具体数学(英文版第2版)的笔记(57)

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  • 大嘴巴灵机一动

    大嘴巴灵机一动 (不逞口腹之欲,何以遣此有涯之生)

    前一页有两个式子: \/公式内容已省略/{align} 然后高爷爷(?)说: By the way, there's a mnemonic for remembering which case uses floors and which uses ceilings: Half-open intervals that include the left endpoint but not the right (such as 0 ≤ θ < 1) are slightly more common than those that include the right endpoint but not the left; and floors are slightl...   (4回应)

    2012-03-13 19:15   2人喜欢

  • 大嘴巴灵机一动

    大嘴巴灵机一动 (不逞口腹之欲,何以遣此有涯之生)

    这里第一次用了repertoire method来解递归,但是讲得有点混乱,因为把归纳法和repertoire method混合起来了(A(n)是猜测出来之后用归纳法证明的,B(n)和C(n)则是用repertoire method得到两个方程,再联立A(n)解出来的)。可以参考 http://pindancing.blogspot.com/2011/02/repertoire-method-in-concrete.html 上面这篇文章提到直接用repertoire method来解,代入/公式内容已省略/三个值,得..   (15回应)

    2012-03-08 14:48   3人喜欢

  • 36°

    36° (仰望星空 脚踏实地)

    方法5的推导跳了一步,补充如下: \/公式内容已省略/{align}   (2回应)

    2012-07-21 13:48   1人喜欢

  • 36°

    36° (仰望星空 脚踏实地)

    关于repertoire method讲的有些小混乱,可以参见国外网友的总结,我觉得非常详实了:http://pindancing.blogspot.com/2011/02/repertoire-method-in-concrete.html 豆瓣网友有个缩略版:http://book.douban.com/annotation/17154454/ 第16页,作者给了一个更快捷的计算方法,即符合下面递归关系的通项: \/公式内容已省略/{align} 这时候的/公式内容已省略/

    2012-07-19 15:53   1人喜欢

  • 大嘴巴灵机一动

    大嘴巴灵机一动 (不逞口腹之欲,何以遣此有涯之生)

    /公式内容已省略/这个数有个很有趣的特性: /公式内容已省略/ 也就是说/公式内容已省略//公式内容已省略/的小数部分是一样的,用第70页3.8式定义的符号来表示:/公式内容已省略/ 假设/公式内容已省略/,即<...   (4回应)

    2012-05-23 13:41   1人喜欢

  • 大嘴巴灵机一动

    大嘴巴灵机一动 (不逞口腹之欲,何以遣此有涯之生)

    5.25式证明: \/公式内容已省略/{align} 5.26式证明: \/公式内容已省略/{align} 5.27式将/公式内容已省略//公式内容已省略/用二项式定理展开,对比两边/公式内容已省略/项的系数,cf. P198。   (8回应)

    2012-04-11 20:02

  • 胡行宇

    胡行宇 (ivy)

    2018-06-01 22:02

  • OrangeCLK

    OrangeCLK

    Skepticism is healthy only to a limited extent. Being skeptical about proofs and programs (particularly your own) will probably keep your grades healthy and your job fairly secure. But applying that much skepticism will probably also keep you shut away working al the time, instead of letting you get out for exercise and relaxation. Too much skepticism is an open invitation to the state of rigor...

    2016-12-01 17:23

  • OrangeCLK

    OrangeCLK

    Incidentally, when we're faced with a "prove or disprove", we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads us to a proof, as soon as we see why a counterex...

    2016-12-01 16:21

  • OrangeCLK

    OrangeCLK

    Here's an "elegant", "impressive" proof that gives no clue about how it was discovered: This logic is seriously floored. 这样的证明还算“好”证明吗?我觉得不算。但这个证明里玩弄的数学技巧应当还是颇有价值的。

    2015-09-25 12:42

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具体数学(英文版第2版)

>具体数学(英文版第2版)