Indian Math Online - Blog

Teach math, science? You're hired!

A friend of mine forwarded this article to me yesterday.

At a recent job fair, a 22-year-old aspiring teacher wore a name tag that said she majored in math. Immediately, Anastasia Batsios became one of the most popular recruits in the room.

School officials from across the nation, including a few from the Houston area, had descended on her Michigan campus, Grand Valley State University, during March.

"They saw 'math' and said, 'Hey, come here. We'll give you a job,' " recalled Batsios, a Michigan native who ended up accepting an offer from the Galena Park school district. "It was overwhelming but encouraging. At least I picked a good major."

You can read the full story here.

As the title says, there is an urgent need for qualified teachers in the American school systems. Good for recent graduates like Anastasia - I am sure it makes them proud to graduate in Math and Science and feel wanted in the work force.

When I read this article, it reminded me of my school days in India. As many of you can guess from my name (Suresh), I was born and raised in India. I am a proud product of the Indian Education system. When I reflect back on my teachers' names and their salutations, it was not uncommon to see the names of "degrees" they had obtained as part of their education. For example, my primary school math teacher (yes, specialization at the primary school level) Bhavani (I will spare the last name for privacy reasons!) had three degrees listed next to her name - "B.Sc, B.Ed, M.Ed".

A little explanation - B.Sc - is for Bachelor of Sciences (3-year program) - typically in Math or Sciences; B.Ed (3 year program) - Bachelor of Education; M.Ed (2 year program) - Masters in Education.

B.Ed and M.Ed are mostly required qualification if a person intends to pursue a teaching profession in primary or high school. Some teachers will go on to do Masters in the chosen Sciences field as well.

At the time I was going through primary-middle-high school, it was an accepted norm that the teacher that was teaching a specific subject (math, physics, chemistry, etc) was specifically trained in that subject. If a school were to hire less qualified teachers, there would be mass exodus by the parents and students.

So, as I read the Houston Chronicle article, I am thrilled to see that being specifically educated and trained in subjects like math and science is REALLY wanted by the school systems here in the US. This is only going to benefit our children!

 

Investing in your Child’s Future

I first met Bob Compton, one of the co-founders of Indian Math Online, and Executive Producer of the documentary film - Two Million Minutes, at a screening in early April 2008. He was on a panel of various high school administrators and students at a private school. He asked one of the students what grade he received in his math class. The student, who was among the top in his class, proudly responded “A’s”.

Bob then asked if he had a tutor for his math classes. Confused by the question, the student responded that he didn’t, and then Bob went on to question the entire audience at-large about why was it that Americans will spend hundreds of thousands of dollars to make their above-average students excel even more in athletics and fine arts, but won’t put forth the additional dollars to help their children shine academically by investing in tutors or academic programs.

Everyone in this country is aware that only a small percentage of students go on to receive athletic scholarships for colleges; and an even more minuscule number become professional athletes later on in their career. However, academic scholarships are abundant, and the brightest students often wind up with the highest-paying jobs down the line.

So rather than investing in athletics and fine arts as much, shouldn’t we be investing in academics?
That is the reason Americans are falling behind developing countries such as India and China, because in those countries, their focus is on academics and the ability to compete in global economy. Meanwhile, American students’ focus is often on the social aspects of life, and most often students wait until college graduation to find out that their global competitors are often acquiring all of the jobs that they sought after.

Investing in Indian Math Online is helping your child prepare for these global competitors by giving him/her the resources necessary to become proficient in mathematics – a subject area where Americans are consistently falling behind. Indian Math Online is designed to help your child challenge him/herself academically, where some school curriculum will not.

Speaking of investing in IMO, there currently is a promotion to save $20 when you sign up for the IMO Summer Program. See below for details -

 

To Learn more about Indian Math Online click here -

 

Why Should I Learn Math?

Whether you are a doctor, a nurse or an airline pilot, you use Math every day. Even professionals such as Artists use Math in their daily life.

We believe Mathematics is the language of the 21st century. We have compiled a presentation titled "Why Math?" which will provide you insights into where Math is being used daily and the careers that involve Math.

Click here to download and read.

How can we apply the Gauss Elimination method to solve m question?

Recently a user to the Indian Math Online web site submitted a question for one of our math experts. The user who we will refer to only by first name - Amresh - submitted this question and picked "Grade 1" as the grade. We do not believe this is a question from a 1st Grader. This is a question for higher grades, perhaps even taught in early years of Engineering programs.

Here we go - the question first;

"How can we apply the Gauss Elemination method to solve m equation? For example z1 = ax^n + bx^(n-1) + ... + m (mod p) z2 = ax^n + bx^(n-1) + ... + m (mod p) ..................................... ..................................... ..................................... zm = ax^n + bx^(n-1) + ... + m (mod p) I want the mod p vale of a,b,c... "

Our answer follows - if after reading the answer, you have more questions or need further clarifications, please click here. A pdf version of the answer can be downloaded here.

Gaussian elimination method:

This is an elementary elimination method & it reduces the system of equations to an equivalent upper triangular system which can then be solved by back substitution.

Although quite general, we shall describe the method by considering the below mentioned system of equations for the sake of clarity & simplicity.

Let the system of equations be

axⁿ+bx^(n-1)+………………….+m(mod p)= z1

axⁿ+bx^(n-1)+………………….+m(mod p) = z2

axⁿ+bx^(n-1)+………………….+m(mod p)= zm

We first form the augmented matrix

a b m(modp) z1

a b m(modp) z2

a b m(modp) zm

    

To eliminate xⁿ from the second equation, we multiply the first equation by –a/a & then add it to the second equation. Similarly, to eliminate xⁿ from the third equation, we multiply the first equation by –a/a & then add it to the third equation. This procedure can be shown thus:

 

   a b m(modp) z1

-a/a   a b m(modp) z2

-a/a   a b m(modp) z3

    a b m(modp) zm

where –a/a & -a/a are called multipliers for the first stage of elimination. In this stage, it is assumed that the first element in the first equation a≠ 0. The first equation is called the pivotal equation & the first element a is called first pivot. At the end of the first stage, the augmented matrix becomes:

    a b m(modp) z1

  0 b’ m(modp)’ z2’

  0 b’ m(modp)’ z3’

 
-a/a   0 b’ m(modp) ‘ zm’

where b’,(modp)’……….. are all changed elements. The first b’ of the second equation is the new pivot & the multiplier is –b’/b’.

After completing all stages, we should have the upper triangular system:

 

   a b m(modp) z1

  0 b’ m(modp)’ z2’

  0 0 m(modp)’ z3’

   0 0    0  zm’

 

from which the values of xⁿ,x^n-1 can be obtained by back substitution.

Those values will be substituted in the original system to get a system of equations

which can be solved to get the values of a,b, c etc

It is clear that this method will fail if one of the pivots vanishes. In such a case , the method can be modified by rearranging the rows so that the pivot is non-zero. This procedure is called partial pivoting & can be implemented on a computer.

If this is not possible, then the matrix is singular & the equations have no solution.

In particular, the number of non zero diagonal elements in the final augmented matrix will represent the rank of the original matrix.

Don't Let Your Child Forget Math This Summer!

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