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…
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…
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…
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…
