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FAQ

What's a cool math fact you can easily tell a layman and look super cool?
Few quick ones...Notches (cuts or indentation) on animal bones prove that humans have been doing mathematics since around 30,000 BC - much before farming or formal writing.The name 'zero' derives from the Arabic word sifr which also gave us the English word 'cipher' meaning 'a secret way of writing' .In 1995 in Taipei, citizens were allowed to remove ‘4‡ from street numbers because it sounded like ‘death‡ in Chinese. Many Chinese hospitals do not have a 4th floor.In working out mathematical equations, the Greek mathematician Pythagoreans used little rocks to represent numbers.Hence the name of Calculus was born which means pebbles in Greek.A fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often.May be tell you mother that next time she meets a big-mouth person at a party, babbling and showing off, she can make a comment like: "I know the exact mathematical equation which proves "An empty vessel makes a bigger sound". The Standing wave solution.When your mother bothers you about your disheveled work desk, you can say there is a theorem which says it is futile to neatly arrange things because in the long run universe is going towards more chaos. dS/dT 0.As in people at a party, there are rational, irrational, complex, perfect, and even surreal numbers :-)And if there are 57 people in that party, there is ~ 99% chance that two of them share same birthday. Refer to: Pigeonhole principleJust a mind-twister- A person who proved that a truth-seeking system will contain statements whose truthfulness it can never prove, also wrote a theorem about a mathematical proof of the existence of God. Refer to: Gödel's ontological proof This one is for middle school students who are just introduced to imaginary numbers but not much into it: That an imaginary number raised to the power of another imaginary number can be a real number.Ever heard of Ponzi scheme of money doubling? There is an equivalent (sort of) in mathematics,The Banach-Tarski theorem: Given a 3-D ball, there exists a decomposition of the ball into finite number of disjoint subsets, which, then can be put back together in a different way to give two identical copies of the original ball. Yes, you make two balls out of one without any stretching, bending, or adding new points :-)One for your movie-loving friend,The rippling muscles of Mr. Incredible in The Incredibles, the exquisitely detailed surfaces of Ratatouille, the effortlessly draped garb of Monsters, Inc., the expressive robots of WALL-E, and the sparkling splashes and eerie lighting of Finding Nemo - all needed solving thousands of equations per frame of the movie.Broken Heater Problem=====================================My water heater broke. I took it to a guy in the neighborhood corner. He changed some spare parts and fixed it.Is this guy likely to be(A) An accountant, OR(B) An accountant and a Plumber?Answer is: (A).Source: The 12 Most Controversial Facts In Mathematics
How can an Indian student get into a top international university?
This question is akin to a common question thrown around in entrepreneur circles how do you start a successful start-up. There is no one definitive answer or formula that works but instead there are a bunch of rules you can follow that would increase your odds. After that, you can only hope that the dice rolls in your favor. Rarely have I met a person and been convinced that there is no way on earth this person is not getting into College X. In fact the only person that comes to my mind is my friend Raghu Mahajan who among other things topped JEE a few years ago. And in case you are updating your model that topping JEE implies getting into one of these colleges, don't do so. Topping JEE was just a byproduct of being Raghu. The man exudes mastery of the sciences like no other. JEE was just a validation of this fact and not really an achievement per se. Yet Raghu is an outlier. He is like Bill Gates in that sense. Those who knew Bill Gates in the 70's had never any doubt that he would start one of the most successful companies in the world. Most of us need the dice to roll in our favor. In my sophomore year, I was advising a friend of mine Vishesh Jain who is now at Stanford. Vishesh is one of the smartest and most original people I know. Yet, I couldn't have said that he was going to surely get into College X. So what we did was what investors call portfolio diversification (known in common parlance as don't put all your eggs in the same basket). Apply to a bunch of good colleges, send a solid application to each and hope variance doesn't hit you adversely. For example let us say the US has ten really good colleges for your program. Each has a historic acceptance rate of 5% from India (its less than a percent for MIT and Harvard but 5 is a good mean figure). And let us make a somewhat of a coarse assumption (right up there with assuming an elephant to be a sphere) and say the entire applicant pool is even, you then are at around 40% to get into at least one college. We shall come back to this model later. Over the last four years, i have read a ton of essays and applications of juniors from my school some of whom are now in the universities you mention. I have known all of them personally. I rarely offer consultation to someone who I do not know well because this prevents me from offering key insights into their application- the reason why they came to me in the first place. Interacting with these juniors has given me enough data to reasonably guess a person's likelihood on getting into a college X he likes. I will begin by debunking some common myths that a lot of Indian students seem to have. Then I will proceed to list out some general rules to follow and not to follow. Common Myths1.  