Aaron Robertson
Mathematician
Professor
Musician
About Me
Mathematician, Professor, Musician
I am a Professor of Mathematics @ Colgate University
I started professing at Colgate University in 1999 and am the mathematics department chair.
I have authored several dozen articles and a few books. My new book Fundamentals of Ramsey Theory, aimed at beginning graduate students, was released in June (2021) on the CRC Press Discrete math imprint. If you are so inclined, you can purchase it on Amazon.
When not doing mathematics or teaching about mathematics or chairing math, I spend my time either with my family or my bandmates or watching Colgate sporting events or recording and writing in my studio. And just so the Colgate basketball coach knows, I still have my 4 years of eligibility.
- Age52
- ResidenceNew York, United States
- Office219 McGregory Hall
- e-mailarobertson@colgate.edu
Teaching
Service Courses
My main service course is Introductory Statistics; however, I have taught all calculus courses, too.
Course in my Area
Combinatorics, Ramsey Theory
Other Majors Courses
Number Theory and Mathematical Reasoning, Probability, Mathematical Statistics, Real Analysis
Thesis Course
Just a few years ago, our department implemented a thesis requirement for our majors. Since then I have directed 45 theses. You can view the titles of recent theses on this Colgate webpage.
Fun Facts
Students Taught
> 2000Pages of math thrown in recycling
31,415Songs written
64Coffee Cups Consumed
101010Resume
Over 25 Years of Experience
Education
1993
B.S. in Actuarial Science
University of MichiganI passed a few tests back then, but realized the business life was definitely not for me.
Experience
July 2012 - Current
Full Professor
Colgate UniversityNow I can relax 😂
July 2005 - June 2012
Associate Professor
Colgate UniversityI thought I was supposed to teach and do research, not service.
July 1999 - June 2005
Assistant Professor
Colgate UniversityWith no power comes no responsibility.
Math Skills
Ramsey Theory
Combinatorics
Other Math
Coding Skills
Maple
Fortran
C
Timex Sinclair 1000
Download CV (updated May 28, 2024)
Teaching
Who put the aching in teaching?
Current / Future Teaching
Fall 24
Math 105: Intro to Stats
MWF: 8:20-9:10101 Ho
Spring 25
Math 105: Intro to Stats
MWF: 8:20-9:10101 Ho
Math 250: Number Theory and Math Reasoning
MWF: 10:20-11:10328 McGregory (Tentatively)
Courses I Have Taught
- Introduction to Statistics (105)
- Calculus I (161)
- Calculus II (162)
- Calculus III (163)
- Number Theory and Math Reasoning (250)
- Combinatorics (310)
- Probability (316)
- Geometry (357)
- Real Analysis I (377)
- Ramsey Theory (410)
- Mathematical Statistics II (416)
- Research Seminar (483)
Research
My Publications
43. ON THE MINIMUM NUMBER OF MONOCHROMATIC 2-DIMENSIONAL SCHUR TRIPLES
Integers 24A, #A16
42. MONOCHROMATIC STRICTLY ASCENDING WAVES AND PERMUTATION PATTERN WAVES
Co-author: B. LandmanAdv. Applied Math 146, Article 102501
41. ARITHMETIC PROGRESSIONS, QUASI PROGRESSIONS, AND GALLAI-RAMSEY COLORINGS
Co-authors: Y. Mao, K. Ozeki, and Z. WangJ. Combin. Theory, Series A 193, Article 105672
40. RAMSEY PROPERTIES FOR INTEGER SEQUENCES WITH RESTRICTED GAPS
Co-authors: B. Landman and Q. RobertsonMoscow J. Comb. and Number Theory 12, 181-195.
