the fact that you graduated high school and university and earned your doctorate so young), I’m wondering if you think you possess something that only a few others have in terms of intellectual ability or not.
I have always believed that if someone applies himself and puts in enough time, effort, concentration, and perseverance they can accomplish whatever they set their mind to.
to expand out the definitions, solve some special cases, and isolate key difficulties) is also a very important measure of progress (see this previous post of mine on this topic), as is the practice of constantly asking yourself “dumb” questions in the subject (as discussed in this post).
One should also not focus on the most difficult questions, but rather on those just outside your current range.
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.
It’s worth persisting in trying to understand how to do these problems, and not just for the immediate goal of getting a good grade; if you have a difficulty with the homework which is not resolved, it is likely to cause you further difficulties later in the course, or in subsequent courses.
For instance, if after failing to solve a problem, you receive the solution and study it carefully, you may discover an insight or problem-solving technique that eluded you before, and will now be able to solve similar problems that were previously out of reach.
One should also bear in mind that being able to partially solve a problem (e.g.
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).
The more important consideration is the extent to which your problem-solving skills are improving over time.
Comments Help Me With Math Problem Solving
Art of Problem Solving
Online school, textbooks, and many other resources for eager math students grades 2-12.…
Problem Solving - National Council of Teachers of Mathematics
A concise discussion of implementing problem solving in the mathematics classroom.…
NU Math Problem Solving Group Web Page
Solve math problems proposed in magazines like Math Horizons, College Mathematics Journal and the Mathematics Magazine. Ideally we should solve at least.…
Synthesis of Research on Problem Solving
Problem solving has a special importance in the study of mathematics. A primary goal of mathematics teaching and learning is to develop the ability to solve a.…
Problem solving & projects - Homeschool Math
Find here an annotated list of problem solving websites and books, and a list of math contests. There are many fine resources for word problems on the net! have.…
Solving mathematical problems What's new - Terence Tao
Problem solving, from homework problems to unsolved problems, is certainly an important aspect of mathematics, though definitely not the only one. Later in.…
Mathematical Problem Solving - Current Themes, Trends, and.
This book continues the accumulation of knowledge about mathematical problem solving by looking at the current themes, trends and research perspectives and.…
Problem Solving Maths
As you study mathematics you will meet more complex problems in early work, problems often require just one step to find a solution; as you progress you will.…
Solving Math Word Problems explanation and exercises
Techniques and strategies for solving math word problems.…
Math Problem Solver Solve math problems for free
This online Math solver can tell you the answer for your math problem, and even show you the steps for a fee.…