Mathematica For Beginners: The Basics

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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’

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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’

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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…

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