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References E.6 Other References

Some books are just interesting, even if they are not primarily about number theory. I enjoyed all of these a great deal and recommend them.

[1]
  
Richard Evans Schwartz, You Can Count on Monsters, A K Peters, (2010) (Website)
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This delightful picture book has a different monster for each prime number, with bizarre combinations for composites. Personal experience says it satisfies for ages three and up.

[2]
  
Nathan Carter, Visual Group Theory, Mathematical Association of America, (2009). (Website)
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Visualize group theory; gorgeous pictures.

[3]
  
John H. Conway and Richard Guy, The Book of Numbers, Springer, (1996). (Website)
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A joyous and pictorially engaging romp.

[4]
  
Arthur T. Benjamin and Ezra Brown (eds.), Biscuits of Number Theory, Mathematical Association of America, (2009). (Website)
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A very good compendium of many articles (published throughout the years) most appropriate for teachers of undergraduate number theory.

[5]
  
Kerins et al., Famous Functions in Number Theory, American Mathematical Society, (2015). (Website)
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Aimed at bringing number theory to in-practice or pre-practice educators, this has a very nice treatment of arithmetic functions. Once you've heard of summation and Moebius inversion as ‘parent’ and ‘child’ relationships, you'll never think of them the same again.

[6]
  
Kerins et al., Applications of Algebra and Geometry to the Work of Teaching, American Mathematical Society, (2015). (Website)
Note

Aimed at bringing algebra and geometry to in-practice or pre-practice educators; manages to bring Gaussian and Eisenstein integers and some quadratic forms in at the ground level.

[7]
  
T. S. Michael, How to Guard an Art Gallery, Johns Hopkins, (2009) (Website)
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The subtitle is “and other discrete mathematical adventures”, and that about says it. Covers a surprising amount of number theory in very visual ways.

[8]
  
Robert Young, Excursions in Calculus: An Interplay of the Continuous and Discrete, Mathematical Association of America, (1992) (Website)
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Unfortunately no longer in print, but a very good source of ideas for connecting what we usually think of as the continuous world of calculus and various discrete topics (not just number theory, though this shows up in several chapters).

[9]
  
Dora Musielak, Prime Mystery: The Life and Mathematics of Sophie Germain, AuthorHouse, (2015) (Website)
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The title says it all, and probably the most comprehensive resource on this intriguing mathematician out there. As is typical for a samizdat, it could use more editing and probably speculates a bit much, but given how little we know about Germain still impressive.

[10]
  
Alan Beardon, Mathematical Exploration, Cambridge, (2016) (Website)
Note

Part of the AIMS Library Series, this book includes plenty of fun, directed, proto-research on topics like families of Pythagorean triples and the conductor. Explore!