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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.

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  • $\begingroup$ Spivak's Comprehensive Introduction to Differential Geometry series contains sections that examine and explain some of the original papers in differential geometry. $\endgroup$ – littleO Apr 18 '16 at 11:49
  • $\begingroup$ Edwards' Riemann's Zeta Function comes to mind. It is an exposition with the explicit aim of allowing the modern reader to understand Riemann's paper "On the Number of Primes Less Than a Given Magnitude" and related primary sources. It includes a translation of Riemann's paper. $\endgroup$ – Bungo Apr 21 '16 at 1:34
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    $\begingroup$ Another pair of books that might be of interest are Theory of Complex Functions and Classical Topics in Complex Function Theory, both by Reinhold Remmert. These books are a rigorous treatment of complex analysis. They have a modern viewpoint but also provide considerable historical context, including extensive quotes from original sources (especially German sources). $\endgroup$ – Bungo Apr 21 '16 at 1:39
  • $\begingroup$ Robin Hartshorne's Euclid and Beyond guides the reader through Euclid's Elements from a modern viewpoint, noting the various subtle gaps and how they were later resolved (Hilbert's axioms, etc.). It then introduces the reader to non-Euclidean geometry. A copy of Euclid is not included, but Hartshorne assumes you are reading it alongside his book, and he refers to it extensively. $\endgroup$ – Bungo Apr 21 '16 at 1:46
  • $\begingroup$ Useful to know - I am grateful. Many thanks. $\endgroup$ – user328032 Apr 21 '16 at 2:22
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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!

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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.

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