标签归档:数学

Deep Learning Specialization on Coursera

那些值得推荐和收藏的线性代数学习资源

关于线性代数的重要性,很多做机器学习的同学可能会感同身受,这里引用“牛人林达华推荐有关机器学习的数学书籍”这篇文章中关于线性代数的一段话:

线性代数 (Linear Algebra):

我想国内的大学生都会学过这门课程,但是,未必每一位老师都能贯彻它的精要。这门学科对于Learning是必备的基础,对它的透彻掌握是必不可少的。我在科大一年级的时候就学习了这门课,后来到了香港后,又重新把线性代数读了一遍,所读的是

Introduction to Linear Algebra (3rd Ed.) by Gilbert Strang.

这本书是MIT的线性代数课使用的教材,也是被很多其它大学选用的经典教材。它的难度适中,讲解清晰,重要的是对许多核心的概念讨论得比较透彻。我个人觉得,学习线性代数,最重要的不是去熟练矩阵运算和解方程的方法——这些在实际工作中MATLAB可以代劳,关键的是要深入理解几个基础而又重要的概念:子空间(Subspace),正交(Orthogonality),特征值和特征向量(Eigenvalues and eigenvectors),和线性变换(Linear transform)。从我的角度看来,一本线代教科书的质量,就在于它能否给这些根本概念以足够的重视,能否把它们的联系讲清楚。Strang的这本书在这方面是做得很好的。

而且,这本书有个得天独厚的优势。书的作者长期在MIT讲授线性代数课(18.06),课程的video在MIT的Open courseware网站上有提供。有时间的朋友可以一边看着名师授课的录像,一边对照课本学习或者复习。

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
(注:这里我修正了一下链接,原文链接已经没有了)

那么这里首推的线性代数学习资源就是 Gilbert Strang 教授的这门线性代数课程了,除了上面链接中官方主页的英文原版外,国内网易公开课也早已引进并有同步翻译。

1. 麻省理工公开课:线性代数

http://open.163.com/special/opencourse/daishu.html

课程介绍:

“线性代数”,同微积分一样,是高等数学中两大入门课程之一,不仅是一门非常好的数学课程,也是一门非常好的工具学科,在很多领域都有广泛的用途。它的研 究对象是向量,向量空间(或称线性空间),线性变换和有限维的线性方程组。本课程讲述了矩阵理论及线性代数的基本知识,侧重于那些与其他学科相关的内容, 包括方程组、向量空间、行列式、特征值、相似矩阵及正定矩阵。

课程主讲人:Gilbert Strang 教授

吉尔伯特-斯特朗:1934年11月27日出生,是美国享有盛誉的数学家,在有限元理论、变分法、小波分析及线性代数方面均有所建树。他对教育的贡献尤为 卓著,包括所著有的七部经典数学教材及一部专著。斯特朗自1962年至今担任麻省理工学院教授,其所授课程《线性代数导论》、《计算科学与工程》均在 MIT开放课程软件(MIT OpenCourseWare)中收录,获得广泛好评。

我大概在2013年学习过这门课程,也花了很多时间找这门课程的书籍资源,最终锁定了这本书的第四版英文版电子版:Introduction to Linear Algebra_4ED_Strang ,感兴趣的同学可以关注我们的公众号AINLP,后台回复”xiandai”获取下载链接。

2. 3Blue1Brown: Essence of linear algebra(线性代数的本质)

如果说上面 Gilbert Strang 教授的线性代数课程和书籍都是大部头,那么鼎鼎大名的3Blue1Brown出品的这个线性代数的本质系列视频就是开胃菜,总共14个小视频,视频控制在9-18分钟之间,很适合短时间快速温习。不过这套视频的评价也很高,以下是来自《3Blue1Brown:“线性代数的本质”完整笔记》的点评:

我最早系统地学习线性代数是在大二时候,当时特意选修了学校物理系开设的4学分的线代,大概也就是比我们自己专业的线代多了一章向量空间的内容,其实最后上完发现,整个课程内容还是偏向于计算,对线性代数的几何直觉少有提起,对线性代数的实际运用更是鲜有涉及。同济的那本薄薄的如同九阴真经一般的教材,把线性代数讲的云里雾里,当时一个人在自习教室度过多少不眠之夜,一点一点去思考其概念定理背后的实际意义,多半也是边猜边想,苦不堪言。直到多年以后,有幸在网上听到了MIT的Strang老师开设的线代公开课,才对一些基础概念渐渐明朗,虽然至今又过去了很多年,但是对一些本质的理解,依然清晰。
不过,仔细想想,国内的教材写的云里雾里,才促使了我自发的思考,如果一切得来太容易,也许就不会那么刻骨铭心。我很早之前就想过这个问题,国内的教科书作者简直就是在下一盘大棋,自己出版的书写的高深莫测,翻译国外的书又翻译的含糊曲折,那么留给学生的只有两条路,要么去看原版的英语书,要么就是自己一点点看云雾缭绕的国产书,边猜边想边证明,不管走哪条路,都能走向成功。

