Mathematics for Data Analysis and Modeling

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

Challenge: Calculating Sum of Geometric Progression

In the previous chapter, we discovered a formula to calculate the sum of elements of an arithmetic progression. There is also a formula for the sum of a geometric progression:

Let's discover the following real-life case: consider a scenario where a population of bacteria doubles every hour. The initial population is 100 bacteria. We might want to calculate the total population after a certain number of hours. This scenario can be modeled as a geometric progression, where each term represents the population at a specific hour, and the common ratio r is 2 (since the population doubles each hour).

Task

Calculate the sum of first n elements of geometric progression using both for loop and the formula described above.

Specify the arguments of the formula.
Specify parameters of for loop.

_{Once you've completed this task, click the button below the code to check your solution.}

Everything was clear?

Section 1. Chapter 4

Course Content

Mathematics for Data Analysis and Modeling

Challenge: Calculating Sum of Geometric Progression

In the previous chapter, we discovered a formula to calculate the sum of elements of an arithmetic progression. There is also a formula for the sum of a geometric progression:

Task

Calculate the sum of first n elements of geometric progression using both for loop and the formula described above.

Specify the arguments of the formula.
Specify parameters of for loop.

_{Once you've completed this task, click the button below the code to check your solution.}

Everything was clear?

Section 1. Chapter 4