标签归档:微积分

Deep Learning Specialization on Coursera

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.

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数学基础公开课汇总

良好的基础是成功的一半。在如今这个时代,数学成为人们社会运行中不可缺少的组成部分,拥有良好的数学基础就等于为自己创造了更多可能,使得人们可以有足够的资本在这个变化繁杂的社会里来调转方向。

大学里有三门数学课是绝大部分专业的学生必修的,分别是:微积分、线性代数、概率统计。课程图谱本次就为这三门课罗列一下目前(2013年)几大MOOC平台收录的相关课程。

微积分公开课
1. 俄亥俄州立大学的Calculus One 是一门口碑非常不错的课程,讲师表情丰富、讲解投入,深得学员的欢迎:

@基佬的愛__ 同学评价“这门 Calculus One 内容比较基础,没有讲拓扑,没有涉及多变量函数,所有的讨论都是在 R 上进行的,差不多等于国内工科高数上的简化版。Jim Fowler 讲课很清楚,耐心很好,推导从来不跳步骤,很显然的步骤也写出来(其实我上过的所有的数学系教授教的 MOOC 的都是这样的),有时候我都有点不耐烦了,所以你跟着他上下来肯定能把这部分内容掌握好。我觉得学过一些函数的高中生甚至初中生就能听懂。印象中每周都会有一两个 lecture 是在室外进行实验。Jim 还提供了一本自己写的教材,教材写的要比他上课讲的严格一些,他上课讲的比较直观、稍欠严谨,可能是希望这门课的受众更广的原因,我建议看完 lecture 把对应的教材也看一遍就完美了。还有一个课程配套的网站 http://mooculus.osu.edu/ ,每周都有 exercises,从最 trivia 的到稍有难度的,总体来说都不是很难的题目,目的在于检查你是否理解了某个概念,不过因为很多都太 trivia 我都是挑着做的。 整个课程有 15 周,可能是最长的 MOOC 跟完很有成就感。Jim Fowler 是我上过的所有 MOOC 里上课最激情的一个讲师,属于表演型的老师,给人的感觉是他很享受整个教书的过程,很能带动学生。Jim 也是我上过的所有课中最愿意和学生互动的讲师,他几乎会回复每一个帖子,而且他不摆架子,允许我们叫它 Jim。Jim 说他在大学的一部分工作就是负责 MOOC,之后可能会开多变量微积分、拓扑、复分析、抽象代数等课程,明年3月会有一门他开的课程,目前还不知道是什么内容,我已经打算上所有 Jim Fowler 的课了。”

@ffffffoouddddd 同学评价“内容很简单,我估计比大学里面要学的微积分内容少70%。这位老师是很有激情的,拍摄视频时离镜头很近,有种身临其境的感觉,并且很有喜感(可能是因为他是光头)。观看视频时你总觉得他下一秒就要把你逗笑那种。而且他们也有一本他自己写的教材,很不错,有自己的俄亥俄州立大学的练习平台,我没怎么去练习因为太简单了。Coursera 上习题可以回答很多次,……”

2. 俄亥俄州立大学的Calculus Two: Sequences and Series 是前一门课程的后续:

@基佬的愛__ 同学评价 “这门课讲数列和级数,相同的内容 Robert Ghrist 的 Calculus: Single Variable 也涉及到了。Jim 讲的要比 Robert 要细致,比如一些数列和级数的收敛性的测试定理,Jim 会花一整个 lecture 讲推导过程, Robert 讲的没那么详细。另外整门课我最喜欢的一个 lecture 是关于 Taylor series 那节,Taylor Series 的 motivation 就是 approximation ,实际上他是 linear approximation 的推广,对某个函数在某点做 Taylor expansion 实现上就是找一个函数,使他在该点的值和原函数相等,并且该点的每一阶导数也和原函数的每一阶导数相等,导数反映的是函数的变化情况,这样我们就找到了一个和原函数在某个区间内相同的函数,说在某个区间内是因为有一个收敛性的问题。我可能记不住 Taylor series 的公式,不过我已经随时能把 Taylor series 推导出来了。还有个很有意思的 lecture,为了说明 geometric series 的收敛性,Jim 举了个造桥的问题,用质量均匀分布、形状相同的长木条造桥,最多能造多远?答案是理想状况下,想多远就多远。只要我们把每一块木条放在下一堆木条的重心处就能保证它不倒,然后你会发现每次增加的长度加起来正好构成一个不收敛的级数,Jim 自己造了这么一座很壮观的桥,你能看到这门课课程介绍的图片就是这样一座桥,实际上 lecture 里 Jim 造的那座还要壮观,比课程介绍里的那座要更长。总体来说这门课内容不多、难度不大、(不过我之前已经上过 Robert 的课,并且自学过一些其他的数学)、占用的时间不多,我基本看完视频就马上能把作业完成,不过这门课还是很有启发性的,有很多有意思的东西,Jim 在课程讨论版里也是一如既往的 supportive。另外这门课也有一本配套的免费教材。”

