After all, functors are well known! When you convert an object into another kind, surely functions in-between those objects also transform into a new breed. Let's look at one example: Objects: Topological Spaces (X) Functions between Objects: Continuous maps (f) Objects: Groups (G) Functions between Objects: Group Homomorphism (\( \phi \)) We wish to convert X into […]
Cauchy's functional equations are very simple. The most familiar one has a simple formula: f(x + y) = f(x) + f(y) But first, for the uninitiated, what is a functional equation after all? What is a functional equation? Usually, functions appear as formulae. For example ( f(x) = x^2 ) is a function. It takes […]
Lets look at Indian National Math Olympiad 2018's Problem 6 which can be solved as an application of Cauchy's Functional Equation.
NBHM grants postdoctoral fellowships, Ph. D. scholarships, M.A./M.Sc. scholarships for research/education in mathematics. The image is a front cover of a book named Real & Complex Analysis by Walter Rudin. Here you can find Jensen's Inequality also this book is very useful for the preparation of NBHM Entrance. Also Visit: College Mathematics Program of Cheenta […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2017. Try them and share your solution in the comments. INMO 2017, Problem 1 In the given figure, \(ABCD\) is a square sheet of paper. It is folded along \(E F\) such that \(A\) goes to a point \(A'\) different from Band \(C\), on the […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2016. Try them and share your solution in the comments. INMO 2016, Problem 1 Let \(ABC\) be triangle in which \(AB=AC\). Suppose the orthocenter of the triangle lies on the incircle. Find the ratio \(AB/BC\). INMO 2016, Problem 2 For positive real numbers \(a, b, […]
It is almost like deflating a balloon. But the effect is exponential. Today (29th January 2018, Monday), we have a special concept building cum problem-solving session on Contraction of a function. When 10 PM I.S.T. (29th January 2018) Where: Online (link will be posted in Cheenta Commons, Open Slate skype group) […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2018. Try them and share your solution in the comments. INMO 2018, Problem 1 Let ABC be a non-equilateral triangle with integer sides. Let D and E be respectively the mid-points BC and C A, let G be the centroid of triangle ABC. Suppose D, […]
In 2018, we are introducing Math Circle memberships. The members have exclusive access to: Weekly live and online Doubt Clearing sessions Exclusive access to Problems and Solutions for I.S.I. & C.M.I. Entrances, TIFR and Math Subject GRE (not available on our general website) Monthly problem lists on school and college mathematics Timely information packet on […]