Mymathware Shafii's math academy

Homeomorphism: the isomorphisms of topological spaces. When studying topological spaces, you will come across homeomorphisms, in one of my papers, i presented a paper on…

Mathematical jokes: the critical jokes for critical thinkers.  Mathematical jokes have served as a form of humor for mathematicians and lovers of mathematics for centuri…

An insight into category theory and epimorphism. To study epimorphism, it will be necessary to study category theory, because epimorphism is a concept used in category t…

Automorphism: the self mapping isomorphic functions.  Automorphism as I wrote in my last post is a type of isomorphism, or we can simply say, it is an extension of an is…

Isomorphism: a special case of homomorphism .  An isomorphic relation between two sets G and H showing the property of injection and inverse. Isomorphism is a mapping be…

The mathematics of homomorphism.  In abstract mathematics (algebra), homomorphism can be defined as a map or relation between two algebraic structures of the same type e…

Why does pi have a constant value of 3.14159265359...?  can we define other values for pi?  $\pi$ is a lowercase greek letter used as a mathematical constant pronounced …

Why do we teach math that won’t ever apply in the real world? This has been such an unflattering question i have gotten from students who don't major in maths and fr…

How to proof that $7$ is irreducible $\mathbb{Z}[\sqrt{6}]$, even though $N(7)$ is not prime.  To solve this, lets look at the rules that govern irreducibles in $\mathbb…

Below is a solution to a 4th order polynomial equation.  Solve the equation $2^4-3x^3-x^2-3x+2=0$ Divide through by $x^2$ $2x^2-3x-1-\frac{3}{x}+\frac{2}{x^2}=0$ Collect…

Graphs of Inequalities in One Variable Graphically, an inequality that involves only one variable $x$  is represented as points on a line: e.g $-2\leq{x}<5$ can …

Introduction to Algebraic Inequalities[Symbols and Properties] Inequality is simply a system of ordering, in mathematics, ordering is very important as it allows…

MTH1301 Test Solutions ( 1 ) Let the universal set be \begin{align*} &\bigcup=\{x:x\ \text{is a natural number less than} 10\}\\ &A=\{x:x\ \text{is an odd…

The 9th Annual National Mathematics Competition For university students (NAMCUS) was recently held at the National Mathematical Centre kwali - sheda, Abuja, it took pla…

PROPOSITION Let $f$ and $g$ be a non-zero polynomial in $k(t)$ show that : there exists a unique polynomial such that (1) $d$ divides $f$ and $g$ (2) if $d$ divi…

Differences between Reducible and Irreducible Polynomial To distinguish between reducible and irreducible polynomial we use the properties of both polynomials which…

(a)Find the Determinant of \begin{equation} A=\left[\begin{array}{ccc} 0 & 1+i & 1+2i\\ 1-i & 0 & 2-3i\\1-2i & 2+3i & 0\end{array}\right] \…

Obtain the following matrices and describe them (a)$A=[a_{ij}]$ is a $3\times3$ matrix such that $a_{ij}=a$ if $i\leq{j}$ and zero otherwise. (b)$B=[b{ij}]$ is …

Question : prove or disprove that $(A+B)^2=A^2+2AB+B^2$ if $A=[a_{ij}]$ is a matrix of $3\times3$ such that $a_{ij}=1$ if i+j is even and it zero otherwise and $B=[b…

Mapping and Function Assignment Mapping: suppose we can assign each element x of a set X in a way, a unique element y of a set Y written as y = f(x) then this is called…