Try to follow the book's lead in experimenting with the basic problem laid out in the appendix section you choose. Don't just follow to the letter the instructions but see how you can try to expand on the theme or support it in some way and go beyond a bit if you can think of a way to do that.
Doing mathematics is more than just following instructions. It is a way of thinking about quantitative problems that suggests more than just the immediate solution of a specific problem. Out in life, if you have a job that really uses your mathematical background, you will have to be your own guide to learning and using mathematical ideas in getting things done. Having a mentor is very valuable, but one has to know how to interact with the mentor in doing new activities. If there is little input from above, you have to struggle with your foundations to make some headway.