• On flipping the classroom in large first year calculus courses
    Jungić, V., Mulholland, J., International Journal of Mathematical Education in Science and Technology. Vol. 46, Issue 4, 2015, 508—520.
    [ link ]
  • On the use of instructor made video lectures in context of flipped classroom.
    Kaur, H., Xin, C., Jungić, V., Mulholland, J., The International Conference of STEM in Education, 2014
  • On instructor experiences in three flipped large undergraduate calculus courses.
    Xin, C., Kaur, H., Jungić, V., Mulholland, J., The International Conference of STEM in Education, 2014
  • Is Close Enough Good Enough? Reflections on the Use of Technology in Teaching Calculus
    Jungić, V., Mulholland, J., International Journal of Mathematical Education in Science and Technology, Vol. 25, Issue 7, 2014, 1075--1084
    [ link ]
  • Twisted Extensions of the Cubic Case of Fermat's Last Theorem
    M. A. Bennett, F. Luca, and J. Mulholland. Ann. Sci. Math. Québec 35, No 1, 2011, 1–15.
    [ pdf ]
  • Online Calculus Course: Combining Two Worlds
    V. Jungic and J. Mulholland. Journal of the Mathematics Council of the Alberta Teachers' Association: delta-K, Vol. 49, No. 1, 2011, 28--33.
  • On the Diophantine equation $x^n+y^n=2^{\alpha}pz^2$.
    M. A. Bennett and J. Mulholland. C. R. Math. Acad. Sci. Soc. R. Can. 28, 2006, no. 1, 6--11.
    [ pdf ]
    This paper contains the results of Chapter 8 of my PhD thesis.
  • Elliptic Curves with Rational 2-Torsion and Relatetd Ternary Diophantine Equations.
    PhD Thesis, UBC July 2006
    [ pdf ] (1.6 MB) - 332 pages ... oh my!
    The main result is a classification fo elliptic curves with rational 2-torsion and good reduction outside 2,3 and a prime p. This extends the work of Hadano, and more recently, Ivorra. A key factor in doing this is to have a method for efficiently computing the conductor of and elliptic curve with 2-torsion, and we specialize the work of Papadopoloous to provide such a method. We then use this classification to study solutions to certain families of ternary Diophantine equations.
  • Local Indicability and Commutator Subgroups of Artin Groups.
    J. Mulholland and D. Rolfsen. arXiv:math.GR/0606116 v1, June 2006
    [ pdf ]
    This paper contains the results of my master's thesis.
  • Artin Groups and Local Indicability
    MSc Thesis, UBC September 2002
    [ pdf ]
    This thesis consists of two parts. The first part (chapters 1 and 2) consists of an introduction to theory of Coxeter groups and Artin groups. This material, for the most part, has been known for over thirty years, however, we do mention some recent developments where appropriate. In the second part (chapters 3-5) we present some new results concerning Artin groups of finite-type. In particular, we compute presentations for the commutator subgroups of the irreducible finite-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the braid groups (see also the paper below). Using these presentations we determine the local indicability of the irredudible finite-type Artin groups (except for $F_4$ which at this time remains undetermined). We end with a discussion of the current state of the right-orderability of the finite-type Artin groups.
  • A Presentation for the Commutator Subgroups of the Braid Groups
    unpublished. June 2002
    [pdf]
    Gorin and Lin [1969] gave a presentation for the commutator subgroups of the braid groups which showed they were finitely presented and, moreover, showed that for n>4 the commutator subgroups are perfect. In this paper we fill in the details of their computation.
  • Algorithms for Trigonometric Polynomials
    M. Monagan, J. Mulholland. Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, (2001), 245--252.
    [ pdf ]
    In the summer of 2000 I worked as an NSERC summer research student with Dr. Michael Monagan and the Computer Algebra Group (CAG) at the Center for Experimental and Constructive Mathematics (CECM) located at Simon Fraser University (SFU). The work we did that summer appears in this paper. We describe algorithms for factoring, and computing gcd's of trigonometric polynomials (polynomials in sin(x) and cos(x)), also, we describe an algorithm for simplifying ratios of trigonometric polynomials. Surprisingly, to simplify a ratio of trigonometric polynomials by canceling gcd's may not give the best result. I have included below; a Maple worksheet describing the simplification problem (can be read as motivation for reading the paper), and the (Maple) source code for all the algorithms described in the paper. The algorithms are implemented in the latest version of Maple.
    [ Example ] [ Source Code ]