39. COMBINATORIAL GAME THEORY. A SPECIAL COLLECTION IN HONOR OF ELWYN BERLEKAMP, JOHN H. CONWAY, AND RICHARD GUY
Co-editors: F. Luca et al.deGruyter
38. NUMBER THEORY AND COMBINATORICS: A COLLECTION IN HONOR OF THE MATHEMATICS OF RONALD GRAHAM
Co-editors: F. Luca et al.deGruyter
37. FUNDAMENTALS OF RAMSEY THEORY
Discrete Math. and Its ApplicationsCRC Press
(click for errata)
36. ON THE DISTRIBUTION OF MONOCHROMATIC COMPLETE SUBGRAPHS AND ARITHMETIC PROGRESSIONS
Co-authors: W. Cipolli and M. DascaluExperimental Math 30, 135-145.
35. DOWN THE LARGE RABBIT HOLE
Rocky Mountain J. Math 50, 237-253.
34. ZERO-SUM ANALOGUES OF VAN DER WAERDEN'S THEOREM ON ARITHMETIC PROGRESSIONS
J. Combinatorics 11, 231-248.
33. ZERO-SUM GENERALIZED SCHUR NUMBERS
J. Combin. and Num. Theory 10, 51-62.
32. THE DETERMINATION OF 2-COLOR ZERO-SUM GENERALIZED SCHUR NUMBERS
Co-authors: Bidisha Roy and Subha SarkarIntegers 18, #A96
31. INTERMINGLED ASCENDING WAVE M-SETS
With C. Cremin, W. Daniel, and Q. XiangDiscrete Math 339, 560-563.
30. A PROBABILISTIC THRESHOLD FOR MONOCHROMATIC ARITHMETIC PROGRESSIONS
J. Combin. Theory, Series A 137, 79-87
29. RAMSEY THEORY ON THE INTEGERS, Second Edition
Co-author: Bruce LandmanAmerican Math Society, STML 73
28. COMBINATORIAL NUMBER THEORY: PROCEEDINGS OF INTEGERS CONFERENCE 2011
Co-editors: B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, and C. PomeranceDe Gruyter, Proceedings in Math
27. VAN DER WAERDEN'S THEOREM AND AVOIDABILITY IN WORDS
Co-authors: Yu-Hin Au and Jeffrey ShallitIntegers 11, #A7
26. MULTIPLICITY OF MONOCHROMATIC SOLUTIONS TO X+Y < Z
Co-authors: W. Kosek, D. Sabo, and D. SchaalJ. Combin. Theory, Series A 8, 1127-1135
25. COMBINATORIAL NUMBER THEORY: PROCEEDINGS OF INTEGERS CONFERENCE 2007
Co-editors: B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, and C. PomeranceDe Gruyter, Proceedings in Math
24. BOUNDS ON SOME VAN DER WAERDEN NUMBERS
Co-authors: Tom Brown and Bruce LandmanJ. Combin. Theory, Series A 115, 1304-1309
23. SOME TWO COLOR, FOUR VARIABLE RADO NUMBERS
Co-author: Kellen MyersAdvances in Applied Math 42, 214-226
22. ON THE ASYMPTOTIC MINIMUM NUMBER OF MONOCHROMATIC 3-TERM ARITHMETIC PROGRESSIONS
Co-authors: Pablo Parrilo and Dan SaracinoJ. Combin. Theory, Series A 115, 185-192
21. AVOIDING MONOCHROMATIC SEQUENCES WITH SPECIAL GAPS
Co-authors: Bruce LandmanSiam J. Discrete Math 21, 794-801
20. A METHOD FOR QUANTIFYING ROTATIONAL SYMMETRY
Co-authors: Frank Frey and Michael BukoskiNew Phytologist 175, 785-791
19. TWO COLOR OFF-DIAGONAL RADO-TYPE NUMBERS
Co-author: Kellen MyersElectronic J. of Combinatorics 14, #R53
18. ON MONOCHROMATIC ASCENDING WAVES
Co-author: Tim LeSaulnierIntegers 7(2), #A23
17. REFINED RESTRICTED INVOLUTIONS
