This repository is dedicated to providing resources, tutorials, and examples on key mathematical and statistical concepts used in data analysis. Whether you're new to the field or looking to refresh your knowledge, this repository covers essential topics that are crucial for any data professional.
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Introduction
- Overview of Mathematics and Statistics in Data Analysis
- Importance of Mathematical Foundations
- Prerequisites
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Basic Mathematics for Data Analysis
- Arithmetic and Algebra
- Functions and Graphs
- Calculus Basics (Differentiation and Integration)
- Linear Algebra (Vectors, Matrices, and Operations)
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Descriptive Statistics
- Measures of Central Tendency (Mean, Median, Mode)
- Measures of Dispersion (Variance, Standard Deviation, Range, IQR)
- Data Distributions (Normal Distribution, Skewness, Kurtosis)
- Data Visualization Techniques (Histograms, Box Plots, Scatter Plots)
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Probability Theory
- Basic Probability Concepts (Events, Sample Space, Probability Axioms)
- Conditional Probability and Bayes' Theorem
- Probability Distributions (Discrete and Continuous)
- Common Distributions (Binomial, Poisson, Normal, Exponential)
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Inferential Statistics
- Hypothesis Testing (Null and Alternative Hypotheses, p-values)
- Confidence Intervals
- t-tests, Chi-square tests, and ANOVA
- Regression Analysis (Linear and Logistic Regression)
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Statistical Modeling
- Model Assumptions and Diagnostics
- Overfitting and Underfitting
- Model Selection Techniques (AIC, BIC, Cross-Validation)
- Advanced Topics (Time Series Analysis, Bayesian Statistics)
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Mathematical Optimization
- Introduction to Optimization
- Linear Programming
- Gradient Descent and its Variants
- Applications in Machine Learning
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Practical Applications
- Case Studies in Data Analysis
- Real-world Data Sets
- Python Code Examples (Using libraries such as NumPy, Pandas, SciPy, and Statsmodels)
- Data Analysis Projects
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Resources
- Recommended Books and Papers
- Online Courses and Tutorials
- Useful Python Libraries for Mathematics and Statistics