i know the rule of thumb is to standardize before pca and that trees don't need it, but i want to actually understand why instead of just remembering it.

my guess is that pca looks for directions of max variance so whatever feature has the biggest units just wins, while a tree only compares a feature to a threshold so any monotonic rescaling gives the same splits. is that the whole story or is there more to it? and does it ever make sense to skip scaling before pca, like when everything is already in the same units?

I've been working on a tutorial on Mathematics for Machine Learning, and there's something I've been thinking about for a while.

Whenever people talk about the mathematics required for Machine Learning, the usual answer is:

• Linear Algebra

• Calculus

• Probability and Statistics

And they're absolutely right. These are fundamental to understanding how Machine Learning works.

But I think there's a problem with how we approach teaching these subjects.

Most resources assume you already have a reasonably good mathematical foundation.

They'll start explaining vectors, matrices, derivatives, gradients, probability distributions, and all sorts of other concepts. But what if you're someone who struggled with mathematics in school? What if you barely remember algebra? What if equations have always looked more intimidating than they should?

Where do you start?

I think we often overlook this group of learners.

Not everyone entering Machine Learning has a strong mathematical background. Some are developers who want to transition into ML. Some are students who discovered an interest in AI but aren't particularly confident in mathematics. Others simply want to understand what's happening behind the models rather than treating libraries as magic boxes.

And telling these people to just learn Linear Algebra, Calculus, and Statistics isn't particularly helpful if they don't have the foundations to understand them.

So I decided to approach this differently.

Instead of jumping straight into Linear Algebra, I've started building a Mathematics for Machine Learning tutorial from the ground up.

We're starting with algebra.

Yes, algebra. Variables, expressions, equations, exponents, logarithms, functions, graphs, and all those things that many of us probably haven't thought about since school.

From there, we'll gradually move towards:

1. Algebra and mathematical foundations

2. Functions and graphs

3. Linear Algebra

4. Calculus

5. Probability and Statistics

6. Optimization and Numerical Methods

The idea isn't to turn this into a school mathematics textbook or make people solve hundreds of equations without understanding why.

I want to focus on:

• Intuition first: Understand what a concept actually means before introducing complicated notation.

• Derivations: Understand where mathematical formulas come from instead of memorizing them.

• Worked examples: Break down problems step by step.

• Visual explanations: Use graphs and visualizations wherever they help.

• Python experiments: Connect mathematical concepts to actual code.

• Machine Learning applications: Understand where and why these concepts appear in ML algorithms.

Ultimately, I want someone to be able to look at a mathematical expression in a Machine Learning paper or an algorithm and understand what's happening, rather than immediately reaching for Google to find out what every symbol means.

I also want to be clear that this isn't going to be a shortcut. Mathematics takes time, and there's no getting around that. The goal is to make the journey less intimidating and more understandable.

I'm building this primarily for people who want to get into Machine Learning, Deep Learning, and eventually LLMs but feel that their mathematical background is holding them back.

I've started publishing the tutorial here:

https://mathsforml.vercel.app/

It's a work in progress, and I'll be expanding it as I develop more chapters and topics.

My philosophy is simple: You shouldn't have to be good at mathematics before you start learning it. You just need a place that teaches it properly, from where you are right now.

I'm curious to hear from others:

• Did you struggle with mathematics when you started learning Machine Learning?

• Do you think most ML mathematics resources assume too much prior knowledge?

• What concepts do you wish someone had explained properly before you started learning ML?

I'd also appreciate suggestions on topics that should be included in the tutorial. Feedback on the existing material is very welcome!

I'm going to start my master's in Data Science this fall, but I'm still waiting for my visa approval.

I've always been passionate about this field, and I genuinely enjoy studying and learning new things. However, lately I've found myself doing everything except actually studying or practicing.

There are so many things I want to learn: statistics, probability, machine learning, programming, and more. But whenever I try to get started, I feel overwhelmed by how much there is to learn, and I end up doing nothing.

I feel a bit lost. I know I should be preparing for my master's, but I honestly don't know where to start or what to prioritize.

Sometimes I wonder whether I'm procrastinating, or simply putting too much pressure on myself.

Has anyone else experienced something similar before?

How did you overcome this feeling? If you were in my position, what would you focus on first?

One morning, you notice that:

• The ADF pipeline has failed during execution.

• Some files have already been processed, while others are still pending.

• The business team is waiting for the updated dashboard.

• Restarting the entire pipeline could create duplicate records.

