John Perram's personal home page

Contents

From this home page, you can learn a little bit about:

My academic career

My activities as coordinator of e-learning at the Faculty of Science and Engineering

My current research interests

The courses I am teaching and how to follow them, even if you are not enrolled as a student at SDU

A list of possible topics for masters theses in the areas of e-learning and analytical mechanics

My spare time activities

by clicking on the orange hyperlinks. The section "Courses I am teaching..." contains information for external students on how to take courses in analytical mechanics and dynamical systems as distance learning.

Biographical

I was born in 1945 in Sydney, Australia, educated at the University of Sydney (BSc in applied mathematics) and University of Manchester (Ph.D. in applied mathematics). I have been professor of applied mathematics at this university since 1975, first in the Department of Mathematics and Computer Science and now in the Maersk Mc-Kinney Moller Institute. I am also currently coordinator (until 1 January 20059 of e-learning for the Faculty of Science and Engineering, where my role is to explain to teachers why and how they should use the Blackboard learning management system.

Apart from e-learning, I am also interested in the technology transfer process, and am a member of the Rektor's Patent Committee.

In the course of my career, I have been awarded Director Ib Henriksen's Prize, the Industrial Prize awarded by the Danish Academy of Natural Sciences, the Funen IT Prize and the Hartmann Brother's Prize.

E-learning

As coordinator of e-learning for the Faculty of Science and Engineering, my role is to help colleagues to use the system to improve the quality and effectiveness of their teaching. It can help you to securely distribute learning material, broadcast announcements, provide you with an up to date electronic list of course participants, send email to students, securely receive project reports and assignments in electronic form, and enable threaded discussions between the students. It can also generate a spreadsheet of participants, which may be useful for grading projects.

Research

After getting my Ph.D. in 1969, I spent the next 15 or so years mainly doing research in statistical mechanics and molecular dynamics, with occasional forrays into other applications of mathematical modelling, such as biophysics, electro- and surface chemistry and computational geometry. These papers are now being cited by researchers in the field of nanotechnology, so I am thinking about returning to work in this area. In fact, I held a lecture recently on charge regulation in colloidal interaction. Click here to download the material in Mathematica notebook (.nb) format. Click here to download the material in .pdf format. The lecture was recorded in compressed .avi format using Camtasia. To watch them, you will need to download the (free) Techsmith Codec by clicking here. Click here to download the first part. Click here to download the second part. Click here to download the third part.

At the end of this period, I realised that some of the techniques from molecular dynamics and computational geometry could be used to move robots as well as molecules, so I moved the focus of my research from statistical mechanics to industrial robotics, within the AMROSE project in industrial robotics, together with Odense Steel Shipyard, which aimed to and succeeded in building an autonomous welding robot. This research got me interested in the whole technology transfer process, where I concluded that the main vehicles for innovation in industry are the graduates we produce, because no organisation can exploit knowledge from the academic world unless they have people who speak the language.

This, and many years of curriculum administration, has made me realise that the main challenge facing universities is how to use IT creatively to improve the quality and usefulness of our teaching, particularly in the areas of applied mathematics and engineering. Universities are largely about developing and imparting knowledge, whereas employers of our graduates are most interested in people who can use their knowledge to solve their employers' problems. I remember an industrial recruiter from my own student days saying: "A graduate who can carry out a measurement competently is worth his weight in lead. A graduate who can improve the measurement is worth his weight in silver. But a graduate who can show that the measurement was never necessary in the first place, is worth his weight in gold."

This research focusses on examining the nature of mathematical knowledge based on our experience in developing electronic learning material for two courses, AM12, a course in analytical mechanics, and AM14, a course in dynamical systems and chaos. This experience suggests that mathematical knowledge can be represented electronically as small, interoperable symbolic, graphical and numerical code fragments, implemented in an environment such as Mathematica. Competences are developed as a kind of meta-knowledge as the students gain experience in learning how to apply their mathematical tools to solving problems relevant to their study program.

Teaching

My courses and how to take them

I currently teach the course AM14, (dynamical systems and chaos, 7.5 ECTS points) in the fall semester and AM12 (analytical and computational mechanics, 9 ECTS points) in the spring. The textbook for each course are a number of interactive modules I have written, written in the Mathematica notebook interface. These courses are particularly suitable for students interested in robotics, who should click here to see an animation of a robot following the Lorenz strange attractor.

These books integrate mathematical text with graphics and symbolic code fragments, which automate most of the mathematical argument, which can be followed by executing them one at a time. This is the format of my lectures, which have been recorded using the Camtasia screen capture system and can be downloaded, along with the text book and the application projects from the respective Blackboard courses.  