最近,在youtube上看到了3Blue1Brown的Essence of linear algebra这门课,有种如获至宝的感觉,整个课程的时间并不长,但是对线性代数的讲解却十分到位,有种浓缩版的Gilbert Strang线代课程的感觉。希望通过这个课程,重温一下Linear Algebra。

这个视频,可以在油管上看官方原版:Essence of linear algebra
也可以在B站上观看:线性代数的本质 – 01 – 向量究竟是什么?
https://www.bilibili.com/video/av5987715/

3. Immersive Linear Algebra

用交互式可视化方法学习数学估计是很多同学梦寐以求的,前两天看到这条微博:

《英文版的线性代数电子书:Immersive Linear Algebra》该书是今天 Hacker News 首页头条。号称是全球第一个全交互式图形的线代电子书。

所以在这里收藏一下,有空的同学可以试一下这个在线学习线性代数的网站,不过看似还有最后两个章节没有完成:http://immersivemath.com/ila/index.html

4. Matrix Algebra for Engineers

http://coursegraph.com/coursera-matrix-algebra-engineers

香港科技大学的面向工程师的矩阵代数(Matrix Algebra for Engineers),该课程介绍的全部是关于矩阵的知识,涵盖了工程师应该知道的线性代数相关知识。学习这门课程的前提是高中数学知识,最好完成了单变量微积分课程之后选修该课程效果更佳。

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. We define matrices and how to add and multiply them, and introduce some special types of matrices. We describe the Gaussian elimination algorithm used to solve systems of linear equations and the corresponding LU decomposition of a matrix. We explain the concept of vector spaces and define the main vocabulary of linear algebra. We develop the theory of determinants and use it to solve the eigenvalue problem. After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed and drop out. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course. The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course.

这门课程有个lecture-notes可以直接下载:
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

5. Mathematics for Machine Learning: Linear Algebra

http://coursegraph.com/coursera-linear-algebra-machine-learning

伦敦帝国理工学院的 面向机器学习的数学-线性代数课程(Mathematics for Machine Learning: Linear Algebra),这个课程属于Mathematics for Machine Learning Specialization 系列,该系列包含3门子课程,涵盖线性代数,多变量微积分,以及主成分分析(PCA),这个专项系列课程的目标是弥补数学与机器学习以及数据科学鸿沟:Mathematics for Machine Learning。Learn about the prerequisite mathematics for applications in data science and machine learning

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets – like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we’re aiming at data-driven applications, we’ll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you’ll write code blocks and encounter Jupyter notebooks in Python, but don’t worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.

6. 可汗学院公开课:线性代数

http://open.163.com/special/Khan/linearalgebra.html

网易公开课引进翻译的可汗学院线性代数公开课,总共143集,每集短小精悍:

在这个课程里面,主讲者介绍了线性代数的很多内容,包括:矩阵,线性方程组,向量及其运算,向量空间,子空间,零空间,变换,秩与维数,正交化,特征值与特征向量,等等。以上这些内容是线性代数的关键内容,它们也被广泛地应用到现代科学当中。

关于线性代数学习资源,还有很多,这里仅仅抛砖引玉,欢迎大家留言提供线索。

最后,提供一个线性代数学习资源的“大礼包”,包括Gilbert Strang 教授线性代数英文教材第四版电子版,香港科技大学的面向工程师的矩阵代数课程notes,以及从其他地方收集的线性代数网盘资源,感兴趣的同学可以关注我们的公众号AINLP,回复”xiandai”获取:

注:原创文章,转载请注明出处“课程图谱博客”:http://blog.coursegraph.com

本文链接地址:那些值得推荐和收藏的线性代数学习资源 http://blog.coursegraph.com/?p=1014

如何学习机器学习:机器学习该怎么入门

首先你要学好英语,因为英文世界的相关资料更加丰富和原创。

其次你得有一定的数学基础,如果你觉得微积分、线性代数和概率统计这些基础课程没有时间回顾的话,那么推荐机器学习强相关的一门课和一本书:

1)面向机器学习的数学课程(Mathematics for Machine Learning Specialization)
http://coursegraph.com/coursera-specializations-mathematics-machine-learning

