Mthod of proof by cases 证明完所有的条件分支,然后得出结论. 证明任意 使用任意 注意,对于一个任意的东西,你不知道它的具体信息.比如对于任意正数,你不知道它是 1 还是 2等等. 使用矛盾 证明相反的结论是错误的 归纳法 Prove the initial step, then apply to the induction step. Prove the mathematical theorems Assignment 解析:首先尝试找到 m, n 使得结论成立.因为…
根据 rubic 打分. 1. 我认为,如果说明 m, n 是自然数,所以最小值是 1 会更清楚.所以 Clarity 我给了 3 分.其他都是 4 分,所以一共是 23 分. 2.  我给出的分数 0 + 4 + 4 + 4 + 4 + 0. 明显可以看出是计算错误,但由于目前是考察数学思考,并不需要像工程师一样精确.所以这个被视为 slip. Logical correctness: 2 分.逻辑正确但是计算错误. Overall valuation: 2 分.同理,逻辑正确但是计算错误.…
错题 评分出错 题目要求的是 "any" ,而答案只给出了一个.所以认为回答者没有理解题意,连 any 都没有理解.所以 0 分. 第一,标准的归纳法只能对自然数使用,而题目要求的是所有整数,所以使用标准归纳法是错误的: 第二,使用标准归纳法,证明 (n+1) 成立时错误,原因是没有使用假设 n 成立时的等式. 得分为: 逻辑正确:并不是说言论对了就给 4 分,还要看它得出这个言论的逻辑是否正确.这里使用归纳法,只能证明自然数,所以给两份.使用归纳法出错,只能给一分了. 理由:由于给出…
Q: Why did nineteenth century mathematicians devote time to the proof of self-evident results? Select the best answer. A: To gain mastery of, and confidence in, the methods of abstract proof to apply them in less obvious cases. (看这个看的想睡觉,可能是没有动手跟上老师的…
否定的逻辑 应该思考符号背后表示的逻辑,而不是像操作算术运算符一样操作逻辑符号. 比如 对于任意的 x,x属于自然数,那么 x 是偶数或者奇数:这是对的 如果使用“乘法分配律”拆分,变成“对于任意的x,x属于自然数,那么x是奇数或者对于任意的x,x属于自然数,那么x是奇数” 这是错的 疑惑 但是做练习的时候,还是把其当做符号来运算.For all 变成 at least one:At least one 变成 for all:v 变成  ^; 计算机也是把逻辑规则抽象成符号来运算的. 注意言论的…
there exists and all there exists 证明根号2是无理数 all 习题 3. Which of the following formal propositions says that there is no largest prime. (There may be more than one. You have to select all correct propositions.) The variables denote natural numbers. [6…
基本数学概念 real number(实数):是有理数和无理数的总称 有理数:可以表达为两个整数比的数(a/b, b!=0) 无理数是指除有理数以外的实数 imply -- 推导出 不需要 A 能推导出 B,而只要 A, B 都是正确的就可以? phi implies psi 与 phi, psi 是否有关联无关.计算机并不需要理解 phi, psi 的意思,不需要知道 phi, psi 是否是正确的,它们只需要知道 phi implies psi 是否是正确的. 那么如何推导出剩下的两个? 通…
Deep Learning and Shallow Learning 由于 Deep Learning 现在如火如荼的势头,在各种领域逐渐占据 state-of-the-art 的地位,上个学期在一门课的 project 中见识过了 deep learning 的效果,最近在做一个东西的时候模型上遇到一点瓶颈于是终于决定也来了解一下这个魔幻的领域. 据说 Deep Learning 的 break through 大概可以从 Hinton 在 2006 年提出的用于训练 Deep Belief…
Technical Development Guide This guide provides tips and resources to help you develop your technical skills (academically and non-academically) through self-paced, hands-on learning. This guide is intended for Computer Science students seeking an in…
Awesome Courses  Introduction There is a lot of hidden treasure lying within university pages scattered across the internet. This list is an attempt to bring to light those awesome courses which make their high-quality material i.e. assignments, lect…
https://www.quora.com/How-do-I-learn-mathematics-for-machine-learning   How do I learn mathematics for machine learning? Promoted by Time Doctor Software for productivity tracking. Time tracking and productivity improvement software with screenshots…
Some books that I really enjoy(ed) It's been quite some time since I blogged about what I've been reading.  That's not because I haven't been reading -- au contraire! -- but rather because I've been busy doing so.  I find these posts interesting for…
原文地址:http://blog.sina.com.cn/s/blog_7e5f32ff0102vlgj.html 入门书单 1.<数学之美>PDF6 作者吴军大家都很熟悉.以极为通俗的语言讲述了数学在机器学习和自然语言处理等领域的应用. 2.<Programming Collective Intelligence>(<集体智慧编程>)PDF3 作者Toby Segaran也是<BeautifulData : The Stories Behind Elegant…
Github上的1000多本免费电子书重磅来袭!   以前 StackOverFlow 也给出了一个免费电子书列表,现在在Github上可以看到时刻保持更新的列表了. 瞥一眼下面的书籍分类目录,你就能知道这个免费电子书库的含金量了吧.记得一定要看几本,千万别下载了大量书籍而束之高阁! 行动重于空想! Github地址:     https://github.com/vhf/free-programming-books/blob/master/free-programming-books.md I…
