Thread by @PiyalBanik

"People need to know Maths to become Data Scientists or Machine Learning Engineer"

- True! 😀

But, how much do we need to know? 🤔⁉️

This thread 🧵 is an outline of the concepts we should know

1. Let's start with Linear Algebra

You can start working on Data Science or ML without knowing them.

But at some time you may wish to dive deeper.

If you ask me, if there was 1 area of Maths that I would suggest you improve before the other, it would be Linear Algebra.

If I could convince you to learn a minimum of Linear Algebra for Machine Learning, it would be the following👇:

- Systems of Linear Equations & Solving them
- Matrices
- Vector Spaces
- Linear Independence
- Basis & Rank
- Linear Mappings / Projections

Still not convinced? Here's the usage👇

- Principal knowledge of Matrix Operations is essential for Vector Calculus

- We need to use projections for dimensionality reduction with PCA

- Linear Algebra plays a central role in solving least-squares problems in Linear Regression.

2. Second is Analytical Geometry:

This one is a sub-section of Linear Algebra.

Here, you add some geometric intuition to all of the concepts mentioned in the previous tweet.

- Norms
- Inner Products
- Lengths & Distances
- Angles & Orthogonality

Application👇

- Inner products and corresponding norms & metrics along with notions of similarity & distances are used to develop the Support Vector Machine.

- Orthogonal projections play a central role in regression via maximum likelihood estimation and PCA

3. Matrix Decompositions:

This completes the topic Linear Algebra😀

Here we need to know
- Determinants
- Eigenvalues & Eigenvectors
- Eigendecomposition and Diagonalization

Don't get demotivated, all these topics are easy to learn with the help of some free online resources👇

Youtube playlists that are goldmine:
- @3blue1brown youtube.com/playlist?list=…

- @khanacademy youtube.com/playlist?list=…

- Free MIT Course youtube.com/playlist?list=…

4. Vector Calculus

This is one of the fundamental mathematical tools we need in Machine Learning. [Do not freak out, I will break it into small components]

Start with
- Basic understanding of what Functions are
- Graph of a Function
- Contour Plots
- Vector Field

Once you feel confident with Functions, move into Differential Calculus

- Derivative of a Function
- Partial Derivatives
- Rules of Differentiation
- Vector-Valued Functions
◦ Derivatives
◦ Partial Derivatives
- Gradient
- Chain Rule
- Jacobian & Hessian Matrix

Did you get overwhelmed? Not yet? Well this is the hardest part [maybe 😐]

Applications of Multi-variable Derivatives
- Critical Points
- Local Maxima, Minima & Saddle Point
- Second Derivative Test
- Lagrange Multipliers
- Least Squares Interpolation
- Gradient Descent

To end Vector Calculus, learn a bit of Integration [not much is required 🎉]

- Area Under the Curve
- Arc Length of Function Graphs and Parametric Curves
- Rules of Integration
- Double Integrals

That's it for this topic, phew 😮‍💨

Again there are few exceptional free resources online which you can follow & become great at it.

- MIT youtube.com/playlist?list=…

- @khanacademy khanacademy.org/math/different…

5. Let's End it with some Probability

Start with some basics
- Probability Models and Axioms
◦ Addition and Multiplication Rule
- Conditional Probability
- Independence
- Total Probability Theorem
- Bayes Rule
- Counting

This is probably the most important part that everyone needs to get right.

- Discrete & Continous Random Variable
- PMF, PDF, CDF
- Expected Value, Variance, & Standard Deviation
- Know about the most popular distributions
- Co-variance and Correlation

Finish it off with

- The Weak Law of Large Numbers
- Central Limit Theorem

In case you love Probability then try Markov Chains

You can follow my favorite youtube channel
youtube.com/c/BrandonFoltz…

or this gold mine -
khanacademy.org/math/statistic…

I could have added Statistics in this thread but decided to keep it separate. Learning the above concepts will make stats much easier.

Credits - "MATHEMATICS FOR MACHINE LEARNING" book

If you're feeling lost then DM me and I will try to convince you how easy it can be for you.

That's it for this tread 👋

Please do add if you feel I have missed something!

A retweet for the first one would really mean a lot 🙏

If you liked my content and want to get more threads on Data Science, Machine Learning & Python, do follow me @PiyalBanik

Here is a ladder🪜 to the top

https://twitter.com/PiyalBanik/status/1416612450376454144?s=20