……给你自己设立以建立更深刻的理解，而且常见问题文章《学习数学》（http://www.epsiloncamp.org/faq/faq_3.php）引述了多位数学家的著作，包括约翰·斯蒂尔韦尔（John Stillwell）的书《数与几何》（Numbers and Geometry），讲述了如何将数学作为一门深刻且融会贯通的学科来欣赏。提交的文章提到：“过去三十年的大量研究表明，任何年龄段的人……
…to set for yourself to build deeper understanding, and the FAQ article "Learning Mathematics" http://www.epsiloncamp.org/faq/faq_3.php points to writings by various mathematicians, including the book Numbers and Geometry by John Stillwell, about how to appreciate mathematics as a deep, connected subject. The submitted article mentioned "Numerous studies over the past thirty years have shown that when people of any age…
……暑期课程。在我大儿子（一个数学迷）成长的过程中，我发现对理解数学很有帮助的书包括：伊恩·斯图尔特（Ian Stewart）的《现代数学概念》（Concepts of Modern Mathematics，Dover 重印版）、约翰·斯蒂尔韦尔的《数与几何》（Numbers and Geometry，Springer 出版）、W. W. 索耶（W. W. Sawyer）的《极简数学视角》（Vision in Elementary Mathematics，Dover 重印版）、桑多尔·莱霍茨基与理查德·鲁斯奇克（Sandor Lehoczky and Richard Rusczyk）的《解题的艺术》（The Art of Problem Solving，Art of Problem Solving 出版）。一本经常被……
…summer course. Books that I found helpful for understanding mathematics when my oldest son, a mathematics-lover, was growing up include Concepts of Modern Mathematics by Ian Stewart (Dover reprint) Numbers and Geometry by John Stillwell (Springer) Vision in Elementary Mathematics by W. W. Sawyer (Dover reprint) The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk (Art of Problem Solving) A frequently…
…that it combines reasoning about discrete, countable things, that is numbers, with reasoning about shapes, that is geometry. An especially good book about both aspects of mathematics is John Stillwell's Numbers and Geometry. http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... I'll quote a bit of Stillwell's preface to give the flavor of the book: "What should every aspiring mathematician know? The answer for…
A suggestion for an addition (or replacement) for the list: http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... Numbers and Geometry by John Stillwell is very readable and full of very interesting math problems, covering a lot of topics that are accessible to anyone with a good high school education but often aren't covered even by…
…maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety." That's from the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998), which is a delight to read and full of thought-provoking problems. http://www.amazon.com/gp/product/0387982892/
…mathematics education in the years indicated, and the author of the submitted article is on to something. One of my favorite authors on mathematics, Professor John Stillwell, writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…
……给你自己设立以建立更深刻的理解，而且常见问题文章《学习数学》（http://www.epsiloncamp.org/faq/faq_3.php）引述了多位数学家的著作，包括约翰·斯蒂尔韦尔（John Stillwell）的书《数与几何》（Numbers and Geometry），讲述了如何将数学作为一门深刻且融会贯通的学科来欣赏。提交的文章提到：“过去三十年的大量研究表明，任何年龄段的人……
…to set for yourself to build deeper understanding, and the FAQ article "Learning Mathematics" http://www.epsiloncamp.org/faq/faq_3.php points to writings by various mathematicians, including the book Numbers and Geometry by John Stillwell, about how to appreciate mathematics as a deep, connected subject. The submitted article mentioned "Numerous studies over the past thirty years have shown that when people of any age…
……暑期课程。在我大儿子（一个数学迷）成长的过程中，我发现对理解数学很有帮助的书包括：伊恩·斯图尔特（Ian Stewart）的《现代数学概念》（Concepts of Modern Mathematics，Dover 重印版）、约翰·斯蒂尔韦尔的《数与几何》（Numbers and Geometry，Springer 出版）、W. W. 索耶（W. W. Sawyer）的《极简数学视角》（Vision in Elementary Mathematics，Dover 重印版）、桑多尔·莱霍茨基与理查德·鲁斯奇克（Sandor Lehoczky and Richard Rusczyk）的《解题的艺术》（The Art of Problem Solving，Art of Problem Solving 出版）。一本经常被……
…summer course. Books that I found helpful for understanding mathematics when my oldest son, a mathematics-lover, was growing up include Concepts of Modern Mathematics by Ian Stewart (Dover reprint) Numbers and Geometry by John Stillwell (Springer) Vision in Elementary Mathematics by W. W. Sawyer (Dover reprint) The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk (Art of Problem Solving) A frequently…
……它将关于离散的、可计数事物的推理（即数）与关于形状的推理（即几何）结合了起来。关于数学这两个方面一本尤为出色的书是约翰·斯蒂尔韦尔的《数与几何》。http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... 我引用一段斯蒂尔韦尔的前言来让大家感受一下这本书的风格：“每个有志于数学的人应该知道什么？20世纪大部分时间的答案都是……
…that it combines reasoning about discrete, countable things, that is numbers, with reasoning about shapes, that is geometry. An especially good book about both aspects of mathematics is John Stillwell's Numbers and Geometry. http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... I'll quote a bit of Stillwell's preface to give the flavor of the book: "What should every aspiring mathematician know? The answer for…
建议为书单补充（或替换）一本：http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... 约翰·斯蒂尔韦尔的《数与几何》非常易读，满是极有趣的数学问题，涵盖了大量只要受过良好的高中教育就能看懂的话题，但这些内容甚至经常连……都未曾涉及。
A suggestion for an addition (or replacement) for the list: http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038... Numbers and Geometry by John Stillwell is very readable and full of very interesting math problems, covering a lot of topics that are accessible to anyone with a good high school education but often aren't covered even by…
……‘保持这些学科之间的联系，不仅有可能呈现出一种更加统一的数学视角，而且同时还能增添更多的趣味和多样性。’这是他那本《数与几何》（纽约：Springer-Verlag，1998）前言里的话，那本书读起来简直是一种享受，而且充满了发人深省的问题。http://www.amazon.com/gp/product/0387982892/
…maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety." That's from the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998), which is a delight to read and full of thought-provoking problems. http://www.amazon.com/gp/product/0387982892/
……在所指那些年份的数学教育，提交文章的作者确实说到了点子上。我最喜欢的数学作家之一，约翰·斯蒂尔韦尔教授，在他那本《数与几何》（纽约：Springer-Verlag，1998）的前言中写道：“每个有志于数学的人应该知道什么？20世纪大部分时间的答案都是：微积分……今天的数学……远不止微积分；……
…mathematics education in the years indicated, and the author of the submitted article is on to something. One of my favorite authors on mathematics, Professor John Stillwell, writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus;…