Hello, this is a discussion page for the college students who are in various prestigious colleges throughout India, and are keen to pursue Mathematics. Abstract Algebra plays a pivotal role in college mathematics, and it mainly focuses on three things GROUPS, RINGS, and FIELDS. Though Field is not in the course of some colleges, eventually […]
Let's discuss a Common but deadly question in Group theory. Question: Is it possible to get an infinite group which has elements of finite order? Discussion To pursue this discussion which is basically a very good concept for the students who are new in group theory, they must know first about the QUOTIENT GROUPS. Particularly […]
Try this problem from TOMATO Problem 7 based on the Parity of the terms of a sequence. Problem: Parity of the terms of a sequence If \( a_0 = 1 , a_1 = 1 \) and \( a_n = a_{n - 1} a_{n - 2} + 1 \) for \( n > 1 \), then: […]
This is a problem from TOMATO Problem number 2, useful for ISI and CMI entrance exam based on Men and Job. Problem: If m men can do a job in d days, then the number of days in which m+r men can do the job is (A) d+r; (B) $\frac{d}{m} (m+r)$ ; (C) $\frac {d}{m+r}$ […]
This is a problem number 3 from TOMATO based on Calculating Average Speed. Problem: Calculating Average Speed. A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is (A) 3; (B) 4; (C) 5; (D) $\sqrt {12}$; Discussion: Suppose the distance from home […]
This is a problem number 95 from TOMATO based on finding the Number of factors of 1800. Problem The number of different factors of $1800$ equals: (A) $12$; (B) $210$; (C) $36$; (D) $18$; Discussion: We may factor $1800$ as $2^3 \times 3^2 \times 5^2 $ Then the number of factors is: $(3+1) \times (2+1) […]
This is an objective problem from TOMATO based on finding the Number of Positive Divisors. Problem: The number of positive integers which divide $240$ is- (A) $18$; (B) $20$; (C) $30$; (D) $24$; Discussion: We use the formula for computing number of divisors of a number: Step 1: Prime factorise the given number $240 = […]
Let us discuss about 'inequality' related problems - Minimum Perimeter Problem. All algebraic inequality problems can be traced back to two key ideas: Positive times positive is positive Square of a real number is nonnegative Though these two notions seem trivial and obvious in nature, they lead to a very rich and diverse theory of […]
A worker suffers a 20% cut in wages. He regains his original pay by obtaining a rise of (A) 20% (B) 22.50% (C) 25% (D) 27.50 % If \( \mathbf {m} \) men can do a job in \( \mathbf {d} \) days , then the number of days in which \( \mathbf {m+r} \) […]
This post contains ISI TOMATO Solutions of Objective Problems from 101 to 200. The number of ways of distributing 12 identical oranges among children so that every child gets at least one and no child more than 4 is (A) 31; (B) 52; (C) 35; (D) 42. The number of terms in the expansion of […]
Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Smallest positive Integer.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Equation of X and Y.
Try this beautiful problem from PRMO, 2018 based on Algebra: Inequality You may use sequential hints to solve the problem.
Try this beautiful problem from PRMO, 2019, problem-4, based on Geometry: Direction & Angles. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry:Tetrahedron box from AMC-10A, 2011. You may use sequential hints to solve the problem
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.
Try this beautiful problem from Geometry:cubical box from AMC-10A, 2010. You may use sequential hints to solve the problem
Try this beautiful problem from Algebra:Roots of cubic equation from AMC-10A, 2010. You may use sequential hints to solve the problem
Try this beautiful Geometry Problem on Equilateral Triangle from AMC-10A, 2010.You may use sequential hints to solve the problem.
To some extent the beauty of number theory seems to be related to the contradiction between the simplicity of the integers and the complicated structure of the primes, their building blocks. This has always attracted people. A. Knauf from "Number theory, dynamical systems and statistical mechanics" This quote is indeed true. If you just think about the […]
Author: Kazi Abu Rousan Here there is $\pi$, there is circle. Today's blog will be a bit different. This will not discuss any formula or any proof, rather it will just contain a python program to compare a $\pi$ formula given by Leibniz and a one discovered by me (blush). How does Leibniz formula looks […]
Author: Kazi Abu Rousan Bottomless wonders spring from simple rules, which are repeated without end. Benoit Mandelbrot Today, we will be discussing the idea for making a simple Mandelbrot Set using python's Matplotlib. This blog will not show you some crazy color scheme or such. But rather the most simple thing you can make from […]
Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.
Author: Kazi Abu Rousan Mathematics is not yet ready for such problems. Paul Erdos Introduction A problem in maths which is too tempting and seems very easy but is actually a hidden demon is this Collatz Conjecture. This problems seems so easy that it you will be tempted, but remember it is infamous for eating […]
What is Mathcounts? MATHCOUNTS is a national middle school mathematics contest held in different places in the U.S. states and territories. It is established in 1983, which provides engaging mathematics programs to the US middle school students of different ability levels to grow their confidence and improve the attitudes about mathematics and problem solving. Who are the […]