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Dr. Craig Erickson
About me
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portfolio
Minneapolis Fire Calls
Streamlit 
app showing locations of confirmed fires responded to by the Minneapolis Fire Department
The Purple States of America
Streamlit app showing county-level results of U.S. Presidential elections.
publications
On nilpotence indices of sign patterns
Published in Commun. Korean Math. Soc., 2010
The work in this paper was motivated by Eschenbach and Li, who listed four 4-by-4 sign patterns, conjectured to be nilpotent sign patterns of nilpotence index at least 3. These sign patterns with no zero entries, called full sign patterns, are shown to be potentially nilpotent of nilpotence index 3. We also generalize these sign patterns of order 4 so that we provide classes of n-by-n sign patterns of nilpotence indices at least 3, if they are potentially nilpotent. Furthermore it is shown that if a full sign pattern A of order n has nilpotence index k with 2≤k≤n−1, then sign pattern A has nilpotent realizations of nilpotence indices k, k+1,…,n.
Recommended citation: C. Erickson and I.-J. Kim. ”On nilpotence indices of sign patterns." Commun. Korean Math. Soc. 25 (2010), No. 1, 11—18. https://doi.org/10.4134/CKMS.2010.25.1.11
Constructions of potentially eventually positive sign patterns with reducible positive part
Published in nvolve, 2011
Potentially eventually positive (PEP) sign patterns were introduced by Berman et al. (Electron. J. Linear Algebra 19 (2010), 108–120), where it was noted that a matrix is PEP if its positive part is primitive, and an example was given of a 3-by-3 PEP sign pattern with reducible positive part. We extend these results by constructing n-by-n PEP sign patterns with reducible positive part, for every n ≥ 3 .
Recommended citation: M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, and A. Ochoa. "Constructions of potentially eventually positive sign patterns with reducible positive part." Involve 4 (2011), No. 4, 405—410. https://doi.org/10.2140/involve.2011.4.405
Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees
Published in Electron. J. Linear Algebra, 2012
The definition of the positive semidefinite zero forcing number for simple graphs is extended to multigraphs; as for simple graphs, this parameter bounds the maximum positive semidefinite nullity from above.
Recommended citation: J. Ekstrand, C. Erickson, D. Hay, L. Hogben, and J. Roat. "Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees." Electron. J. Linear Algebra 23 (2012), 79—87. https://doi.org/10.13001/1081-3810.1506
Sign patterns that allow strong eventual nonnegativity
Published in Electron. J. Linear Algebra, 2012
A new class of sign patterns contained in the class of sign patterns that allow eventual nonnegativity is introduced and studied. A sign pattern is potentially strongly eventually nonnegative (PSEN) if there is a matrix with this sign pattern that is eventually nonnegative and has some power that is both nonnegative and irreducible. Using Perron-Frobenius theory and a matrix perturbation result, it is proved that a PSEN sign pattern is either potentially eventually positive or r-cyclic. The minimum number of positive entries in an n-by-n PSEN sign pattern is shown to be n, and PSEN sign patterns of orders 2 and 3 are characterized.
Recommended citation: M. Catral, C. Erickson, L. Hogben, D.D. Olesky, and P. Van den Driessche. "Sign patterns that allow strong eventual nonnegativity." Electron. J. Linear Algebra 23 (2012), 1—10. https://doi.org/10.13001/1081-3810.1502
Potentially eventually exponentially positive sign patterns
Published in Involve, 2013
We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all 2-by-2 and 3-by-3 PEEP sign patterns is given.
Recommended citation: M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, and A. Ochoa. "Potentially eventually exponentially positive sign patterns." Involve 6 (2013), No. 3, 261—271. https://doi.org/10.2140/involve.2013.6.261
Positive semidefinite zero forcing
Published in Linear Algebra Appl., 2013
We establish a variety of properties of positive semidefinite zero forcing: Any vertex of G can be in a minimum positive semidefinite zero forcing set (this is not true for standard zero forcing). Graphs having extreme values of the positive semidefinite zero forcing number are characterized. The effect of various graph operations on positive semidefinite zero forcing number and connections with other graph parameters are studied.
Recommended citation: J. Ekstrand, C. Erickson, H.T. Hall, D. Hay, L. Hogben, R. Johnson, N. Kingsley, S. Osborne, T. Peters, J. Roat, A. Ross, D.D. Row, N. Warnberg, and M. Young. “Positive semidefinite zero forcing.” Linear Algebra Appl. 439 (2013), 1862–1874. https://doi.org/10.1016/j.laa.2013.05.020
Sign patterns that require eventual exponential nonnegativity
Published in Electron. J. Linear Algebra, 2015
Sign patterns that require exponential nonnegativity are characterized. A set of conditions necessary for a sign pattern to require eventual exponential nonnegativity are established. It is shown that these conditions are also sufficient for an upper triangular sign pattern to require eventual exponential nonnegativity and it is conjectured that these conditions are both necessary and sufficient for any sign pattern to require eventual exponential nonnegativity. It is also shown that the maximum number of negative entries in a sign pattern that requires eventual exponential nonnegativity is (n-1)(n-2)/2 + 2.