Co-authors: E. Deutsch and D. SaracinoEuropean J. of Combinatorics 28, 481-498
16. ON THE DEGREE OF REGULARITY OF GENERALIZED VAN DER WAERDEN TRIPLES
With N. Frantzikinakis and B. LandmanAdvance in Applied Math 37, 124-128
15. SOME NEW EXACT VAN DER WAERDEN NUMBERS
Co-authors: Bruce Landman and Clay CulverIntegers 5(2), #A10
14. RESTRICTED PERMUTATIONS FROM CATALAN TO FINE AND BACK
Sém. Lotharingien de Combin. 50, #B50G
13. RAMSEY THEORY ON THE INTEGERS
Co-author: Bruce LandmanAmerican Math Society, STML 24
12. REFINED RESTRICTED PERMUTATIONS
Co-authors: D. Saracino and D. ZeilbergerAnnals of Combinatorics 6, 427-444
11. REFINED RESTRICTED PERMUTATIONS AVOIDING SUBSETS OF PATTERNS OF LENGTH 3
Co-authors: Toufik MansourAnnals of Combinatorics 6, 407-418
10. ON GENERALIZED VAN DER WAERDEN TRIPLES
Co-authors: Bruce LandmanDiscrete Math 256, 279-290
9. NEW LOWER BOUND FORMULAS FOR SOME MULTICOLORED RAMSEY NUMBERS
Electronic J. of Combinatorics 9, #R13
8. PERMUTATIONS RESTRICTED BY TWO DISTINCT PATTERNS OF LENGTH THREE
Advances in Applied Math 27, 548-561
7. OFF-DIAGONAL GENERALIZED SCHUR NUMBERS
Co-authors: Dan SchaalAdvances in Applied Math 26, 252-257
6. DIFFERENCE RAMSEY NUMBERS AND ISSAI NUMBERS
Advance in Applied Math 25, 153-162
5. PERMUTATION PATTERNS AND CONTINUED FRACTIONS
Co-authors: Herb Wilf and Doron ZeilbergerElectronic J. Combinatorics 56, #R38
4. PERMUTATIONS CONTAINING AND AVOIDING 123 AND 132 PATTERNS
Disc. Math and Theor. Comp. Sci. 3, 151-154
3. NEW LOWER BOUNDS FOR SOME MULTICOLORED RAMSEY NUMBERS
Electronic J. of Combinatorics 6, #R3
2. A 2-COLORING OF [1,N] CAN HAVE N2/22 + O(N) MONOCHROMATIC SCHUR TRIPLES, BUT NOT LESS
Co-authors: Doron ZeilbergerElectronic J. of Combinatorics 5, #R19
1. REVIEW OF SOCIAL SECURITY FINANCING AND RELATED MATTERS
Co-authors: C. Nesbitt and F. MessnerARCH 1993.1, 249-282
Computer Code
Fortran, Maple, C++
- GALRAD: a Maple package that accompanies Gallai-Rado Numbers and Their Multiplicities, which aids in the determination of the minimal integer n such that every 3-coloring of [1,n] admits a monochromatic or rainbow solution to x+y+b=z.
- Colorings/main.c: a C++ program written by Quinn Robertson that accompanies Ramsey Properties for Integer Sequences with Restricted Gaps that calculates the minimal n such that every 2-coloring of [1,n] admits a monochromatic arithmetic progression of color 1 with common difference from a given set D or a monochromatic sequence of color 2 with all consecutive gaps from the same set D.
- ZSAP.f, ZSAP2.f, MZSAP.f, and MZSAP2.f are Fortran programs that accompany Zero-sum Analogues of van der Waerden's Theorem on Arithmetic Progressions.
- ZSGS.f and ZSGS2.f are Fortran programs that accompany Zero-sum Generalized Schur Triples.
