EDUCATION
B.A. (Mathematics), Rutgers University, May 1989
M.A. (Mathematics), The Pennsylvania State University, August 1994
Additional Graduate Study (22 credits in Statistics), Texas A&M University and University of Kentucky, 1994-1999
Ph.D. (Mathematics), University of Kentucky, May 2002

FULL-TIME ACADEMIC APPOINTMENTS
1995           Lecturer of Mathematics, Sam Houston State University, Huntsville, TX
1996-1997 Instructor of Mathematics and Statistics, Lexington Community College, Lexington, KY
2000-2002 Instructor of Mathematics, Pennsylvania State University, University Park, PA
2002-2003 Visiting Assistant Professor of Mathematics, Pennsylvania State University, University Park, PA
2003-2006 Hill Assistant Professor of Mathematics, Rutgers University, New Brunswick, NJ
2006-2007 Assistant Professor of Mathematics, Rutgers University, New Brunswick, NJ
2007-2011 Tenure-Track Assistant Professor of Mathematics, Georgia Southern University, Statesboro, GA
2011-present, Associate Professor of Mathematics (tenured August 1, 2012), Georgia Southern University, Statesboro, GA

RESEARCH INTERESTS
Number theory, combinatorics, classical analysis, symbolic computation, mathematics of Ramanujan.

DOCTORAL DISSERTATION
Computer Assisted Explorations of Rogers-Ramanujan Type Identities

Ph.D. THESIS ADVISOR
George E. Andrews, Evan Pugh Professor of Mathematics, The Pennsylvania State University

POSTDOCTORAL ADVISORS
2002-2003: George E. Andrews, Evan Pugh Professor of Mathematics, The Pennsylvania State University.
2003-2007: Doron Zeilberger, Board of Governors Professor of Mathematics, Rutgers University.

