- Calculus and analysis 27
- Linear algebra and matrices 20
- Probability and distributions 28
- Statistical inference 47
- Time series and stochastic 16
All 138 notes, A to Z
- Algebraic Functions and Projective Curves in Python8 min
Algebraic functions and projective curves are fundamental concepts in algebraic geometry, linking algebra and geometry. They provide powerful tools for...
- Algebraic Topology Using Python6 min
Algebraic topology is a branch of mathematics that uses algebraic structures to study topological spaces. It provides powerful tools for analyzing the shape...
- Calculus Fundamentals for Python16 min
The concept of limits forms the foundation for analyzing continuous financial processes. In quantitative finance, limits help evaluate how financial...
- Calculus III Concepts and Theorems in Python13 min
Vector functions map scalar inputs to vector outputs, often used to represent curves in three-dimensional space. These functions are crucial in understanding...
- Complex Analysis Functions of a Complex Variable11 min
Complex analysis, also known as function theory, is a branch of mathematics that studies complex-valued functions of a complex variable. It extends the...
- Differential Analysis on Complex Manifolds with Python9 min
Differential analysis on complex manifolds is a branch of mathematics that combines complex analysis, differential geometry, and topology. It studies the...
- Distribution Theory and Functional Analysis Using Python7 min
Distribution theory, developed by Laurent Schwartz, extends the notion of functions to generalized functions or distributions. This theory provides a...
- Euler's Identity and Fourier Transform in Python6 min
Euler's Identity is a mathematical equation that connects five fundamental constants in a single, elegant expression. It's often considered one of the most...
- Exploring General Topology with Python7 min
General Topology is a branch of mathematics that deals with the study of spaces and their properties. In Python, we can represent topological spaces using...
- Exploring Graph Theory Concepts with Python7 min
Graph Theory is a branch of mathematics that studies the relationships between objects. It has numerous applications in computer science, networking, and...
- Exploring Modern Fourier Analysis with Python7 min
Modern Fourier Analysis is a powerful mathematical technique used to decompose complex signals into simpler, periodic components. It has applications in...
- Exploring Moduli Spaces of Algebraic Curves with Python7 min
Moduli of curves is a fundamental concept in algebraic geometry, dealing with the classification of algebraic curves. This field explores the space of all...
- Generative Modeling on Data Manifolds17 min
The mathematical foundation of Riemannian Flow Matching requires understanding differential geometry concepts. We'll implement basic geometric operations and...
- Hyperbolic Manifolds using Python9 min
Hyperbolic geometry is a non-Euclidean geometry that challenges our intuition about parallel lines and the nature of space. In hyperbolic space, the sum of...
- Information Theory and Density Analysis in Python6 min
Information theory is a mathematical framework for quantifying, storing, and communicating information. It was developed by Claude Shannon in 1948 and has...
- Introduction to Calculus I in Python7 min
Introduction to Calculus I This slide will provide an overview of Calculus I and its applications in Python.
- Introduction to Calculus II in Python8 min
Calculus II is a continuation of Calculus I, covering more advanced topics such as techniques of integration, infinite sequences and series, parametric...
- Introduction to Calculus III in Python7 min
Introduction to Calculus III in Python Calculus III deals with multivariable calculus, including partial derivatives, multiple integrals, and vector...
- Introduction to Fourier Transforms in Python6 min
The Fourier transform is a powerful mathematical tool that decomposes a signal into its constituent frequencies. It is widely used in various fields...
- Jacobian Matrix Slideshow with Python Examples9 min
A Jacobian matrix is a fundamental concept in multivariable calculus and linear algebra. It represents the best linear approximation of a differentiable...
- Numerical Methods Optimization and Mathematical Modeling in Python8 min
Numerical methods are techniques used to approximate solutions to mathematical problems using numerical approximations and iterative methods. These methods...
- Optimizing on the Stiefel Manifold8 min
The Stiefel manifold St(n,p) consists of n×p orthonormal matrices, forming a crucial space for optimization problems where orthogonality constraints must be...
- Raincloud Plots Revealing Hidden Data Distributions18 min
Traditional visualization methods like histograms and box plots can mask important patterns in data distributions. Box plots may show identical statistics...
- Smooth Manifolds and Observables in Python13 min
Smooth manifolds are fundamental objects in differential geometry, generalizing the concept of curves and surfaces to higher dimensions. They provide a...
- Third-Order Derivative Tensors in AI and ML11 min
Third-order derivative tensors play a crucial role in advanced machine learning and artificial intelligence algorithms. These mathematical structures extend...
- Topological Vector Spaces Using Python7 min
Topological vector spaces are a fundamental concept in functional analysis, combining linear algebra with topology. They provide a framework for studying...
- Weakly Differentiable Functions using Python11 min
Weakly differentiable functions are a generalization of differentiable functions in the context of functional analysis and partial differential equations....
- Advanced Linear Algebra for Data Science9 min
Advanced linear algebra forms the backbone of many sophisticated algorithms in data science and machine learning. It enables us to manipulate...
- Elementary Linear Algebra with Applications using Python6 min
Vectors are fundamental objects in linear algebra and can represent various quantities in mathematics, physics, and computer science. In Python, vectors can...
- Intuition for Eigenvalues and Eigenvectors13 min
Linear transformations represent mappings between vector spaces that preserve vector addition and scalar multiplication. In machine learning, understanding...