Mathematic books with historical and original view

Question

I am looking for books along the lines of history of mathematics but I have some conditions;

• History must not be the main aim of the book, the main aim of using historical context should be teaching mathematics somewhat topdown.

• For the part it teaches, it should teach it for real. It should include rigirous proofs and discussion.

• By original view I meant, using original papers and publications where these ideas are first considered.

I know some good books along these lines like Journey through Genius. Or I know some books that are more on history and that are not about teaching mathematics. I am more into complete and coherent marriage of this two approaches while also incorporates rigor and original sources.

Answer 1

A general book that includes exercises to do is 'Mathematics And It's History', Stilwell, J.

For analysis 'Analysis By It's History', Hairer, E.& Wanner, G. Both of these are published by Springer. This book includes copies of work out of Newton's oeuvre among others.

For geometry try 'Geometry By It's History', Ostermann, A. & Wanner, G. - another Springer book.

I haven't had a look at the last but the first two are proving (no pun intended) very useful and include exercises. So I expect this one does as well. The first book has excellent reviews and is very useful indeed. All 3 are aimed at undergraduates.

Finally, typing 'history of mathematics' into this website's search box will bring up a boatload of suggestions.

Great entertainment for time traveler's!

Answer 2

A History of Mathematics by Uta Merzbach, and Carl Boyer or The History of Mathematics: An Introduction by David Burton are both excellent books. Both might be historically focused if you are looking for something strictly mathematical. However both are written with the upper level undergraduate Math student in mind. Both provide some original proofs and have practice problems included at the end of each chapter. The problems emphasis the Mathematics highlighted in the chapter asking students to grapple with the problems that the mathematicians dealt with in the chapter.

I am not exactly sure if that is what you are looking for. I am an undergraduate Mathematics and History major, and I was able to enjoy both books from a mathematical perspective.