## 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 couple of 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 39 theses. You can view the titles of recent theses on this Colgate webpage.

### Fun Facts

#### Students Taught

> 2000#### Pages of math thrown in recycling

31,415#### Songs written

64#### Coffee Cups Consumed

10^{1010}

## Resume

##### Over 20 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

## Teaching

##### Who put the aching in teaching?

### Current Teaching

### 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

## 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 S
_{n}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
N
^{2}/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.