SAT ScoreIt is understandable that everyone tries to maximize this one metric for seemingly it is the one objective score in an otherwise subjective application. More objective and in fact a fairer reflection of your basic academic abilities are your school marks from 9th to 12th. If you scored a 2100 or more then do not take the SAT I again. For no other reason except that it is unnecessary, a royal waste of time and it is going to make you dumb.2. Social ServiceI don't know when this phenomenon started. But over the last decade or so, I have seen so many kids who get into class 11, and it occurs to them that they should apply abroad for college. Unfortunately, all these realizations seem to coincide with their first visit to the blind school or the old age home in their city. The act is itself a very noble one but when laced with an insincere intention it plunges to a heinous and perverse one. Besides, none of the people I consulted with ever did social service and they all got into college X. Bill Gates did not do any social service when he was a kid because his priorities then were computers. Now he runs the largest philanthropic organization in the history of the world. Rules to follow:DO’s1. Maintain a solid academic recordThis goes a long way in showing basic academic abilities of the student. All you need is a consistent record. Nothing fancy, nothing spectacular. A solid 90% in all grades from 9-12. That's it. In India, it is often the case, that people score unusually high marks in class 10, then plunge in class 11 and kind of recover in 12th. This is concrete evidence that the kid likes to slack which is not exactly a vice but definitely not a virtue. Also, if you are trying really hard to get 95% but can score an effortless 90%, i would settle for the latter and invest my time in more fruitful activities than to shine in the Indian education system. 50% of the applicant pool will not have a solid academic record. 2. Take your hobbies seriouslyWe are all born curious. This curiosity leads us to pick up hobbies at a very early age. Somewhere along time we find less and less time for these hobbies and get caught up more and more in the rat race. We must make a conscious effort to avoid this situation. You can avoid it by turning these hobbies into more than just hobbies. Say the one thing you are fascinated about is the Rubik's cube and you find that slowly and slowly, for various reasons, you are devoting less and less time on it. Solution: start a Rubik's cube club in school. Spread the joy. Hold time trials. Observe what the theoretical limit is. In the case of the 3x3 rubik's cube it would be around 2 seconds if you could solve the entire cube in your head before touching it. This is a ridiculous number to achieve but try to see how close you can get to it. Make challenges out of mundane things and lo! without even realizing it you are on the path to mastery.Even if you don't eventually attain the lofty goals you set yourself, you would have gained a ton of insight and lessons that you can now apply to other hobbies. This all comes together quite beautifully when you write your application. It is also something that is hard to feign if you haven't lived through it. 70% of the applicant pool would not have pursued a hobby seriously.  3. Be Creative but not pompous in your essaysThis one is kind of hard. It would be hard to give advice on what a good essay is because it would vary from prompt to prompt. But a key insight to keep in mind is to write something that comes out like a fresh breeze into the otherwise bored admissions officer’s head who has to read around 200-300 essays a day. A good essay would usually have a fresh insight into things, be sincere and articulate, and would avoid any hint of pomposity or narcissism. It is easier said than done though.  With a couple of iterations and a level head you can at least avoid all signs of pomposity, narcissism or insincerity in your essays. Creativity is a little harder. It is mostly luck. And like all things that involve luck your odds of hitting upon a creative idea can also be dramatically improved through mostly a few basic but hard to achieve habits. Creativity comes with obsession. When you take a hard problem and figure that none of the existing techniques in your mental cache seem to work, one of two things can happen in your brain, a) it can either go into panic mode which eventually results in a crash and burn b) it can go into a totally calm and relaxed mode- for a few moments you would have no thoughts at all and then the brain suddenly goes into overdrive and thoughts from all over the place, thoughts that  you didn’t even know existed, come pouring in and your job then