William Hackborn, Ph D, M Sc, B Math

Professor, Augustana - Sciences

Contact

Professor, Augustana - Sciences
Phone
(780) 679-1106
Address
C152 AG03 Classroom Building
4901-46 Ave
Camrose AB
T4V 2R3

Overview

Research

Prof. Hackborn's research interests include applied mathematics (especially fluid dynamics), chaos theory (the study of the surprising patterns and apparent randomness present in some basic processes of the natural world), the history of mechanics (part of the history of physics and mathematics), and projectile motion (including ballistics and the somewhat dark roles both mathematics and computing science have played in the birth and development of this black art). Most recently, he has also been doing research on social networks, both in a practical way (via a survey of the connections between U Alberta professors) and, more theoretically, using differential equations to approximate social networks that capture some of the ways in which human communities adopt ideas and build consensus.


Teaching

Brief Teaching Philosophy

The most important ingredient in learning computing science and mathematics (like music) is practice, practice, practice!  So, Prof. Hackborn likes to give students lots of opportunities for practicing their course work both during class and afterwards in a variety of ways, including group activities and individual assignments.  He also likes to impress upon his students the utility and beauty of mathematics and computing, and the important roles they have played in the development of the modern world, because students cannot be expected to learn a subject unless and until they see why it is worth learning (and the passion it excites in its disciples).

Courses Taught since Fall 2003

  • AUCSC 110  Introduction to Computing Science  (Fall 2003)
  • AUCSC 120  Abstraction, Design and Object-Oriented Programming  (Winter 2009)
  • AUCSC 210  Algorithm Analysis and Data Structures  (Fall 2012)
  • AUCSC 315  Theory of Computing  (Winter 2013, cross listed with AUMAT 355)
  • AUCSC 340  Numerical Methods  (Fall 2003, cross-listed with AUMAT 340 & AUPHY 340)
  • AUCSC 330  Database Management Systems I  (Winter 2018)
  • AUCSC 430  Database Management Systems II  (Fall 2004)
  • AUIDS 211  Interdisciplinary Science Projects (Winter 2019)
  • AUMAT 110  Elementary Calculus I  (Fall 2018)
  • AUMAT 116  Elementary Calculus I, Enriched  (Fall 2015)
  • AUMAT 112  Elementary Calculus II  (Winter 2018)
  • AUMAT 212  Intermediate Calculus II  (Winter 2016)
  • AUMAT 229  Introduction to Group Theory  (Winter 2015)
  • AUMAT 260  Topics in Geometry  (Fall 2007)
  • AUMAT 315  Complex Variables  (Winter 2019)
  • AUMAT 332  Mathematical Ecology and Dynamical Systems  (Fall 2014)
  • AUMAT 480  History of Mathematics and Physics  (Fall 2015)

Courses

AUCSC 340 - Numerical Methods

Computer arithmetic and errors, solution of systems of linear equations, root finding, interpolation, numerical quadrature, and numerical solutions of ordinary differential equations. Applications from physics are included. Prerequisites: AUCSC 111, AUMAT 120, AUMAT 112; or consent of the instructor. Note: Credit may be obtained for only one of AUCSC 340, AUMAT 340, AUPHY 340.

Fall Term 2020
AUMAT 315 - Complex Variables

Complex numbers, functions of a complex variable, analytic functions, Cauchy and related theorems, Taylor and Laurent expansions, the residue calculus and applications, harmonic functions, conformal mapping, applications. Prerequisite: AUMAT 212.

Winter Term 2021
AUMAT 332 - Mathematical Ecology and Dynamical Systems

Mathematical analysis of problems associated with ecology, including models of population growth (e.g., discrete, continuous, age-structured, limited carrying capacity), the population dynamics of ecosystems, the spread of epidemics, the transport of pollutants, and the sustainable harvesting of vegetation and animal populations. Fundamental concepts of discrete and continuous dynamical systems, both linear and nonlinear. Prerequisites: AUMAT 120 and 211.

Fall Term 2020
AUMAT 340 - Numerical Methods

Computer arithmetic and errors, solution of systems of linear equations, root finding, interpolation, numerical quadrature, and numerical solutions of ordinary differential equations. Applications from physics are included. Prerequisites: AUCSC 111, AUMAT 120, AUMAT 112; or consent of the instructor. Note: Credit may be obtained for only one of AUMAT 340, AUCSC 340, AUPHY 340.

