{"topic":{"id":14811,"title":"个人认为适合计算机（等非数学专业）的离散数学课程设计","slug":"topic","categoryId":54,"createdAt":"2025-06-24 01:53:06.975816","bumpedAt":"2025-06-30 11:15:04.24683","views":340,"postsCount":5,"highestPostNumber":5,"likeCount":14,"closed":false,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"第一章：集合与自然数 1.1 定义集合，子集，空集，运算 1.2 用集合定义自然数的枚举 1.3 群的定义，对自然数集合引入逆元形成整数加法群 1.4 非交换群的两个例子：矩阵乘法群，二面体群 Dn 第二章：函数与关系 2.1 关系与函数的定义 2.2 等效关系 2.3 全序关系，半序关系，整数加法群的半序关系 2.4 左右伴群，商群，余数等效关系的整数商群 Z/pZ 第三章：环与域 3.1 环的定义，整数环，多项式环 3.2 域的定义…","deletedAt":null,"isAnonymous":false,"category":{"id":54,"name":"学术专区","slug":"academic","color":"9EB83B"},"author":{"id":601,"username":"m0rsun","name":null,"avatarUrl":"/uploads/image/37/7f/377f4ae853850691ab959270f01d52509ee07caf808041ddb0ab22488a0e9f85.avif"},"tags":[]},"posts":[{"id":57953,"postNumber":1,"raw":"**第一章：集合与自然数**\n1.1 定义集合，子集，空集，运算\n1.2 用集合定义自然数的枚举\n1.3 群的定义，对自然数集合引入逆元形成整数加法群\n1.4 非交换群的两个例子：矩阵乘法群，二面体群 Dn\n\n**第二章：函数与关系**\n2.1 关系与函数的定义\n2.2 等效关系\n2.3 全序关系，半序关系，整数加法群的半序关系\n2.4 左右伴群，商群，余数等效关系的整数商群 Z/pZ\n\n**第三章：环与域**\n3.1 环的定义，整数环，多项式环\n3.2 域的定义，整数环引入逆元得到有理数域，进一步得到实数域，虚数域\n3.3 质数商群 Z/pZ 的域性质\n\n以上是我认为更适合 cs 等非数学专业的离散数学课程设计，其中重点强调了自然数集合 - 整数加法群 - 整数环 - 模 p 整数域的构建过程，同时保留了现有设计中大量的抽象证明训练，为算法设计、密码学等领域中可能用到的离散数学（不含组合数学）打下了良好的基础。\n\n免责声明：本人了解的非数学专业离散数学课只有 xjtu 离散数学一门，因此内容可能与现有高质量课程雷同","cooked":"

第一章：集合与自然数
\n1.1 定义集合，子集，空集，运算
\n1.2 用集合定义自然数的枚举
\n1.3 群的定义，对自然数集合引入逆元形成整数加法群
\n1.4 非交换群的两个例子：矩阵乘法群，二面体群 Dn

第二章：函数与关系
\n2.1 关系与函数的定义
\n2.2 等效关系
\n2.3 全序关系，半序关系，整数加法群的半序关系
\n2.4 左右伴群，商群，余数等效关系的整数商群 Z/pZ

第三章：环与域
\n3.1 环的定义，整数环，多项式环
\n3.2 域的定义，整数环引入逆元得到有理数域，进一步得到实数域，虚数域
\n3.3 质数商群 Z/pZ 的域性质

以上是我认为更适合 cs 等非数学专业的离散数学课程设计，其中重点强调了自然数集合 - 整数加法群 - 整数环 - 模 p 整数域的构建过程，同时保留了现有设计中大量的抽象证明训练，为算法设计、密码学等领域中可能用到的离散数学（不含组合数学）打下了良好的基础。

免责声明：本人了解的非数学专业离散数学课只有 xjtu 离散数学一门，因此内容可能与现有高质量课程雷同

\n","createdAt":"2025-06-24 01:53:07.066245","updatedAt":"2025-06-24 01:53:07.066245","replyToPostNumber":null,"replyCount":0,"likeCount":8,"wordCount":380,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"👍️","count":1,"users":[{"id":30,"username":"一只玉米人","name":"玉米🌽"}],"hasReacted":false},{"reaction":"❤️","count":8,"users":[{"id":30,"username":"一只玉米人","name":"玉米🌽"},{"id":1835,"username":"Dusk","name":"夕大画家"},{"id":2899,"username":"wing","name":"wingqwq"},{"id":2902,"username":"1313","name":"ᐕ)ﾉ"},{"id":4668,"username":"IO","name":null},{"id":5905,"username":"PipaQinse233","name":"PipaQinse233"},{"id":7245,"username":"anon42647320","name":null},{"id":7364,"username":"青年杰出贡献上交大門人","name":"紫金港第一皮革<・)))><<"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":601,"username":"m0rsun","name":null,"avatarUrl":"/uploads/image/37/7f/377f4ae853850691ab959270f01d52509ee07caf808041ddb0ab22488a0e9f85.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}},{"id":57977,"postNumber":2,"raw":"[grid mode=\"tile\"]\n![1103797986|361x500](/uploads/image/0b/b9/0bb9af6edb2b783be95e76d9aea9c6dc33fe9b9a0e34f91a29605076d8dd20ff.avif)\n\n![Screenshot_2025-06-24-14-19-56-066_com.douban.frodo-edit|341x500](/uploads/image/f6/c6/f6c6118ff7e0d55eeb3a492a5a3cc74650846f2cae84bbe0b16cde696b95907a.avif)\n[/grid]\n\n\n\n这本就是面向 CS 的","cooked":"

