Classes

Mathematics

  • Fall 2006, Fall 2007

    Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think.

    Each professor in the mathematics department teaches this course differently, with different materials. This Math 103 section is a hands-on discovery course with somewhat odd materials:  the card game SET; a series of handouts and worksheets; the Japanese pencil puzzle book PENPAMIX; and some knot-making materials.

  • Spring 2007

    Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think.

    In this class we will use origami as the vehicle for exploring mathematical topics such as divisibility, the Euler characteristic, the Mandelbrot set, Platonic solids, semi-regular polyhedra, Buckyballs, Menger sponges, and graph theory.

  • Fall 2009

    Sets, logic, numeration systems, development of real numbers, number operations, number theory, geometry, measurement, algebra, functions, probability and data analysis. Sequence is required for early childhood, elementary, or middle school teacher licensure.

  • Fall 2012Spring 2013Fall 2013Spring 2014

    Review of fundamental mathematics required to be successful in Calculus, including graphs of functions, factoring, simplifying, solving equations and inequalities, and exponential/logarithmic/trigonometric functions. Self-paced study with required proctored tests.

  • Fall 2001Fall 2002Spring 2003Fall 2003Fall 2004Fall 2005Fall 2008Spring 2011Fall 2013Fall 2016Fall 2018

    First semester of a sequence that combines first-semester calculus with algebra and trigonometry. The sequence is designed for students whose pre-calculus skills are not strong enough for the standard STEM Calculus sequence. Calculus material includes limits and derivatives of algebraic functions and their applications.

  • Spring 2002Fall 2002Spring 2003Spring 2004Spring 2009Fall 2011Spring 2012Spring 2014Spring 2017Spring 2018Spring 2019

    Second semester of a sequence that combines first-semester calculus with algebra and trigonometry. The sequence is designed for students whose pre-calculus skills are not strong enough for the standard STEM Calculus sequence. Calculus topics include limits and derivatives of transcendental functions, the theory of integration and basic integration techniques.

  • Fall 2000Fall 2010Fall 2012Spring 2013

    Differential and integral calculus of functions of one variable.

  • Spring 2001Summer 2002Spring 2011

    Differential and integral calculus of functions of one variable. Sequences and infinite series.

  • Fall 2005Spring 2006Fall 2009Fall 2012Fall 2018

    Logic, set theory, relations and functions, mathematical induction and equivalent forms, recurrence relations, counting techniques. Introduction to proof and proof techniques.

  • Fall 2008Spring 2013

    Graphs and their applications. Possible topics include trees, Euler paths and Hamiltonian circuits, planar graphs, digraphs, adjacency matrices, connectivity and coloring problems.

  • Spring 2004Fall 2004Spring 2005

    An introduction to groups, rings and fields.

  • Fall 2007Spring 2012

    A proof-based linear algebra course covering such topics as vector spaces, linear transformations and matrices, eigenvalues and eigenvectors, inner product spaces, and canonical forms.

  • Fall 2006

    Metric spaces, limits, continuous maps and homeomorphisms, connectedness, compact topological spaces and applications. This particular class also included topics such as the fundamental group, classification of surfaces, and basic knot theory.

Mentored Mathematical Research

  • Fall 2012, Spring 2013

    Students pursue advanced research in a selected area of mathematics and/or statistics. Student must make arrangements with a supervising instructor prior to registration. This course centered on an active research project concerning determinants of spiral knots.

  • Spring 2006, Fall 2006, and Spring 2007

    Three-semester sequence fulfilling the planning, research, and writing phases of the JMU Undergraduate Honors Thesis program. This particular course centered on new research concerning Shidoku configurations and minimal clue sets.

  • Spring 2014, Fall 2014, Spring 2015

    Three-semester sequence fulfilling the planning, research, and writing phases of the JMU Undergraduate Honors Thesis program. This particular course centered on new research concerning determinants of spiral knots.

  • Summer 2010 Consultant, with Roger Thelwell and Anthony Tongen

    The focus of the research project is Mancala, an ancient family of board games popular in Africa and Asia. While there are many possible rule variants, this ‘sowing’ type game is based on moving stone seeds from one container to others according to prescribed deterministic rules. Play can be surprisingly involved, with a large number of legal moves possible each turn. Surprisingly, there has been little published mathematical research of this very interesting game. John Conway developed his own variant, ‘Sowing,’ which led to some simple mathematical language and structure which could be further developed. The primary research question for this project is “Is there an optimal strategy, against which no other competing strategy can win.” Mancala has been played for more than ten thousand years, suggesting that no obvious optimal strategy exists.