- PERMPROG.f: a
Fortran77 program that accompanies
Monochromatic Strictly Ascending Waves
and Permutation Pattern Waves that calculates
the minimal n such that every 2-coloring of
[1,n] admits a monochromatic π-wave.
- RADONUMBERS:
a zip file of a C++ program that accompanies
Some Two Color,
Four Variable Rado Numbers.
It was written by Kellen Myers and Joseph Parrish.
It determines, given
k andj , the minimum integerN such that any 2-coloring of[1,N] admits a monochromatic solution tox+y+kz=jw . - FVR:
is a (very short) Maple package that accompanies
Some Two Color,
Four Variable Rado Numbers.
It determines, given a 2-coloring, those
values of
k for whichx+y+kz=(k+c)w has a monochromatic solutions (whenc is given). - PABLO:
is a Maple package that accompanies
On the Asymptotic
Minimum Number of Monochromatic 3-Term
Arithmetic Progressions.
It verifies the lower bounds given
in the article.
- SCHAAL:
is a Maple package that accompanies
Two Color
Off-diagonal Rado-type numbers.
It determines bounds for the
Rado numbers of certain
linear homogeneous equations.
- AB.f:
is a Fortran77 program that accompanies
the article
On the Degree of Regularity of
Generalized van der Waerden Triples
In particular, it proves that the degree
of regularity of (2,2) is
not 1, 2, or infinity. - AARON:
AARON is a Maple package written by Doron
Zeilberger with additions by me. It accompanies
the article
Refined Restricted Permutations.
One use is the enumeration, for small n, of the set of
permutations in Sn with
k fixed points which contain
r instances of a given pattern of length 3.
- DIFFSEQ.f:
DIFFSEQ.f is a Fortran program which accompanies the
article Avoiding Monochromatic Sequences
With Special Gaps. It will calculate
f(S,k;2) for many small values of k and
an inputted set S.
- VDW.f:
VDW.f is a Fortran program which accompanies the
article On Generalized
Van der Waerden Triples. It will calculate
N(a,b;2) for many small values of a and b by
a recursive search similar to that used in DF.f.
- AUTOISSAI:
AUTOISSAI is a Maple package which accompanies the
article Off-diagonal
Generalized Schur Numbers. It was used to help
determine the exact values of these numbers, and
is another step towards automated theorem proving.
- MIKLOS:
MIKLOS is a Maple package accompanying the article
Permutation Patterns and Continued Fraction.
It will find, quite quickly thanks to Herb Wilf,
the generating functions for the number of
permutations with either 0 or 1 (132)-patterns
and a prescribed number of (123)-patterns.
- DF.f,
DF3.f, and
ISSAI: DF.f
(and its 3-colored cousin DF3.f) is a Fortran program
which finds the maximal Difference Ramsey number.
ISSAI is a small Maple package for finding lower
bounds and exact values for the newly defined
Issai Numbers, also called Off-diagonal
Generalized Schur Numbers.
These programs accompany the article
Difference Ramsey Numbers and
Issai Numbers.
- RES: RES is a Maple package
accompanying the article New Lower Bounds
for Some Multicolored Ramsey Numbers. By mating the finite
field method of Greenwood and Gleason with today's computing
power, we are able to find good bounds for some large Ramsey numbers.
- RON, GENRON, and SCHUR : RON is a Maple package accompanying the article A 2-Coloring of [1,N] Can Have N2/22 + O(N) Monochromatic Schur Triples, But Not Less!. It will find the number of Schur Triples (asymptotically) of any coloring you enter, along with many other useful tools to attact this problem posed by Ron Graham. GENRON is a Maple package which performs the same tasks as RON, except that we are trying to find the minimum number of monochromatic solutions of x+ay=z (if a=1 then we are counting Schur triples). This extension was posed to me by Ron Graham.
Music
Some Music
My band, dangerboy, is mostly a cover band. We play alternative rock, focusing on 90s alternative. We did record some of my original songs way back in the day. Below are a couple of demos from back then.