Recommended citation: C. Erickson. "Sign patterns that require eventual exponential nonnegativity." Electron. J. Linear Algebra 30 (2015), 171--195. https://doi.org/10.13001/1081-3810.3027
Rainbow arithmetic progressions
Published in J. Comb., 2016
In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers n and k, the expression aw([n], k) denotes the smallest number of colors with which the integers {1,…,n} can be colored and still guarantee there is a rainbow arithmetic progression of length k.
Recommended citation: S. Butler, C. Erickson, L. Hogben, K. Hogenson, L. Kramer, R.L. Kramer, J.C.-H. Lin, R.R. Martin, D. Stolee, N. Warnberg, M. Young. "Rainbow arithmetic progressions." J. Comb. 7 (2016), No. 4, 595—626. https://doi.org/10.4310/JOC.2016.v7.n4.a3
Restricted power domination and zero forcing problems
Published in J. Comb. Optim., 2019
A power dominating set of a graph is a set of vertices that observes every vertex in the graph, following a set of rules for power system monitoring. A practical problem of interest is to determine the minimum number of additional measurement devices needed to monitor a power network when the network is expanded and the existing devices remain in place. In this paper, we study the problem of finding the smallest power dominating set that contains a given set of vertices X.
Recommended citation: C. Bozeman, B. Brimkov, C. Erickson, D. Ferrero, M. Flagg, L. Hogben. "Restricted power domination and zero forcing problems." J. Comb. Optim. 37 (2019), No. 3, 935—956. https://arxiv.org/abs/1711.05190
Properties of a q-analogue for zero forcing
Published in Graphs Combin., 2020
This paper investigates a q-analogue of zero forcing. Basic properties of this game are established including determining all graphs which have minimal cost 1 or 2 for all possible q, and finding the zero forcing number for all trees when q=1.
Recommended citation: S. Butler, C. Erickson, S. Fallat, H.T. Hall, B. Kroschel, J.C.H. Lin, B. Shader, N. Warnberg, B. Yang. “Properties of a q-analogue for zero forcing.” Graphs Combin. 36 (2020), No. 5, 1401—1419. https://arxiv.org/abs/1809.07640
talks
Strongly Eventually Nonnegative Matrices
Published:
Potentially eventually positive and potentially eventually exponentially positive sign patterns
Published:
Zero forcing and other games on graphs
Published:
Restricted power domination
Published:
teaching
Introduction to Programming
teaching, Hamline University, 1900
Goals: To help students develop greater precision in their algorithmic thinking by writing moderate-sized programs for a variety of applications, including but not limited to biology, chemistry, economics, literary studies, and mathematics.
Introduction to Computational Data Science
teaching, Hamline University, 1900
Goals: To continue the study of computational techniques using Python, with an emphasis on applications in data science and analytics.
Elements of Statistical Learning
teaching, Hamline University, 1900
Goals: This is a continuation course for MATH 1200, introducing techniques of statistical learning.
Computational Data Science Capstone
teaching, Hamline University, 1900
Goals: To help students integrate the knowledge and skills attained in the Computational Data Science program.
Introduction to Computer Science
teaching, Hamline University, 1900
Goals: To help students develop greater precision in their algorithmic thinking by writing moderate-sized programs for a variety of applications, including but not limited to biology, chemistry, economics, literary studies, and mathematics.
Programming in MATLAB
teaching, Hamline University, 1900
This course introduces MATLAB as a programming language and as a software environment for mathematical computing and graphics. No prior use of MATLAB or computer programming is assumed. Topics will include: data input/output, plots, if-else statements, loops and vectorization, using built-in MATLAB functions, and creating your own scripts and functions that extend the language.
First Year Seminar: Uses and Misuses of Algorithms
teaching, Hamline University, 1900
Data scientists have used algorithms for many great things: Netflix’s recommendation system; building teams that go on to win the World Series or the Stanley Cup; proving the existence of the Higgs boson; and early detection of cancer. Other data scientists have used algorithms with malicious intent: targeting of vulnerable people by payday loan companies and for-profit higher education companies that provide little—if any—benefit to their students; using of social network bots to spread misinformation and sow discontent within a country. Sometimes algorithms have unintended negative effects: the firing of skilled teachers in Washington, D.C.; racial discrimination in the lengths of prison sentences and the granting (or not granting) of parole; and discriminating against job applicants (including racism, sexism, and ableism).
Introduction to Algebra
teaching, Grand View University, 1900
This course is a college preparatory course designed for students who need to learn or revisit concepts typically taught in a high school Algebra I course. This course covers the fundamentals of arithmetic skills necessary in daily life and builds a foundation of algebraic understanding. Topics included are: operations with real numbers, percent, ratio, proportion, expressions, linear equations, polynomials, and radicals.
Intermediate Algebra
teaching, Grand View University, 1900
This course will include a brief review of: sets, integers, algebraic expressions and operations, polynomials, rational expressions, and equations. This course will emphasize: roots, radicals and complex numbers, linear equations/functions and graphing, systems of linear equations and inequalities, quadratic functions, and exponential and logarithmic functions.
