作者：吴恩达

译自：Quora

我觉得机器学习需要的最重要的数学领域，降序排列：

I think the most important areas of math for machine learning are, in decreasing order:

1. 线性代数（Linear algebra）
2. 概率统计（Probability and statistics）
3. 微积分（包含多变量） （Calculus (including multivariate calculus)）
4. 优化 （Optimization）

除了这些，我觉得其他意义不大。我觉得信息论也是有用的。你可以在Coursera或者大多数大学找到这些课程。

After that, I think it falls off quickly. I’ve also found Information Theory helpful. You can find courses on all of these on Coursera or at most universities.

虽然很难争辩说不用学那么多数学，但是我觉得学好机器学习，或者拿到一个机器学习PhD，所需要的数学水平，这些年来一直在下降。这是因为这个领域越来越经验化（基于实验），没那么理论化了，特别是随着深度学习的兴起。

While it’s hard to argue against knowing more math, I think the level of math needed to do machine learning effectively, or to get a PhD in machine learning, has decreased over the years. This is because machine learning has become more empirical (based on experiments) and less theoretical, especially with the rise of deep learning.

作为PhD学生我曾经热爱实分析（real analysis），研究过微分几何（differential geometry），测度论（measure theory），以及代数几何（algebraic geometry）等。当然你知道这些肯定比不知道更好，但是你往往只有有限的时间，最好花更多的时间研究机器学习本身，甚至多花点时间研究构成人工智能系统的其他技术基础，比如构建大数据系统背后的算法，如何组织大型数据库，加上高性能计算（HPC (high performance computing)）。

As a PhD student I had loved real analysis, and also studied differential geometry, measure theory, and algebraic geometry. While you’re certainly be better off knowing these areas than not, in a world in which you have limited time, consider just spending more time studying machine learning itself, and even studying some of the other technical foundations for building AI systems, such as the algorithms that underly building big data systems and how to organize giant databases, plus HPC (high performance computing).

祝好运！

Best of luck!