In this article, I have shared a 3-month plan to learn mathematics for machine learning. As we know, almost all machine learning algorithms make use of concepts of Linear Algebra, Calculus, Probability & Statistics, etc. Some advanced algorithms and techniques also make use of subjects such as Measure Theory

在本文中，我分享了一個為期3個月的計劃，學習用於機器學習的數學。 眾所周知，幾乎所有的機器學習演算法都使用線性代數，微積分，概率和統計

The plan that I have shared in this article can be used to prepare for data science interviews, to strengthen mathematical concepts, or to start researching in machine learning. The plan will not only help in understanding the intuition behind machine learning but can also be used in many other advanced fields such as statistical signal processing, computational electrodynamics, etc.

我在本文中分享的計劃可用於準備資料科學訪談，加強數學概念或開始進行機器學習研究。 該計劃不僅有助於理解機器學習的直覺，而且還可以用於許多其他高階領域，例如統計訊號處理，計算電動力學等。

After following the plan, I aced the Microsoft interview for Data Science Internship and received an offer from Microsoft for 2021. My interview experience can be viewed in the following article:

按照計劃執行後，我獲得了Microsoft對Data Science Internship的採訪，並收到了Microsoft提出的2021年的錄取通知。我的採訪經驗可以在以下文章中檢視：

In addition to that, one should be understood the papers presented at top conferences/journals, which might be overwhelming earlier. It can also help to start with a research career.

除此之外，應該理解在頂級會議/期刊上發表的論文，而這些論文可能早些時候就不堪重負了。 它還可以幫助您開始研究生涯。

The plan is mainly divided into four parts:-

該計劃主要分為四個部分：

1. Linear Algebra

   線性代數

2. Probability Theory

   概率論

3. Multivariable Calculus

   多變數微積分

4. Multivariate Statistics

   多元統計

線性代數(Linear Algebra)

Linear Algebra is one of the most important concepts required in machine learning and deep learning. The best available course to learn linear algebra is a collection of 35 lectures by Dr. Gilbert Strang on MIT OCW. This course can take at most one month to complete for a complete beginner. But since most of the folks doing machine learning are aware of introductory linear algebra and matrices. They should be able to complete it in 2 hours per lecture. In addition to the lectures, one should also try to complete the homework and exams given in the course for proper practice. The most important skill from this course can visualize multidimensional vectors and understand the relation between them. Visualization of vectors is one of the most skill in data science.

線性代數是機器學習和深度學習中最重要的概念之一。 最好的學習線性代數的課程是Gilbert Strang博士在MIT OCW上發表的35堂課。 對於一個完整的初學者來說，該課程最多可能需要花費一個月的時間。 但是由於大多數從事機器學習的人們都瞭解線性代數和矩陣的入門知識。 他們每堂課應能在2小時內完成。 除了授課外，還應嘗試完成課程中的功課和考試，以進行適當的練習。 本課程中最重要的技能是視覺化多維向量並瞭解它們之間的關係。 向量的視覺化是資料科學中最熟練的技能之一。

For better understanding the visualization in Linear Algebra, one can watch the playlist “Essence of Linear Algebra” uploaded by the YouTube Channel “3blue1brown”. The channel also has other videos describing the beauty of mathematics through visualizations.

為了更好地瞭解Linear Algebra中的視覺化效果，可以觀看YouTube頻道上載的播放列表“ Linear Algebra的實質” 3blue1棕色” 。 該頻道還有其他視訊，通過視覺化描述了數學的美麗。

概率論 (Probability Theory)

Probability is a set of principles to understand the science behind uncertainty. With enough observations, uncertainties can be modeled using deterministic principles. The best course on probability theory is the lectures by Dr. John Tsitsiklis on MIT OCW. The course discusses the basics of probability theory and discusses the Poisson Process, Markov Chains, Central Limit Theorem, and much more. The assignments and exams are also available on MIT OCW, and one should do all the assignments and exams to test the concepts learned during the course. Solutions are also provided for the same. If you are someone who likes to learn from a textbook, then you can go through the book “Introduction to Probability, 2nd ed.” by Bertsekas, Dimitri, and John Tsitsiklis, which is accompanied for this course.

