Watch the video to learn more about opportunities after Mathematical Olympiads in India, the United States and other countries.
Watch the video to learn more about opportunities after Mathematical Olympiads in India, the United States and other countries.
reading a book written by a true master is like learning from him or her directly. It is an outstanding opportunity that none of us should miss. Here are some of those walks with the masters, that has transformed my life and the way I do mathematics. You may use this list of beautiful mathematics books to stay inspired.
If you are preparing for Mathematics Olympiads, ISI-CMI Entrances or challenging College level entrances then this article is for you. We will describe the no short-cut approach of Cheenta Programs and how you can use them.
Dear parent, One of the key contributions of modern mathematics is its tryst with infinity. As parents and teachers we can initiate thought provoking communication with our children using infinity. Consider the following set: N = {1, 2, 3, … } Notice that N contains infinitely many elements. Take a subset of N that consists […]
‘Teachers for Tomorrow’ is a unique program for parents and teachers who wish to take their kids / students an extra mile in mathematical training. Cheenta uses modern tools (such as Latex, GeoGebra, STACK etc.) to deliver its courses. It also uses carefully experimented teaching methods developed in USSR, United States, and India. We firmly believe that these tools and methods are very valuable in stimulating creativity in young mind.
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 Euclidean geometry. We were traveling in Kausani. After days of frustration and failed attempts, I could put together the ‘reason’ that made ‘everything fit together perfectly’. The problem was […]
In the world of fake olympiads and thousands of contests, it is important to select the right ones and focus on them. Children take hundreds of tests these days under peer pressure. No good comes out this rat race. We urge kids to learn deep mathematical science and prepare for 1 or 2 real contests […]
Try this Algebra challenge for Math Olympiad and ISI-CMI entrance
American Math Competition 8 (AMC 8) 2024 Problems, Solutions, Concepts and discussions.
PART - I Problem 1 In a convex polygon, the number of diagonals is 23 times the number of its sides. How many sides does it have?(a) 46(b) 49(c) 66(d) 69Answer: B Problem 2 What is the smallest real number a for which the function \(f(x)=4 x^2-12 x-5+2a\) will always be nonnegative for all real […]
PART I Problem 1 The measures of the angles of a pentagon form an arithmetic sequence with common difference \(15^{\circ}\). Find the measure of the largest angle. (a) \(78^{\circ}\)(b) \(103^{\circ}\)(c) \(138^{\circ}\)(d) \(153^{\circ}\) Answer : C Problem 2 If \(x-y=4\) and \(x^2+y^2=5\), find the value of \(x^3-y^3\). (a) -24(b) -2(c) 2(d) 8 Answer : B Problem […]
High school research projects and journals that accept papers from high school students in mathematical science.
Part I Problem 1 Let \(XZ\) be a diameter of circle \(\omega\). Let Y be a point on \(XZ\) such that \(XY=7\) and \(YZ=1\). Let W be a point on \(\omega\) such that \(WY\) is perpendicular to \(XZ\). What is the square of the length of the line segment \(WY\) ? (a) 7(b) 8(c) 10(d) […]
PART I Problem 1 Answer: A Problem 2 Answer: D Problem 3 Answer: D Problem 4 Answer: A Problem 5 Answer: D Problem 6 Answer: D Problem 7 Answer: D Problem 8 Answer: C Problem 9 Answer: B Problem 10 For positive real numbers a and b, the minimum value of\( \left18 a+\frac{1}{3 b}\right\left3 b+\frac{1}{8 […]
Problem 1 Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
Question 1 The instructions on a $350-$ gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag? (a) 16 (b) […]
