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Mathematics for Data Science Roadmap

Mathematics is the backbone of data science, machine learning, and AI. This roadmap covers essential topics in a structured way.


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1. Prerequisites

Basic Arithmetic (Addition, Multiplication, etc.)
Order of Operations (BODMAS/PEMDAS)
Basic Algebra (Equations, Inequalities)
Logical Reasoning (AND, OR, XOR, etc.)


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2. Linear Algebra (For ML & Deep Learning)

🔹 Vectors & Matrices (Dot Product, Transpose, Inverse)
🔹 Linear Transformations (Eigenvalues, Eigenvectors, Determinants)
🔹 Applications: PCA, SVD, Neural Networks

📌 Resources: "Linear Algebra Done Right" – Axler, 3Blue1Brown Videos


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3. Probability & Statistics (For Data Analysis & ML)

🔹 Probability: Bayes’ Theorem, Distributions (Normal, Poisson)
🔹 Statistics: Mean, Variance, Hypothesis Testing, Regression
🔹 Applications: A/B Testing, Feature Selection

📌 Resources: "Think Stats" – Allen Downey, MIT OCW


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4. Calculus (For Optimization & Deep Learning)

🔹 Differentiation: Chain Rule, Partial Derivatives
🔹 Integration: Definite & Indefinite Integrals
🔹 Vector Calculus: Gradients, Jacobian, Hessian
🔹 Applications: Gradient Descent, Backpropagation

📌 Resources: "Calculus" – James Stewart, Stanford ML Course


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5. Discrete Mathematics (For Algorithms & Graphs)

🔹 Combinatorics: Permutations, Combinations
🔹 Graph Theory: Adjacency Matrices, Dijkstra’s Algorithm
🔹 Set Theory & Logic: Boolean Algebra, Induction

📌 Resources: "Discrete Mathematics and Its Applications" – Rosen


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6. Optimization (For Model Training & Tuning)

🔹 Gradient Descent & Variants (SGD, Adam, RMSProp)
🔹 Convex Optimization
🔹 Lagrange Multipliers

📌 Resources: "Convex Optimization" – Stephen Boyd


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7. Information Theory (For Feature Engineering & Model Compression)

🔹 Entropy & Information Gain (Decision Trees)
🔹 Kullback-Leibler Divergence (Distribution Comparison)
🔹 Shannon’s Theorem (Data Compression)

📌 Resources: "Elements of Information Theory" – Cover & Thomas


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8. Advanced Topics (For AI & Reinforcement Learning)

🔹 Fourier Transforms (Signal Processing, NLP)
🔹 Markov Decision Processes (MDPs) (Reinforcement Learning)
🔹 Bayesian Statistics & Probabilistic Graphical Models

📌 Resources: "Pattern Recognition and Machine Learning" – Bishop


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Learning Path

🔰 Beginner:

Focus on Probability, Statistics, and Linear Algebra
Learn NumPy, Pandas, Matplotlib

Intermediate:

Study Calculus & Optimization
Apply concepts in ML (Scikit-learn, TensorFlow, PyTorch)

🚀 Advanced:

Explore Discrete Math, Information Theory, and AI models
Work on Deep Learning & Reinforcement Learning projects

💡 Tip: Solve problems on Kaggle, Leetcode, Project Euler and watch 3Blue1Brown, MIT OCW videos.



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Mathematics for Data Science Roadmap

Mathematics is the backbone of data science, machine learning, and AI. This roadmap covers essential topics in a structured way.


---

1. Prerequisites

Basic Arithmetic (Addition, Multiplication, etc.)
Order of Operations (BODMAS/PEMDAS)
Basic Algebra (Equations, Inequalities)
Logical Reasoning (AND, OR, XOR, etc.)