伦敦帝国理工学院的面向机器学习的数学专项课程系列(Mathematics for Machine Learning Specialization),该系列包含3门子课程,涵盖线性代数,多变量微积分,以及主成分分析(PCA),这个专项系列课程的目标是弥补数学与机器学习以及数据科学鸿沟,感兴趣的同学可以关注:Mathematics for Machine Learning。Learn about the prerequisite mathematics for applications in data science and machine learning

2)机器学习中的数学(https://mml-book.github.io/):新书,看章节安排的很合理。

如果想学习更多的数学课程打基础,这里有:

3) Coursera上数学类相关课程(公开课)汇总推荐

除了数学基础,你还应该有一定的编程基础,如果你还是编程小白,那么推荐从Python入门:

4)Coursera上Python课程(公开课)汇总推荐

当然,一定的数据结构和算法接触还是要有的:

5)Coursera上数据结构 & 算法课程(公开课)汇总推荐

然后重点推荐推荐2门机器学习入门课程:

6) 还是首推Andrew Ng老师的机器学习课程了:http://coursegraph.com/coursera_ml

7) 其次是最近比较火的fast.ai的课程:fast.ai 新课程:面向程序员的机器学习导论(Introduction to Machine Learning for Coders)

不过到了这里,也只是入门而已,你需要动手做相关的项目,如果没有项目,我推荐你去参加一下类似Kaggle的项目。如果想更深入的学习更多的机器学习课程,这里有一份Coursera课程汇总:

8)Coursera上机器学习课程(公开课)汇总推荐

最后,如果想更进一步,学习深度学习,依然首推Andrew Ng的深度学习专项课程

9)Deep Learning Specializationhttp://coursegraph.com/coursera-specializations-deep-learning

再奉上一份更详细的深度学习课程资源,仅供参考:

10)深度学习课程资源整理

注:原创文章,转载请注明出处“课程图谱博客”:http://blog.coursegraph.com

本文链接地址:http://blog.coursegraph.com/如何学习机器学习-机器学习该怎么入门 http://blog.coursegraph.com/?p=904

Coursera上数学类相关课程(公开课)汇总推荐

数学课程是基础,Coursera上有很多数学公开课,这里做个汇总,注意由于Coursera上有一批很有特色的统计学相关的数学课程,我们将在下一期里单独汇总。

1 斯坦福大学 Introduction to Mathematical Thinking(数学思维导论)

http://coursegraph.com/coursera-mathematical-thinking

引用老版课程一个同学的评价,供参考:

这门课是高中数学到大学数学的一个过度。高中数学一般重计算不太注重证明,这门课讲了基本的逻辑,数学语言(两个 quantifier,there exists, for all)和证明的几个基本方法,比如证明充要条件要从两个方向证、证伪只需要举个反例,原命题不好证的时候可以证等价的逆否命题以及很常用的数学归纳法。课程讲了数论里一些基本定理,然后通过让你证一些看起来显然而不需要证明的证明题来训练你证明的技能和逻辑思考的能力,看起来显然的命题也是要证明才能说服人的,课程最后简略的讲了下数学分析里面实数的引入,但这部分讲的不完整。Keith Devlin 是个 old school 的讲师,上课只用纸和笔,也是属于比较热情的讲师,他每周都会录几个答疑的视频。这门比较适合大一的新生上,开得也比较频繁。

课程简介:

Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

2 加州大学尔湾分校 初级微积分系列课程

1)Pre-Calculus: Functions(初级微积分:函数)

http://coursegraph.com/coursera-pre-calculus

This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic properties

2)Pre-Calculus: Trigonometry(初级微积分:三角)

http://coursegraph.com/coursera-trigonometry

This course covers mathematical topics in trigonometry. Trigonometry is the study of triangle angles and lengths, but trigonometric functions have far reaching applications beyond simple studies of triangles. This course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Evaluate trigonometric functions using the unit circle and right triangle approaches 2. Solve trigonometric equations 3. Verify trigonometric identities 4. Prove and use basic trigonometric identities. 5. Manipulate trigonometric expressions using standard identities 6. Solve right triangles 7. Apply the Law of Sines and the Law of Cosines

3 宾夕法尼亚大学的 单变量微积分系列课程

1)Calculus: Single Variable Part 1 – Functions(单变量微积分1:函数)
http://coursegraph.com/coursera-single-variable-calculus

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this first part–part one of five–you will extend your understanding of Taylor series, review limits, learn the *why* behind l’Hopital’s rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O.

2)Calculus: Single Variable Part 2 – Differentiation(单变量微积分2:微分)

http://coursegraph.com/coursera-differentiation-calculus

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this second part–part two of five–we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.

3)Calculus: Single Variable Part 3 – Integration(单变量微积分3:积分)

http://coursegraph.com/coursera-integration-calculus

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this third part–part three of five–we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals.

