Local Linear Approximation

Local Linear Approximation

  May 08, 2021    Roy John

---

You might have seen the famous approximation $\sin(x) \approx x$ for $x$ near 0. We can use derivatives to approximate non-linear functions by simpler linear functions. We can better understand this by looking at the graph a function $f$ under magnification.The blue curve is the graph of $f(x) = \sin(x)$ and the yellow line is its tangent at $x = 0$. We can see that, under magnification of the curve...

Read More

Generating Sexy Prime Pairs using Python

Generating Sexy Prime Pairs using Python

  April 06, 2021    Roy John

---

Sexy Primes, What are they?They are prime numbers that differ by 6. For example, 5 & 11,  7 & 13. The name comes from the Latin word for six; sex. What we are going to do is, write a program to generate all the sexy prime pairs within a given interval of natural numbers. Sexy Prime PairsThis is a program to generate all the sexy prime pairs below 10000.Programdef check_prime(n): ...

Read More

Monte Carlo Integration using Python

Monte Carlo Integration using Python

  August 18, 2020    Roy John

---

 Monte Carlo IntegrationMonte Carlo integration is a  powerful method of computing the value of complex integrals using probabilistic techniques. This technique uses random numbers to compute the definite integral of a function. Here we are going to use the python...

Read More

Generating Pseudorandom Numbers Using Congruence Theory In Python

Generating Pseudorandom Numbers Using Congruence Theory In Python

  August 18, 2020    Roy John

---

Pseudorandom NumbersA sequence of random numbers, chosen from the interval between 1 and some fixed integer $M$, is a sequence of numbers $x_0, x_1, \ldots $ such that for each $i$, the values of $x_i$  has a $1/M$ chance of being any given number between 1 and $M$,...

Read More

Making an Encryption Application in Python Using the RSA Algorithm

Making an Encryption Application in Python Using the RSA Algorithm

  August 16, 2020    Roy John

---

 The RSA CryptosystemRSA algorithm is an asymmetric cryptography algorithm. Asymmetric actually means that it works on two different keys i.e. Public Key and Private Key. As the name describes that the public key is given to everyone and the private key is kept private.The...

Read More

Modular Designs With Python (Congruence Theory)

Modular Designs With Python (Congruence Theory)

  August 15, 2020    Roy John

---

Modular DesignsCongruence theory can be used to generate beautiful designs. It is really a fun way to study congruences. Two such designs are created using python. $m$-pointed stars and $(m,n)$ residue designs.$m$ - Pointed StarsTo construct an $m$-pointed star, mark $m$...

Read More

Visualization of Collatz Conjecture using Python

Visualization of Collatz Conjecture using Python

  August 10, 2020    Roy John

---

The Collatz ConjectureThe ProblemThe Collatz conjecture (a.k.a the hailstone problem or the $3n + 1$ problem) was proposed by Lother Collatz in 1937. Although the problem on which the conjecture is based is really simple that even a fourth-grader can easily understand...

Read More