……纯粹是“定义-定理-证明”那种结构。但在本科及以上阶段，许多其他纯数学领域也都是以类似套路呈现的。（我推荐 Nathan Carter 的书《Visual Group Theory》，它是对这种主流趋势的一个极其精彩的反例，从具体实例切入，非常通俗好懂。http://web.bentley.edu/empl/c/ncarter/vgt/）
…a pure definition–theorem–proof kind of structure. But many other areas of pure mathematics at the undergraduate level and above are presented in a similar fashion. (I recommend Nathan Carter’s book Visual Group Theory for a lovely counter-example to the prevailing trend, which starts with the concrete, and is very accessible. http://web.bentley.edu/empl/c/ncarter/vgt/)
……只要肯下功夫，高中生也是能看懂本科群论课程里那些更高级的内容（西罗定理等等）的。把 Nathan Carter 那本写得极好的《Visual Group Theory》推荐给任何一个聪明的15岁孩子，我连眼都不会眨一下。但对于一个（比如）10岁的孩子来说，光是学习图形和镶嵌的对称性，就已经包含足够多既实用又有趣的数学了。
…fancier parts of an undergraduate group theory course (Sylow theorems, etc.) are accessible to high school students who go through the work. I wouldn’t hesitate to recommend Nathan Carter’s lovely book Visual Group Theory to any bright 15 year old. But for a (say) 10-year-old, just learning about the symmetries of shapes and tilings is plenty of useful and interesting math.
如果你喜欢图解，还有两本很棒的书：Nathan Carter 的《Visual Group Theory》（可视化群论）和 Marty Weissman 的《Illustrated Theory of Numbers》（图解数论），只要是有自驱力的高中生应该都能看懂。http://web.bentley.edu/empl/c/ncarter/vgt/ http://illustratedtheoryofnumbers.com
If you like pictures, another couple nice books are Nathan Carter’s Visual Group Theory and Marty Weissman’s Illustrated Theory of Numbers, both of which should be accessible to motivated high school students. http://web.bentley.edu/empl/c/ncarter/vgt/ http://illustratedtheoryofnumbers.com
……本科工科教育。要学习群论、环论等，你最好从储备一批生动具体的实例并进行深入探究开始（对于有高中数学或工科本科背景的人，我会推荐 Nathan Carter 的书《Visual Group Theory》作为起点）。否则，那些定理和证明无非就是在摆弄符号，机械地去 pattern-matching 老师布置下来的某项作业……
…undergraduate technical education. To learn group theory, ring theory, etc., you want to start with a nice stable of explicit concrete examples, explored deeply (I would recommend Nathan Carter’s book Visual Group Theory as a start for someone with a high school math or undergraduate engineering background). Otherwise the theorems and proofs are just symbol twiddling and pattern-matching to some assignment handed down…
……需要2个生成元，所以你不可能只对床垫不断重复单一的翻转/操作就得到所有可行的摆放位置。对于想学群论的朋友，我推荐 Nathan Carter 的书《Visual Group Theory》，这是一本入门门槛很低的导论，通篇采用口语化风格，包含大量精彩的配图（不像大多数抽象且堆满符号的群论教材）。http://web.bentley.edu/empl/c/ncarter/vgt/…
…needs 2 generators, so you can’t keep performing a single flip/operation on your mattress and get all viable positions out of it. For folks trying to learn group theory, I recommend Nathan Carter’s book Visual Group Theory, an approachable introduction written in conversational style, full of great pictures (unlike most group theory textbooks, which are abstract and symbol-heavy). http://web.bentley.edu/empl/c/ncarter/vgt/…
有一本没有前面讨论的那些毛病的神书，那就是 Nathan Carter 写的《Visual Group Theory》，之前在 HN 上讨论过。它在深入定理之前提供了极其充分的动机阐述和实例支撑。https://news.ycombinator.com/item?id=11745486
A wonderful book that doesn't suffer the discussed flaw is Visual Group Theory by Nathan Carter, discussed on HN earlier. It provides ample motivation and examples before diving into the theorems. https://news.ycombinator.com/item?id=11745486
