Here is a practical comment for the typical economics graduate student: Buy this book if you want to start using Mathematica!What does a typical economics graduate student need? First, s/he needs to review her/his knowledge of mathematics. Second, s/he needs to learn how to use the tool (math) to solve an economic problem. Cliff J. Huang and Philip S. Crooke's book is helpful in both respects. While they are introducing the basic language of Mathematica they review most of the undergraduate math. And they teach with a hands-on approach--that is, you solve almost every problem using Mathematica.
Mathematica is a great tool for economics graduate students, it helps you out in understanding the basic intuitions behind mathematical concepts--because you do not have to solve complex problems (Mathematica solves them for you), you just have to understand them. Of course, students are advised to consult their professors to choose the right computer software or programming language. Mathematica can do a lot, but some other software might be much more practical for your PhD thesis project...
[Also consider Differential Equations: An Introduction with Mathematica by Clay C. Ross]
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