HOW STUDENTS CAN PREPARE THEIR MATH FOR THE MACHINE-LEARNING COURSES At TU KAISERSLAUTERN

Machine learning uses basic tools from mathematics to formulate its concepts. In order to understand machine learning, you need to first understand the math behind it. In the following, we have collected mathematical material that is, to the best of our knowledge, ideally taylored to machine learning. In particular, we are not suggesting you to study areas of math that are irrelevant for machine learning. The following material is ideally taylored to the TUK courses on machine learning: ML1, ML2, and ML3.


Option 1 (workload: medium)
========================

1.1 Lecture notes on "Mathematics for Machine Learning'
-------------------------------------------------------
A good summary of the most basic prerequisites is contained in the following reference: 
https://ipvs.informatik.uni-stuttgart.de/mlr/marc/teaching/18-Maths/paper.pdf
- The following sections/subsections can be ommitted: 3.5,3.6.1
As a prerequisite for ML 1:
- study sections 1,2, and 3.
As a prerequisite for ML 2, section 5 should also be read. 
As a prerequisite for ML 3:
- study Section 4 and Section 5.1
In order to master the material, it is crucial that you have a hands-on experience: 
- you need attempt some (or better: all) of the exercises!

1.2 Video Lecture
-----------------
If you are not confident in your mathematics skills, or if you prefer learning by watching video lectures, you can watch the following video lectures. Make sure, however, that, subsequently, you study the above material.
- Mathematics for machine learning: https://www.coursera.org/learn/machine-learning
- Multivariate calculus: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives 
Except the following sections: "Parametric curves", "curvature", "divergence", "curl", "divergence (articles)" 
- Probability: https://www.youtube.com/playlist?list=PLUl4u3cNGP60A3XMwZ5sep719_nh95qOe 
- Linear algebra: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ 


Option 2 (workload: high)
===========================

If you want to invest more time into your math, consider studying the following material:
- Linear algebra (basics): https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2012-2013/linear-algebra.pdf (Except chapters 4 and 5)
  For exercises, see the example sheets from the same website: https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/ (2018-2019)
  We recommended the following exercises (starred exercises are harder). Sheet 1: 1,2,4,5,6,12*. Sheet2: 1,7,8,12*. Sheet 3: 1,2,12*. Sheet4: none.
- Linear algebra (review): basic diagonalisation exercises with solutions. https://www3.nd.edu/~gszekely/Linear%20Algebra/practice%20final%20solutions.pdf
- Probability (basics): http://www.statslab.cam.ac.uk/~james/Lectures/p.pdf (except the following chapters: 13,14,19,20).
  Exercises: see example sheets on the same webpage (http://www.statslab.cam.ac.uk/~james/Lectures/). 
  We recommended the following exercises. Sheet 1: 1,2,4,5,6,14*. Sheet 2:1,2,3,7,12**. Sheet 3: 2,3,6,7. Sheet 4 : 1,2,4,7,8. 
  Motivated students are  encouraged to attempt more excercises.
After studying the above, you can check your learning success by attempting to solve the following three questions.
- Question 1: 
 (a) Prove that eigenvectors corresponding to different eigenvalues of a real symmetric matrix are orthogonal.
 (b) Prove that the eigenvalues of a real symmetric matrix are real.
 (c) Prove that every real symmetric matrix is diagonalisable.
- Question 2: See exercise 5 in the following reference. http://www.statslab.cam.ac.uk/~rrw1/markov/exmarkov1.pdf.
- Question 3 (harder, only for highly motivated students): How many n\times n matrices $A$ are there whose entries are either 0 or 1, and such that $A^2=0$?


Option 3 (workload: very high)
==============================

Option 3 is for highly motivated students only. The following reference is a highly complete resource for probability: 
https://eng.uok.ac.ir/mfathi/Courses/Stochastic%20Process/ebooksclub.org__Probability_and_Random_Processes_for_Electrical_and_Computer_Engineers.pdf
You may also want to read the following books for linear algebra: 
- Matrix Methods in Data Mining and Pattern Recognition, by Lars Elden
- Matrix Analysis for Scientists & Engineers, by Alan J. Laub