3. 宾夕法尼亚大学的Calculus: Single Variable 在今年年初获得了美国官方的认可,成为可以获得正式学分的在线课程

@基佬的愛__ 同学评价 “Robert Ghrist 这门课和 Jim Fowler 的 Calculus One 有重叠的部分,不过内容更深入,课程周期也挺长的。课程总共分五个部分,Functions,Differentiation,Integration,Applications(主要是积分的),Discretization(主要讲数列和级数)。积分的应用部分略有难度,讲的内容比我以前上的高数课讲的积分的应用要多 centroids 和 moments and gyrations 我是第一次学,第一部分的 Taylor series 我觉得没有 Jim Fowler 讲的好。这门课作业量挺大的,每周大概是五个 lecture(外加一亮个 bonus),每个 lecture 对应一个 core 和 一个 challenge 作业,core 一般10道左右,challenge 一般2-5道左右,我做了所有的 core 和一部分的 challenge 。作业是不计分的,某个单元会有一次 quiz,期末会有个 exam。另外,讲师是个 geek,他的 lecture 里很多彩蛋。”

@52nlp 评价 “Coursera在今年一月份同时推出了两门微积分课程,一门是这个单变量微积分,另一个是微积分上(Calculus One)。我同时跟了这两门课,不过由于工作及春节等等缘故,大概跟了一半就放弃了,不过还是可以点评一下。相对来说,这门课制作的课件非常有意思,但是Calculus One讲得更生动一些。

这门课程的一个参考书是不到50页的一个小册子:FLCT: the Funny Little Calculus Text ,这个在google book上能阅读免费电子版,google play 上也只有0.45美元的价格,课件的确很有趣并且动感实足,这样导致感觉老师讲得有点不生动了。不过总体来说,这门微积分入门课还是非常不错的。”

线性代数公开课
线性代数是一门非常实用的课程,但是国内绝大多数的同学在学习这门课程的时候并不能很好理解线性代数的重要性,究其原因可能是因为教学方式相对于现实运用的滞后性。目前国外MOOC平台的线性代数课程往往结合了计算机编程,通过动手解决问题来加深对于这门课程的理解。

1. 布朗大学的Coding the Matrix: Linear Algebra through Computer Science Applications 通过Python来解决现实中的实际问题,来帮助学生对于知识的理解。不过有趣的是,对于这门课程大家的反响不一:

@ototsuyume 同学评价“值得吐槽的很多:
1.老师讲课水平不咋样,课程内容也有问题,很多基本概念没有说清楚
2.作业量偏大,而且大部分是重复的计算,比如上上周作业是要实现matrix类各种运算,然后作业里面还要用另外的方法算matrix的乘法,不明白这样做的意义何在
3.课程介绍说这门课很偏向应用,但貌似基础概念讲不好应用讲得也很浅,从作业上没看到这点,你将线性变换好歹在作业里让学生拉长一张图片都比实现vector、matrix类要好吧
4.svd分解等内容因为课程长度问题不会讲,这门课的含金量进一步降低。
另外虽然吐槽的是这个老师主页上还写着拿过布朗大学的优秀讲师奖项的,从他讲课的方式来看我不明白这个奖到底是怎么评的…”

@大家都叫我瑞爷 同学评价“这门课不能算是一门入门课,尤其是不能视为线性代数入门课,因为关于数学部分的课程材料过于简略。此外,这门课还有编程作业较多的特点。因此此课比较适合:了解线代,但是不懂如何将线代应用到计算机上解决问题。我见过有人吐槽这门课线性代数教的太少了。所以想学线性代数的guys请移步到mit公开课网站直接修线性代数。”

2. UTAustin的Linear Algebra – Foundations to Frontiers 将于明年在Edx平台上开课,本课同样也是希望通过计算机编程来帮助学生理解线性代数的概念,让学生充分理解这门课的重要性。由于这门课尚未正式开课,质量究竟如何让我们拭目以待!

