Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics)

It has many good ideas on developing the skills of understanding and using proofs (something that always needs to be worked on) and seems to be one of the unique approaches to this subject. I find no fault in the method and I am working through the book to see if I can glean some of the wisdom from it.

Until I came across this book, I did not believe there existed a decent book to teach proofs that one can use for SELF-STUDY.The stated aim of this book is to introduce the idea of proofs and analysis on subject matter that is not too difficult. In the ~230 pages one gets introduced to proofs in a total variety of contexts - algebra and geometry and number theory and complex numbers. About 20% of the proofs require calculus -but not at an advanced level.A number of proofs are demonstrated in these different contexts in a way that one can follow and understand.It would be great to take a class based upon this book where the instructor follows the author's suggestion of assigning problems to teams and they present to the class.The author also makes the statement that at the high school level, instead of one year geometry and one year algebra it should be 2 years of a combined class. I think this is a real good idea; the two subjects are articifically separated. This is also the idea of "Numbers and Geometry" by John Stillwell - which I am currently reading and will review in a couple months.I think this is an excellent book for a good solid introduction to real non-trivial mathematical proofs, but where one is at the same time not really struggling with advanced concepts like one would in a standard analysis class. There are some good digressions with some mathematical history as well; such as the Chinese really had Pascal's triangle centuries before Blasie Pascal. I really recommend it for someone who is looking for a self-study guide AND with Dover you know the price is right!

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The book has a very interesting approach to a wide range of topics in maths. Uses lots of anecdotes and historical facts to motivate the reader. I haven't really sat down to the exercises, but I love the stories and pointers.. sure shall get at the sources mentioned, sometime.