Online Math
Online Math
OnlineMath_Introduction
Think that math is just a tad too easy? Bored without much competition? Here’s a chance to prove yourself!
Online Math is expected to be one of the most interesting events of Shaastra 2009, because it gives the participant an excellent opportunity to exercise his grey cells. The event is all about testing the ingenuity and analytical skills of a person and making mathematics fun.
Mathematics is one of those branches of science which has many beautiful applications and intriguing problems, beautiful solutions and in all, a subject where one can exercise their creativity by giving many different solutions for the same problem! Mathematics has always been considered the sacred pattern which describes all of the wonders of nature.
As Einstein summed it up: "Pure mathematics is, in its way, the poetry of logical ideas".
Do register for Shaastra in the userportal http://www.shaastra.org/userportal/home/ so that we can contact you for giving the prizes and other related issues.In case you are unable to register for the userportal, please send us your details (name, school/college, country, college id/roll number and year) along with the solutions of the problem set. We shall inform you as soon as the userportal is updated and then, you can register yourself in the userportal.
RESULTS HAVE BEEN UPLOADED IN THE PROBLEM SETS TAB! OUR HEARTIEST CONGRATULATIONS TO THE WINNERS!
OnlineMath_EventFormat
- The event will consist of 5 problem sets.
- Each problem set will consist of 6 problems.
- Each problem set will be available for a fixed time period.
- Participants will have a time limit to submit their solutions (about 4 days).
- Keep watching the 'Problem Sets' tab for updates on the date and timings of the problem sets.
OnlineMath_Rules and Regulations
Only individual participation is allowed.
No prior registration is necessary for participation.
The login and password are same as that acquired while registering for Shaastra in the user portal (which will be up shortly).
Solutions should be presented in a clear and legible manner and only then will they be subjected to correction.
The idea is more important than the solution itself, hence the idea must be clearly highlighted. Elegant solutions will be given greater credit.
Solutions should be mailed to the coordinators, preferably LaTeXified (you could also scan the solutions).
OnlineMath_Problem Statement
The problem sets will be uploaded on this page. Watch this page for further details on the time and date of the problem sets.
Please see the corrections tab for corrections of ambiguities in the problem sets.
Problem set 5 uploaded! Happy Problem Solving!
Deadline for submission is 30th September, 17:00 hours, Indian Standard time. Hope you had a great time solving our problems, and hope you end it on a high! :)
Please see the corrections tab for corrections of ambiguities in the problem sets.
Problem set 5 uploaded! Happy Problem Solving!
Deadline for submission is 30th September, 17:00 hours, Indian Standard time. Hope you had a great time solving our problems, and hope you end it on a high! :)
| Attachment | Size |
|---|---|
| Online Math Problem Set 1.pdf | 238.19 KB |
| Online Math Problem Set 2.pdf | 370 KB |
| Online Math Problem Set 3.pdf | 246.64 KB |
| Online Math Problem Set 4.pdf | 232.79 KB |
| Online Math Problem Set 5.pdf | 241.45 KB |
| Online Math Results.pdf | 78.84 KB |
OnlineMath_Corrections
Note: This page will contain updated corrections in the problem sets
Problem Set 1:
In problem 1 (An inequality), the summation is cyclic as expected.
In problem 2 (Workaholic Clerks!), the constant alpha should be taken as a natural number.
Problem Set 2:
In problem 6 (Casino Royale!), part a, the condition is 1 <= i, j, k, m <= 4 and not 1 <= i, j, l, m <= 4.
Problem Set 3:
In problem 2 (United we root, divided we leaves?), a, b and c are distinct positive integers. Also, it is sufficient to prove that |z|=1. One need not prove that z is some nth root of unity, which is a stronger condition.
Problem Set 4:
In problem 5 part b, you must include the condition that (alpha*beta,gamma*delta) = 1, where (a,b) denotes the GCD of a,b.
Problem Set 5:
In problem 6, the term 'square free' does not refer to the mathematical definition of the term square free in wikipedia (or any other site) but corresponds only to the definition given in the problem.
Problem Set 1:
In problem 1 (An inequality), the summation is cyclic as expected.
In problem 2 (Workaholic Clerks!), the constant alpha should be taken as a natural number.
Problem Set 2:
In problem 6 (Casino Royale!), part a, the condition is 1 <= i, j, k, m <= 4 and not 1 <= i, j, l, m <= 4.
Problem Set 3:
In problem 2 (United we root, divided we leaves?), a, b and c are distinct positive integers. Also, it is sufficient to prove that |z|=1. One need not prove that z is some nth root of unity, which is a stronger condition.
Problem Set 4:
In problem 5 part b, you must include the condition that (alpha*beta,gamma*delta) = 1, where (a,b) denotes the GCD of a,b.
Problem Set 5:
In problem 6, the term 'square free' does not refer to the mathematical definition of the term square free in wikipedia (or any other site) but corresponds only to the definition given in the problem.
OnlineMath_FAQ
What is the focus of the event?
The event is meant to test your 'mathematical thinking' and focuses on a number of elementary problems,for which you are expected to come up with complete and elegant solutions. Each problem set will revolve around some theme.
What will be the level of problems that I am expected to solve?
The problems will be simple to understand, but will contain some 'tricks' to challenge your brains. The problems will roughly be on the lines of the National Olympiad level.
What topics will the problem sets cover?
You need to know a bit on algebra, combinatorics, functional analysis, geometry, inequalities, number theory. Questions may also be from fun topics like game theory and some puzzles. We plan to include aspects of both pure and applied mathematics in our sets to strike a balance.
When will be the problem sets be posted?
The problem sets will be posted at regular intervals starting mid September or so. Keep checking the web site for updates.
How and When do I submit my solutions?
Your solutions may be scanned (provided the handwriting is legible) or type-set using LaTeX (or any such typesetting application) and mailed to us at onlinemath [at] shaastra [dot] org (onlinemath@shaastra.org). The official solution and/or good solutions provided by the participants will be put up in the web-site. Please send us your Shaastra username along with your solutions.
Is there any age limit for participation?
You can participate as long as you are registered as a student of any school or college.
What is LaTeX and where do I learn it from?
LaTeX is a typesetting application widely used by mathematicians, scientists, engineers, etc. It improves the presentation and enhances readability. There are many sites with tutorials for LaTeX. One such link is http://www.artofproblemsolving.com/LaTeX/AoPS_L_About.php
I am not able to send the solutions in Latex. Are there other ways by which I can submit the solutions?
Definitely. You can scan your solutions, send them in a word document, or send them by any other format. The only requirement is that your solutions need to be legible so that there are no discrepancies in the evaluation.
Any links for practice problems?
The forum http://www.mathlinks.ro/index.php (or) http://www.artofproblemsolving.com/Forum/index.php provides an excellent database of problems.
OnlineMath_Contact
Rohit Kannan
G. Vignesh Mail us at onlinemath [at] Shaastra [dot] org (onlinemath@shaastra.org) for further queries.