About

Michael Maltenfort received his PhD from the University of Chicago in 1997. Following graduation, he was a Peace Corps volunteer in Kenya. He then returned to Chicago, where he briefly taught at DePaul University and Loyola University before joining the faculty at Truman College, where he taught from 2002 to 2013. He joined the faculty at Northwestern University as a Weinberg College Advisor in 2013. Maltenfort's research is in simple mathematics, including problems that are accessible to those whose background is limited to calculus.

Research topics

• Mathematics
• Combinatorics
• Pure mathematics
• Arithmetic
• Discrete mathematics
• Mathematics education

Selected publications

• Balanced Stirling numbers

  Aequationes Mathematicae · 2024

  1st authorCorresponding
  • Mathematics
  • Combinatorics
  • Discrete mathematics
  PublisherDOI

• Counting Spaces

  Mathematics Magazine · 2021

  Senior authorCorresponding
  • Mathematics
  • Mathematics education
  PublisherDOI

• The Associativity of Infinite Matrix Multiplication, Revisited

  College Mathematics Journal · 2021

  1st authorCorresponding
  • Mathematics
  • Arithmetic
  • Pure mathematics

  SummaryWe give a simple approach to determine when multiplication is associative for matrices of infinite size, extending recent results of Bossaller and López-Permouth.

  PublisherDOI

• Decimal Selection Functions

  American Mathematical Monthly · 2019-07-09 · 1 citations

  article1st authorCorresponding

  When we take a decimal form of a number in the unit interval [0,1], we can form a new number by selecting certain digits and discarding the others. We analyze the properties of this process, particularly in relationship to a recent Monthly article.

  PublisherDOI

• New definitions of the generalized Stirling numbers

  Aequationes Mathematicae · 2019-10-05 · 8 citations

  article1st authorCorresponding
  PublisherDOI

• Pascal Functions

  American Mathematical Monthly · 2018-01-30 · 1 citations

  article1st authorCorresponding

  We define Pascal functions by adapting the arithmetic rule that creates the Pascal triangle. By developing and applying properties of Pascal functions, we discover new identities and find new perspectives of old identities. The identities all involve binomial coefficients, with some also involving Stirling numbers, Stirling polynomials, associated Stirling numbers of the second kind, or Bell numbers.

  PublisherDOI

• A Function Worth a Second Look

  College Mathematics Journal · 2017-01-01

  article1st authorCorresponding

  SummaryWe take a closer look at an interesting function introduced in a recent Classroom Capsule by Denis Bell.

  PublisherDOI

• Characterizing Additive Systems

  American Mathematical Monthly · 2017-01-01 · 1 citations

  article1st authorCorresponding

  An additive system is a collection of sets that gives a unique way to represent either all nonnegative integers, or all nonnegative integers up to some maximum. A structure theorem of de Bruijn gives a certain form for an additive system of infinite size. This form is not, in general, unique. We improve de Bruijn's theorem by finding a unique form for an additive system of arbitrary size. Our proof gives a concrete construction that allows us to test easily whether a collection of sets is an additive system. We also show how to determine most of the structure of an additive system if we are only given its union.

  PublisherDOI

• A Canine Conundrum, or What Would Elvis Do?

  College Mathematics Journal · 2016-03-01 · 1 citations

  article1st authorCorresponding

  SummaryThe dog Elvis became famous by finding optimal paths that solve various calculus problems. Not all problems, however, have solutions. By giving an unsolvable problem very similar to those Elvis solved, we provide a reminder that it is necessary to prove, rather than assume, that optimal paths exist.

  PublisherDOI

• Secants, Tangents, Rotations, and Reflections

  College Mathematics Journal · 2015-01-01

  article1st authorCorresponding

  SummaryGiven the graph of a continuous function on an interval, if we know the slopes of all the secant lines, then we can determine which rotations and reflections of the graph are also graphs of functions and, for those that are, whether the new functions are one-to-one. Provided that the original function is differentiable on the interior of the interval, we can determine the slopes of all secant lines by calculating the range of the function's derivative, provided that we know any subintervals where the function is linear.

  PublisherDOI

Frequent coauthors

• Bailey Fluegel

  Woods Hole Oceanographic Institution

  1 shared

• Dominic Hatch

  Northwestern University

  1 shared

• Michael Gilgenbach

  1 shared

• Benjamin Frank

  1 shared

Education

• Ph.D., Mathematics

  University of Chicago

  1997

• M.S., Mathematics

  University of Chicago

  1992

• A.B., Mathematics

  Cornell University

  1991