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Number Theory: In Context and Interactive

Karl-Dieter Crisman

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
 66 
www.richardevanschwartz.com/monsters.html
)
Note.
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
 67 
www.maa.org/publications/ebooks/visual-group-theory
)
Note.
Visualize group theory; gorgeous pictures.
[3]
John H. Conway and Richard Guy, The Book of Numbers, Springer, (1996). (Website
 68 
www.springer.com/us/book/9780387979939
)
Note.
A joyous and pictorially engaging romp.
[4]
Arthur T. Benjamin and Ezra Brown (eds.), Biscuits of Number Theory, Mathematical Association of America, (2009). (Website
 69 
www.maa.org/press/books/biscuits-of-number-theory
)
Note.
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
 70 
bookstore.ams.org/sstp-3/
)
Note.
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
 71 
bookstore.ams.org/sstp-2
)
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
 72 
jhupbooks.press.jhu.edu/content/how-guard-art-gallery-and-other-discrete-mathematical-adventures
)
Note.
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
 73 
www.maa.org/publications/books/excursions-in-calculus
)
Note.
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
 74 
www.authorhouse.com/BookStore/BookDetails/703856-Prime-Mystery
)
Note.
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
 75 
www.cambridge.org/core/books/mathematical-explorations/F926A2DFE3FEC8B34542EC598C8D7DE3
)
Note.
Part of the AIMS
 76 
aims.ac.za
Library Series, this book includes plenty of fun, directed, proto-research on topics like families of Pythagorean triples and the conductor. Explore!
[11]
Apostolos Doxiadis, Uncle Petros and Goldbach’s Conjecture, Bloomsbury, (2000) (Website
 77 
apostolosdoxiadis.com/book/uncle-petros-and-goldbachs-conjecture/
)
Note.
This ‘novel of mathematical obsession’ is a Bildungsroman of sorts that does a surprisingly good job of also introducing the still-unproven conjecture that any even number greater than four is the sum of two odd primes.
[12]
Riley Tipton Perry, Quantum Computing from the Ground Up, World Scientific, (2012) (Website
 78 
www.worldscientific.com/worldscibooks/10.1142/8515
)
Note.
The best elementary introduction to quantum computing I’ve yet found. That doesn’t make it easy, but it could certainly be used with undergraduates with a modicum of linear algebra and familiarity with complex numbers (and circuitry!). Yes, Shor’s algorithm and QFT is outlined at this level, rather remarkably.
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