……纯粹是“定义-定理-证明”那种结构。但在本科及以上阶段，许多其他纯数学领域也都是以类似套路呈现的。（我推荐 Nathan Carter 的书《Visual Group Theory》，它是对这种主流趋势的一个极其精彩的反例，从具体实例切入，非常通俗好懂。http://web.bentley.edu/empl/c/ncarter/vgt/）
…a pure definition–theorem–proof kind of structure. But many other areas of pure mathematics at the undergraduate level and above are presented in a similar fashion. (I recommend Nathan Carter’s book Visual Group Theory for a lovely counter-example to the prevailing trend, which starts with the concrete, and is very accessible. http://web.bentley.edu/empl/c/ncarter/vgt/)
……只要肯下功夫，高中生也是能看懂本科群论课程里那些更高级的内容（西罗定理等等）的。把 Nathan Carter 那本写得极好的《Visual Group Theory》推荐给任何一个聪明的15岁孩子，我连眼都不会眨一下。但对于一个（比如）10岁的孩子来说，光是学习图形和镶嵌的对称性，就已经包含足够多既实用又有趣的数学了。
…fancier parts of an undergraduate group theory course (Sylow theorems, etc.) are accessible to high school students who go through the work. I wouldn’t hesitate to recommend Nathan Carter’s lovely book Visual Group Theory to any bright 15 year old. But for a (say) 10-year-old, just learning about the symmetries of shapes and tilings is plenty of useful and interesting math.
如果你喜欢图解，还有两本很棒的书：Nathan Carter 的《Visual Group Theory》（可视化群论）和 Marty Weissman 的《Illustrated Theory of Numbers》（图解数论），只要是有自驱力的高中生应该都能看懂。http://web.bentley.edu/empl/c/ncarter/vgt/ http://illustratedtheoryofnumbers.com
If you like pictures, another couple nice books are Nathan Carter’s Visual Group Theory and Marty Weissman’s Illustrated Theory of Numbers, both of which should be accessible to motivated high school students. http://web.bentley.edu/empl/c/ncarter/vgt/ http://illustratedtheoryofnumbers.com
……本科工科教育。要学习群论、环论等，你最好从储备一批生动具体的实例并进行深入探究开始（对于有高中数学或工科本科背景的人，我会推荐 Nathan Carter 的书《Visual Group Theory》作为起点）。否则，那些定理和证明无非就是在摆弄符号，机械地去 pattern-matching 老师布置下来的某项作业……
…undergraduate technical education. To learn group theory, ring theory, etc., you want to start with a nice stable of explicit concrete examples, explored deeply (I would recommend Nathan Carter’s book Visual Group Theory as a start for someone with a high school math or undergraduate engineering background). Otherwise the theorems and proofs are just symbol twiddling and pattern-matching to some assignment handed down…
……需要2个生成元，所以你不可能只对床垫不断重复单一的翻转/操作就得到所有可行的摆放位置。对于想学群论的朋友，我推荐 Nathan Carter 的书《Visual Group Theory》，这是一本入门门槛很低的导论，通篇采用口语化风格，包含大量精彩的配图（不像大多数抽象且堆满符号的群论教材）。http://web.bentley.edu/empl/c/ncarter/vgt/…
…needs 2 generators, so you can’t keep performing a single flip/operation on your mattress and get all viable positions out of it. For folks trying to learn group theory, I recommend Nathan Carter’s book Visual Group Theory, an approachable introduction written in conversational style, full of great pictures (unlike most group theory textbooks, which are abstract and symbol-heavy). http://web.bentley.edu/empl/c/ncarter/vgt/…
有一本没有前面讨论的那些毛病的神书，那就是 Nathan Carter 写的《Visual Group Theory》，之前在 HN 上讨论过。它在深入定理之前提供了极其充分的动机阐述和实例支撑。https://news.ycombinator.com/item?id=11745486
A wonderful book that doesn't suffer the discussed flaw is Visual Group Theory by Nathan Carter, discussed on HN earlier. It provides ample motivation and examples before diving into the theorems. https://news.ycombinator.com/item?id=11745486