Bertrand Russell, in his book The Principles of Mathematics, proposes the following as a definition of pure mathematics. Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth. The Princeton Companion to Mathematics could be said to be about everything that Russell’s definition leaves out. Russell’s book was published in 1903, and many mathematicians at that time were preoccupied with the logical foundations of the subject. Now, just over a century later, it is no longer a new idea that mathematics can be regarded as a formal system of the kind that Russell describes, and today’s mathematician is more likely to have other concerns. In particular, in an era where so much mathematics is being published that no individual can understand more than a tiny fraction of it, it is useful to know not just which arrangements of symbols form grammatically correct mathematical statements, but also which of these statements deserve our attention. Of course, one cannot hope to give a fully objective answer to such a question, and different mathematicians can legitimately disagree about what they find interesting. For that reason, this book is far less formal than Russell’s and it has many authors with many different points of view. And rather than trying to give a precise answer to the question, “What makes a mathematical statement interesting?” it simply aims to

The Princeton Companion to Mathematics.pdf

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普林斯顿项目 普林斯顿大学主持的算法1和2的编程任务 作者：大二CS学生杨达恩 渗滤：确定NxM矩阵是否渗滤（具有从上到下的路径），并通过蒙特卡洛模拟计算渗滤阈值-使用不相交的集合数据结构和加权联合查找wihout路径压缩-顶部和底部虚拟节点，用于在检查是否存在连接时将运行时间从O（N ^ 2）减少到O（1）-源文件：Percolation.java PercolationStats.java PercolationVisualizer.java 共线点：给定具有不同点的图，确定哪些点形成4点或更多点的线，并重现这些线而无重复。 -使用快速排序按升序对斜率进行排序，以便计算O（N ^ 2 Lg（n））中的所有线，而不是O（N ^ 4） -源文件：LineSegment.java Point.java FastCollinearPoints.java 8Puzzle ：使用A *算法，找

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