PiHard: Mathematics in Python ℼ( ◡̀_◡́)ᕤ

This repo houses code for implementing various mathematical concepts in Python.

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Statistics (ง'̀-'́)ง

• ✅ classical_statistics.ipynb - Exploring Classical Statistics with Practical Python Implementation

Application	Topic	Status
Location	Confidence Limits for the Mean	✅
Location	One sample t-Test	✅
Location	Two sample t-Test for Equal Means	✅
Location	One-Way ANOVA test	✅
Scale or variability or spread	Bartlett Test	✅
Scale or variability or spread	Levene Test	✅
Skewness and Kurtosis	Skewness and Kurtosis	✅
Distributional Measures	Quantile-Quantile Plot	✅
Distributional Measures	Shapiro-Wilk test	✅
Distributional Measures	D’Agostino’s K^2 Test	✅
Distributional Measures	Anderson Darling Test	✅
Distributional Measures	Chi-Squared Goodness of Fit Test	✅
Distributional Measures	Kolmogorov-Smirnov Test	✅
Outlier Detection	Isolation Forest	✅
Outlier Detection	Grubbs Test	✅
Outlier Detection	Box plot and scatter plot	✅
Outlier Detection	Z-Score	✅
Outlier Detection	IQR Score	✅
Outlier Detection	Generalized Extreme Deviate Test	✅
Outlier Detection	Distance-based outlier detection	✅
Outlier Detection	Outlier detection based on polynomial fit	✅
Feature Selection	Univariate Selection	✅
Feature Selection	Recursive Feature Elimination	✅
Feature Selection	Principal Component Analysis	✅
Feature Selection	Linear Discriminant Analysis	✅
Feature Selection	Feature Importance	✅

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Linear Algrebra (ง'̀-'́)ง

• ✅ vector_operations_and_norms - Finding the $L_p$ norm of a vector

Topic	Status
Quick intro to Vectors	✅
Element-wise vector operations	✅
Scalar broadcasting in Vector operations	✅
Dot, Cross, Scalar Triple and Vector Triple Products	✅
$L_0$, $L_1$, $L_2$, $L_\infty$ and $L_p$ norms	✅

• ✅ activation_functions_in_ML.ipynb - Exploring Activation Functions in Machine Learning

Topic	Status
Sigmoid Function	✅
tanh Function	✅
Rectified Linear Unit (ReLU) Function	✅
Leaky Rectified Linear Unit (LeakyReLU) Function	✅
Parametric Rectified Linear Unit (PReLU) Function	✅
Exponential Linear Unit (ELU) Function	✅
Scaled Exponential Linear Unit (SELU) Function	✅
Swish Function	✅
Gaussian Error Linear Unit (GELU) Function	✅
Softmax Function	✅
Gated Linear Unit (GLU) Function	✅
ReGLU (ReLU + GLU) Function	✅
GeGLU (GELU + GLU) Function	✅
SwiGLU (Swish + GLU) Function	✅

• ✅ linear_algebra_study_notes.ipynb - For Quick Revision

Topic	Status
Basics of Vector and real coordinate spaces	✅
Addition and subtraction of vectors	✅
Parameterizing lines in any dimensions	✅
Linear combination of vectors and span	✅
Linear dependence and independence	✅
Linear subspaces and basis	✅
Dot product of vectors	✅
Cauchy-Schwarz and Vector Triangle Inequality	✅
Angle between two vectors and orthogonal vectors	✅
Cross product of vectors	✅
Vector projections	✅
Reduced Row Echelon Form (RREF)	✅
System of Linear Equations	✅
Matrix Multiplication, Null Space and Column Space	✅

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Physics (ง'̀-'́)ง

• ✅ fast_fourier_transform.ipynb - Performing Fourier Transform in O(nlogn) Time Complexity

Topic	Status
Quick intro to Fourier Transform	✅
Fourier Transform using Discrete Fourier Transform (DFT) vs Fast Fourier Transform (FFT)	███░░
Implementing Fast Fourier Transform	✅

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Natural Language Processing (ง'̀-'́)ง

• ✅ similarity_search.ipynb - A Collection of Similarity Search Algorithms

Topic	Status
Jaccard Similarity	✅
W-shingling	✅
Levenshtein distance	✅
TF-IDF	✅
Best Matching 25 (BM25)	✅
FAISS (IndexFlatL2)	✅
FAISS (IndexFlatL2 with IndexIVFFlat)	✅
FAISS (IndexFlatL2 with IndexIVFPQ)	✅
FAISS (IndexFlatIP)	✅
FAISS (IndexLSH)	✅
FAISS (IndexHNSWFlat)	✅

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Calculus (ง'̀-'́)ง

• ✅ calculus_study_notes.ipynb - For Quick Revision

Topic	Status
Limit	✅
Squeeze Theorem	✅

Quantum Computing (ง'̀-'́)ง

• ✅ complex_numbers.ipynb - Complex Numbers in Python

Topic	Status
Introduction	✅
Addition	✅
Subtraction	✅
Multiplication	✅
Division	✅
Polar Representation	✅