These courses, which are taught in English, can be taken free of charge as distance learning by students from within the EU as part of the Erasmus program, or, by paying a small fee, under the University of Southern Denmark's Open University program. The interface between the University's learning management system (Blackboard) and the other student administrative systems is currently being updated, so that students for AM12 should be able to get at my learning material from the middle of January, 2005.

Getting started for International Masters' students

If you want to prepare for your arrival here in September, a good thing to do is to find out how to use Mathematica, which is integrated into several of our courses, such as AM11 and AM14, which you will take in the coming semester. Click here to download Module 0 of AM14 in .nb format.

I have also made 3 short video presentations of this material. To view these videos, you will need a Windows machine and download the free Camtasia player and CODEC, which can be done by clicking here.

http://www.mip.sdu.dk/~jperram/AM14_2003/module0_1.avi

Click here to download the first video

Click here to download the second video

Click here to download the third video

AM14: dynamical systems and chaos (7.5 ECTS)

This course uses Mathematica and knowledge about vector calculus and linear algebra to study the qualitative behaviour of low dimensional systems of differential and difference equations. Click here to see the official course description. Using a package such as Mathematica, with its symbolic, graphical and numerical capabilities, allows us to introduce a few novel features, such as:

Using curvature to diagnose the limit cycle in the van der Pol system

The van der Pol equations

are a model for an active electronic circuit. For any positive value of ε, the trajectories converge to a closed curve, called a limit cycle. For this system it is possible to compute the curvature as

and to use Mathematica to find the curves where it is zero. These curves (shown in green), and the red curve of vertical tangents are shown below

superimposed on the flow field plot, a rectangular array of arrows pointing in the direction of the tangents to the trajectories. Simple geometric arguments show that trajectories starting in or entering the region between the two green curves cannot leave it, trajectories starting close to the origin spiral outwards, trajectories entering from outside spiral inwards, so we can conclude that all trajectories are attracted to a single closed curve.

How to build a dynamical system with a predefined limit cycle

The picture below, taken from Module 6,

shows the trajectory, the red curve, of a dynamical system whose limit cycle is a cardioid. This curve is superimposed on the flow field plot.

Finding the chaotic parameter space of the Lorenz system

Lorenz's famous dynamical system

can exhibit extremely complex behaviour for some values of the 3 dimensionless, non-negative parameters  σ, r and b, such as the trajectory shown below

one of the most famous pictures in applied mathematics.

For values of r less than unity, it has a single stable fixed point at the origin. For values of r greater than 1, this fixed point becomes an unstable saddle with a 2-dimensional unstable manifold and two new fixed points emerge from it, which are situated in the two circular holes in the trajectories

In his original paper, Lorenz (E.N. Lorenz, Deterministic nonperiodic flows, J. Atmos. Sci., 20, 130, (1963)) showed that the system's behaviour was chaotic for σ=10, b=8/3 and  values of r greater than about 24.74. In a later numerical study, Kaplan and Yorke (J.L. Kaplan and J.A. Yorke, Preturbulence: a regime observed in a fluid flow by Lorenz, Comm. Math. Phys., 67, 93, (1979)) discussed the behaviour of the system for Lorenz's parameter set.

The shape of the trajectories suggests that complicated behaviour occurs when the two fixed points become unstable. Using Mathematica, we show that this occurs when

For the numerical case studied by Lorenz, this occurs when r is greater than 470/19, whose value to 6 decimal places is 24.736842.

Who should take the course

Apart from science and engineering students, this course might be interesting for students of artificial intelligence, since dynamical systems can be regarded as simple kind of agent. Since the course only uses freshman mathematics, it could also be interesting for anyone with this knowledge who is interested in finding out more of one of the more exciting areas of modern mathematics. To follow the course, you will need to obtain a student license for the Mathematica package, about which you can find out more by clicking here.

AM12: analytical and computational mechanics (9 ECTS)

This course uses Mathematica and knowledge about vector calculus and linear algebra to study the behaviour of mechanical systems modelled as constrained particle systems. Constrained particle systems model solid bodies as a collection of point masses connected by massless, rigid constraints, such as the model humanoid shown below.

Click here to see the official course description.

The course has a number of novel features, including:

The extensive use of simulation to visualise and animate mechanical systems such as blast wheels, robots and spinning tops

The derivation of the approximate expression

for the dependence of the frequency of the simple pendulum on its amplitude Θ (the angle the pendulum makes with the downward vertical direction when it is released from rest).