---

2. Linear Algebra (For ML & Deep Learning)

🔹 Vectors & Matrices (Dot Product, Transpose, Inverse)
🔹 Linear Transformations (Eigenvalues, Eigenvectors, Determinants)
🔹 Applications: PCA, SVD, Neural Networks

📌 Resources: "Linear Algebra Done Right" – Axler, 3Blue1Brown Videos


---

3. Probability & Statistics (For Data Analysis & ML)

🔹 Probability: Bayes’ Theorem, Distributions (Normal, Poisson)
🔹 Statistics: Mean, Variance, Hypothesis Testing, Regression
🔹 Applications: A/B Testing, Feature Selection

📌 Resources: "Think Stats" – Allen Downey, MIT OCW


---

4. Calculus (For Optimization & Deep Learning)

🔹 Differentiation: Chain Rule, Partial Derivatives
🔹 Integration: Definite & Indefinite Integrals
🔹 Vector Calculus: Gradients, Jacobian, Hessian
🔹 Applications: Gradient Descent, Backpropagation

📌 Resources: "Calculus" – James Stewart, Stanford ML Course


---

5. Discrete Mathematics (For Algorithms & Graphs)

🔹 Combinatorics: Permutations, Combinations
🔹 Graph Theory: Adjacency Matrices, Dijkstra’s Algorithm
🔹 Set Theory & Logic: Boolean Algebra, Induction

📌 Resources: "Discrete Mathematics and Its Applications" – Rosen


---

6. Optimization (For Model Training & Tuning)

🔹 Gradient Descent & Variants (SGD, Adam, RMSProp)
🔹 Convex Optimization
🔹 Lagrange Multipliers

📌 Resources: "Convex Optimization" – Stephen Boyd


---

7. Information Theory (For Feature Engineering & Model Compression)

🔹 Entropy & Information Gain (Decision Trees)
🔹 Kullback-Leibler Divergence (Distribution Comparison)
🔹 Shannon’s Theorem (Data Compression)

📌 Resources: "Elements of Information Theory" – Cover & Thomas


---

8. Advanced Topics (For AI & Reinforcement Learning)

🔹 Fourier Transforms (Signal Processing, NLP)
🔹 Markov Decision Processes (MDPs) (Reinforcement Learning)
🔹 Bayesian Statistics & Probabilistic Graphical Models

📌 Resources: "Pattern Recognition and Machine Learning" – Bishop


---

Learning Path

🔰 Beginner:

Focus on Probability, Statistics, and Linear Algebra
Learn NumPy, Pandas, Matplotlib

Intermediate:

Study Calculus & Optimization
Apply concepts in ML (Scikit-learn, TensorFlow, PyTorch)

🚀 Advanced:

Explore Discrete Math, Information Theory, and AI models
Work on Deep Learning & Reinforcement Learning projects

💡 Tip: Solve problems on Kaggle, Leetcode, Project Euler and watch 3Blue1Brown, MIT OCW videos.

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Export WhatsApp stickers to Telegram on Android

From the Files app, scroll down to Internal storage, and tap on WhatsApp. Once you’re there, go to Media and then WhatsApp Stickers. Don’t be surprised if you find a large number of files in that folder—it holds your personal collection of stickers and every one you’ve ever received. Even the bad ones.Tap the three dots in the top right corner of your screen to Select all. If you want to trim the fat and grab only the best of the best, this is the perfect time to do so: choose the ones you want to export by long-pressing one file to activate selection mode, and then tapping on the rest. Once you’re done, hit the Share button (that “less than”-like symbol at the top of your screen). If you have a big collection—more than 500 stickers, for example—it’s possible that nothing will happen when you tap the Share button. Be patient—your phone’s just struggling with a heavy load.On the menu that pops from the bottom of the screen, choose Telegram, and then select the chat named Saved messages. This is a chat only you can see, and it will serve as your sticker bank. Unlike WhatsApp, Telegram doesn’t store your favorite stickers in a quick-access reservoir right beside the typing field, but you’ll be able to snatch them out of your Saved messages chat and forward them to any of your Telegram contacts. This also means you won’t have a quick way to save incoming stickers like you did on WhatsApp, so you’ll have to forward them from one chat to the other.

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