REFEREED PUBLICATIONS

1. (with J. P. O. Santos) "q-Pell sequences and two identities of V. A. Lebesgue," Discrete Mathematics 257/1 (2002) 125-142.
2. "Finite Rogers-Ramanujan type identities," Electronic J. Combin. 10(1) (2003) #R13, 122 pp.
3. (with J. Sellers and G. Mullen) "Bijections and congruences for generalizations of partition identities of Euler and Guy," Electronic J. Combin. 11(1) (2004) #R43, 19 pp.
4. "RRtools---a Maple package for aiding the discovery and proof of finite Rogers-Ramanujan type identities," J. Symbolic Comput., 37 (2004) 415-448.
5. "A combinatorial proof of a partition identity of Andrews and Stanley," Int. J. Math. Math. Sci 2004/47, 2495-2503.
6. "On identities of the Rogers-Ramanujan type," Ramanujan J. 11 (2006) 403-429.
7. "On series expansions of Capparelli's infinite product," Adv. Appl. Math. 33/2 (2004) 397-408.
8. "Identitites of the Rogers-Ramanujan-Bailey type," J. Math. Anal. Appl. 308/2 (2005) 669-688.
9. "q-Difference equations and identities of the Rogers-Ramanujan-Bailey type," J. Difference Equ. Appl. 10 (2004) 1069-1084.
10. (with D. Zeilberger) "Disturbing the Dyson conjecture (in a GOOD way)," Experimental Math. 16:2 (2006) 187-191.
11. "On simplifications of certain q-multisums," Adv. Appl. Math. 39/2 (2007) 260-268.
12. "Disturbing the Dyson conjecture, in a generally GOOD way," J. Combin. Theory, Ser. A 113/7 (2006) 1368-1380.
13. "Identities of the Rogers-Ramanujan-Slater type," Int. J. Number Theory 3 (2007) 293-323.
14. "A partition bijection related to the Rogers-Selberg identities and Gordon's theorem," J. Combin. Theory, Ser. A 115/1 (2008) 67-83.
15. (with D. Bowman and J. McLaughlin) "Some more identities of Rogers-Ramanujan type," Ramanujan J. 18 (2009) 307-325.
16. "Disturbing the q-Dyson conjecture," Tapas in Experimental Mathematics, ed. Tewodros Amdeberhan and Victor H. Moll, Contemp. Math. 457 (2008) 265-271.
17. (with J. McLaughlin) "Ramanujan-Slater type identities related to the moduli 18 and 24," J. Math. Anal. Appl. 344/2 (2008) 765-777.
18. "On the ordinary and signed Göllnitz-Gordon partitions," South East Asian J. Math. Math. Sci 6 (2008) 63-68.
19. (with J. McLaughlin) "Combinatorics of Ramanujan-Slater type identities," Integers 9 (supplement) (2009) paper #10, 14 pp.
20. (with J. McLaughlin and P. Zimmer) "Lifting Bailey pairs to WP-Bailey pairs," Discrete Math. 309 (2009) 5077-5091.
21. (with J. McLaughlin and P. Zimmer) "Rogers-Ramanujan computer searches," J. Symbolic Comput. 44 (2009) 1068-1078.
22. (with J. McLaughlin and P. Zimmer) "Rogers-Ramanujan-Slater type identities," Electronic J. Combin. 15 (2008) #DS15, 59 pp.
23. "A Rademacher type formula for partitions and overpartitions," Int. J. Math. Math. Sci. 2010 (2010) Article ID 630458, 21 pp. doi:10.1155/2010/630458.
24. "The Apostles and brothers of Jesus," in The Tomb of Jesus and His Family?: Exploring Ancient Jewish Tombs Near Jerusalem's Walls, ed. James H. Charlesworth and Arthur Boulet, Eerdmans press, 2013.
25. (with S. Corteel and C. Savage) "Lecture hall sequences, q-series, and asymmetric partition identities," Partitions, q-Series, and Modular Forms, ed. K. Alladi and F. Garvan, Springer, 2012, 53-68. Developments in Mathematics, Vol. 23. ISBN 978-1-4614-0027-1.
26. "Towards an automation of the circle method," Gems in Experimental Mathematics, ed. T. Amdeberhan, L. Medina, and V. H. Moll, Contemp. Math. 517 (2010) 325-338.
27. "Rademacher-type formulas for restricted partition and overpartition functions," Ramanujan J. 23 (2010) 253-264.
28. (with J. McLaughlin and P. Zimmer) "Some implications of Chu's ₁₀ψ₁₀ generalization of Bailey's ₆ψ₆ summation formula," Online Journal of Analytic Combinatorics 5 (2010), 24 pp.
29. (with C. D. Savage) "On an identity of Gessel and Stanton and the new little Göllnitz identities," Adv. Appl. Math. 46 (2011) 563-575.
30. (with J. McLaughlin) "On a pair of identities from Ramanujan's lost notebook," Ann. Combin., 16 (2012) 581-607.
31. (with J. McLaughlin) "Polynomial generalizations of two-variable Ramanujan type identities," Electronic J. Combin. 18(2) (2011) #P15, 10 pp.
32. (with D. Eichhorn and J. McLaughlin) "Hybrid proofs of the q-binomial theorem and other identities," Electronic J. Combin. 18(1) (2011) #P60, 21 pp.
33. "Compositions, partitions, and Fibonacci numbers," The Fibonacci Quarterly 40 (2011) 348-354.
34. (with H. Wang) "On the maximal Wiener index and related questions," Discrete Appl. Math. 160 (2012) 1615-1623.
35. (with D. Zeilberger) "Formulæ for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)," Advances in Applied Mathematics, 48 (2012) 640-645.
36. (with D. Zeilberger) "Rademacher's infinite partial fraction conjecture is (almost certainly) false," Journal of Difference Equations and Applications 19 (2013) 680-689.
37. (with H. Wang) "The minimal number of subtrees of a tree," Graphs and Combinatorics 31 (2015) 255-264.
38. (with L. Lindroos and H. Wang) "Odd fibbinary numbers and the golden ratio," Fibonacci Quarterly 52 (2014) 61-65.
39. (with Y. Choliy) "A formula for the partition fucntion that 'counts'," Ann. Combin., to appear.
40. (with S. Kanade, J. Lepowsky, and M. C. Russell) "Ghost series and a movtivated proof of the Andrews-Bressoud identities," submitted.