is to simply collect the best ones and note them down lest you forget. Once you have ideas for what you want to write, the only thing left is articulation which comes from practice. Articulation is key, because no matter how good your ideas are, if you can't get them across, the people reading your application won't care. 65% of the applicant pool would fail at no. 3DON’Ts:1. Don't be phonyA lot of people figure that they want to apply to abroad when they enter class 11. You suddenly find new clubs springing up every second day, a hoard of eager students who suddenly want to get into the computer club, do quizzing, MUN and what not. Some genius even started a Youth Congress in my school in the middle of class 11, not because he had a profound plan for what it'd do but because he systematically went through the list of all the clubs our school had and decided this one didn’t exist. 75% of the applicant pool would have done phony stuff and proudly highlighted it2. Do Not ImitateAnd this encompasses a lot of things people the world over err at. People try to blindly emulate a classmate or a senior who has been there done that. If your friend has an IMO gold and got into MIT, that doesn't mean the way to get into MIT is through an IMO Gold. Your friend got an IMO gold because his motivations exceeded beyond getting into MIT- mainly the thrill that comes from Mastery of a field, to know that few people in the world can see things the way he can. If your motivation is to get into MIT, then you will not get an IMO gold in a million years. However instead of trying to imitate your friend, you can squeeze out the essence of his achievement and try to attain that. Essence in this case was pure mastery and if you apply the same dedication to a craft you are good at, then you are automatically one step closer to your goal. There is a Zen saying "If you try to seek happiness, you never will" and nothing rings truer in the case of college applications.This is not going to hurt your chances except that you are doing injustice to your life. You are wasting time on mastering skills your friend has rather than perfecting your own. This leads us to infer that if you follow all of the above rules, in the worst case you'll be in the top 30% applicant pool (we assume everyone in this 30% pool is equally strong) of India. Coming back to our original calculation, this implies that if you apply it to your favorite ten colleges, your chances of getting in just increased to about 84%. Favorable odds indeed :D. Yet this is not a 100%. I have seen pretty mediocre people getting into these colleges and pretty solid people being left out. The head girl in my batch was my friend Shraddha, who had scored an effortless 2370 in her SAT I, had effortless scores of 95% throughout her high school, was one of the more formidable quizzers in delhi, and had amongst many academic achievements topped the NTSE in Delhi. I had the privilege of reading her essays and they were marked with creativity and finesse beyond her years. The phenomenon where such applicants miss out is popularly known as Bad Luck. She didn't get in but nevertheless continued to do what she liked and is doing better than most of the people whom luck was kinder to back then. Thus, even if you don't get into college X and continue to follow the above rules, I think you'll do fine.A small note on financial aid:If you do get into these top universities without financial aid, you'll be chunking out around 200K over your four years. If your plan is to study something technical and get a job then you are indeed positive ROI. Top quartile in these schools can easily get 100k a year jobs. It still depends on how risk averse you are and if such a hefty loan on your head makes you lose sleep at night. I was very lucky to get away super cheap so I never had to make this decision. All these institutions have world class faculty, research opportunities and facilities. If you plan to make the best out of these then you should probably take the loan.  Startup Idea:I talked about startups, so while writing this piece I had a start-up idea. Every year 500,000 undergrads from around the world come to the USA to study. I am sure there are definitely more than that number who apply and don't get in. The decision on whether they'll get in probably depends on around 100 factors. I don't know which 100 factors though but i am guessing 100 factors with perhaps 20 really strong indicators. If you can collect the data for these factors for applicants of say the last 8 years. You would have a training set of 8 million. An international undergrad on average spends 1,000 dollars on applications and 80,000 dollars as tuition over his four year years in the US. Thus, it is not far-fetched that he would be easily willing to pay to the tune of 300-500 dollars to get access to a software that predicted his current chances and also told him how he could tweak stuff around to increase his chances. That translates to roughly 300-500 million a year. Thus, if you can go through the arduous task of data collecting, you will be a very rich man at the end of it all. If you do happen to collect all the data, but don't know how to train your classifier then ping me and i shall happily do it for a tiny share of the pie :D.
