Course Content

Matlab Basics

1. Basic Syntax and Coding with a Text Editor

Matlab's Place and Dark Mode The Command Window Installing a Text Editor and Its Packages Finishing Off the Text Editor Creating Snippets and Writing Programs

2. Coding Foundations

Messin with Matrices Importing and Exporting Data to and from Excel For Loops If Statements Modular Programming

3. Learning Through Applications

Application: Nuclear Plant Data Analysis Application: Medical Data Analysis Generating Combinations Application: Logistics Problem The Sortrows and Find Functions

4. Visualizations

Graphing Basics Automating Graph Creation Application: Calculating 3D Trajectories While Loops Application: Graphing 3D Trajectories and Multiple Plots System Function

5. Recursion and Matrix Multiplication

Recursive Programming Understanding Matrices and Matrix Multiplication Applying Matrix Multiplication: Transforming Vectors and Coordinate Systems Applying Matrix Multiplication: Solving Systems of Equations Applying Matrix Multiplication: Derivatives and Integrals Career Prospects for a MATLAB Programmer

Generating Combinations

Analyzing combinations comes up frequently in all sorts of analysis, and here you'll dive into generating three types of combinations in Matlab and complete the first module of our logistics data analysis (next chapter):

Unordered combinations with replacement;
Unordered combinations without replacement;
Ordered permutations.

Note

Matlab has many safety features built in to prevent it from ever harming your computer, but you can still run code that will take forever to finish! In these cases, instead of shutting Matlab down, you can simply hit:

Ctrl + C;
Cmd + C.

To stop code in progress.

Task

The number of ways of forming ordered permutations (with replacement) of $m$ elements from a larger set of $n$ elements is given by the formula: $n^m$ . That's $n$ choices for each element in the permutation, multiplied together $m$ times to get the total number of possibilities.

The average sentence contains between 15-20 words. Let's consider a 20-word sentence.

1. Derive the Permutations Formula

Assuming that the vocabulary size is $n$ , how many unique sentences can be formed?

2. Calculate the Number of Permutations

Take 3 different vocabulary sizes: 1000 words, 10000 words, 100000 words. For each of them, calculate how many unique sentences can be formed.

3. Compare to the Number of Atoms

Compare each of these numbers to the estimated number of atoms in the universe: $10^{80}$ .

In the formula, vocabulary size is represented by $n$ , while the number of words is $m$ .

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Section 3. Chapter 3

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