Fall Term 2020
AUPHY 340 - Numerical Methods in Physics

Computer arithmetic and errors, solution of systems of linear equations, root finding, interpolation, numerical quadrature, and numerical solutions of ordinary differential equations. Applications from physics are included. Prerequisite: AUCSC 111, AUMAT 120, AUPHY 120 or 250, AUMAT 112. Note: Credit may be obtained for only one of AUPHY 340, AUCSC 340, AUMAT 340.

Fall Term 2020

Browse more courses taught by William Hackborn

Scholarly Activities

Research - Alberta Mathematics Dialogue (AMD) 2019

20190502 - 20190503

I am the principal organizer of the Alberta Mathematics Dialogue (AMD) 2019, to be held at the Augustana Campus on Thursday-Friday, 2-3 May 2019.

Our talented line-up of invited speakers is well-balanced. All have confirmed their attendance. They are (in alphabetical order):

  • Melania Alvarez, UBC, Mathematics Education & Indigenous Outreach
  • Greg Forest, U North Carolina, Mathematical Biology & Big Data
  • Thomas Hillen, U Alberta, Public Lecture (on Math & Music)
  • Vakhtang Putkaradze, U Alberta, Theoretical Mechanics (applied to figure skating)
  • Jonathan Schaeffer, U Alberta, Banquet Speaker (on artificial intelligence)
  • John Stockie, Simon Fraser University, Industrial Mathematics
  • Steph van Willigenburg, UBC, Algebraic Combinatorics

We're excited about these speakers. They have all won awards of various kinds. Parallel sessions (associated with the areas of our invited speakers and other areas popular at previous AMDs) to be held at AMD 2019 include:

  • Algebraic Combinatorics
  • Big Data (and other areas of Comp Sci, where mathematics plays a big role)
  • Industrial and Applied Mathematics
  • Mathematical Biology
  • Mathematics Education, Pedagogy & Outreach
  • Number Theory
  • Statistics (both pedagogy & research)
  • K-12 Math Curriculum (and how it relates to post-secondary education)
  • Undergraduate Research

We particularly encourage the participation of post-doctoral fellows, graduate students, and undergraduates. One of the mandates of AMD has always been to nurture the talents of aspiring mathematicians. Please note the last session topic above: Undergraduate Research.

AMD 2019 will also include a special panel/roundtable on jobs in mathematics. We plan to invite Alberta math/stats graduates who now work in sectors that rely heavily on mathematics (such as computer science, financial analysis, data science, etc.) to address this panel. This is another reason why young mathematicians will want to attend -- academia alone is not big enough to hold all the mathematical talent in Alberta.

The deadline for abstract submission is Friday, 5 April 2019.

Publications

Euler's Discovery and Resolution of D'Alembert's Paradox
Author(s): William W. Hackborn
Publication: Research in History and Philosophy of Mathematics. Proceedings of the Canadian Society for History and Philosophy of Mathematics.
Volume: 4
Issue: 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics
Page Numbers: 43-57
External Link: https://rd.springer.com/chapter/10.1007%2F978-3-319-90983-7_3
On motion in a resisting medium: A historical perspective
Author(s): William W. Hackborn
Publication: American Journal of Physics
Volume: 84
Issue: 2
Page Numbers: 127-134
External Link: https://www.researchgate.net/publication/291391679_On_motion_in_a_resisting_medium_A_historical_perspective
Pattern Formation in Reaction–Diffusion Models with Nonuniform Domain Growth
Author(s): Edmund J. Crampin, William W. Hackborn, Philip Maini
Publication: Bulletin of Mathematical Biology
Volume: 64
Issue: 4
Page Numbers: 747-769
External Link: https://www.researchgate.net/publication/11173643_Pattern_Formation_in_Reaction-Diffusion_Models_with_Nonuniform_Domain_Growth
Projectile Motion: Resistance Is Fertile
Author(s): William W. Hackborn
Publication: The American Mathematical Monthly
Volume: 115
Issue: 9
Page Numbers: 813-819
External Link: https://www.researchgate.net/publication/233649871_Projectile_Motion_Resistance_Is_Fertile
The Science of Ballistics: Mathematics Serving the Dark Side
Author(s): William W. Hackborn
Publication: Proceedings of the Canadian Society for History and Philosophy of Mathematics
Volume: 19
Page Numbers: 109-119
External Link: https://www.researchgate.net/publication/319459791_The_Science_of_Ballistics_Mathematics_Serving_the_Dark_Side