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.
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.
🚀 Fun Facts About Data Science 🚀
1️⃣ Data Science is Everywhere - From Netflix recommendations to fraud detection in banking, data science powers everyday decisions.
2️⃣ 80% of a Data Scientist's Job is Data Cleaning - The real magic happens before the analysis. Messy data = messy results!
3️⃣ Python is the Most Popular Language - Loved for its simplicity and versatility, Python is the go-to for data analysis, machine learning, and automation.
4️⃣ Data Visualization Tells a Story - A well-designed chart or dashboard can reveal insights faster than thousands of rows in a spreadsheet.
5️⃣ AI is Making Data Science More Powerful - Machine learning models are now helping businesses predict trends, automate processes, and improve decision-making.
Stay curious and keep exploring the fascinating world of data science! 🌐📊
#DataScience #Python #AI #MachineLearning #DataVisualization
1️⃣ Data Science is Everywhere - From Netflix recommendations to fraud detection in banking, data science powers everyday decisions.
2️⃣ 80% of a Data Scientist's Job is Data Cleaning - The real magic happens before the analysis. Messy data = messy results!
3️⃣ Python is the Most Popular Language - Loved for its simplicity and versatility, Python is the go-to for data analysis, machine learning, and automation.
4️⃣ Data Visualization Tells a Story - A well-designed chart or dashboard can reveal insights faster than thousands of rows in a spreadsheet.
5️⃣ AI is Making Data Science More Powerful - Machine learning models are now helping businesses predict trends, automate processes, and improve decision-making.
Stay curious and keep exploring the fascinating world of data science! 🌐📊
#DataScience #Python #AI #MachineLearning #DataVisualization