Mymathware Shafii's math academy

What is a transcendental number, examples and properties? Happy new year to all my readers and followers. Today, i will be celebrating the new year with you by writing o…

Why the natural logarithm are not as confusing as you think. This is my last post for the year 2020, by tomorrow Jan 1st, 2021, we are going to be marking a new decade, …

What are the real applications of pure mathematics? I have utterly no evidence to support this, but my sense is that  bright minds seek tough targets, regardless of thei…

Proving the Madhava-Leibniz series for pi(π)  One of the earliest known approximations of $\pi$ was done by an Indian mathematician Madhava of Sangamagrama during th…

The Fermat's last theorem, the exegesis, Andrew Wiles contribution and the quest for a solution. A photo of Andrew Wiles The Fermat's last theorem is a 358 years…

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 …

Find the unit tangent vector at the point $(2,0,\pi)$ for the curve with parametric equations $x=2\sin\theta; y=3\cos\theta; z=2\theta$, we see that the point $(2,0,\pi)…

If $A=3i+2j-3k$ &B= 2i-2j-k$ $C=2i-j-3k$ What is $2C-[2A.(2B+4C)]B?$ We will be breaking down the solution one step at a time. First we begin with $2A=2(3i+2j…

Are good mathematicians merely good at memorizing math formulas?  Answer by Alan Bustany on Quora.  Far from it! The typical good mathematician cannot remember many form…

Find the second derivative of $y=\sqrt{3x^2-2x+1}$ By indices $y=(3x^2-2x+1)^\frac{1}{2}$ We use chain rule to evaluate $y$.  Formula $\frac{dy}{dx}=\frac{dy}{du}\times…

Evaluate the complex number into real and imaginary parts $\sqrt{i}^\sqrt{i}$.  Solution From indices we know that $\sqrt{i}=i^\frac{1}{2}$ $i^\frac{1}{2}=[\cos\frac{\pi…

Why study calculus in real analysis when we can study it in elementary mathematics? Real analysis is an area of analysis that studies concepts such as sequences and thei…

How do mathematicians memorise theorems and equations? Answer by kevin Coombes on Quora In most cases, they don’t. Mathematicians are  way  too lazy to waste time or ene…

The mathematics department of Usmanu Danfodiyo University in sokoto has added another PhD scholar to their folder of doctors.  Dr. Kazeem Aremu, a man of few words and m…

Why should we learn math? Written by jan Meww, author of jan papers.  Mathematics is the only subject that deals with most complex ideas in the most precise, concise, an…

Evaluate the integral $\int{(2x+3)}\sqrt{x-4}dx=I$ Let $3=-8+11$ $\therefore$, $I=\int{(2x-8+11)}\sqrt{x-4} dx$.  $=\int{[2(x-4)}+11]\sqrt{x-4}dx$.  $2\int{(x-4)}^{\fra…

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…

What can one learn from real analysis that is not taught in high school? There's no universal standard for what “real analysis” means as an undergraduate course, nor…

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…