Mathematica For Beginners: The Basics
This tutorial explains how to manipulate the basic objects underlying the Mathematica (and the Wolfram Language), by using many examples. We explain how to achieve many tasks by coding in Mathematica:
How to make lists, tables and arrays in mathematica. How to plot lists, generate random numbers. How to make and manipulate matrices. How to apply functions in Mathematica iteratively,
using riffle shuffling of cards as an example. How to define functions in mathematica, How to do number theory, and we illustrate these methods by generating a network related to the Collatz Conjecture (the 3n+1 Problem).
Way to perform many of the most fundamental operations in Mathematica are also discussed:
How to form if statements, while loops and how to deal with local variables. How to manipulate strings. How expressions can be transformed to strings, and vice versa. These ideas are illustrated by making complex rewrite system with a couple of lines of code.
(See `Mining the Space of Rewrite Systems'
• Mining the Space of Rewrite Systems
for a more detailed discussion of how complex patterns can be generated by simple string rewrite systems).
This tutorial can be considered to be a more in depth sequel to
`Mathematica For Beginners'
• Mathematica For Beginners
This tutorial makes for an excellent introduction to functional programming. There is particular focus on explaining:
How to use lists.
How to do a screen capture.
How to use tables.
How to apply functions to a list.
How to define variables and control output in mathematica.
How to find the size of a list.
How to use nest list.
How to do a while loop.
How to use mathematica to manipulate vectors, matrices and linear algebra.
How to perform set theoretic operations such as union, intersection, and determination of subsets.
How to join lists.
How to take or drop elements from the beginning of a list.
How to do array plots.
How to form 'if' statements, with inequalities to test inputs.
How to use the modulo function.
How to make networks/graphs by forming an adjacency matrix, using the array command.
How to plot graphs in different ways, like in 3D.
How to determine the positions of different entries within a list.
How to flatten lists by deleting internal parenthesis. How to select entries which satisfy a given criterion, and how to sort lists by a given condition.
How to use modules to define variables locally. The difference between local and global variables is also explained.
How to create and manipulate string in mathematica.
How to do joining, and replacement operations on strings.
How to cut up strings according to the occurrence of particular patterns.
How to get a list of the characters in a string.
More information can be found at my website
https://sites.google.com/site/richard...
The hyperbolic platonic solids shown in the thumbnail were generated using code from the Wolfram Demonstration: `Hyperbolization of a Dodecahedron' by Michael Trott
http://demonstrations.wolfram.com/Hyp...
Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page
/ richardsouthwell
Any support would really help me produce more videos and software.
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