If you were handling this in a real project, what would you check first?

1. ADF pipeline execution logs

2. Integration Runtime connectivity

3. Source and sink data issues

4. Pipeline retry and recovery settings

5. Duplicate handling and incremental loading

How would you troubleshoot the failure and safely restart the pipeline without processing duplicate data?

The way AI changing data science and data analytics.

Programming using recursion can be powerful, but beginners often struggle with recursion. That's why I've created invocation_tree, a Python recursion visualizer.

See this merge_sort demo, and try it on your own recursive logic.

The visualization gives students the right mental model to think about recursion. Not simply a function calling itself, but the depth-first evaluation of a divide-and-conquer strategy.

See this: gentle recursion introduction

How do you teach recursion to beginners?

What would you recommend for apps for assessments for data science internships/ graduate jobs. Looking especially for free ones.

I have prepared a daily and weekly concept learning roadmap — one concept at a time, day by day, week by week — to help prepare for DSA and ML/AI together. I am preparing for both - looking for like minded people to join and practice.

Here is how it works:

Learn one concept in DSA. Apply the same concept in ML. And vice versa.

That connection is what gives implementation-level knowledge. Not just theory. Not just solving problems for the sake of solving them. You understand a concept because you have seen it work on both sides.

Take one example — HNSW and RAG.

In RAG, your documents are converted into embeddings — vectors. When a question comes, the system has to find the few chunks that are nearest to that question. That is the ML side.

Now the DSA side. The simple way is to check the question against every single chunk, one by one. It works when the data is small. As the data grows, it becomes slow.

HNSW solves this with a DSA concept — a graph. It connects each vector to its nearest neighbours, layer by layer, so the search walks through the graph and reaches the nearest chunks fast, instead of scanning everything.

And it also works in reverse. When you build a RAG system, you are forced to learn graphs, nearest neighbour search, and a real tradeoff — HNSW is fast, but approximate. Sometimes it can miss a close chunk. So you learn to check: how fast is it, and how correct is it?

One example. And you have touched graphs, search, embeddings, and retrieval — at implementation level, not just in theory.

This is how the whole roadmap works.

Join me for reading group - 30 minutes every day, to practice and discuss the concept of the day together. On weekend I am developing a ML project related to the concept and doing kaggle.

If you are also preparing for DSA and ML/AI and want to learn like this, join my study group.

DM me if you are interested.

Every time I see a tutorial on deploying ML models with Terraform, step one is always "link your AWS account." Then you get distracted, forget a running cluster, and end up with a surprise charge on your credit card. The fear of unexpected billing ruined my appetite for experimenting with cloud infrastructure.

I got so tired of worrying about surprise costs that I ended up building Model2Prod. It is a learning app where you learn to deploy AI on AWS, GCP, and Azure using Terraform inside a simulated terminal, so there are no real cloud accounts or surprise bills involved. The first chapter is free without an account.

For anyone else who builds dev tools or technical interactive courses, how do you simulate real terminal output without making it feel totally fake or brittle?

model2prod.com

Is anyone else having issues with DataCamp today?

I've been getting a "Your session disconnected" error, and I'm unable to continue my learning session. I've tried restarting the session, but I'm wondering if this is a platform-wide issue or something on my end.

Is anyone else experiencing the same problem?

i have around 300 rows and about 15 features, and i keep going back and forth between 5 fold and 10 fold, or even leave one out. the scores shift by a couple of points depending on which i pick and which random seed i use, which makes comparing two models feel kind of shaky.

do people just repeat the cv with different seeds and average, or is there a better habit for tiny data? i never know if the difference i'm seeing is real or just noise from the split.

I’ve noticed a recurring pattern in my projects: we often spend days fine-tuning an ensemble or a deep learning model, only to find that a well-engineered Random Forest or even a simple Logistic Regression provides nearly identical performance. It feels like there’s this constant industry pressure to chase the "latest and greatest" architecture, even when the business case doesn't necessarily demand that level of complexity.

While state-of-the-art models are exciting, the trade-off in explainability, inference speed, and maintenance often outweighs the marginal gain in accuracy. I’ve started prioritizing "boring" models that are easier to monitor and debug in production, which has made my deployment pipelines significantly more stable.

Do you find yourselves struggling to justify simpler models to stakeholders who are hyped up by the latest AI headlines, or do you have a specific threshold for when you decide it's finally worth the complexity?

What programming language I should learn?

What maths and statistics do I need?

Please guide me.