Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

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1. Basic Mathematical Concepts and Definitions

Let's start with some basic definitions and concepts we'll use later. Consider the idea of a function, a numerical sequence, and its sum, and also understand what a coordinate system's basis is.

What is a Function?

What are Number Series?

Sum of Elements of The Series

Challenge: Calculating Sum of Geometric Progression

Vectors and Matrices

2. Linear Algebra

The simplest and most commonly used type of relationship is the linear relationship. Linear algebra is a branch of higher mathematics entirely devoted to linear functions and linear spaces. Let's look at some of the most important topics in linear algebra: vectors, matrices, solving linear equations, and solving the spectral problem for matrices.

Numerical Operations on Vectors and Matrices

Challenge: Calculate the Matrix Multiplication Result

Matrix Determinant

Scaling Factor of the Linear Transformation

Challenge: Figures' Linear Transformations

Inversed and Transposed Matrices

System of Linear Equations

Challenge: Solving the Task Using SLE

Eigenvalues and Eigenvectors

3. Mathematical Analysis

Mathematical analysis is a discipline that allows you to analyze functions according to various criteria. Consider how to check numerical sequences for convergence, find the maximum/minimum values of functions, solve nonlinear equations, and use integrals to solve applied problems.

Derivative of the Function

Partial Derivative of the Function

Challenge: Solving Task Using Derivative

Optimization Problem

Challenge: Solving the Optimisation Problem

Gradient Descent Method

Challenge: Optimising Function Of Multiple Variables

Contenido del Curso

Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

Challenge: Figures' Linear Transformations

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Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

Rotation transformation rotates a figure around a specific point or axis.
Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
Apply the rotation_matrix to the square.
Apply the scaling_matrix to the result of the previous transformation.

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¿Todo estuvo claro?

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Sección 2. Capítulo 5

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Challenge: Figures' Linear Transformations

Tarea

Swipe to show code editor

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

Rotation transformation rotates a figure around a specific point or axis.
Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
Apply the rotation_matrix to the square.
Apply the scaling_matrix to the result of the previous transformation.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

¡Gracias por tus comentarios!

Sección 2. Capítulo 5

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

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