  • Summer 2012

    Open exploration of determinant patterns for spiral knots, using the Online Encyclopedia of Integer Sequences.

  • Summer 2003

    Two Fox m-colorings of a knot or link K are said to be equivalent if they differ only by a permutation of colors. The set of equivalence classes of m-colorings under this relation is the set Cm(K) of Fox m-coloring classes of K. We develop a combinatorical formula for |Cm(K)| for any knot or link K that depends only on the m-nullity of K. As a practical application, we determine the m-nullity, and therefore the value of |Cm(P(p,q,r))|, for any any (p, q, r) pretzel link P(p,q,r). Resulted in published paper Counting m-coloring classes of knots and links.

  • Summer 2004

    We classify by elementary methods the p-colorability of torus knots, and prove that every p-colorable torus knot has exactly one nontrivial p-coloring class. As a consequence, we note that the two-fold branched cyclic cover of a torus knot complement has cyclic first homology group. Resulted in published paper p-Coloring Classes of Torus Knots.

  • Summer 2007, with Len Van Wyk

    Spiral knots are a generalization of torus knots we define by a certain periodic closed braid representation. For spiral knots with prime power period, we calculate their genus, bound their crossing number, and bound their m-alternating excess. Resulted in published paper Spiral Knots.

  • Summer 2011, with Anthony Tongen

    We introduce a new matrix tool for the sowing game Tchoukaillon that enables us to non-iteratively construct an explicit bijection between board vectors and move vectors. This allows us to provide much simpler proofs than currently appear in the literature for two key theorems, as well as a non-iterative method for constructing move vectors. We also explore extensions of our results to Tchoukaillon variants that involve wrapping and chaining. Resulted in published paper Mancala Matrices.

  • Summer 2013, with Len Van Wyk

    An open-ended experimental exploration of singular knots and their classification. Specifically, how can we generate a complete enumeration of 1-singular and 2-singular knots?

  • Summer 2018, with Brant Jones

    The game of best choice, also known as the secretary problem, is a model for sequential decision making with many variations in the literature. Notably, the classical setup assumes that the sequence of candidate rankings is uniformly distributed over time and that there is no expense associated with the candidate interviews. Here, we weight each ranking permutation according to the position of the best candidate in order to model costs incurred from conducting interviews with candidates that are ultimately not hired. We compare our weighted model with the classical (uniform) model via a limiting process. It turns out that imposing even infinitesimal costs on the interviews results in a probability of success that is about 28%, as opposed to 1/e (about 37%) in the classical case. Resulted in the published paper Opportunity costs in the game of best choice.

3D Printing and Design

  • Fall 2017

    Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think.

    Our explorations of mathematics in this course will be supported by 3D printing and design in the JMU 3SPACE Classroom. This will be a highly digital course and we will be using the internet as our primary textbook. We will also make use of online collaboration and publication tools, and use 3D design software and coding to create and explore mathematical objects. Main topics will include fractals and the fourth dimension, but we may also investigate puzzles, knots, polyhedra, graph theory, computational geometry, topology, squircles, splines, or whatever we find interesting.

  • Fall 2013Spring 2014Fall 2017Spring 2019

    A study of topics selected to allow students to participate in mathematical and scientific problem solving approaches to knowledge.

    Our explorations of problem solving and iteration in this course will be supported by 3D printing and design in the JMU 3SPACE Classroom. This will be a highly digital course and we will be using the internet as our primary textbook. We will use both online and locally installed 3D design software and coding programs, and make use of online collaboration and publication tools. The main objective of this class is to put you in a hands-on environment where you can apply modern problem solving approaches such as design thinking, project iteration, and independent learning.

  • Spring 2013

    Topics or projects in mathematics which are of interest to the lower-division student. In this particular course, students will explore new 3D printing technologies at IVS, Engineering, and the new Math MakerLab, and learn how to create 3D-printable mathematical forms using 3D design software.

  • Spring 2018

    Designed to give students an opportunity to complete independent study and/or research under faculty supervision in university studies. This semester’s research projects were chosen by students and were electoral maps, GIS data, facial recognition, and tactile floorplans, designed and 3D printed in the JMU 3SPACE classroom.

  • Spring 2014

    A multi-week exploratory workshop for faculty interested in getting started with the 3D printing technologies available through JMU 3SPACE and the Library Makeries.

  • Summer 2017, Summer 2019

    A multi-session exploration of current 3D scanning technologies including scanners, photogrammetry, apps, and mesh manipulation software.

