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Comment Tasktop (Score 1) 428

You may want to look into Tasktop. You can connect the task list to one or more task system back ends or just use local tasks. The advantage of Tasktop is that it can track context for each task. That way, when you want to return to a task that you haven't touched in two weeks, restoring the task in Tasktop can get you right back to the web pages, e-mails, etc. that you were accessing while working on the task last time. It also has integration with Eclipse if you do your development in Eclipse.

Comment The Knot Book by Colin Adams (Score 1) 630

I'd add Adams's The Knot Book to your list. I've been out of the field for some time, but I remember that this book gave an accessible introduction to knot theory and some notions of topology, presented at a high school level.

It's not exactly a new book, so some of the unsolved problems listed in the book may now be solved. In any case, it's one of the few I know that help a younger student go into more depth in an area where there's still active research going on. It's a difficult subject where many of the theorems can be proved without resorting to higher mathematics.

I'd imagine that there are probably similar texts for some areas of number theory and game theory, but nothing springs to mind. Non-Euclidean geometry may also be an option if the students have already taken geometry, and there were some text books that I found at least partially accessible in high school.

The Mathematical Tourist is even more out-of-date by this time. Since it's really a survey of many areas, it doesn't really meet your need, but you may find it useful yourself for looking into other areas that may be accessible to your students.

Finally, contact your local mathematics and math education departments. The math education folks may have some good suggestions. Many mathematics departments also do some sort of outreach to high school students, so there may also be some faculty there who could offer ideas.

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