• Editor, Selected Works of George E. Andrews, Imperial College Press, a division of World Scientific, 2013.
• Guest Editor, Ramanujan Journal 13 (2013) 1-238, Special issue in honor of Mourad Ismail and Dennis Stanton; Proceedings of q-Series 2011: an International Conference on q-Series, Partitions, and Special Functions, held at Georgia Southern University, Statesboro, GA, March 14-16, 2011

• A. Sills, Grant for Professional Travel, Georgia Southern University Faculty Development, Spring 2008
• A. Sills, PI; S. B. Damelin, Co-PI: "q-Series: 2011: an International Conference on q-series, Partitions, and Special Functions," National Science Foundation Grant DMS 1100964, February 1, 2011-January 31, 2013.
• A. Sills, "Supplemental funding for q-Series: 2011: an International Conference on q-series, Partitions, and Special Functions," Georgia Southern Department Foundation Grant, October 2010.
• A. Sills, "Computer Assisted Research in Additive and Combinatorial Number Theory and Allied Areas," National Security Agency Standard Research Grant H98230-14-1-0159, 2014-2015.

1. "Computer Algebra and Rogers-Ramanujan Type Identities," Special session in Special Functions and q-series, AMS/MAA Joint Meetings (no. 983), Baltimore, MD, January 16, 2003.
2. "A Combinatorial Proof of a Partition Identity of Andrews and Stanley," Special session in q-series, AMS sectional meeting (no. 984), Baton Rouge, LA, March 15, 2003.
3. "Rogers-Ramanujan-Bailey Type Identities," Conference on Additive Number Theory, University of Florida, Gainesville, November 17, 2004.
4. "Rogers-Ramanujan-Slater Type Identities," Maine-Québec Number Number Theory Conference, University of Maine, Orono, ME, October 1, 2005. (30 minutes)
5. "Multiparameter Bailey Pairs and Rogers-Ramanujan-Slater Type Identities," Special session on Theory of Infinite Dimensional Lie Algebras, Vertex Operator Algebras, and Related Topics, AMS Sectional Meeting (no. 1009), Annandale-on-Hudson, NY, October 9, 2005.
6. "A Partition Bijection Related to the Rogers-Selberg Identities," Maine-Québec Number Number Theory Conference, Université Laval, Québec City, Canada, October 1, 2006.
7. "Disturbing the Dyson Conjecture (in a GOOD Way)," Special Session on Experimental Mathematics, AMS/MAA Joint Meetings (no. 1023), New Orleans, LA, January 5, 2007.
8. "Identities of the Ramanujan-Slater type," Integers Conference 2007, University of West Georgia, Carrollton, GA, October 26, 2007.
9. "A Partition Bijection Relating the Rogers-Selberg Identities to a Special Case of Gordon's Theorem," Conference on Partitions, q-Series and Modular Forms, University of Florida, Gainesville, March 12, 2008
10. "Computer Algebra and Rademacher Type Partition Formulas," Combinatory Analysis 2008: A Conference in Honor of George Andrews' 70th Birthday, Pennsylvania State University, State College, PA, December 5, 2008.
11. "Computer Algebra and Rademacher Type Partition Formulas," PANTS IX (Palmetto Number Theory Series), Clemson University, February 8, 2009. (30 minutes)
12. "A new look at some partition theorems of Göllnitz," Conference on Quadratic Forms, Sums of Squares, Theta Functions and Integral Lattices, University of Florida, March 14, 2009.
13. "A new look at the partition identities of Göllnitz," Special Session on Applications of Algebraic and Geometric Combinatorics, AMS Southeast Sectional Meeting (no. 1048), Raleigh, NC, April 4, 2009.
14. "Rademacher's Infinite Partial Fractions Conjecture is (Almost Certainly) False," Rademacher 125 Conference, University of Florida, Gainesville, November 5, 2012.
15. "Rademacher's Infinite Partial Fractions Conjecture is (Almost Certainly) False," AMS Special Session on the influence of Ramanujan at his 125th birthday, AMS-MAA Joint Meetings in San Diego, CA, January 10, 2013.
16. "A Formula for the Partition Function that 'Counts'," Special Session on Partitions, q-series, and Modular Forms, AMS-MAA Joint Meetings in San Antonio, TX, January 10, 2015.