Index Ada Agda Alef Android APL Arduino ASP.NET MVC Assembly Language Non-X86 AutoHotkey Autotools Awk Bash Basic BETA C C# C++ Chapel Cilk Clojure COBOL CoffeeScript ColdFusion Cool Coq D Dart DB2 Delphi / Pascal DTrace Elasticsearch Emacs Erlang F#…
I 开篇 1. 绪论 II 离散数学 2. 数 (已看) 3. 集合 4. 笛卡尔 5. 类型 6. 函数 7. λ演算 8. 代数 9. 数理逻辑 III 简单RSL 10. RSL中的原子类型和值 11. RSL中的函数定义 12. 面向性质与面向模型的抽象 13. RSL中的集合 14. RSL中的笛卡尔 15. RSL中的列表 16. RSL中的映射 17. RSL中的高阶函数 IV 规约类型 18 RSL中的类型 19. 应用式规约程序设计 20. 命令式规约程序设计 21. 并发式规…
https://onlinecourses.science.psu.edu/statprogram/programs Graduate Online Course Overviews Printer-friendly versionPrinter-friendly version Picture of Thomas Building where the Eberly College of Science and the Department of Statistics resides.The D…
https://ocw.mit.edu/courses/find-by-topic/#cat=mathematics Course # Course Title Level 1.010 Uncertainty in Engineering Undergraduate 1.017 Computing and Data Analysis for Environmental Applications Undergraduate 2.003J Dynamics and Control I (Fall 2…
8.02  Physics II (电磁学基础) Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric curr…
Source: Connected Brain Figure above: Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems.[J]. Nature Reviews Neuroscience, 2009, 10(3):186-198. Graph measures A graph G consisting of a set of…
The author has a course on web: http://brickisland.net/DDGSpring2016/ It has more reading assignments and sliders which are good for you to understand ddg. ------------------------------------------------------------- DISCRETE DIFFERENTIAL GEOMETRY :…
-------------------------------------------------------------- Chapter 1: Introduction to Discrete Differential Geometry: The Geometry of Plane Curves . A better approximation than the tangent is the circle of curvature. . If the curve is sufficientl…
List of mathematical abbreviations From Wikipedia, the free encyclopedia 数学缩写列表 维基百科,自由的百科全书 This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology. 这篇文章是一个数学函数,类似于函数的操作符和其…
Chapter 1 Introduction 1.1 What Is Machine Learning? To solve a problem on a computer, we need an algorithm. An algorithm is a sequence of instructions that should be carried out to transform the input to output. For example, one can devise an algori…
A beginner’s introduction to Deep Learning I am Samvita from the Business Team of HyperVerge. I joined the team a few months back to help out on User Growth, PR and Marketing. From when I first heard about HyperVerge, I had one question – What is thi…
Introduction to Gaussian Processes Gaussian processes (GP) are a cornerstone of modern machine learning. They are often used for non-parametric regression and classification, and are extended from the theory behind Gaussian distributions and Gaussian…
Around September of 2016 I wrote two articles on using Python for accessing, visualizing, and evaluating trading strategies (see part 1 and part 2). These have been my most popular posts, up until I published my article on learning programming langua…
John M. Lee is a famous mathematician, who bears the reputation of writing the classical book "Introduction to Smooth Manifolds". In his article, "Some Remarks on Writing Mathematical Proofs", he gives us concrete and complete suggesti…
Introduction Optimization is always the ultimate goal whether you are dealing with a real life problem or building a software product. I, as a computer science student, always fiddled with optimizing my code to the extent that I could brag about its…
[翻译] 提升树算法的介绍(Introduction to Boosted Trees) 1. 有监督学习的要素 XGBoost 适用于有监督学习问题.在此类问题中,我们使用多特征的训练数据集 \(x_i\) 去预测一个目标变量 \(y_i\) .在专门学习树模型前,我们先回顾一下有监督学习的基本要素. Elements of Supervised Learning XGBoost is used for supervised learning problems, where we use th…