4) Calculus: Single Variable Part 4 – Applications(单变量微积分4:应用)

http://coursegraph.com/coursera-applications-calculus

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this fourth part–part four of five–we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.

4 杜克大学 Data Science Math Skills(数据科学中的数学技巧)

http://coursegraph.com/coursera-datasciencemathskills

这门课程主要介绍数据科学中涉及的相关数学概念,让学生了解基本的数学概念,掌握基本的数学语言,内容涵盖集合论、求和的Sigma符号、数学上的笛卡尔(x,y)平面、指数、对数和自然对数函数,概率论以及叶斯定理等:

Data science courses contain math—no avoiding that! This course is designed to teach learners the basic math you will need in order to be successful in almost any data science math course and was created for learners who have basic math skills but may not have taken algebra or pre-calculus. Data Science Math Skills introduces the core math that data science is built upon, with no extra complexity, introducing unfamiliar ideas and math symbols one-at-a-time. Learners who complete this course will master the vocabulary, notation, concepts, and algebra rules that all data scientists must know before moving on to more advanced material.

5 加州大学圣迭戈分校 Introduction to Discrete Mathematics for Computer Science Specialization(面向计算机科学的离散数学专项课程)

http://coursegraph.com/coursera-specializations-discrete-mathematics

面向计算机科学的离散数学专项课程(Introduction to Discrete Mathematics for Computer Science Specialization),这个系列包含5门子课程,涵盖证明、组合数学与概率、图论,数论和密码学,配送问题项目等,感兴趣的同学可以关注: Build a Foundation for Your Career in IT-Master the math powering our lives and prepare for your software engineer or security analyst career

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses.

1) What is a Proof(什么是证明)

http://coursegraph.com/coursera-what-is-a-proof

There is a perceived barrier to mathematics: proofs. In this course we will try to convince you that this barrier is more frightening than prohibitive: most proofs are easy to understand if explained correctly, and often they are even fun. We provide an accompanied excursion in the “proof zoo” showing you examples of techniques of different kind applied to different topics. We use some puzzles as examples, not because they are “practical”, but because discussing them we learn important reasoning and problem solving techniques that are useful. We hope you enjoy playing with the puzzles and inventing/understandings the proofs. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

2)Combinatorics and Probability(组合和概率)

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics. In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations. One of the main `consumers’ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop. In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

3)Introduction to Graph Theory(图论导论)

We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

4) Number Theory and Cryptography(数论和密码学)

We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest! As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

5)Solving Delivery Problem(解决旅行商问题)

http://coursegraph.com/coursera-delivery-problem

We’ll implement together an efficient program for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. How to find an optimal solution to this problem quickly? We still don’t have provably efficient algorithms for this difficult computational problem and this is the essence of the P versus NP problem, the most important open question in Computer Science. Still, we’ll implement several efficient solutions for real world instances of the travelling salesman problem. While designing these solutions, we will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. We’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.

6 伦敦帝国理工学院 Mathematics for Machine Learning Specialization(面向机器学习的数学专项课程系列)

http://coursegraph.com/coursera-specializations-mathematics-machine-learning

伦敦帝国理工学院的面向机器学习的数学专项课程系列(Mathematics for Machine Learning Specialization),该系列包含3门子课程,涵盖线性代数,多变量微积分,以及主成分分析(PCA),这个专项系列课程的目标是弥补数学与机器学习以及数据科学鸿沟,感兴趣的同学可以关注:Mathematics for Machine Learning。Learn about the prerequisite mathematics for applications in data science and machine learning

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in maths – stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialisation aims to bridge that gap, getting you up to speed in the underlying maths, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimise fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Components Analysis, uses the maths from the first two courses to do simple optimisation for the situation where you don’t have an understanding of how the data variables relate to each other. At the end of this specialisation you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning.

1) Mathematics for Machine Learning: Linear Algebra(面向机器学习的数学:线性代数)

http://coursegraph.com/coursera-linear-algebra-machine-learning

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets – like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we’re aiming at data-driven applications, we’ll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you’ll write code blocks and encounter Jupyter notebooks in Python, but don’t worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.

2)Mathematics for Machine Learning: Multivariate Calculus(面向机器学习的数学:多变量微积分)

http://coursegraph.com/coursera-multivariate-calculus-machine-learning

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you’ll still come away with the confidence to dive into some more focused machine learning courses in future.

