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Mathematics for Data Analysis and Modeling
course content

Course Content

Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

1. Basic Mathematical Concepts and Definitions
What is a Function?What are Number Series?Sum of Elements of The SeriesChallenge: Calculating Sum of Geometric ProgressionVectors and Matrices
2. Linear Algebra
Numerical Operations on Vectors and MatricesChallenge: Calculate the Matrix Multiplication ResultMatrix DeterminantScaling Factor of the Linear TransformationChallenge: Figures' Linear TransformationsInversed and Transposed MatricesSystem of Linear EquationsChallenge: Solving the Task Using SLEEigenvalues and Eigenvectors
3. Mathematical Analysis
Derivative of the FunctionPartial Derivative of the FunctionChallenge: Solving Task Using DerivativeOptimization ProblemChallenge: Solving the Optimisation ProblemGradient Descent MethodChallenge: Optimising Function Of Multiple Variables

bookChallenge: 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.

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

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

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Section 1. Chapter 4
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bookChallenge: 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.

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

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

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 1. Chapter 4
toggle bottom row

bookChallenge: 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.

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

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

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

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.

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

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

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 1. Chapter 4
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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