**Refereed Research Papers**

[43] *Residual smallness in commutative algebra* (with Adam Salminen), Communications in Algebra, 16 pages (to appear)

[42] *Residually small commutative rings* (with Adam Salminen), Journal of Commutative Algebra, 25 pages (to appear)

[41] *Elementarily lambda-homogeneous binary functions*, Algebra Universalis **78** (2017), no. 2, 147-157.

[40] *Factorization theory of root closed monoids of small rank* (with Jim Coykendall), Communications in Algebra **45** (2017), no. 7, 2795-2808.

[39] *Polynomial and power series rings with finite quotients* (with Adam Salminen), Houston Journal of Mathematics **43** (2017), no. 1, 31-38.

[38]* Turning automatic continuity around: automatic homomorphisms* (with Ryan Berndt), Real Analysis Exchange **41** (2016), no. 2, 271-286.

[37] *Divisible multiplicative groups of fields*, Journal of Algebra **453** (2016), 177-188.[36]

[35]

[34]

[33]

[32]

[31]

[30]

[29]

[28]

[27]

[26]

[25]

[24]

[23]

[22]

[21]

[20]

[19]

[18]

[17]

[16]

[15]

[14]

**Refereed Survey Papers**

[13] *Unifying some notions of infinity in ZC and ZF*, Reports on Mathematical Logic** 51** (2016), 43-56.

[12] *Jonsson and HS modules over commutative rings*, International Journal of Mathematics and Mathematical Sciences (2014), 120907, 13 pp.

**Miscellaneous Refereed Publications**

[11] *A short proof of the Bolzano-Weierstrass Theorem* (with Katrina Biele), College Mathematics Journal **48** (2017), no. 4, 288-289.

[10] *A radical excursion: from irrational roots to Prufer domains and back* (with Ben Griffith), Pi Mu Epsilon Journal, **14** (2016), no. 5, 327-332.

[9] *Game show shenanigans: Monty Hall meets mathematical logic *(with Greg Morrow and Adam Salminen), Elemente der Mathematik **71** (2016), no. 4, 145-155.

[8] *I'm thinking of a number... *(with Adam Hammett), Missouri Journal of Mathematical Sciences **28** (2016), no. 1, 31-48.

[7] *A characterization of the cyclic groups by subgroup indices *(with Victoria Slattum), College Mathematics Journal **47** (2016), no. 1, 29-33.

[6] *The converse of the Intermediate Value Theorem: from Conway to Cantor to cosets and beyond*, Missouri Journal of Mathematical Sciences **26** (2014), no. 2, 134-150.

[5] *Groups whose subgroups have distinct cardinalities*, Pi Mu Epsilon Journal **14** (2014), no. 1, 31-37.

[4] *Group permutations which preserve subgroups* (with Veronica Marth), Pi Mu Epsilon Journal **13** (2012), no. 7, 407-414.

[3] *The number of homomorphic images of an abelian group*, International Journal of Algebra **5** (2011), no. 3, 107-115.

[2] *An independent axiom system for the real numbers*, College Mathematics Journal **40** (2009), no. 2,78-86.

**Book Chapter**

[1] *Jonsson modules over commutative rings*, Chapter 1 of "Commutative Rings: New Research", Nova Science Publishers, New York (2009), 1-6. (invited chapter)

**Problems Posed**

[46] *Problem #???* (with Logan Robinson), College Mathematics Journal (to appear)

[45] *Problem #???* (with Adam Salminen), American Mathematical Monthly (to appear)

[44] *Problem #???*, College Mathematics Journal (to appear)

[43] *Problem #1106*, College Mathematics Journal **48** (2017), no. 4, p. 292

[42] *Problem #2019*, Mathematics Magazine **90** (2017), no. 2, p. 145.

[41] *Problem #353* (with Adam Hammett), Math Horizons **23** (2017), no. 3, p. 30.

[40] *Problem #1104*, College Mathematics Journal **48** (2017), no. 3, p. 220.