3)Mathematics for Machine Learning: PCA(面向机器学习的数学:主成分分析)

http://coursegraph.com/coursera-pca-machine-learning

This course introduces the mathematical foundations to derive Principal Component Analysis (PCA), a fundamental dimensionality reduction technique. We’ll cover some basic statistics of data sets, such as mean values and variances, we’ll compute distances and angles between vectors using inner products and derive orthogonal projections of data onto lower-dimensional subspaces. Using all these tools, we’ll then derive PCA as a method that minimizes the average squared reconstruction error between data points and their reconstruction. At the end of this course, you’ll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you’ll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge.

注:原创文章,转载请注明出处“课程图谱博客”:http://blog.coursegraph.com

本文链接地址:http://blog.coursegraph.com/coursera上数学类相关课程数学公开课汇总推荐 http://blog.coursegraph.com/?p=804

Coursera上博弈论相关课程(公开课)汇总推荐

博弈论(Game Theory)很有意思,大家可能首先想到的就是赌博,据说博弈论最早源于赌博策略和数学,下面是来自维基百科的解释:

博弈论(英语:game theory),又译为对策论,或者赛局理论,应用数学的一个分支,1944年冯·诺伊曼与奥斯卡·摩根斯特恩合著《博弈论与经济行为》,标志着现代系统博弈理论的的初步形成,因此他被称为“博弈论之父”。博弈论被认为是20世纪经济学最伟大的成果之一。目前在生物学、经济学、国际关系、计算机科学、政治学、军事战略和其他很多学科都有广泛的应用。主要研究公式化了的激励结构(游戏或者博弈)间的相互作用。是研究具有斗争或竞争性质现象的数学理论和方法。也是运筹学的一个重要学科。

作为互联网广告研发人员,应该或多或少了解一点计算广告学,其中支撑Google, 百度等互联网巨头广告业务的竞价排名机制的核心之一就是博弈论。另外经济学中有很多博弈论的影子,电影“美丽心灵”中的主角数学家约翰纳什,由于他与另外两位数学家在非合作博弈的均衡分析理论方面做出了开创性的贡献,对博弈论和经济学产生了重大影响,而获得1994年诺贝尔经济学奖,纳什均衡则是博弈论课程中不可或缺的一节课。Coursera上有好几门博弈论(Game Theory)相关的课程,这里做个汇总整理。

1. 斯坦福大学的 博弈论(Game Theory)

这门课程早在Coursera诞生之初就有了,后经多次优化,现在有上和下两个部分,这门课程属于博弈论上,重在博弈论基础,需要学习者有一定的数学思维和数学基础,例如基础的概率理论和一些微积分基础知识:

This course is aimed at students, researchers, and practitioners who wish to understand more about strategic interactions. You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; but you should be familiar with basic probability theory (for example, you should know what a conditional probability is), and some very light calculus would be helpful.

2. 斯坦福大学的 博弈论二: 高级应用(Game Theory II: Advanced Applications)

上门博弈论课程的续集,关注博弈论的应用,包括机制设计,拍卖机制等:

Popularized by movies such as “A Beautiful Mind”, game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Over four weeks of lectures, this advanced course considers how to design interactions between agents in order to achieve good social outcomes. Three main topics are covered: social choice theory (i.e., collective decision making and voting systems), mechanism design, and auctions. In the first week we consider the problem of aggregating different agents’ preferences, discussing voting rules and the challenges faced in collective decision making. We present some of the most important theoretical results in the area: notably, Arrow’s Theorem, which proves that there is no “perfect” voting system, and also the Gibbard-Satterthwaite and Muller-Satterthwaite Theorems. We move on to consider the problem of making collective decisions when agents are self interested and can strategically misreport their preferences. We explain “mechanism design” — a broad framework for designing interactions between self-interested agents — and give some key theoretical results. Our third week focuses on the problem of designing mechanisms to maximize aggregate happiness across agents, and presents the powerful family of Vickrey-Clarke-Groves mechanisms. The course wraps up with a fourth week that considers the problem of allocating scarce resources among self-interested agents, and that provides an introduction to auction theory.

3. 东京大学的 博弈论入门课程(Welcome to Game Theory)

入门级博弈论课程,由东京大学推出,英文授课:

This course provides a brief introduction to game theory. Our main goal is to understand the basic ideas behind the key concepts in game theory, such as equilibrium, rationality, and cooperation. The course uses very little mathematics, and it is ideal for those who are looking for a conceptual introduction to game theory. Business competition, political campaigns, the struggle for existence by animals and plants, and so on, can all be regarded as a kind of “game,” in which individuals try to do their best against others. Game theory provides a general framework to describe and analyze how individuals behave in such “strategic” situations. This course focuses on the key concepts in game theory, and attempts to outline the informal basic ideas that are often hidden behind mathematical definitions. Game theory has been applied to a number of disciplines, including economics, political science, psychology, sociology, biology, and computer science. Therefore, a warm welcome is extended to audiences from all fields who are interested in what game theory is all about.