3. 最后隆重推荐网易公开课上收录的“麻省理工公开课:线性代数”:

这门课程虽然是老一代的公开课,但是讲得确实确实非常好,更详细的信息可参考这篇文章《线性代数的学习及相关资源》。

概率论公开课
生活中充满不确定性,如何更好地理解和面对这种不确定,正是概率和统计学所主要面对的议题。正因为如此,概率统计是适合每个人去学习的一门课程
1. 台湾大学的機率

@基佬的愛__ 同学评价 “这门课半途弃了。讲师是个 EE 背景的教授,虽然第一周第一个 lecture 叶老师明确说了这门课比较注重生活中的应用,还是有些小失望,如果叶老师选择自己更擅长的 EE 方便的课程可能会效果会更好。这门课不合我口味是因为太不严肃,推导少了点。课程前几周有一课里叶老师引入了一个事件域/空间(event field)的概念,我不记得他用的哪个名词了,反正他给出的定义是样本空间的幂集。事件域(event field)我用英文在 google 搜没有搜到这个概念,只有 wolfram 的 wiki 说它指的就是样本空间,和叶老师的定义不一样,用 baidu 搜发现国内的教材里确实有这个概念,定义也是和叶老师的课里一样的,但是叶老师引入这个概念后面的课里(至少在我上完的那几周里)没用到这个概念,那引入这个定义有什么意思,我受不了这种不严谨。另外叶老师喜欢在每周花一整节课的时间讲大道理让我非常反感,人之患在好为人师,客观的真理是可以教的,但是怎么做人就不太好教了,我觉得人不是从别人的建议里学到东西的,人是从自己的经验,犯过的错中学习的。对于叶老师不公布作业解答的做法也不太认同。叶老师也鲜有在论坛上回复同学数学上的问题,有个 TA 还是很认真的。值得肯定的是叶老师也是属于教学非常热情的讲师,不过他在课上用的梗很烂,没得到我的共鸣……我觉得他过于花心思在课上一些讨人欢喜的梗上而忽略了课程内容讲解的重要性。”

2. MIT的Introduction to Probability – The Science of Uncertainty 将于明年(2014)二月开课,课时很长,或许将是一门很实的课程,讲师John Tsitsiklis在MIT讲授的概率论课程在MIT的OCW上也有公布。由于课程尚未开始,究竟课程质量如何,让我们拭目以待!

统计学公开课
目前MOOC平台上涌现了很多统计学的课程,课程图谱曾经对统计学的课程进行了收录,详细点击《统计学公开课大盘点》:
http://blog.coursegraph.com/统计学公开课大盘点

还有一门华盛顿大学的Mathematical Methods for Quantitative Finance也受到了广泛的好评,想要快速的过一遍基础数学的朋友不妨关注一下这门课程:

@钛合金蛙眼:内容包括微积分,线性代数,最优化再捎带一些金融知识,都是数据挖掘和机器学习数学基础(除了概率统计),老师也讲的很清楚,只可惜没有证书,UW开的几门课程都不错
@算文解字:搞statistical NLP自然要吃透了概率、统计和随机过程,但适当的微积分、线性代数和数值计算基础也很重要。没时间系统恶补?No problem! Coursera上推出了一门 Mathematical Methods for Quantitative Finance ,虽然原本针对金融,但8周的课程提供的浓缩版数学对NLPer也很实用。

以上是对数学基础课进行的简单汇总,难免会有缺失和遗漏,还望谅解。如果有朋友发现不错的数学基础公开课在上文中尚未收录,希望能够留言告知。

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

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