What are the best ways to reduce and eliminate belly, abdominal, and thigh fat?
One of the biggest questions I get is “how do I lose my belly fat? I’ve tried several things but nothing worked”. When I ask what you tried I hear 100 daily sit-ups, cutting calories drastically, excess cardio, fat burners, etc.If you can’t lose your belly fat, you’re using the wrong approach. You don’t need endless sit-ups, supplements, starving yourself or worse surgery. Here are the 10 best ways to lose your belly fat ‡ quickly and naturally.1. Stop Doing Crunches. Crunches will strengthen your stomach muscles, but won’t burn the belly fat that covers your abs. Spot reduction is a myth. You’re wasting time & effort doing 200 daily crunches.Crunches can also cause lower back pain, slouching shoulders & forward head posture. The Reverse Crunch doesn’t cause these problems, but again: spot reduction is a myth. To lose your belly fat, you need more. Keep reading.2. Get Stronger. Strength training builds muscle mass, prevents muscle loss and helps fat loss. The Squat & Deadlift work best to build strength.Your lower back keeps you upright from the back. Your abs from the front. Both muscles will work hard during heavy Squats & Deadlifts at keeping you from collapsing under the weight.Squats & Deadlifts allow you to stress your body with heavy weights, working all your muscles from head to toe. This helps getting stronger quickly and building muscle fast, including ab muscles.Spot reduction still doesn’t exist, so Squats & Deadlifts won’t burn your belly fat directly. However they’ll strengthen your abs and lower your waist size. If you never did both exercises, check StrongLifts 5×5. Only takes 3x45mins/week.3. Eat Healthy. As the saying goes “abs are built in the kitchen”. You can train hard & build muscular abs, but if you eat junk food all day, you won’t lose your belly fat. Stop eating processed food. Eat whole, unprocessed foods.Proteins. Meat, poultry, fish, whey, eggs, cottage cheese, …Veggies. Spinach, broccoli, salad, kale, cabbage, …Fruits. Banana, orange, apple, pineapple, pears, …Fats. Olive oil, fish oil, real butter, nuts, flax seeds, …Carbs. Brown rice, oats, whole grain pasta, quinoa, …No need to be perfect. Eating junk food actually helps fat loss by keeping your hormones sharp. Don’t overdo it though. Eat junk food 10% of the time max. That’s 4 junk meals/week if you eat 6 meals/day.4. Limit Alcohol Consumption. To lose your belly fat, what you drink is as important as what you eat. Alcohol from time to time is OK. But forget about losing your belly fat if you drink beer & sweet alcohols daily.Beer drinkers always have a pear shape: belly fat & man boobs ‡ especially as they get older. Alcohol also stresses your liver which has to overwork to clear the toxins. This can get in the way of building muscles.Drink alcohol 10% of the time. Example Friday & Saturday night. Normal alcohol consumption, not the get drunk. Rest of the time: water, water with squeezed lemon, green tea, etc. Either that or forget about losing your belly fat.5. Eat Less Carbs. You need carbs for energy. Problem is that most people eat way more carbs than they need. Your body will stock the carbs it doesn’t need as fat. And this is often how you get belly fat.Unless you’re a skinny guy who needs to gain weight, lower your carb intake. Keep eating fruits & veggies with each meal. But cut back on potatoes, pasta, rice, breads, ‡ Eat these post workout only.6. Eat More. Eating tons of healthy foods won’t make you fat. Especially not if you exercise 2-3x/week. Starving yourself is the number 1 nutritional mistakes. Healthy nutrition is important for 3 reasons:Energy. Food is energy. Your body uses food for weight lifting, working, digestion, etc. Lack of food means lack of energy, in all areas of life.Fat Loss. Eating the right foods helps fat loss: protein has the highest thermic effect and satiates, healthy fats promote fat loss, …Maintain Muscle. If you starve yourself, your body will burn muscle for energy ‡ NOT fat. You’ll become skinny + fat.Hunger means you’re not eating enough. Don’t worry about calories. Just eat breakfast and eat every 3 hours from there on, including post workout. Eat healthy foods 90% of the