CONJECTURES IN MATHEMATICS

Dear All,

Generalization is a very important tool for obtaining new results in mathematics. We first experiments with numbers and geometrical shapes and observe some patterns emerging and then we make some conjectures on the basis of these observations. These conjectures do not get the status of theorems unless these can be deducted either from certain axioms or can be deduced from other results which have been earlier proved in mathematics.

Let us consider some examples of valid as well as invalid generalizations.

CONJECTURES BASED ON PRIME NUMBERS:

SOME MORE CONJECTURES:

Conjectures are obtained by generalizations but only those generalizations are valid which can be proved rigorously. We must continue to generalize, but we must generalize with care.

So, what did you conjecture today!

Note: I could not type mathematical symbols on the blog. So, I have attached images in this post. Click here to download pdf file for printing.

Mathematics Movement Phase II - held at SDPS Pitam Pura

Dear All,

S.D. Public School, Pitam Pura in collaboration with NCSTC, Department of Science and Technology is organized “Mathematics Movement - (Phase II)” from 3rd to 5th October 2013. There were many interactive sessions for the teachers and the students. The main focus of the event was to enhance the student’s skills in various areas of Mathematics.

I had my sessions on all three days with class IX and X students.

@ Mathematics Movement held at SDPS Day 1:

An interdisciplinary activity relating mathematics with environment was taken. This activity was planned by Mr. Ajay Marwah (HOD – Math’s) from SDPS.

Activity

The calculations were based on rough estimation.

While preparing myself for this activity, I came across another area where mathematics is used. It's about various paper sizes like A4, A3 etc. Some interesting results are here. I will be doing a project soon on this topic with my students.

1     2      3  

@ Mathematics Movement held at SDPS Day 2:

An activity based on counting without counting was taken. Students took actively part and interest in it and enjoyed beauty of mathematics.

Activity   Follow up 

@ Mathematics Movement held at SDPS Day 3:

On day 3, I took session on the theme “Thought Provoking Mathematical Problems”.

Activity   Follow up

If anyone is interested to check solutions, he/she can email to me at amitbajajcrpf@gmail.com

I am thankful to Mrs. Anita Sharma, Principal SDPS Pitam Pura for having trust in me and giving an opportunity to interact with the kids. I am also thankful to my Principal Sir Sh. H. R. Sharma for allowing me to attend this mega event. My sincere thanks to Mrs. Rashmi Kathuria, a Math's teacher from Kulachi Hansraj School, Ashok Vihar who is a true passionate math's teacher I have ever met. 

It was a great teaching and learning experience.