• "Rogers-Ramanujan Toolkit for Maple," East Coast Computer Algebra Day, Queens, NY, May 18, 2002.
• "On the Rogers-Selberg Identities and Gordon's Theorem," Southeast Regional Meeting On Numbers, University of North Carolina at Greensboro, April 18, 2009.
• "Identities of the Ramanujun-Slater Type," SERMON 2010, Davidson College, Davidson, NC, April 17, 2010.
• "All I Really Need To Know, I Learned From Dr. Z," Conference in Honor of Doron Zeilberger's 60th Birthday, Rutgers University, Piscataway, NJ, May 28, 2010.

• "The RRtools Maple package," Special Functions in the Digital Age, IMA Workshop, Minneapolis, MN, July 29, 2002.

• "An Algorithmic Approach to Rogers-Ramanujan Type Identities," University of South Florida, November 22, 2002.
• "Integer Partitions and Identities of the Rogers-Ramanujan Type," Kent State University, February 17, 2006.
• "Rogers-Ramanujan-Slater Type Identitites," West Chester University, October 4, 2006.
• "Polynomial Generalizations of q-Series Identities," Georgia Southern University, October 15, 2007.
• "Maximizing the Wiener Index," Georgia Southern University, August 27, 2010.
• "A Revival of Sylvester's Wave Theory of Partitions," Georgia Southern University, September 15, 2011
• "A Formula for the Partition Function that 'Counts'," Georgia Southern University, August 29, 2014

• "Partitions of Integers," Special lecture in the Rutgers Mathematical Careers and Ideas series, March 30, 2005.

1. "Computer Explorations of Rogers-Ramanujan Type Identities," Penn State Partitions Seminar. Part 1: April 19, 2001; Part 2: May 3, 2001.
2. "Maple and Mathematica for Research in q-series," Penn State Partitions Seminar, September 6, 2001.
3. "Computer Proofs and the WZ method," Penn State Partitions Seminar, September 13, 2001.
4. "The Colorful Combinatorics of Lebesgue's Identity," Penn State Partitions Seminar, November 2001.
5. "Bijections for Certain Equivalent Partition Ideals of Order 1," University of Florida Number Theory Seminar, June 18, 2002.
6. "Bijective Proofs for Some Equivalent Partition Ideals," Ohio State University Combinatorics Seminar, August 22, 2002.
7. "A Combinatorial Proof of a Partition Identity of Andrews and Stanley," Penn State Partitions Seminar, March 6, 2003.
8. "Computer Algebra and Rogers-Ramanujan," Rutgers Experimental Mathematics Seminar, September 25, 2003.
9. "A Rogers-Ramanujan Computer Search," Rutgers Experimental Mathematics Seminar, February 12, 2004.
10. "Rogers-Ramanujan-Bailey Identities," University of Pennsylvania Combinatorics Seminar, November 9, 2004.
11. "Disturbing the Dyson Conjecture (in a GOOD Way)," Rutgers Experimental Mathematics Seminar, March 10, 2005.
12. "Disturbing the Dyson Conjecture (in a generally GOOD Way)," Rutgers Experimental Mathematics Seminar, October 27, 2005.
13. "Polynomial Generalizations of Rogers-Ramanujan Type Identities," Binghamton University Algebra Seminar, December 6, 2005.
14. "Integer Partitions and Identities of Rogers-Ramanujan Type," University of Akron, March 16, 2006.
15. "Rogers-Ramanujan Type Identities and Partitions," Penn State Partitions Seminar, June 28, 2005.
16. "Integer Partitions and Identities of Rogers-Ramanujan Type," Georgia Southern University, November 30, 2006.
17. "On Dyson's q-Series Identities," Rutgers Experimental Mathematics Seminar, February 22, 2007.
18. "Finding Polynomial Generalizations of q-Series Identities," Clemson University Algebra and Discrete Mathematics Seminar, September 27, 2007.
19. "A Generalization of the Euler-Glaisher Bijection," North Carolina State University Algebra and Combinatorics Seminar, September 26, 2008.
20. "A Generalization of the Euler-Glaisher Bijection," University of South Carolina Number Theory Seminar, February 25, 2009.
21. "Instances of Gordon's Theorem Have Been Hiding in Slater's List!" University of Florida Graduate Number Theory Seminar, March 16, 2010.
22. "Maximizing the Wiener Index," Rutgers Experimental Mathematics Seminar, October 7, 2010.
23. "A Revival of Sylvester's Wave Theory of Partitions," Rutgers/DIMACS Summer Seminar Series, July 11, 2011.
24. "Rademacher's Infinite Partial Fraction Conjecture," Georgia Southern Discrete Mathematics Seminar, February 1, 2012.
25. "Rademacher's Infinite Partial Fraction Conjecture is (almost certainly) False," University of Florida Number Theory Seminar, March 22, 2012.
26. "A Formula for the Partition Function that 'counts'," Discrete Mathematics Seminar, Armstrong Atlantic State University, Savannah, GA, April 22, 2014.