time to lose your belly fat fast.7. Eat More Protein. Protein has a higher thermic effect than other foods: your body burns more energy processing proteins than it does processing carbs and fat. That’s why high protein diets work great at burning your belly fat.How much protein do you need daily? Do like I do: eat whole protein with each meal without worrying about the numbers. Check the 10 cheapest sources of protein to keep it budget-friendly.8. Eat More Fat. Fat doesn’t make you fat. Bad nutrition and lack of exercise do. Eating fat actually helps fat loss. Your body won’t stock fat as easily if your give it a constant intake of healthy fats.Fish oil is the best source of fat to lose your belly fat. Fish oil naturally increases testosterone levels and increases fat loss. 6g omega-3 per day is a good start. Check Carlson Fish Oil: 1600mg omega-3 per tbsp.Stay away from trans-fatty fats present in products like margarine. Trans-fatty fats are bad for your health. Eat whole unprocessed foods 90% of the time as I recommend in point 3 and you’ll avoid trans-fatty fats easily.9. Lower Your Body Fat. As a man, your belly is the last place where you’ll get rid of fat. If you have man boobs and a double chin, you’ll have to lower your body fat to lose your belly fat. Here’s how:Get Stronger. Strength training builds & maintains muscle, increases fat loss, helps sticking to diet, ‡ Check StrongLifts 5×5 if you don’t know where to start: it only takes 3x45mins/week.Eat Healthier. Apply the 8 nutrition rules. Eat breakfast. Eat every 3 hours. Proteins, veggies & fruits with each meal. Carbs post workout only. 2 cups of water with each meal. Whole foods 90% of the time.Add Cardio. 15mins post workout, build up to 3x45mins/week. If you have less than 15% body fat, just get stronger and eat healthier. That will lower your body fat and make you lose your belly fat.Check the fat loss guide for more info about how to lower your body fat.10. Stay Motivated. Looking at your belly or in the mirror gives you inaccurate feedback. What you see is influenced by food intake, water retention, light and your own perception. Self-image issues can make the last one tricky.Measure Body Fat. Every 2 weeks using a fat caliper. It doesn’t need to be accurate. What matters is that the trend goes down.Measure Your Waist. Also every 2 weeks. If you get stronger and eat healthy, your waist will go down fast. Your pants will start to feel loose.Take Pictures. Shoot pictures of yourself every 2 weeks: front, back & side. The side pictures will show the most change.Success breeds success. Track progress accurately so you know where you are and stay motivated to keep working at losing your belly fat. Don’t just read this post and go back to what you were doing. Take action. Lose your belly fat.
Which five world leaders will actually make the world a better place?
There are dearth of worth emulating leaders these days. There is no other way out except making ourselves that perfect leader whom we want to emulate in life. As a matter of fact our five sense organs are the real leaders which if controlled properly can do miracles. History is replete with many such examples where the ordinary persons by controlling their sense organs did extraordinary works. many time we fall in the trap of religions. religions are real culprit which doesn't allow the advance form of civilization to take its root in the world so that world may become a better place to live in. many religious scriptures directly orders discrimination based on religion and which eventually germinates the hatred towards other religion and their followers. Unfortunately many such leaders which creates antagonism and hatred in the society commands tremendous respect in the societies world over. We have to read virtuous book like Bhagwadgita and Vedanta philosophy as illustrated by Swami Vivekananda which prescribes lot of panacea and mantras for imbibing and assimilating virtues and thereby transforming the society as a whole. So, we have to transcend beyond caste, creed and religion to establish virtues all around us by becoming perfect epitome and icon in the world. Hate the haters and love the lovers!;"";""
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