  • Fall 2016

    Research findings about teaching in the content area will be used to identify the most effective instructional strategies for teaching that content to students in grades 9-12.  Emphasis will be on developing plans for employing the strategies and making appropriate instructional decisions based on instructional goals, the learner, and available resources. This particular class will also introduce students to Desktop Fabrication tools such as 3D printing, 3D design, and Lasercutting.

  • Fall 2013, Spring 2014

    Explorations of cutting-edge technology and beta-level hardware for multimaterial 3D printing.

  • Spring 2017

    Explore using Sketchup in JMU 3SPACE to design 3D models based on historical blueprints, then experience your structures in Virtual Reality at the Carrier Makery.

  • Fall 2017

    Did you know that desktop fabrication is more than 3D printing? In the JMU Library Makeries we have cababilities to use CNC machines like the Carvey and ShopBot to design and carve into wood and other materials. Come learn with us how to design and create projects using these tools!

  • Fall 2017

    Have you wondered if it was possible to 3D print objects in a material other than plastic? In this session we will explore 3D printing using silicone, food, and resin.  Join us to explore the benefits of being able to print objects in alternative materials.

  • Summer 2018 and Fall 2018

    Already know some 3D design basics? Expand your toolbox with Scribble, Fusion 360, and OpenSCAD and learn three ways to create 3D-printable spiralized vase designs.

  • Spring 2018 and Fall 2018

    Join us in JMU’s 3D printing classroom 3SPACE to take your 3D design skills to the next level. We will use Fusion 360 to design a ring from scratch that we will have 3D printed in Metal at Shapeways. 3D design and printing experience not required.

  • Summer 2018 and Fall 2018

    Join us to learn how to color your 3D prints to print on the da Vinci Full Color 3D Printer! This desktop 3D printer uses CMKY inkjet technology and color absorbing PLA to create full color 3D prints. We will explore how to design in color utilizing TinkerCad, how to blend colors using Meshmixer as well as how to design in XYZ Maker. We will schedule times for everyone to print their designs in full color.

Mentored Design Research

  • Spring 2014

    Students pursue research in a selected area of mathematics and/or statistics. Topics include knot theory, in particular knot classification and special knot types, and 3D modeling skills required to design and print physical models of various knot types.

  • Spring 2017

    Students pursue research in a selected area of mathematics and/or statistics. Topics include knot classification, homotopies, and graph theory, as well as 3D modeling skills using OpenSCAD and Fusion 360 to create relevant 3D-printable models.

  • Fall 2017

    Students pursue research in a selected area of mathematics and/or statistics. Topics in graph theory include generalized Petersen graphs, intrinsically linked graphs, intrinsically knotted graphs, and representations of non-planar graphs. Students will also learn 3D modeling skills in order to create new physical models of spatial graphs that exhibit symmetry or particular efficiency.

  • Summer 2013

    Two students will lead the construction and administration of the new Math/Stat MakerLab, and along the way explore new software and hardware solutions to support this new technology.

  • Fall 2018, Spring 2018

    By changing parameters in equation for tritangentless trefoils we get different tritangentless conformations. Some of these conformations roll better than others; which one is optimal? And can we prove that one is optimal? We will experiment with 3D printed conformations of tritangentless trefoils, and also try to use calculus, linear algebra, and geometry to arrive at an optimal solution.

  • Fall 2018, Spring 2018

    The model shown in the image is a 3D spatial representation of the complete bipartite graph K4,4. When drawn in the plane, this graph necessarily intersects itself, and it has quite a few overlapping edges. When working in three dimensions, we can arrange the vertices so that the edges do not intersect. Determining the “best” way to do this is an aesthetic and artistic challenge.

  • Fall 2018, Spring 2018

    One of the ways in which engineers reduce rocket launch noise is through the use of a trench which channels the rocket exhaust away. The shape of this trench is very important. In particular, Dr. Lubert has been working with Orbital ATK (now Northrop Grumman) – one of the two commercial resuppliers of the International Space Station, together with SpaceX – who launch their Antares rocket from NASA’s Wallops Flight Facility on the Eastern Shore of Virginia. We will use engineering drawings of the Wallops trench to create a 3D printed version of it, so that we can more easily visualise and understand the flow processes that take place inside it.

  • Spring 2017

    Explorations of advanced 3D printing topics such as mid-print error detection, mathematical visualization, and algorithmic infill generation.

  • Fall 2017Spring 2018

    Explorations of advanced 3D printing topics, including representations of generalized Petersen graphs, large-scale scanning and printing, and the creation of an inversive geometry library.