4. 佐治亚理工学院的 组合博弈论(Games without Chance: Combinatorial Game Theory)

这门课程主要关注组合博弈论,覆盖不靠运气游戏背后的数学理论和分析:This course will cover the mathematical theory and analysis of simple games without chance moves.

本课程将讲解如何运用数学理论,分析不含运气步骤(随机步骤)的简单游戏。本课程将探索不含运气步骤(随机步骤)的两个玩家游戏中的数学理论。我们将讨论如何简化游戏,什么情况下游戏等同于数字运算,以及怎样的游戏才算公正。许多例子都是有关一此简单的游戏,有的你可能还没有听说过:Hackenbush(“无向图删边”游戏)、Nim(“拈”游戏)、Push(推箱子游戏)、Toads and Frogs(“蟾蜍和青蛙”游戏),等。虽然完成这门课程并不能让你成为国际象棋或围棋高手,但是会让你更深入了解游戏的结构。

5. 国立台湾大学的 实验经济学: 行为博弈论 (Experimental Economics I: Behavioral Game Theory)

台湾大学王道一副教授 (Associate Professor)的实验经济学课程-行为博弈论:

人是否会如同理论经济学的预测进行决策?这门课将透过每周的课程视频以及课后作业带你了解实验经济学的基本概念。每周将会有习题练习以及指定阅读的期刊论文。你将会参与一些在线的实验、报告论文并且互评其他同学的报告。❖课程介绍(About the course)这是一门进阶的经济学课程,课程目标为介绍实验经济学的基本概念,并且让学生们能开始在这个领域从事自己的相关研究。详细课程目标如下:1.实验经济学的介绍:在上完这堂课之后,学生应能列举经济学各个领域的数个知名实验,并且解释实验结果如何验证或否证经济理论及其他实地数据。2.评论近期相关领域研究:上完这堂课之后,学生应能阅读并评论实验经济学相关的期刊论文。在课堂中,学生将会阅读指定的期刊论文,并且(在视频中)亲自上台报告一篇论文。❖授课形式(Course format)1.本堂课将以视频的形式为主,搭配课后作业的形式来进行。每个同学将阅读一篇实验经济学论文,并录像成两段各10分钟的介绍视频并后上传至Coursera(或上传到Youku,再复制连接到作业上传区)。第一段期中报告视频请同学介绍该论文所描述的实验设计,第二段,也就是期末报告视频则介绍实验结果。此外每位同学至少需观看其他两位同学的呈现内容,并给予评论。2.这堂课将简单地运用以下赛局(博弈)概念:奈许均衡/纳什均衡(Nash Equilibrium)混合策略均衡(Mixed Strategy Equilibrium)子赛局完美均衡/子博弈精练纳什均衡(SPNE)共识/共同知识(Common Knowledge)信念(Belief)

注:原创文章,转载请注明出处“课程图谱博客”:http://blog.coursegraph.com

本文链接地址:http://blog.coursegraph.com/coursera上博弈论课程博弈论公开课汇总推荐 http://blog.coursegraph.com/?p=782

Coursera课程下载和存档计划五:其他课程资源

本期整理了手头剩下的其他课程,限于个人精力有限,不整理归类了,请自取。这些公开课资源一些来自于之前课程图谱群内朋友的或者微博上的朋友的分享,另外一些这里做了下载补充,主要针对Coursera旧课程平台的课程进行备份和分享,对于一些已经迁移至新课程平台的课程,希望大家直接去Coursera新课程平台上去上课,这样会有更好的学习体验。最后特别说明的是,课程网盘资源仅供个人备份学习使用。

关于“Coursera课程下载和存档计划”,请参考:

  1. Coursera Downloader 下载工具
  2. Coursera课程速查表
  3. 机器学习 & 自然语言处理 & 推荐系统 & 数据挖掘相关公开课
  4. 计算机科学基础公开课

以下课程资源备份,相关信息我们也会同步到“Coursera Archive”项目上去:

29. 计算机科学入门课程: Computer Science 101

链接: http://pan.baidu.com/s/1dEXhOU9 密码: 6efk

30. 社交网络分析: Social Network Analysis

链接: http://pan.baidu.com/s/1kVheUMV 密码: pr7d

31. 台大概率课程:機率

链接: http://pan.baidu.com/s/1mis8w8C 密码: gqun

32. 科学计算:Scientific Computing

链接: http://pan.baidu.com/s/1mhN0sJI 密码: iiyn

33. 高性能科学计算:High Performance Scientific Computing

链接: http://pan.baidu.com/s/1kUP4jUB 密码: n8b5

34. Python入门课程:Learn to Program: The Fundamentals

链接: http://pan.baidu.com/s/1eSlZbR8 密码: fwr6

35. 函数式编程:Programming Languages

这门课程直接分享有问题,压缩了一下分享出来:

