The seminar is based on Richard Guy's book *Unsolved Problems in Number Theory*.

Each student chooses an unsolved problem (usually from Guy's book) and investigates it for the semester, culminating in a final paper and presentation.

Here is a paper describing the seminar: (pdf) published in Primus, http://www.tandfonline.com/doi/full/10.1080/10511970.2013.837566#.VAz_wk2YbIU

Volume 24, Issue 2, February 2014, pages 95-103.

*Some class resources:*

*List of student topics from the number theory seminars*- Some Villanova Seminar Seminar Syllabi

*SyllabusStyer*

SyllabusNorton

SyllabusKnecht

SyllabusFreyVolpert

SyllabusDeanin (for the graduate seminar but very similar to her undergrad seminar syllabus) *Homework Assignments (docx file)**Peer Review Sheet**Stylistic Advice handout**Maple worksheet to introduce primes (Maple, pdf)**Synopsis of Euler's argument for an infinitude of primes**Heuristic Arguments for Mersenne and Fermat primes (Maple, pdf)**Final Paper Grading Rubric*

*Some articles students published from
the senior seminars:*

*William Berrigan, The Mathematical Modeling
behind Duchenne's Muscular Dystrophy, published in Vol 2, Issue 2 (2012)
Rose-Hulman
Undergraduate Mathematics Journal*

*Daniel Lyons, *
Smallest N
beginning a sequence of 14 and 15 consecutive happy numbers, published in
Involve: a journal of mathematics
Vol 6 (2013), no. 4, 461-466. (more
info)

Stephanie Perez and Robert Styer, Persistence: A Digit Problem. Involve: a journal of mathematics Vol 8, Issue 3 (2015), pp. 439-446. (more info)

Brent Johnson, An Introduction to the Birch and Swinnerton-Dyer Conjecture,
published in Vol 16, # 1 (2015)
Rose-Hulman Undergraduate Mathematics Journal (not written during the
seminar but for an independent study following up on his seminar topic)

Colin Lubner and Robert Styer, Multiplicative Persistence of nonzero fixed point digits. Submitted to Involve: a journal of mathematics 2017. (more info)

Styer home page 02/21/2017