Learning Plan: Data Science Mathematics

Structured Learning Plan for Data Science Mathematics

This 12-week learning plan breaks down each topic into digestible weekly goals with recommended exercises and applications in data science.

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Week 1: Fundamentals of Linear Algebra

📌 Topics
- Introduction to Vectors and Matrices
- Matrix Operations: Addition, Multiplication, Transpose
- Identity, Inverse, and Special Matrices

📚 Resources
- Gilbert Strang’s Linear Algebra and Its Applications
- Khan Academy: Linear Algebra Fundamentals

📝 Exercises
- Solve basic matrix operations and vector manipulations
- Compute determinants and inverses manually and using NumPy

🔍 Applications in Data Science
- Representing datasets as matrices
- Feature scaling and transformations

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Week 2: Advanced Linear Algebra for Data Science

📌 Topics
- Eigenvalues and Eigenvectors
- Singular Value Decomposition (SVD)
- Principal Component Analysis (PCA)

📚 Resources
- Deep Learning by Ian Goodfellow (Chapter on Linear Algebra)
- 3Blue1Brown’s Essence of Linear Algebra series

📝 Exercises
- Compute eigenvalues and eigenvectors using Python
- Perform PCA on a dataset using sklearn.decomposition.PCA

🔍 Applications in Data Science
- Dimensionality reduction in high-dimensional datasets
- Image compression using SVD

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Week 3: Differential Calculus

📌 Topics
- Limits and Continuity
- Derivatives and Partial Derivatives
- Chain Rule and Gradient Calculation

📚 Resources
- Calculus by James Stewart
- MIT OpenCourseWare: Single Variable Calculus
- 3Blue1Brown’s The essence of calculus series

📝 Exercises
- Manually compute derivatives of polynomial and exponential functions
- Implement gradient computation in Python

🔍 Applications in Data Science
- Compute loss function gradients in machine learning

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Week 4: Integral & Vector Calculus

📌 Topics
- Definite & Indefinite Integrals
- Gradient, Hessian, and Jacobian Matrices
- Applications in Probability

📚 Resources
- Mathematics for Machine Learning by Deisenroth et al.

📝 Exercises
- Compute multiple integrals manually and with Python (sympy.integrate())

🔍 Applications in Data Science
- Computing expectations in probability distributions

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Week 5: Probability Theory

📌 Topics
- Basics of Probability
- Bayes’ Theorem & Conditional Probability
- Discrete & Continuous Distributions

📚 Resources
- Probability and Statistics for Engineering and the Sciences by Jay Devore
- Khan Academy: Probability & Statistics

📝 Exercises
- Solve probability problems manually
- Simulate probability distributions using NumPy

🔍 Applications in Data Science
- Naïve Bayes classifier for text classification

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Week 6: Statistics & Inference

📌 Topics
- Descriptive Statistics
- Hypothesis Testing (T-tests, Chi-Square)
- Maximum Likelihood Estimation

📚 Resources
- The Elements of Statistical Learning by Hastie, Tibshirani, Friedman
- Think Stats by Allen B. Downey

📝 Exercises
- Perform hypothesis testing using scipy.stats
- Compute confidence intervals on sample datasets

🔍 Applications in Data Science
- Feature selection and A/B testing

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Week 7: Optimization Techniques

📌 Topics
- Gradient Descent & Variants (SGD, Adam, RMSprop)
- Lagrange Multipliers
- Convex vs. Non-Convex Optimization

📚 Resources
- Convex Optimization by Boyd & Vandenberghe

📝 Exercises
- Implement gradient descent from scratch in Python
- Optimize logistic regression parameters using gradient descent

🔍 Applications in Data Science
- Training machine learning models efficiently

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Week 8: Numerical Methods

📌 Topics
- Newton’s Method
- Matrix Factorization (LU, QR)
- Iterative Methods (Jacobi, Gauss-Seidel)

📚 Resources
- Numerical Methods for Scientists and Engineers by R.W. Hamming

📝 Exercises
- Solve non-linear equations using Newton’s method in Python

🔍 Applications in Data Science
- Efficient computations in large-scale datasets

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Week 9: Information Theory & Entropy

📌 Topics
- Entropy and Mutual Information
- KL Divergence & Cross-Entropy
- Shannon’s Theorem

📚 Resources
- Information Theory, Inference, and Learning Algorithms by David MacKay

📝 Exercises
- Compute entropy of a dataset using Python

🔍 Applications in Data Science
- Feature selection in decision trees

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Week 10: Graph Theory

📌 Topics
- Graph Representations & Adjacency Matrices
- Graph Traversal (DFS, BFS)
- PageRank Algorithm

📚 Resources
- Networks, Crowds, and Markets by Easley & Kleinberg

📝 Exercises
- Implement DFS and BFS in Python
- Compute PageRank on a sample graph

🔍 Applications in Data Science
- Knowledge graph creation and analysis

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Week 11: Time Series Analysis

📌 Topics
- Stationarity & Differencing
- Autoregressive Models (AR, MA, ARIMA)
- Fourier Transforms

📚 Resources
- Time Series Analysis and Its Applications by Shumway & Stoffer

📝 Exercises
- Implement ARIMA models using statsmodels

🔍 Applications in Data Science
- Financial and economic forecasting

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Week 12: Final Project & Consolidation

🎯 Objective: Apply all learned concepts in a capstone project

📝 Project Ideas
- Build a predictive model using PCA + Regression
- Implement an ML model and optimize it using gradient descent
- Perform statistical hypothesis testing on a real-world dataset

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