链接: http://pan.baidu.com/s/1c1AjzNE 密码: 8hb2

36. 线性代数应用课程:Coding the Matrix: Linear Algebra through Computer Science Applications

链接: http://pan.baidu.com/s/1cHVpsa 密码: qb4v

37. 异构并行编程 Heterogeneous Parallel Programming

关键词:GPU,CUDA

链接: http://pan.baidu.com/s/1pLznR2j 密码: taxa

38. 博弈论:Game Theory

链接: http://pan.baidu.com/s/1bFDh9s 密码: etxp

39. 大数据暑期学校:The Caltech-JPL Summer School on Big Data Analytics

链接: http://pan.baidu.com/s/1gfHffn9 密码: wfc3

40. 大数据课程:Web Intelligence and Big Data

链接: http://pan.baidu.com/s/1skWd9Nn 密码: dikb

41. Audio Signal Processing for Music Applications

链接: http://pan.baidu.com/s/1i5vwuQp 密码: 7di2

42. 图像和视频处理: Image and video processing: From Mars to Hollywood with a stop at the hospital

链接: http://pan.baidu.com/s/1i5NMCvj 密码: jq55

43. 离散优化: Discrete Optimization

链接: http://pan.baidu.com/s/1i49ZlgL 密码: cy2u

44. 线性优化和离散优化:Linear and Discrete Optimization

链接: http://pan.baidu.com/s/1gf7BFEz 密码: q5q6

45. 计算机视觉基础:Computer Vision: The Fundamentals

链接: http://pan.baidu.com/s/1qYgUX1i 密码: a2gm

46. 计量金融中的数学方法:Mathematical Methods for Quantitative Finance

链接: http://pan.baidu.com/s/1pKYP1H5 密码: eu5z

47. 模型思维:Model Thinking 模型思维

链接: http://pan.baidu.com/s/1nvvomQt 密码: x8g9

48. 统计学 & R语言:Statistics: Making Sense of Data

链接: http://pan.baidu.com/s/1c0utwM 密码: bs3b

49. 数字信号处理:Digital Signal Processing

链接: http://pan.baidu.com/s/1slgmZjJ 密码: wc9u

50. 逻辑导引:Introduction to Logic

链接: http://pan.baidu.com/s/1jIffsKQ 密码: fdm2

51. 软件定义网络:Software Defined Networking

链接: http://pan.baidu.com/s/1qXE4DIk 密码: bw62

52. Principles of Reactive Programming

链接: http://pan.baidu.com/s/1skSFMOl 密码: ht3j

53. 创业工程:Startup Engineering

链接: http://pan.baidu.com/s/1c2AzEuc 密码: j8jw

54. 台湾大学:中國古代歷史與人物--秦始皇

链接: http://pan.baidu.com/s/1boD9nWV 密码: fb99

55. 人类简史:A Brief History of Humankind

链接: http://pan.baidu.com/s/1mibD2vY 密码: pbx6

最后再推荐一个神器:coursera-dl-all

Extend the Coursera Downloader by downloading quizzes and assignments (and hopefully forum posts soon!). Uses coursera-dl in the process.

作为Coursera Downloader的扩展,可以下载问题和作业,今晚才发现,有点迟了,感兴趣的同学可以试用一下,这确实是一个很好的补充。

注:原创文章,转载请注明出处“课程图谱博客”:http://blog.coursegraph.com

本文链接地址:http://blog.coursegraph.com/coursera课程下载和存档计划五

2014年4月份MOOC部分热门课程汇总

近期MOOC的内容呈现出爆炸式的增长,各式各样的课程让人应接不暇。本文将对各大平台4月份预计比较热门的课程进行简单的汇总,各位可以根据自身的需求挑选合适的课程。

Coursera平台:

1. 美国西北大学的Everything is the Same: Modeling Engineered Systems 将于4月6日开课。本课主要讲述一些简单的物理工程实例,对物理学、工程学感兴趣的朋友可以关注。同时这门课程中会穿插Matlab和Python的内容,适合懂得一点编程的朋友。

2.马里兰大学的Exploring Quantum Physics将于4月7日开课,本课讲述的是量子物理。目前讲述量子物理方面的课程还不多,这门课或许是个不错的选择

3. 约翰霍普金斯大学的Getting and Cleaning Data将于4月7日开课。本课属于约翰霍普金斯大学 Data Science Specialization(“微专业”)的一部分

