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Textbook: Mathematical Maturity via Discrete Mathematics. Here is the table of contents, here is an excerpt including front matter, first chapter, and end matter, here are the errata.

Navigation: main courses, side dishes, dessert, aged wine.


Additive Number/Group Theory (MSC Classification 20D60/20M14/11P99):

Squarefree Divisor Complexes of Certain Numerical Semigroup Elements (with J. Autry, P. Graves, J. Loucks, C. O'Neill, and S. Yih). Under review.

Elasticity in Apery Sets (with J. Autry, T. Gomes, C. O'Neill). To appear in American Mathematical Monthly.

Membership and Elasticity in Certain Affine Monoids (with J. Autry). To appear in Pi Mu Epsilon journal.

On Numerical Semigroups with Almost-Maximal Genus (with J. Arroyo, J. Autry, C. Crandall, J. Lefler). The PUMP Journal of Undergraduate Research (3) 2020, pp. 62-67.

Augmented Hilbert Series of Numerical Semigroups (with J. Glenn, C. O'Neill, and B. Sepanski). INTEGERS: The Electronic Journal of Number Theory (19) 2019, #A32.

Numerical Semigroups on Compound Sequences (with C. Kiers and C. O'Neill). Communications in Algebra 44 (9) 2016, pp. 3842-3852.

Arithmetic of Congruence Monoids (with A. Fujiwara, J. Gibson, M. Jenssen, D. Montealegre, and A. Tenzer). Communications in Algebra 44 (8) 2016, pp. 3407-3421.

On the Set of Catenary Degrees of Finitely Generated Cancellative Commutative Monoids (with C. O'Neill, R. Tate, and G. Webb). International Journal of Algebra and Computation 26 (3) 2016, pp. 565-576.

Arithmetic of Semigroup Semirings Ukrainian Mathematical Journal 67 (2) 2015, pp. 213-229.

Accepted Elasticity in Local Arithmetic Congruence Monoids (with L. Crawford, J. Steinberg, M. Williams). Results in Mathematics 66 (1) 2014, pp. 227-245.

Arithmetic-Progression-Weighted Subsequence Sums (with D. Grynkiewicz, A. Philipp). Israel Math Journal 193 (1) 2013, pp. 359-398.

Irreducible Factorization Lengths and the Elasticity Problem Within N (with M. Jenssen, D. Montealegre). American Mathematical Monthly 120 (4) 2013, pp. 322-328.

Two Semigroup Elements Can Commute With Any Positive Rational Probability (with N. Selinski). College Mathematics Journal 43 (4) 2012, pp. 334-336.

Diversity in Inside Factorial Monoids (with U. Krause, J. Maney). Czechoslovak Mathematics Journal 62 (3) 2012, pp. 811-827.

Diversity in Monoids (with J. Maney). Czechoslovak Mathematics Journal 62 (3) 2012, pp. 795-809.

The Multi-Dimensional Frobenius Problem (with J. Amos, I. Pascu, E. Trevino, Y. Zhang). Involve 4 (2) 2011, pp. 187-197.

On Image Sets of Integer-Valued Polynomials (with S. Chapman). Journal of Algebra (348) 2011, pp. 350-353.

Number Theory of Matrix Semigroups (with D. Adams, R. Ardila, N. Baeth, D. Hannasch, A. Kosh, H. McCarthy, R. Rosenbaum). Journal of Linear Algebra and its Applications (434) 2011, pp. 694-711.

Determining Integer-Valued Polynomials From Their Image Proceedings of the CIRM Meetings 2 (2) 2010, pp. 51-52.

Distinct Solution to a Linear Congruence (with D. Adams). Involve 3 (3) 2010, pp. 345-347.

Numerical Semigroups From Open Intervals (with R. Rosenbaum). Involve 3 (3) 2010, pp. 341-344.

Bifurcus Semigroups and Rings (with D. Adams, R. Ardila, D. Hannasch, A. Kosh, H. McCarthy, R. Rosenbaum). Involve 2 (3) 2009, pp. 351-356.

Invariant Polynomials and Minimal Zero Sequences (with B. Finklea, T. Moore, Z. Turner), Involve 1 (2) 2008, pp. 159-165. Also available are the associated big table (in Excel format), and software.

The Frobenius Number of Geometric Sequences (with D. Ong). INTEGERS: The Electronic Journal of Number Theory (8) 2008, #A33.

Robert Gilmer's Contributions to the Theory of Integer-Valued Polynomials (with S. Chapman, W. Smith) "Multiplicative Ideal Theory in Commutative Algebra", Springer, New York, 2006, pp. 109-122.

The Extraction Degree of Cale Monoids (with K. Cervello, D. Terry, L. Zhu), Semigroup Forum 72 (1) 2006, pp. 149-158.

The Catenary and Tame Degree in Finitely Generated Commutative Cancellative Monoids (with S. Chapman, P.A. Garcia-Sanchez, D. Llena, J.C. Rosales), Manuscripta Mathematica (120) 2006, pp. 253-264.

Minimal Zero Sequences of Finite Cyclic Groups Integers: The Electronic Journal of Combinatorial Number Theory (4) 2004, article A24.


Various Other Papers:

Applying Iterating Mapping to the No-Three-in-a-Line Problem (with C. Brower). Under review.

The Power Mean Test (with T. Kulhanek). to appear in PUMP.

