Getting Started with Mathematica

This guide gives a stream-lined, but fairly extensive introduction to Mathematica. It primarily covers Mathematica 5.0, although references to earlier versions are included in cases where significant changes have been made.

Each of the Guide's 28 Chapters has been structured around an area of undergraduate mathematics (e.g., one-variable differential Calculus, multiple integration, differential equations, linear algebra). Each chapter defines relevant commands used in that area, addresses their syntax, and provides basic examples. Each chapter ends with one or more sections which include more technical examples, offer useful tips, and diagnose common problems that users are likely to encounter. Two appendices are also included that explain how to work in the Mathematica notebook environment and use certain input features.

This book is written at a freshman/sophomore level, and includes enough basics to be useful for a Calc I through Calc 3 student, Linear Algebra student, and Intro Statistics student. Some of the 3D plots are truly beautiful, such as the hyperboloid in one sheet. These authors have a full grasp of parameterization, which is necessary for some plots (e.g., the hyperboloid in one sheet).

So--a great intro, with more content than other intro Mathematica books.


Getting Started with Mathematics   September 2, 2007
Peano (Trentham, Vic, Australia)
An excellent small book to work with when trying to learn how to use Mathematica. I found it very easy to follow and I particularly liked the progression from easy topics to more advanced topics. The examples that are used to demonstrate the Mathematica approach have been well chosen. It is so easy to play around with these examples to really see what is going on. I am very pleased that the graphics functions are interspersed with the other commands. This really helps to see what is going on, as well, it also acts as appropriate repetition for learning the Mathematica syntax. Not only that, the mathematics being used as a context for the examples simply comes alive as well. So I felt that I was getting more from this book than just how to use Mathematica. One small point that may be of use. Mathematica version 6 has changed a number of the commands, particularly for graphics. Although it is still possible to complete the examples it is necessary to do a bit of detective work first. But that just helps with the learning, so not a big deal.


A must for mathematica beginners!   February 3, 2000
7 out of 7 found this review helpful

This book helped me a lot getting started with mathematica . It gives easy examples in all basic math areas. The examples can easily be reproduced and modified for personal use. The only critique is that there is no disk included...everything needs to be punched in.


Good, and small enough to hold comfortably, too.   December 31, 2007
C. Bailey (Maryland United States)
I like and recommend this general introduction to Mathematica (MMA) and am almost halfway through. Getting Started with Mathematica is much smaller than The Mathematica Book, or Mathematica Navigator, or the 4 volume Mathematica GuideBook series, and is the only general Mathematica book I've found that's small enough to hold comfortably.

Clearly, they made some choices to keep the book small. For example, MMA has a bewildering wealth of ways to type expressions in the graphically complicated mathematical notation you'd see on a blackboard, with Greek letters, subscripts and superscripts, fractions many layers high, and symbols that aren't on the keyboard. Other than brief mention of palettes where you can click on some characters, they let all of this go, along with the several MMA ways of representing them from the keyboard. For this level of detail you need one of the 5 pound books.

To be very picky, here are some things I didn't like.

There are different ways of packaging information in this book. For example, there's a Useful Tips section near the end of every chapter. The tip saying that natural logs are written "Log[]" rather than "Ln[]" rates 3 stars, and the more useful tip not to use spaces to show multiplication only ranked 1 star.

Then there are Troubleshooting Q&A sections, after the Tips. Why are some things offered in the body of the chapter, some as tips, and some in question-and-answer form? This scatters things unnecessarily. For example, Mathematica's built-in names always start with a capital letter, so it's a good idea for users to start the names they define with a lowercase letter. But in the "Rules for Names" section, they don't mention this, and in fact offer "Perimeter" and "Batman" as "examples of legitimate names that you could use". Starting with lowercase only turns up 4 pages later as a Useful Tip.

"Immediate assignment" and "delayed assignment" are explained in a Troubleshooting Q&A section. "The difference between them is about when the expression on the right side of the assignment gets evaluated. Our rules of thumb are: use immediate assignment '=' when you give a name to an expression or result. Use delayed assignment ':=' when you define a function." I gather that immediate assignment evaluates the thing being assigned once, when the line is processed, while delayed assignment evaluates it afresh every time the assignee is evaluated. Their "rules of thumb" just obscure this.

Things are sometimes introduced out of order. For example, we learn to assign Solve's answer to a rootfinding problem to "ans", and then isolate each of the two roots as "ans[[1]]" and "ans[[2]]", which is new unexplained notation. Two pages later, a Useful Tip says that the purpose of [[ double square brackets ]] notation is to "Specify by position". Only in the next chapter do we learn about lists (MMA's form of vectors, arrays, and the like) and find that double brackets are notation for indexing into them.

Now for some things I did like.

One example of a Troubleshooting Q&A that works well as a troubleshooting question: you're told in Mathematica class to "Clear All" to erase previous assignments, so you type "Clear All", and MMA answers "All Clear". You think MMA is confirming it cleared everything, but it actually assumed "Clear" and "All" were unresolveable arguments to a multiplication, and just echoed that multiplication, but with the arguments alphabetized. Another example that works well describes the confusion that results when you request a function that lives in a separate package before loading the package, and how to recover from this error.

The chapter on "Making Graphs" introduces many plotting functions and many options for them. It's impressive how clearly they did this. Several examples of why you'd want to do things, and the code showing how you do them, and the resulting graphs, are on each page. Seventeen nice examples build in complexity and subtlety.

"Part 3", about "Mathematica for One-Variable Calculus", starts with a chapter on "Limits and Derivatives", where I am now reading. Beginning with a run through a tidy development of derivatives is wise. They explain just enough about calculus to help rusty readers keep up, but really are mostly explaining how MMA treats it. They balance this difficult feat very successfully.

Finally, the book's sturdy and well printed and has a pretty good index, importantly including the Mathematica symbols that are punctuation marks. There's also a good appendix explaining working with Notebooks (MMA's live document user interface metaphore).



needs revision   August 9, 2007
Frank J. Carter (Hood River, OR USA)
5 out of 5 found this review helpful

This book covers version 3 of Mathematica and version 6 is the current release. This author has written some good Mathematica books, this book is just not that relevant anymore.