1. "Partitions and q-series," a series of three talks given in the University of Kentucky Algebra seminar, September 1998
2. "Fractional Calculus," University of Kentucky Algebra Seminar, Spring 1998
3. "Magic Squares and Ehrhart Polynomials," University of Kentucky Algebra Seminar, September 2, 1999.
4. "Recounting the Rationals," based on the article of the same title by N. Calkin and H. S. Wilf, Amer. Math. Monthly 107 (2000) no. 4, 360-363. Penn State Partitions Seminar, October 18, 2001.
5. A series of talks explaining the WZ theory, Penn State Partitions Seminar, September--October, 2002.
6. "Some Partition Identities," Rutgers Graduate Student Combinatorics Seminar, February 2, 2004.
7. "An Introduction to WZ Theory," DIMACS REU Seminar, July 6, 2004.
8. "Computer Proofs via the Algorithms of Sister Celine and Zeilberger," Rutgers Graduate Student Combinatorics Seminar, April 18, 2005.
9. "An Introduction to Integer Partitions," DIMACS REU Seminar, June 8, 2006.
10. "Hypergeometric Series and the WZ Method," Georgia Southern Analysis Seminar, January 22, 2008.
11. "WZ Method and q-Hypergeometric Series," Georgia Southern Analysis Seminar, January 29, 2008.
12. "q-Series and Bailey Chains," Georgia Southern Analysis Seminar, February 5, 2008.
13. "Combinatory Analysis," Georgia Southern Analysis Seminar, February 26, 2008.

LIST OF COURSES TAUGHT
Have taught essentially all college mathematics courses from the remedial level through the sophomore level, including:

• Developmental Mathematics
• Introductory, Intermediate, and College Algebra
• Trigonometry
• Finite Mathematics
• Pre-Calculus
• Business Calculus
• Calculus and Analytic Geometry I & II
• Mathematics for Elementary Education Majors
• Multivariable Calculus
• Introductory Linear Algebra
• Elementary Differential Equations

• Introductory Statistics
• Intermediate Statistics
• Probability and Statistics for Engineers (Calc II prerequisite)

• Introduction to Mathematical Reasoning
• Linear Optimization
• Number Theory
• Modern Algebra I & II
• Introductory Complex Analysis
• Mathematical Theory of Statistics
• Combinatorics and Graph Theory
• Individual Study in Mathematics (reading course)

• Analytic Number Theory
• Applied Nonparametric Statistics

• Served as co-mentor, along with Doron Zeilberger, for REU student Sterling Stein, Summer 2003
• Served as mentor to Rutgers Undergraduate Research Fellow Yuriy Choliy in the R.E.U. program, Summer 2004
• Math 494, Individual Study in Mathematics: a reading course for Rutgers undergraduate Slava Kiria on Integer Partitions (G.E. Andrews and K. Erickson), Spring 2007
• Served as mentor for Christine Bowman in the undergraduate seminar program, Spring 2008.
• James Diffenderfer, "Restricted Compositons," Spring 2011.