Eigenvalues of the Sum and Product of Anticommuting Matrices (with L. Selstad) to appear in Involve.

A Cauchy-Schwarz Type Inequality for Differences (with R. Farhadian) to appear in American Mathematical Monthly.

Surprises in Knockout Tournaments (with T. Kulhanek). Mathematics Magazine 93 (3) 2020, pp. 193-199.

On the monotonicity of the number of positive entries in nonnegative four element matrix powers (with C. Brower). The PUMP Journal of Undergraduate Research (3) 2020, pp. 26-36.

On the Monoid of Monic Binary Quadratic Forms (with J. Dimabayao, O. Tigas). Miskolc Mathematical Notes 20 (2) 2019, pp. 863-871.

Primes in (0,n] vs. (n,m] (with F. Huppe). American Mathematical Monthly 126 (10) 2019, p.942.

Dilated Floor Functions that Commute Sometimes (with T. Kulhanek, J. McDonough). The PUMP Journal of Undergraduate Research (2) 2019, pp. 107-117.

Subsums of the Harmonic Series (with B. Lubeck). American Mathematical Monthly 125 (4) 2018, pp. 351-355.

Asymptotic Formula for (1+1/x)^x, Revisited American Mathematical Monthly 122 (6) 2015, p. 587.

Fibonacci Nim and a Full Characterization of Winning Moves (with C. Allen). Involve 7 (6) 2014, pp. 807-822.

Multivariate analysis of functional metagenomes (E. Dinsdale, R. Edwards, B. Bailey, I. Tuba, S. Akhter, K. McNair, R. Schmieder, N. Apkarian, M. Creek, E. Guan, M. Hernandez, C. Isaacs, C. Peterson, T. Regh, V. Ponomarenko). Frontiers in Statistical Genetics and Methodology 41 (4) 2013.

How to Play the One-Lie Renyi-Ulam Game (with R. Ellis, C. Yan). Discrete Mathematics 308 (2008), pp. 5805-5808.

Characterizing Pseudodendrimers. I. Graph Representations of Pseudodendrimers Formed by Enhancements to Propagation of Linear Units (with D. Johnson, J. Wang). Macromolecular Theory and Simulations 18 (8) 2007, pp. 727-731.

Geometry of Jump Systems (with V. Lyubashevsky, C. Newell), Rocky Mountain Journal of Mathematics, Volume 35 (5) 2005, pp. 1675-1688.

The Renyi-Ulam Pathological Liar Game with a Fixed Number of Lies (with R. Ellis and C. Yan), Journal of Combinatorial Theory, Series A, Volume 112 (2) November 2005, pp. 238-336.

The Convergence of Difference Boxes (with A. Behn, C. Kribs Zaleta) American Mathematical Monthly 112 (5) May 2005, pp. 426-439.

Jump Systems and Laminated Manhattan Sets (with J. Cuomo, N. Nwasokwa) Australasian Journal of Combinatorics (31) February 2005, pp. 135-144.

Faa di Bruno's Formula and Nonhyperbolic Fixed Points of One-Dimensional Maps (corrected) International Journal of Mathematics and Mathematical Sciences (29) 2004, pp. 1543-1549.

Reduction of Jump Systems Houston Journal of Mathematics 30 (1) 2004, pp. 27-33.

DRILL (Depository of Repetitive Internet-based probLems and Lessons) Journal of Online Mathematics and Applications (3) 2003.

Stability of Hyperbolic and Non Hyperbolic Fixed Points of One-Dimensional Maps (with F. Dannan, S. Elaydi) Journal of Difference Equations and Applications 9 (5) 2003, pp. 449-457.

Mimeomatroids Ars Combinatoria (66) 2003, pp. 103-107.


Pseudo-mathematical pieces:

The United States of America Prime under review

The Mathematical Association fo America Prime American Mathematical Monthly 127 (7) 202, p. 672.

Proof Techniques for the New Millennium American Mathematical Monthly 127 (5) 2020, p. 443.

Count to Six in Six Languages (with M. Kutzman) American Mathematical Monthly 126 (8) 2019, p.747.

The Color of Pi MAA FOCUS 39 (5) 2019, p. 6.

Solution to the Hardest Jumbles (with B. LeTourneau) American Mathematical Monthly 126 (5) 2019, p. 479.

The Hardest Jumbles (with B. LeTourneau) American Mathematical Monthly 126 (5) 2019, p. 436.

Help with the Jumble American Mathematical Monthly 126 (1) 2019, p. 77.

A Base Conversion Surprise American Mathematical Monthly 122 (5) 2015, pp. 366, 402.

Anagrams of "American Mathematical Monthly" American Mathematical Monthly 121 (3) 2014, p. 243.

Most Active Mathematical Fields, in the American Mathematical Monthly (with R. Devitt-Ryder) American Mathematical Monthly 121 (2) 2014, p. 166.

Most Active Mathematical Fields (with R. Devitt-Ryder) American Mathematical Monthly 121 (2) 2014, p. 119.

Growth Rate of Calculus Textbooks American Mathematical Monthly 120 (9) 2013, p.786.

Famous American Mathematical Monthly Authors American Mathematical Monthly 120 (5) 2013, p. 408.

The Music of Pi American Mathematical Monthly 119 (8) 2012, p. 711. (associated sound file)


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