From Introduction to Programming with Mathematica, Third Edition

Mathematica is a very large and seemingly complex system. It contains hundreds of functions for performing various tasks in science, mathematics, and engineering, including computing, programming, data analysis, knowledge representation, and visualization of information. In this introductory chapter, we introduce the elementary operations in Mathematica and give a sense of its computational and programming breadth and depth. In addition, we give some basic information that users of Mathematica need to know, such as how to start Mathematica, how to get out of it, how to enter simple inputs and get answers, and finally how to use Mathematica's documentation to get answers to questions about the system.

1.1 A brief overview of Mathematica

Numerical computations

Mathematica has been aptly described as a sophisticated calculator. With it you can enter mathematical expressions and compute their values.

You can store values in memory.

    <i class="emphasis">In[2]:=</i> <b class="bold">rent = 350</b>    <i class="emphasis">Out[2]=</i> 350    <i class="emphasis">In[3]:=</i> <b class="bold">food =175</b>    <i class="emphasis">Out[3]=</i> 175    <i class="emphasis">In[4]:=</i> <b class="bold">heat = 83</b>    <i class="emphasis">Out[4]=</i> 83<a name="26"></a><a name="page2"></a>    <i class="emphasis">In[5]:=</i> <b class="bold">rent + food + heat</b>    <i class="emphasis">Out[5]=</i> 608

Yet Mathematica differs from calculators and simple computer programs in its ability to calculate exact results and to compute to an arbitrary degree of precision.

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Topics of Interest

Expressions are the basic building blocks from which everything is built. Their structure, internal representation, and how they are evaluated are essential to understanding Mathematica. In this...

The use of rules to transform expressions from one form to another is one of the most powerful and useful tools available in the Mathematica programming language. The thousands of rules built in to...

Programming in Mathematica is essentially a matter of writing user-defined functions that work like mathematical functions; when applied to specific values, they perform computations producing...

4.2 Functions for manipulating expressions Three of the most powerful and commonly used functions by experienced Mathematica programmers are Map, Apply, and Thread. They provide very sophisticated...

4.5 Auxiliary functions There are several major drawbacks to the deal function created in the previous section. In order to use deal, the definition of removeRand and the value of cardDeck must be...