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

Conteúdo do Curso

Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

Challenge: Figures' Linear Transformations

Tarefa

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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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Seção 2. Capítulo 5

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Challenge: Figures' Linear Transformations

Tarefa

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.

Mude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo

Tudo estava claro?

Obrigado pelo seu feedback!

Seção 2. Capítulo 5

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