4.约翰霍普金斯大学的R Programming将于4月7日开课。本课属于约翰霍普金斯大学 Data Science Specialization(“微专业”)的一部分,R语言日益成为数据分析领域的首选工具,本门课程可以作为对这个工具入手的入门课程。

5. 约翰霍普金斯大学的The Data Scientist’s Toolbox将于4月7日开课。本课属于约翰霍普金斯大学 Data Science Specialization(“微专业”)的一部分,主要介绍了目前数据分析中会经常用到的工具,例如:Github,  MarkDown, R Console, R Studio等等

6. 上海交通大学的“唐诗宋词人文解读”将于4月8日开课。课程从喜闻乐见的唐诗宋词入手,触摸一段历史与一群文人的体温,领悟人生旅途的趣味和智慧。

7. 上海交通大学的“媒介批评:理论与方法”将于4月8日开课。“媒介批评”是现代大众传播学的重要分支,简单而言,就是批评媒介,是 对大众传播媒介本身进行批评,属于应用传播学的研究领域。

8. 密歇根大学的Programming for Everybody将于4月10日开课。在众多编程基础课中这门课属于新的成员,适合编程零基础的朋友。

9. 慕尼黑大学的Competitive Strategy将于4月11日开课:

@ototsuyume:

其实就是简单易懂的博弈论入门,课程量少老师讲得作业难度不高而且每道题都有说明,大概是大学里面公共通选课的难度,有空可以看看

10.科罗拉多大学博尔德分校的Physics 1 for Physical Science Majors将于4月14日开课。本课属于比较传统的大学物理,之前获得了不错的反响

11.慕尼黑大学的Introduction to Mathematical Philosophy将于4月14日开课。在现代的哲学研究中越来越多的需要思考很多底层的问题,在这期间免不了需要思考很多数学层面的问题,本课推荐给对数学或哲学领域感兴趣的朋友。

12.匹兹堡大学的Warhol将于4月21日开课。出生于匹兹堡市的Andy Warhol是20世纪最伟大的艺术家之一,波普艺术的创始人,对当代的艺术和文化产生了巨大的影响。本课将介绍Andy Warhol的生平和作品,让大家一睹大师的风采。

13.香港中文大学的“中國人文經典導讀”将于4月24日开课。本課程是以四堂演講的方式,分別討論中國文化的四個主要面向,彙文學、歷史、哲學、藝術于一爐。每一個主題以一篇或兩篇經典文本爲基礎,指導學生如何精讀作品,學習以欣賞和批判的雙重角度重新解讀經典,同時獲得對中國文字的陶冶和享受。它本爲大學一年級學生所設,但不限於中文系本科專業,希能為學生鑒賞中國傳統文化開啟新的視野。

14.瑞士洛桑联邦理工学院(EPFL)的Functional Programming Principles in Scala将于4月25日开课。本课之前几轮获得了极高的评价,主要通过Scala语言讲述函数式编程的思想。本课的讲师正是Scala语言的发明人。

15. 斯坦福大学的Algorithms: Design and Analysis, Part 1将于4月29日开课:

@超級現實的超現實理想主義者:

这门课对我的影响非常大,直接改变了我的思维方式,并且为日后的学习打下了很好的基础。

edX平台

1. MIT的Street-Fighting Math将于4月8日开课。如同街头打架一样,不论你使用什么招式,打架的唯一目的就是寻求胜利。各位接受了多年“严谨”的数学教育,不妨感受一下“Quick and Dirty”的数学方法。

2.哈佛大学的Justice将于4月8日开课。这门“公正”课早在MOOC出现之前就已经红遍国内互联网,想要重温或者学习这门经典课程的朋友不妨关注一下这门MOOC形式呈现的课程。

3.京都大学的The Chemistry of Life将于4月10日开课。该课属于化学和生物的入门课程。

学堂在线:

1. 清华大学的组合数学将于4月10日开课。随着计算机科学的发展,组合数学在这段时间里获得了极大的发展。不同于传统数学领域侧重于“连续”层面,组合数学解决的是“离散”层面的问题。本课将从基础的排列组合开始,逐步深入了解计数问题的不同解决思路,通过对现实生活中计数问题的演绎和学生们共同体会组合计数问题不断抽象深入的挖掘过程,引导学生共同感受数学知识的精妙,从而深入理解组合数学对计算机理论发展的推动作用。

2. 加州大学伯克利分校的云计算与软件工程—第一部分将于4月21日开课。本课的讲师是软件工程和计算机科学领域的大牛,课程主要通过Ruby on Rails等目前热门的互联网开发技术阐述诸如“云计算”、“敏捷开发”等软件工程领域热门的主题。

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