$\"1103797986\"$

$\"Screenshot_2025-06-24-14-19-56-066_com.douban.frodo-edit\"$

这本就是面向 CS 的

\n","createdAt":"2025-06-24 06:19:17.690411","updatedAt":"2025-06-24 06:20:19.781372","replyToPostNumber":null,"replyCount":1,"likeCount":3,"wordCount":13,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"👍️","count":2,"users":[{"id":30,"username":"一只玉米人","name":"玉米🌽"},{"id":1835,"username":"Dusk","name":"夕大画家"}],"hasReacted":false},{"reaction":"❤️","count":3,"users":[{"id":30,"username":"一只玉米人","name":"玉米🌽"},{"id":1835,"username":"Dusk","name":"夕大画家"},{"id":7364,"username":"青年杰出贡献上交大門人","name":"紫金港第一皮革<・)))><<"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":4148,"username":"sad-dharma-vipralopa","name":"Echo est ubi sum","avatarUrl":"/uploads/image/fd/e3/fde3022e639c0b35239b5c831c0f8ea3600eceb69353bcc2fb5e795f79d789ca.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":58153,"postNumber":3,"raw":"最后讲群和对称性吗，感觉这个思路可能适合一些思维方式是自顶向下的人，从现实庞大的系统中一点点剔除规则得到抽象。我主楼的顺序适合我这种从零构建体系的自底向上思维方式","cooked":"

最后讲群和对称性吗，感觉这个思路可能适合一些思维方式是自顶向下的人，从现实庞大的系统中一点点剔除规则得到抽象。我主楼的顺序适合我这种从零构建体系的自底向上思维方式

\n","createdAt":"2025-06-24 21:27:24.791784","updatedAt":"2025-06-24 21:27:24.791784","replyToPostNumber":2,"replyCount":1,"likeCount":0,"wordCount":81,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":601,"username":"m0rsun","name":null,"avatarUrl":"/uploads/image/37/7f/377f4ae853850691ab959270f01d52509ee07caf808041ddb0ab22488a0e9f85.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}},{"id":58218,"postNumber":4,"raw":"我倒是没多大偏好，两种顺序都可以","cooked":"

我倒是没多大偏好，两种顺序都可以

\n","createdAt":"2025-06-25 08:48:44.632253","updatedAt":"2025-06-25 08:48:44.632253","replyToPostNumber":3,"replyCount":0,"likeCount":0,"wordCount":16,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":4148,"username":"sad-dharma-vipralopa","name":"Echo est ubi sum","avatarUrl":"/uploads/image/fd/e3/fde3022e639c0b35239b5c831c0f8ea3600eceb69353bcc2fb5e795f79d789ca.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":58834,"postNumber":5,"raw":"要速通一遍离散了","cooked":"

要速通一遍离散了

\n","createdAt":"2025-06-30 11:15:04.24683","updatedAt":"2025-06-30 11:15:04.24683","replyToPostNumber":null,"replyCount":0,"likeCount":3,"wordCount":8,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"hugging_face_exploding_head","count":2,"users":[{"id":200,"username":"Srotseiticar","name":null},{"id":7014,"username":"兴庆宫第一迷路幽灵","name":"post deleted by author"}],"hasReacted":false},{"reaction":"🥰️","count":1,"users":[{"id":7970,"username":"Yau-20070205","name":"小姚"}],"hasReacted":false},{"reaction":"❤️","count":3,"users":[{"id":200,"username":"Srotseiticar","name":null},{"id":7014,"username":"兴庆宫第一迷路幽灵","name":"post deleted by author"},{"id":7970,"username":"Yau-20070205","name":"小姚"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":2877,"username":"Zerick","name":null,"avatarUrl":"/uploads/image/a7/a3/a7a3f86ac04b30a3177766813966fa48ce68b0e1cc009a8d274e34ab13a43ce9.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}}],"hasMore":false,"lastReadPostNumber":5,"hasUrlPostNumber":true}