概率是理解不確定性背後的科學的一組原則。 有了足夠多的觀察，就可以使用確定性原理對不確定性進行建模。 關於概率論的最佳課程是John Tsitsiklis博士在MIT OCW上的講座。 該課程討論了概率論的基礎，並討論了泊松過程，馬爾可夫鏈，中心極限定理等等。 作業和考試也可以在MIT OCW上獲得，並且應該完成所有作業和考試，以測試在課程中學習的概念。 還提供了相同的解決方案。 如果您是喜歡學習教科書的人，則可以閱讀《概率概論》第二版。 由Bertsekas，Dimitri和John Tsitsiklis撰寫，並隨本課程一起提供。

多變數微積分 (Multivariable Calculus)

Knowing Multivariable Calculus is crucial for understanding many machine learning algorithms since most of the machine learning algorithms use more than one parameter(millions in deep learning), and thus calculating the gradient and backpropagation matrix cannot be done by just single variable calculus. Hence, the knowledge of multivariable calculus is essential for machine learning.

知道多變數演算對於理解許多機器學習演算法至關重要，因為大多數機器學習演算法使用多個引數(深度學習中為數百萬個)，因此僅通過單變數演算就無法完成梯度和反向傳播矩陣的計算。 因此，多變數演算的知識對於機器學習至關重要。

Before going for any course on multivariable calculus, revise the concepts for single variable calculus first. One of the best courses available on this topic is lectures by Dr. Denis Auroux on MIT OCW. Also, as always, practice assignments and exams form this course. The course discusses Lagrange Multipliers, Partial Differential Equations, Vector Fields, Flux, etc. There is a series of short(5–10 min) video playlist by “3blue1brown” on this topic, which uses visualization to explain this topic. It is strongly advisable to watch the videos for a better understanding.

在學習多變數微積分的任何課程之前，請先修改單變數微積分的概念。 關於該主題的最佳課程之一是Denis Auroux博士關於MIT OCW的講座。 同樣，與以往一樣，練習和考試構成了本課程。 該課程討論了拉格朗日乘數，偏微分方程，向量場，通量等。該主題上有一系列由“ 3blue1brown ”組成的簡短(5-10分鐘)視訊播放列表，使用視覺化解釋了該主題。 強烈建議觀看視訊以更好地理解。

多元統計 (Multivariate Statistics)

Many machine learning algorithms use the concepts of statistics in a multivariate setting. The concepts of these topics are derived from linear algebra and probability & statistics for high dimensional feature space. There is no specified course for studying this topic. However, it is advised to follow any one of the following resources to learn this topic:

許多機器學習演算法在多元設定中使用統計的概念。 這些主題的概念源自線性代數以及高維特徵空間的概率和統計量。 沒有學習此主題的特定課程。 但是，建議遵循以下任何一種資源來學習此主題：

• Chapters 4, 7, and 8 of the book by R. Johnson: Applied Multivariate Statistical Analysis.

  R. Johnson的書的第4、7和8章：應用多元統計分析。

• Chapters 2,3 and 11 of the book by T W. Anderson: An Introduction to Multivariate Statistical Analysis.

  T W. Anderson的書第2、3和11章：多元統計分析簡介。

Now, you can sit back and look back at what you have learned during the three-month plan. But this is not the end.

現在，您可以坐下來，回顧一下在三個月計劃中學到的知識。 但這還沒有結束。

Now take any conference paper or any advanced machine learning book or online courses, etc. Most of the folks have already watched the coursera course on Machine Learning by Dr. Andrew Ng. Now, you can try to watch the original lectures of CS229 at Stanford and try to understand machine learning concepts in depth with mathematical rigor.

現在參加任何會議論文或任何高階機器學習書籍或線上課程等。大多數人已經看過Andrew Ng博士的機器學習課程。 現在，您可以嘗試在斯坦福大學觀看CS229的原始演講，並嘗試通過嚴格的數學知識深入瞭解機器學習概念。

Also, you can go for any of the book mentioned below to learn machine learning:

此外，您可以閱讀下面提到的任何書籍來學習機器學習：

1. Pattern Recognition and Machine Learning Book by Christopher Bishop.
   模式識別和機器學習書，克里斯托弗·畢曉普(Christopher Bishop)。
2. Introduction to Computational Thinking and Data Science.
   計算思維與資料科學導論。
3. Machine Learning by Prof. Tommi Jaakkola.
   Tommi Jaakkola教授的機器學習。

I anybody has any questions regarding this, feel free to discuss.

我對此有任何疑問，請隨時討論。