There are of course several other problem-solving books, such as Polya’s classic “How to solve it“, which I myself learnt from while competing at the Mathematics Olympiads.Solving homework problems is an essential component of learning a mathematical subject – it shows that you can “walk the walk” and not just “talk the talk”, and in particular identifies any specific weaknesses you have with the material.But I find math hard and i often make many mistakes now.
Does that mean you don’t consider yourself a genius or you don’t really see a distinction between yourself and others who apply themselves and are ambitious?
I am not saying I don’t believe some people are naturally more gifted at certain things or develop stronger skills or have stronger talents than others.
A good rule of thumb is that if you cannot adequately explain the solution of a problem to a classmate, then you haven’t really understood the solution yourself, and you may need to think about the problem more (for instance, by covering up the solution and trying it again).
For related reasons, one should value partial progress on a problem as being a stepping stone to a complete solution (and also as an important way to deepen one’s understanding of the subject). Note: My English is quite poor, you may experience this in the solution.
Today, a reports that most people make a common computing mistake with the fraction (1/3) in the problem.
At first glance, you’d probably assume that the 1/3 is meant to be a fraction representing one-third. And if you guessed wrong, don’t worry — we’re right there with you scratching our heads.Later in your research career, you will find that problems are mainly solved by knowledge (of your own field and of other fields), experience, patience and hard work; but for the type of problems one sees in school, college or in mathematics competitions one needs a slightly different set of problem solving skills.I do have a book on how to solve mathematical problems at this level; in particular, the first chapter discusses general problem-solving strategies.But, if you put the problem into a calculator or Google search, the slash would be interpreted as a division symbol, which would change the order of operations used to solve the problem, producing a different answer. Watch the video below, which explains the common mistake that is made and how to correctly solve the problem. Problem solving, from homework problems to unsolved problems, is certainly an important aspect of mathematics, though definitely not the only one.I hope you are interested in elementary geometry, too, nice to meet you here! Hi Prof Tao, As an undergraduate student I often face the problem of deciding how many textbooks problems I should do before moving on, for example, Is ten questions per chapter of Rudin’s Principles of Math Analysis adequate?The more problems I do on a specific topic the slower it takes to reach graduate level mathematics. Tao: I hava translated this essay into chinese, I’m sorry I couldn’t translated it well enough, as my ability in english is as poor as mathematics.And I know you say similar things on your career advice blog, and I know it’s important to be realistic and plan for graduate school and beyond I just really don’t like how people put this label of genius or prodigy on certain people to (in my opinion) make them seem able to achieve things that most other people cannot–even the levels of Einstein or Mozart.And I don’t think that’s arrogant or unrealistic.I wanted to get your honest opinion. Hey Leif, This book might be useful in pursuing the answer for your question: Disclaimer: I just read the summary and reviews of that book. I’m, at the moment, too busy with studying Maths stuff. Tao, I am a high school student, I loved math got good grades in my middle school years.But i am very nervous during my math exams and i almost forget everything i have learnt. I am currently self-studying some non-rigorous calculus. Try to see if you’ve learned everything in regular calculus, and then go onto . Since research is about hard problems, does that mean I don’t have what it takes to be a mathematician?As you are still several years away from having to attack research-level mathematics problems, your current skill in solving such problems is not particularly relevant (much as the calculus-solving skill of, say, a seventh-grader, has much bearing on how good that seventh-grader will be at calculus when he or she encounters it at the college level).