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The book has five chapters, [3] each largely self-contained [4] [5] and loosely organized around different techniques used to solve problems in this area, [4] with an appendix on the background material in number theory needed for reading the book. [3]
Problem Solving Through Recreational Mathematics is based on mathematics courses taught by the authors, who were both mathematics professors at Temple University. [1] [2] It follows a principle in mathematics education popularized by George Pólya, of focusing on techniques for mathematical problem solving, motivated by the idea that by doing mathematics rather than being told about its ...
First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones.
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