[39] *Problem #1103*, College Mathematics Journal **48** (2017), no. 3, p. 220.

[38] *Problem #1332*, Pi Mu Epsilon Journal, Spring 2017, p. 3.

[37] *Problem #1331*, Pi Mu Epsilon Journal, Spring 2017, p. 2.

[36] *Problem #1096* (with Adam Salminen), College Mathematics Journal **48** (2017), no. 2, p. 138.

[35] *Problem #1095 *(with Keith Kearnes), College Mathematics Journal **48** (2017), no. 1, p. 59.

[34] *Problem #1093*, College Mathematics Journal **48** (2017), no. 1, p. 58.* *

[33] *Problem #2009*, Mathematics Magazine **89** (2016), no. 5, p. 379.

[32] *Problem #11943* (with Keith Kearnes), American Mathematical Monthly **123** (2016), no. 10, p. 1050.

[31] *Problem #1078*, College Mathematics Journal **43** (2016), no. 3, pp. 221-222.

[30] *Problem #1998*, Mathematics Magazine **89** (2016), no. 3, pp. 223-224.

[29] *Problem #11887 *(with Luke Harmon), American Mathematical Monthly **123** (2016), no. 2, p. 197.

[28] *Problem #1067*, College Mathematics Journal **47** (2016), no. 1, p. 61.

[27] *Problem #1054*, College Mathematics Journal **46** (2015), no. 3, p. 221.

[26] *Problem #326* (with Alan Loper), Math Horizons **23** (2015), no. 1, p. 30.

[25] *Problem #318*, Math Horizons **22** (2015), no. 3, p. 30.

[24] *Problem #11813*, American Mathematical Monthly **122** (2015), no. 1, p. 76.

[23] *Problem #11750*, American Mathematical Monthly **121** (2014), no. 1, p. 83.

[22] *Problem #1934*, Mathematics Magazine **86** (2013), no. 5, p. 382.

[21] *Problem #1011*, College Mathematics Journal **44** (2013), no. 5, p. 437.

[20] *Problem #1006*, College Mathematics Journal **44** (2013), no. 4, p. 325.

[19] *Problem #11702*, American Mathematical Monthly **120** (2013), no. 4, p. 365.

[18] *Problem #11658*, American Mathematical Monthly **119** (2012), no. 7, p. 608.

[17] *Problem #985*, College Mathematics Journal **43** (2012), no. 4, p. 338.

[16] *Problem #1900*, Mathematics Magazine **85** (2012), no. 3, p. 229.

[15] *Problem #977*, College Mathematics Journal **43** (2012), no. 3, p. 257.

[14] *Problem #968*, College Mathematics Journal **43** (2012), no. 1, p. 95.

[13] *Problem #11617*, American Mathematical Monthly **119** (2012), no. 1, p. 68.

[12] *Problem #946*, College Mathematics Journal **42** (2011), no. 2, p. 151.

[11] *Problem #940*, College Mathematics Journal **41** (2010), no. 5, p. 410.

[10] *Problem #1211*, Pi Mu Epsilon Journal, Fall 2009, p. 560.

[9] *Problem #11451*, American Mathematical Monthly **116** (2009), no. 7, p. 648.

[8] *Problem #1825 *(with Kevin Schoenecker), Mathematics Magazine **82** (2009), no. 3, p. 228.

[7] *Problem #892*, College Mathematics Journal **40** (2009), no. 1, p. 55.

[6] *Problem #1810*, Mathematics Magazine **81** (2008), no. 5, p. 376.

[5]* Problem #871*, College Mathematics Journal **39** (2008), no. 2, p. 153.

[4] *Problem #11284*, American Mathematical Monthly **114** (2007), no. 4, p. 358.

[3] *Problem #203*, Math Horizons, **14** (2006), no. 1, p. 40.

[2] *Problem #820*, College Mathematics Journal **37** (2006), no. 1, p. 60.

[1] *Problem #11166*, American Mathematical Monthly **112** (2005), no. 7, p. 654.

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719-255-8227 (UCCS), 800-990-8227