Q. What is smallest prime? A. The smallest prime is 2, which is divisible by 2 (itself) and 1. Cardinality of Primes Infinite Number..

Ordinary Differential Equations $y'(x) = f(x,y)$ Euler's Method > extremely simple approximation with low accuracy > Suppose tha twe know an initial state $y(x_0) = y_0$ > Approximate $y$ at $x = x_0 + h$, $h$ is a small step size $\frac{y(x_0+h) -y_0}{h} = f(x,y)$ => $y(x_0 +h) = y_0 + h f(x,y)$ - General formula > $x_{i+1} = x_i +h$ > $y_{i+1} = y_i + h f(x_i, y_i)$ Talyor Series - Approximati..

More tips to work with others Logging/ searching / debugging git grep - Allows to easily look for where a term exists in our working directory $ git grep -n README - git grep vs grep (linux) > Much faster and more convenient than grep > git grep is optimized for Git repositories --no-index : earch files in the current directory that is not managed by Git --untracked : search both tracked & untra..

Topics - Solution of Nonlinear Equations > Bracketing Methods > Bisection Method - Open Methods > Newton-Raphson Method > Secant Method Basis of Bisectio Method - An equation $f(x) =0$, where $f(x)$ is real continuous function, has at least one root between $x_1$ and $x_u$ if $f(x_1) f(x_u) roots of the equation may still exist between the two points > there may not be any roots for the equation..

Goals of segmentation - Group together similar-looking pixels for efficiency of further processing > simplify and / or change the representation of a image into something that is more meaningful and easier to analyze Major processes for segmenation - Separate image into coherent 'object' > Bottom-up : group tokens with similar features > Top-down : group tokens that likely belong to the same obj..

Parametric (global) warping - Transformation T is coordinate-changin machine : $p' = T(p)$ - What does it mean that $T$ is global? > is the same for any point $p$ > can be described by just a few numbers (parameters) - For linear transformations, we can represent T as a matrix $p' = Tp$ Common transformations - Translation - Rotation - Aspect - Affine - Perspective Scaling - Scaling a coordinate..

Network Layer Introduction Routing protocols ICMP Network-layer functions Recall : two network-layer functions - Forwarding : move packets from routers' input to appropriate router output -> data plane - Routing : determine route taken by packets from source to destination -> control plane Two approaches to structuring network control plane - per-router control (tranditional, still popular) - lo..

Github The single largest host for Git repositories - The central point of collaboration for millions of developers and projects Github and Git - Github is as remote repository of our project - By using Git commands, we can work for the project on our local computing machines Github workflow for a private project Gentralized workflow - one central hub can accept code and everyone synchronizes th..

IP Internet Protocol The Internet network layer - host, router network layer functions : physical layer -> link layer -> network layer ( routing protocols, IP protocol, ICMP protocol ) -> transport layer (TCP, UDP) IP datagram format - IP header : 5 x 32bits ( 5 x 4bytes = 20Bytes + options ) - IP payload : data Header component -- -- ver : IP protocol version number [ 4 bits ] -- head.len : Hea..