Mymathware Shafii's Math Academy

Dumelang guys!!! In this post, we will explore the real and imaginary parts of the complex logarithm function \( w = \log{z} \), and show that they satisfy the Cauchy-Ri…

Sanbonani guys!!!  This is MMTC081 (Complex Analysis Module).  Here we look into some uncommon problems we have encountered in the course of studying this module.   (1) …

What is a Polynomial Ring? It's properties and Examples  Polynomial rings are fundamental mathematical structures that allow us to study polynomials and …

Exploring the Fascinating World of Graph Symmetry When we think about symmetry, images of perfectly balanced objects or reflections often come to mind. Howev…

In ring theory, a ring divisor of zero refers to an element of a ring that, when multiplied by another element, yields zero. These divisors of zero play a significant ro…

Accessing Machine Learning Impact In Mathematics - Trends and Application Machine learning has revolutionized the field of mathematics, enabling mathematicians to develo…

From UDUS to KMUTT: The journey of a thousand miles ends with a PhD in Mathematics by Abubakar Muhammad Shafii Dr. Ibrahim Hassan Abdulkareem An anonymous sp…

Evaluate $x$ in the equation $\frac{x^2-10}{x-3}+\frac{1}{x-3}=\frac{1}{5}$ Solution First we need to find the Lowest Common Multiple (LCM) of the left hand …

Echoes of Victory from KMUTT - An epistle of accolades on Dr. Jamilu Abubakar Academia is a field of patience and resilience, only those who are willing to …

Let $f:A\rightarrow{A}$ with $f(x)=\frac{x+2}{x-3}$ for $A=\mathbb{R}/\{1,3\}$ Show that $f$ is a one-to-one function. Proof: we are given $f:A\rightarrow{A}…

Let $a,b\in\mathbb{R}$. Prove th inequality $\frac{a}{b}+\frac{b}{a}\geq{2}$ Proof We are given $\frac{a}{b}+\frac{b}{a}\geq{2}$, . Let $(a-b)^2\geq{0}$ so t…

a) We are to find area of $\bigtriangleup{ABC}$ This is quite simple, all we need to do is to use the idea of similar triangles, to do this, simply extract the $\bigtria…

Proof that for any integer $n>1$ the number $n^5+n^4+1$ is not a prime. Simply rewrite $n^5+n^4+1$ as $n^5+n^4+n^3-n^3-n^2-n+n^2+n+1$ Factor out common terms  $n^3(n^…

The product of the third and the sixth terms of an arithmetic sequence is $406$. The ninth term of the sequence divided by the fourth term gives a quotient of $2$ and a …

Find the sum of all natural numbers between $1$ and $1000$ that are not divisible by $13$. Let $S$ be the unknown sum and $M$ multiples of $13$ less than $1000$, then $S…

Lecture series by Dr Kamran Khan on Complex Integration Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim Universi…

Solve the equation $2\cosh{2x}+10\sinh{2x}=5$ ................. 🆔 This is a hyperbolic trigonometric function equation, in order to solve the given equation, we must re…

Find the integer solution $x^2+3x+9=9y^2$.............(1) This is a beautiful quadratic Diophantine's equation that requires an integer solution. So how …

Find the value of $x$ $\frac{x^{\sqrt{x}}} {\sqrt{x}}=\frac{{\sqrt{x}}^x}{\sqrt{x}}$ Since both sides of the equation have a common denominator, multiply through by $\sq…

Find the integer solution for $3^x+27^y+81^z=10935$ This is a rather thickish question so we have to be very careful in our simplifications. The left hand side of the eq…