Math with Joy

This site is currently for Mr. Jung’s Algebra 1 students at El Camino Real Charter High School and their families. Hopefully you will find all the information you need to stay current with course requirements, informed of current grade status, and reminded of class rules and procedures.

Here’s a link to the first quiz.

The following is a list of links to pages related to the class:

Posted in Algebra 1 | Leave a comment

RSA cryptosystem

Posted on May 24, 2011 by mathwithjoy

I developed a web application that will encrypt a message given the enciphering modulus $n$ and the public key $e$ . $n$ must be a positive integer that is a product of two very large and distinct primes ( $p$ and $q$ ) and $e$ must be a positive integer such that $\left(e$ , $\phi(n)\right)=1$ .

The web application will calculate the private key $d$ by solving the congruence $de \equiv 1 \left(mod \phi(n) \right)$ .

The web application can also decrypt a message given the private key $d$ and the enciphering modulus $n$ .

Here’s the link:

Please note that I developed this application for fun and that it is not meant for commercial, business, or professional use.

Posted in Mathematics, Web Tools | Leave a comment

Solving cubic equations

Posted on May 6, 2011 by mathwithjoy

I developed a web application that calculates the real root of a cubic equation for one of the classes I’m taking at CSUN.

Here’s the link: http://mathwithjoy.com/apps/cubic/cubic.htm.

Given a cubic equation of the form $ax^{3}+bx^{2}+cx+d=0$ , the web application calculates the coefficient $p$ of the first-degree term and the constant $q$ of the depressed cubic equation that is the result of substituting in $y-\dfrac{b}{3a}$ for $x$ .

$p=\dfrac{3ac-b^{2}}{3a^{2}}$

$q=-\dfrac{2b^{3}-9abc+27a^{2}d}{27a^{3}}$

The web application then calculates $u$ and $v$ ( $y=u+v$ ).

$u=\sqrt[3]{\dfrac{q+\sqrt[2]{q^{2}+\dfrac{4p^{3}}{27}}}{2}}$

$v=\sqrt[3]{\dfrac{q-\sqrt[2]{q^{2}+\dfrac{4p^{3}}{27}}}{2}}$

The web application then calculates the real root $x$ of the cubic equation.

$x=u+v-\dfrac{b}{3a}$

There are fields below the value of $x$ on the web application. These are for the other two roots of the cubic equation. I have not finished writing the code for this yet. I also have to figure out how to non-real numbers in the calculations.

Posted in Mathematics, Web Tools | Leave a comment

My math notes

Posted on December 30, 2010 by mathwithjoy

I just finished developing the structure for a web application I call “My Math Notes” that will contain basic mathematical concepts and definitions for classes I’ve taken at CSUN. This web application is optimized for mobile operating systems like iOS and Android.

The link is http://www.mathwithjoy.com/apps/mymathnotes/.

Whenever I add an entry related to a math class I’m taking or have taken, I will add a link to that entry in the web application.

Posted in Mathematics, Web Tools | Leave a comment

Wheel

Posted on December 29, 2010 by mathwithjoy

I developed a web application (“Wheel”) that calculates pro rate and short rate factors. The web application is optimized for mobile operating systems like iOS and Android.

Here’s the link: http://www.mathwithjoy.com/apps/wheel/wheel.htm.

Please note that I cannot guarantee the accuracy of the results of this application. I just developed it for fun, not for actual business use.

Posted in Insurance, Web Tools | Leave a comment

Notepad for math proofs

Posted on August 20, 2010 by mathwithjoy

I developed a web application that might help you type math proofs for posting on websites and inserting into documents. I call the tool “Mathpad.”

Here is the link: http://mathwithjoy.com/apps/mathpad/mathpad.htm.

Posted in Web Tools | Leave a comment

Calculating the traditional short rate unearned factor

Posted on August 7, 2010 by mathwithjoy

The traditional short rate unearned factor is not 90% of the pro rate unearned factor. The traditional short rate unearned factor can be greater or less than 90% of the pro rate unearned factor depending on the policy term and number of days the policy stayed in force. You can calculate the traditional short rate unearned factor using the following method:

$d =$ the number of days the policy stayed in force

$u =$ the unearned factor we are calculating

$\left[x\right]$ symbolizes “round $x$ down to the nearest integer”

12-Month Terms

If $d < 23$ then $u = \dfrac{\left[(90-\dfrac{d}{3.65})+5.55-\dfrac{d}{4}\right]}{100}$
If $23 \leq d \leq 186$ then $u = \dfrac{\left[90-\dfrac{d}{3.65}\right]}{100}$
If $186 < d$ then $u = \dfrac{\left[(90-\dfrac{d}{3.65})+(\dfrac{d}{18.29})-9.98\right]}{100}$

6-Month Terms

Id $d\cdot2 < 23$ then $u = \dfrac{\left[(90-\dfrac{d\cdot2}{3.65})+5.55-(\dfrac{d\cdot2}{4})\right}}{100}$
If $23\leq d\cdot2 \leq 186$ then $u = \dfrac{\left[90-\dfrac{d\cdot2}{3.65}\right]}{100}$
IF $186 < d\cdot2$ then $u = \dfrac{\left[(90-\dfrac{d\cdot2}{3.65})+(dfrac{d\cdot2}{18.29})-9.98\right]}{100}$