Imagination and reason in Mathematics

Module Starting Date: 22nd November, 2019, Friday, 6:30 PM Go to Joining Section Math-Olympiad Module: Day 0 Problem ListDownload Philosophical Remarks When did we first fall in love with mathematics? For me, it was in class 6. My father exposed me to a problem from...
An excursion in Linear Algebra

An excursion in Linear Algebra

Pick up any odd book on linear algebra. Matrices, base changes, eigen-values will pop up. It is hard to appreciate why an intelligent person should spend hours and days, mastering these skills. Our excursion, begins with an attempt to understand that very thing:...
RMO 2019 (Maharashtra Goa) Adding GCDs

RMO 2019 (Maharashtra Goa) Adding GCDs

Understand the problem For each ( n  in mathbb{N} ) let ( d_n ) denote the G.C.D. of n and (2019 – n). Find the value of (  d_1 +  d_2 + … + d_{2019} ). Source of the problem Regional Math Olympiad, 2019, Maharashtra, Goa Region Problem 1 Topic Number...
Inequality in RMO 2019 Problem 3 Solution

Inequality in RMO 2019 Problem 3 Solution

Understand the problem Let a, b, c be positive real numbers such that a + b + c = 1. Prove that $$ frac {a} {a^2 + b^3 + c^3} + frac {b}{ b^2 + c^3 + a^3 } + frac {c} { c^2 + a^3 + b^3 } leq frac{1}{5abc} $$ Source of the problem Regional Math Olympiad, 2019 Problem 3...
Rational form – RMO 2019 Problem 1 Solution

Rational form – RMO 2019 Problem 1 Solution

Understand the problem Suppose x is a non zero real number such that both ( x^5 ) and ( 20 x + frac{19}{x} ) are rational numbers. Prove that x is a rational number.  Source of the problem Regional Math Olympiad, 2019 Problem 1 Topic Algebra Difficulty Level 3/10...