• Michael Hammock, M.S., Georgia Southern University, December 2009
• Vyacheslav Kiria-Kaiserberg, M.S., Georgia Southern University, May 2011
• Linus Lindroos, M.S., Georgia Southern University, December 2012
• James Diffenderfer, M.S., Georgia Southern University, May 2013
• Yiran Zhang, M.S., Georgia Southern University, August 2014 (co-advised with Charles Champ)

• Have served as referee for
• Acta Arithmetica
• Advances in Applied Mathematics
• Advances in Mathmatics
• Annals of Combinatorics
• Applicable Analysis and Discrete Mathematics
• Ars Combinatoria
• Bulletin of the London Mathematical Society
• Computers and Mathematics with Applications
• Discrete Mathematics
• Electronic Journal of Combinatorics
• European Journal of Combinatorics
• Fibonacci Quarterly
• Forum Mathematicum
• Indian Journal of Pure and Applied Mathematics
• International Journal of Mathematics and Mathematical Sciences
• International Journal of Number Theory
• International Mathematics Research Notices
• Involve
• Journal of Combinatorial Theory, Series A
• Journal of the Indian Mathematical Society
• Journal of the Korean Mathematical Society
• Journal of Mathematical Analysis and Applications
• Journal of Number Theory
• New Zealand Journal of Mathematics
• Portugaliae Mathematica
• Quaestiones Mathematicae
• Ramanujan Journal
• Rocky Mountain Journal of Mathematics
• Transactions of the American Mathematial Society
• Reviewer for Math Reviews, 2003-present (56 reviews published to date)
• Co-organizer (with Michael Mossinghoff, Davidson College) special session in combinatorial number theory, MAA southeast section meeting, Charleston, SC, March 28, 2008.
• Principal Organizer, q-Series 2011: an International Conference on Partitions, q-Series, and Special Functions. March 14-16, 2011 at Georgia Southern University, Statesboro, GA.
• AMS Library Committee, 2011-2014.
• MAA Polya Prize Committee, 2012-2015.

• At Penn State Department of Mathematics
  • Served on examination writing committee for calculus sequence, 2000-2002 (chairmanship for Spring 2002 and Fall 2002 final exams)
  • Secretary for Partitions Seminar, 2001-2002
• Rutgers University Department of Mathematics
  • Co-founder and Co-organizer of the Rutgers/DIMACS Experimental Mathematics Seminar, 2003-2007
• Georgia Southern University Department of Mathematical Sciences
  • Colloquium Committee, 2007-2009, 2011-2012.
  • Math Tournament Committee, 2007-2008
  • Hosted Distinguished Lecturer, 2008, 2010, and 2012
  • Library Representative, 2008-present
  • Graduate Coordinating Committee, 2008-2012
  • Curriculum Committee, 2008-2010
  • Tenure-track Assistant Professor Search Committee, 2008-2009, 2012-2013
  • Course Coordinator, Math 1113 Precalculus, Fall 2009.
  • Calculus textbook selection committee, Spring 2010.
  • Course Coordinator, Math 2242 Calculus II, Spring 2011.
  • Elections Committee, 2011-2012
  • Grants and Scholarships Committee, 2011-2013
  • Department Chair search committee, 2014-2015

EMPLOYMENT OUTSIDE ACADEMIA
Actuarial Assistant, Insurance Services Office, New York, NY, 1990-1992

Last update: March 18, 2015.