How to prepare for studying Mathematics

You have finished high school, have been admitted to study Mathematics at Jacobs University, and wonder what you can do over the summer to smooth your start into university mathematics. Here are a few suggestions for things you can do to bridge the long gap between your high school exam and the start of the university semester.

Revise

Have a second look at everything you did at high school
Can you reliably manipulate algebraic expressions?
Can you find at least two independent explanations for every concept? E.g., one that is geometric/graphical, one that is algebraic/formal?
Can you prove the main mathematical theorems you know? What are the assumptions, what other results does the argument depend on? You high-school text books may or may not do a good job in this department - start to look beyond!

Read

Build perspective by reading up on mathematics and mathematicians
Visit your local library, or the library of your local university
This reading list maintained by the University of Cambridge has some excellent suggestions
Another good reading list by the NRICH project

Work problems

Working problems is the most important skill and pastime of a mathematician
The NRICH project has a collection of beautiful mini-projects - try the pure as well as the applied mathematics collection, both cover important aspects of the mind-set and skill-set of a mathematician.

Further links

Preparing for your Maths Degree (IMA)
How To Study Math (Paul Dawkins)
Tips for Success in Undergraduate Math Courses (Jessica Purcell)