Introductory & Intermediate Algebra
teaching, Grand View University, 1900
This course covers: operations with numeric and algebraic expressions, polynomials, rational expressions and equations, roots, radicals and complex numbers, linear equations/functions and graphing, systems of linear equations and inequalities, quadratic functions, and exponential and logarithmic functions.
High School Algebra
teaching, Iowa State University, 1900
Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only.
College Algebra
teaching, Minnesota State University, 1900
Concepts of algebra (real numbers, exponents, polynomials, rational expressions), equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations and inequalities, matrices and determinants, conic sections, sequences and series, probability, and binomial theorem.
Finite Mathematics
teaching, Grand View University, 1900
Topics include elementary linear functions, systems of equations, linear inequalities, matrices, linear programming (using the graphical method and optionally the Simplex Method), set theory, mathematics of finance, introductory statistics and probability. Game theory, decision making, and counting may be included. Applications to such diverse fields as business, economics, life sciences, and social sciences are covered.
Calculus I
teaching, Hamline University, 1900
Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus.
Statistics
teaching, Hamline University, 1900
Goals: To cover the fundamentals of statistical data analysis.
College Algebra
teaching, Iowa State University, 1900
Coordinate geometry, quadratic and polynomial equations, functions, graphing, rational functions, exponential and logarithmic functions, inverse functions, quadratic inequalities, systems of linear equations.
Introduction to Discrete Structures
teaching, Grand View University, 1900
This course is an introduction to set theory, logic, integers, combinatorics, and functions for today's computer scientists.
Calculus I
teaching, Iowa State University, 1900
Differential calculus, applications of the derivative, introduction to integral calculus.
Calculus II
teaching, Iowa State University, 1900
Integral calculus, applications of the integral, parametric curves and polar coordinates, power series and Taylor series.
Applied Calculus
teaching, Grand View University, 1900
This course investigates applications of modeling techniques used in a variety of disciplines, including the natural sciences, mathematics, computer science and business. The nature and use of calculus (both differential and integral) is a primary focus of the course.
Applied Statistics
teaching, Grand View University, 1900
This course introduces students to modeling techniques for probabilistic processes and data analysis methods used in descriptive and inferential statistics. It develops students' abilities in employing technology as an analytical tool.
Elementary Differential Equations & Laplace Transforms
teaching, Iowa State University, 1900
Solution methods for ordinary differential equations. First order equations, linear equations, constant coefficient equations. Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis. Laplace transforms and power series solutions to ordinary differential equations.
Introduction to Mathematical Reasoning
teaching, Grand View University, 1900
This course introduces students to the basics of propositional and predicate logic in symbolizing natural language and determining validity, and introduces such topics as the logic of set theory, functions, relations, and transfinite sets. Emphasis is placed upon strategies involved in constructing proofs.
Introduction to Mathematical Modeling
teaching, Grand View University, 1900
Introduction to Mathematical Modeling is a mathematical tool for solving real world problems. In this course, students study a problem-solving process. They learn how to identify a problem, construct or select appropriate models, figure out what data needs to be collected, test the validity of a model, calculate solutions and implement the model. Emphasis lies on model construction in order to promote student creativity and demonstrate the link between theoretical mathematics and real world applications.
Multivariable and Vector Calculus
teaching, Hamline University, 1900
Goals: To extend concepts of calculus in two variables to the calculus of several variables.
Discrete Computational Structures
teaching, Grand View University, 1900
Topics included are propositional logic, set theory, graph theory and combinatorial analysis, and Boolean algebra. Applications and theory are discussed.
Discrete Mathematics
teaching, Hamline University, 1900
Goals: To introduce the concept of the discrete as well as techniques used in higher non-continuous mathematics, providing the necessary background material required by computer scientists for algorithm analysis.
Introduction to Numerical Analysis
teaching, Grand View University, 1900
Topics included are: error analysis, curve fitting, function approximation, interpolation, numerical methods for solving equations and systems of equations, numerical differentiation and integration, optimization, numerical solutions of ODE and PDE and eigenvalues/eigenvectors.
Senior Seminar
teaching, Grand View University, 1900
This course represents the capstone course for Mathematics majors. Emphasis is placed on further development of skills in the areas of written and oral communication, problem solving, and research. Students, with guidance from an instructor, choose a topic. On their chosen topic, students prepare a research paper and give an oral presentation to mathematics faculty and other mathematics students.
Calculus I
teaching, Drake Univeresity, 1900
Very brief review of algebra, logarithms, and trigonometry; functions; introduction to continuity, limits, differentiation, and integrals, with applications.
Topics in Advanced Mathematics
teaching, Hamline University, 1900
This course will consider various recently defined graph parameters that can be viewed as the result of playing different games on graphs, e.g., the cop number of a graph (which comes from the game of cops and robbers on graphs), the burn number, power domination number, and the standard and several variations of the zero forcing number of a graph.
Calculus II
teaching, Drake Univeresity, 1900
Advanced applications of differentiation; advanced techniques and applications of integration; simple examples of differential equations.