A different side of analytic number theory, with a different set of amazing formulas and brilliant analytic tricks. In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. If you decide to check it out, I think you will find it worthwhile. Thoughts on many parts of mathematics from one of the most exciting mathematicians today. It is a small book, but filled with mathematical gems. The book is focused on the kind of problems encountered in mathematics competitions: It is conversational and pleasant to read.
I really appreciate this style of presentation - all in the voice of a 15-year old. A different side of analytic number theory, with a different set of amazing formulas and brilliant analytic tricks.
Analytic number theory terrence trial#
Many folks new to problem solving will see a fully formed solution and do not understand that there may have been quite a bit of trial and error involved in coming up with that solution. Thus, the most common question I get from these newbies is "how do I know where to start"? Tao addresses this question by including with his solutions a discussion of alternative approaches and why he chose not to use them. Modern number theory is a broad subject that is classified into subheadings such as elementary number theory, algebraic number theory, analytic number.
While these books are good, I really like the tone of "Solving Mathematical Problems." Tao does a very good job of describing the experimental aspects of problem solving. In the past, I have used the books by Polya (here is one and another) on problem solving heuristics. I work with a lot of folks on developing their problem solving abilities. Today at 36, he is one of the world's top mathematicians. The book was written when Tao was a 15 year old mathematics prodigy competing in international mathematics competitions. While on my vacation to Ireland, I brought along a book called "Solving Mathematical Problems: A Personal Perspective" by Terence Tao.
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