A discussion of the nature of time dependent constraints (such as Foucault's pendulum) and how to avoid them, by realising that they are approximations to reality when one subsystem is very much bigger (the earth) than the other (the pendulum rotating with it). According to Newton's third law, Foucault's pendulum will affect the motion of the earth, and when this is taken into account, the constraints are independent of time. This avoids the need to struggle mentally with the principle of virtual work

Who should take the course

Apart from science and engineering students, this course might be interesting for anyone with appropriate mathematical knowledge interested in experiencing a traditional, mathematical (but elementary) treatment of mechanics, in which secondary principles are deduced as mathematical consequences of Newton's laws, one of the towering human intellectual achievements. To follow the course, you will need to enroll as a student at SDU and obtain a student license for the Mathematica package, about which you can find out more by clicking here.

Masters' projects

Below is a list of short masters' project descriptions. If any of them appeal to you, please contact me.

E-learning in applied mathematics education

This is meant to be a large project in which a number of students participate on their own aspect of it, while all collaborating on establishing a framework.

Procedures for generating electronic learning material in Mathematica

In writing the modules for the AM12 and AM14 learning material, I have experimented with various formats for presenting material, which consists of equations, explanatory and connecting text and fragments of Mathematica code which have to be executed to generate the figures, animations and equations. This project is about investigating what is the best way to do this, also examining such questions as the semi-automatic generation of connecting text. All the students will participate in this sub-project.

The nature of mathematical knowledge and meta-knowledge

In the courses AM12 and AM14, knowledge is represented as small Mathematica code fragments, which participants use to solve problems, by putting these fragments together into composite tools. This leads us to the model that mathematical knowledge can be largely represented as small fragments of Mathematica symbolic, graphical and numerical code. Mathematical competence then becomes the ability to put these tools together to solve more complicated problems. This project sets out to investigate the extent this is true by examining the high school mathematics curriculum, and the extent to which students could learn how to use Mathematica in the process of building a toolbox of Mathematica code fragments to reinforce their knowledge of high school mathematics. Yu Zhang and Zhiyong Fang have expressed an interest in this project.

Just in time applied mathematics

The aim of this project is devise a methodology for developing mathematical meta-knowledge by learning mathematics in the context of using it to solve problems in mathematical modelling of the physical world. The mathematical models in this project are taken from the components of the classical freshman physics curriculum, mechanics, electricity, optics and thermodynamics. The question to be answered is: can they be ordered in such a way that they serve as platforms for introducing the standard freshman mathematics curriculum in calculus and linear algebra?

Partial differential equations and Fourier series

This project is about designing a Mathematica based course in this important area of applied mathematics, treating initial and boundary value problems for the standard wave, diffusion and Laplace equations, both using the classical solutions in terms of infinite series and numerical methods contained in Mathematica. A possibly interesting issue is using animation and sound as methods for "visualising" periodic phenomena. Yinan Liang is interested in this project.

Fine grained curriculum design

As learning on the web becomes more prevalent, learners will want to free themselves from the place and time constraints imposed by situated education. An external student wanting to learn about the theory of rigid bodies should be able to see which pieces of a modularised curriculum they need to study in order to gain this competence. This project is about building tools for generating the dependency graph associated with competences in a modularised curriculum, using as test material, the nested HTML files generated from the AM12 and AM14 learning material.

Analytical mechanics

For those who wish to look at mechanics beyond AM12, I have a couple of advanced projects in:

Friction modelling in robots

Frictional forces at moving robot joints are proportional to the velocity associated with each degree of freedom and the normal reaction. The normal reaction is related to the constraint forces acting on the joint. A document deriving these equations for the pendulum is available if anyone is interested.

Non-holonomic mechanics

Non-holonomic constraints are associated with rolling, such as a ball rolling on a surface or a mobile robot car trying to park itself. These constraints usually have the form of Pfaffian differential equations, of the form

which may not be integrable (eg, expressed as the time derivative of a scalar function of the coordinates). The project is about building a simulator for such systems which can be used in connection with computer games and trajectory planning.

Systems with time-dependent constraints

In AM12, we discussed systems with time dependent constraints, such as the blast wheel and Foucault's pendulum, showing that these constraints are an approximation to reality when we ignore, for example, the force of Foucault's pendulum on the earth. The derivation of the equations of motion for systems with time dependent constraints involves invoking the principle of virtual work, in which the student is invited to study the work done by the forces of constraint in a displacement consistent with the instantanous constraints. The project is about making sense of the statement in Goldstein's book: "We now restrict ourselves to systems for which the virtual work of the forces of constraint is zero. We have seen that this is true for rigid bodies, and it is valid for a large number of other constraints" by answering "why and which constraints".

Spare time interests

When I am not developing my ideas about education, I am an avid golf player (handicap 6.8)  at Sct. Knud's Golf Club in Nyborg. I am currently the captain of the club's senior (over 55) golf team, which plays in the elite division of the Danish Championship for club teams. If you understand Danish, you can follow our progress by clicking here.

Created by Mathematica  (December 21, 2004)