Question 1 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1: 30$, traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at $2: 30$, traveling due east at a steady 12 miles per hour. At what time will they […]
Question 1 In the year 2001, the United States will host the International Mathematical Olympiad. Let $I, M$, and $O$ be distinct positive integers such that the product $I \cdot M \cdot O=2001$. What's the largest possible value of the sum $I+M+O$ ? (a) 23 (b) 55 (c) 99 (d) 111 (e) 671 Question 2 […]
Question 1 The median of the list \[ n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15 \] is 10 . What is the mean? (a) 4 (b) 6 (c) 7 (d) 10 (e) 11 Question 2 A number \(x\) is 2 more than the product of its reciprocal and its additive inverse. In which […]
Question 1 The ratio \(\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\) is closest to which of the following numbers? (a) 0.1 (b) 0.2 (c) 1 (d) 5 (e) 10 Question 2 For the nonzero numbers \(a, b, c\), define \((a, b, c)=\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\). Find \((2,12,9)\). (a) 4 (b) 5 (c) 6 (d) 7 (e) 8 Question 3 According to the standard convention […]
Question 1 What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers? (a) 0 (b) 1 (c) 2 (d) 2003 (e) 4006 Question 2 Members of the Rockham Soccer League buy socks and T-shirts. Socks cost \($ 4\) per pair and […]
Question 1 You and five friends need to raise \($ 1500\) in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise? (a) 250 (b) 300 (c) 1500 (d) 7500 (e) 9000 Question 2 For any three real numbers \(a, b\), and \(c\), with \(b \neq c\), […]
Question 1 While eating out, Mike and Joe each tipped their server 2 dollars. Mike tipped \(10 %\) of his bill and Joe tipped \(20 %\) of his bill. What was the difference, in dollars between their bills? (a) 2 (b) 4 (c) 5 (d) 10 (e) 20 Question 2 For each pair of real […]
Question 1 Sandwiches at Joe's Fast Food cost \($3\) each and sodas cost \($ 2\) each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? (a) 31 (b) 32 (c) 33 (d) 34 (e) 35 Question 2 Define \(x \otimes y=x^{3}-y\). What is \(h \otimes(h \otimes h)\) ? (a) \(-h\) (b) […]
Question 1 What is $10 \cdot\left(\frac{1}{2}+\frac{1}{5}+\frac{1}{10}\right)^{-1}$ ? (a) 3 (b) 8 (c) $\frac{25}{2}$ (d) $\frac{170}{3}$ (e) 170 Question 2 Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing 6 cans […]
মানচিত্র আঁকছিলাম। রাস্তা গুলো সোজা সোজা। উত্তর, দক্ষিণ, পুব, পশ্চিমে যাওয়া যায়। এক ধাপ ডাইনে গেলে, সঙ্গে সঙ্গে এক ধাপ বাঁয়ে ফেরার নিয়ম নেই। (তাহলে আর ডাইনে গেলাম কেন!) তেমনি একধাপ উত্তরে গেলে, সঙ্গে সঙ্গে একধাপ দক্ষিণে ফেরাও মানা।
মানচিত্র আঁকতে আঁকতে দেখলাম এক উদ্ভট দেশ তৈরি হচ্ছে। সে দেশের প্রতি চৌমাথায় অসীম সব রাস্তা। সে সব রাস্তা আবার একে অপরের সঙ্গে তেমন দেখা সাক্ষাৎ করে না। এ হেন দেশের সীমান্ত নিয়ে আমাদের যত মাথা ব্যাথা। খুঁজতে খুঁজতে বেড়িয়ে পড়ল এক আজব কিস্যা!
সীমান্তে একলা দাঁড়িয়ে আছেন ক্যান্টর।
বাকি আড্ডা ভিডিও তে।
লিনিয়ার বীজগণিত নিয়ে আমরা একটি ভিডিও সিরিজ তৈরী করছি। 'চিন্তা'-র কলেজ গণিত প্রোগ্রামে যদিও প্রধানত ইংলিশে আলোচনা হয়, আমরা চেষ্টা করি বিভিন্ন আঞ্চলিক ভাষা গুলোতে কিছু আলোচনা করতে। পরবর্তী আলোচনা গুলো খুব আসছে এই পাতায়।
গ্রুপ থিয়োরি নিয়ে বাংলায় একটা কোর্স তৈরি করার ইচ্ছা বহুদিনের। এই ভিডিও সিরিজটা তারই শুরুয়াদ। আমরা প্রচুর ইংরেজি শব্দ ব্যাবহার করব। তারই সাথে চলতি বাংলা থেকে কিছু ছবি, কিছু কথা, কিছু ধ্বনি আনিত হবে। গ্রুপ কয় কাহারে? আমরা 'ডেফিনেশন' দিয়ে শুরু করতে পারি। কিন্তু তার বদলে শুরু করছি একটা বেশ কৌতূহলোদ্দীপক উদাহরণ দিয়ে। ভিডিওটা দেখার […]
সংখ্যাতত্ত্ব লেখাটিতে আমরা Pythagorean triplet বা পিথাগোরীয়ান ত্রয়ী নিয়ে আলোচনা করা হয়েছে ।
দৈনন্দিন জীবনে বস্তু গোনবার পদ্ধতি খুব কাজের জিনিস । এই পোস্ট থেকে একটি পদ্ধতি সম্বন্ধে জানব যা ডিরিশিলিটের বাক্স নীতি বা ইংরেজিতে Pigeonhole principle বলে।
A post on homological triangles... topic of our math camp August 2014 (in Scotland)