MaplePrimes Announcement

Reporting from Amsterdam, it's a pleasure to report on day one of the 2014 Maple T.A. User Summit. Being our first Maple T.A. User Summit, we wanted to ensure attendees were not only given the opportunity to sit-in on key note presentations from various university or college professors, high school teachers and Maplesoft staff, but to also engage in active discussions with each other on how they have implemented Maple T.A. at their institution.

We started things off by hearing an encouraging talk by Maplesoft’s president and CEO Jim Cooper. Jim started things off with a question to get everyone thinking; “How will someone born today be educated in the 2030s?” From there, we heard about Maplesoft’s vision on education, learning, and questions we have to ask ourselves today to be prepared for the future.

Up next was Louise Krmpotic, Director of Business development. Louise discussed content and Maple T.A. This included an overview of our content team operations, what content is currently available today, and how users can engage themselves in the Maple T.A. community and get involved in sharing their own content with other users.

We then heard our first keynote presentation by Professor Steve Furino and Rachael Vanbruggen of the University of Waterloo.  We were provided with a brief history of the University of Waterloo and mathematics as well as their ever expanding initiative in brining math courses into an online environment both at the university level and high school level. We then heard in detail of how Maplesoft technologies have been implemented in various math courses and the successes and challenges of creating their own content.

I (Jonny Zivku, Product Manager of Maple T.A.) then delivered a presentation on all the new features in Maple T.A. 10. I won’t get into detail about the new features in this post, but if you’d like to read more about it, check out my previous post from a few weeks ago.

Meta Keijzer-de Ruijter of TU Delft University then took the floor and delivered our second keynote presentation. She discussed the history of Delft as well as the new initiative, the Delft Extension School. She then went on to discuss Delft’s experiences with implementing Maple T.A. at their campus and maintaining it since 2007 as well as how they’ve managed to maintain their academic integrity while using online tools. We also had the opportunity of seeing several examples of some of their excellent questions they’ve created which included adaptive, math apps, algorithms, maple-graded and more.

After a delicious lunch break, Paul DeMarco from Maplesoft, Director of Maple and Maple T.A. Development, talked about the future of testing and assessment. Paul went over various topics and how we envision them changing which included partial marks, skills assessment, learning, feedback, and content.

Jonathan Kress from the University of New South Wales was up next and discussed their experiences with implementing Maple T.A. into their mathematics and statistics courses at a first year, second year, and higher level of learning. He then discussed the various scenarios for how Maple T.A. is deployed which included both formative and summative testing. Moving on, we then were briefed on Maple T.A. use from a student's perspective and an overview of various pieces of content.

We then moved on to an engaging panel discussion which featured Grahame Smart, math and e-learning consultant, Professor Marina Marchisio of the University of Turin and Dr. Alice Barana also from the University of Turin. Grahame first started things off by discussing how he doubled the pass rates in his prevoius high school using investigative and interactive learning with Maple T.A. Marina and Dr. Barana then gave us a brief overview of Maple T.A. at the University of Turin and their exciting PP&S project. The panel then answered various questions from the audience

William Rybolt of Babson College then closed off the presentations with a discussion about how his school has been a long time user of EDU, Maple T.A.’s predecessor.  Going from ungraded web pages, web forms, and Excel, we heard about Babson’s attempts at converting paper-based assignments into an online format until 2003 when they decided to adopt EDU.

To end the day, we enjoyed a nice cruise on the canals of Amsterdam while enjoying a delicious three course meal. Not a bad way to end the day!

Jonny
Maplesoft Product Manager, Maple T.A.


Featured Posts

Last week the Physics package was presented in a talk at the Perimeter Institute for Theoretical Physics and in a combined Applied Mathematics and Physics Seminar at the University of Waterloo. The presentation at the Perimeter Institute got recorded. It was a nice opportunity to surprise people with the recent advances in the package. It follows the presentation with sections closed, and at the end there is a link to a pdf with the sections open and to the related worksheet, used to run the computations in real time during the presentation.

COMPUTER ALGEBRA FOR THEORETICAL PHYSICS

 

  

Generally speaking, physicists still experience that computing with paper and pencil is in most cases simpler than computing on a Computer Algebra worksheet. On the other hand, recent developments in the Maple system implemented most of the mathematical objects and mathematics used in theoretical physics computations, and dramatically approximated the notation used in the computer to the one used in paper and pencil, diminishing the learning gap and computer-syntax distraction to a strict minimum. In connection, in this talk the Physics project at Maplesoft is presented and the resulting Physics package illustrated tackling problems in classical and quantum mechanics, general relativity and field theory. In addition to the 10 a.m lecture, there will be a hands-on workshop at 1pm in the Alice Room.

 

... Why computers?

 

 

We can concentrate more on the ideas instead of on the algebraic manipulations

 

We can extend results with ease

 

We can explore the mathematics surrounding a problem

 

We can share results in a reproducible way

 

Representation issues that were preventing the use of computer algebra in Physics

 

 

Notation and related mathematical methods that were missing:


coordinate free representations for vectors and vectorial differential operators,

covariant tensors distinguished from contravariant tensors,

functional differentiation, relativity differential operators and sum rule for tensor contracted (repeated) indices

Bras, Kets, projectors and all related to Dirac's notation in Quantum Mechanics

 

Inert representations of operations, mathematical functions, and related typesetting were missing:

 

inert versus active representations for mathematical operations

ability to move from inert to active representations of computations and viceversa as necessary

hand-like style for entering computations and texbook-like notation for displaying results

 

Key elements of the computational domain of theoretical physics were missing:

 

ability to handle products and derivatives involving commutative, anticommutative and noncommutative variables and functions

ability to perform computations taking into account custom-defined algebra rules of different kinds

(problem related commutator, anticommutator, bracket, etc. rules)

Vector and tensor notation in mechanics, electrodynamics and relativity

   

Dirac's notation in quantum mechanics

   

 

• 

Computer algebra systems were not originally designed to work with this compact notation, having attached so dense mathematical contents, active and inert representations of operations, not commutative and customizable algebraic computational domain, and the related mathematical methods, all this typically present in computations in theoretical physics.

• 

This situation has changed. The notation and related mathematical methods are now implemented.

 

Tackling examples with the Physics package

 

Classical Mechanics

 

Inertia tensor for a triatomic molecule

 

 

Problem: Determine the Inertia tensor of a triatomic molecule that has the form of an isosceles triangle with two masses m[1] in the extremes of the base and mass m[2] in the third vertex. The distance between the two masses m[1] is equal to a, and the height of the triangle is equal to h.

Solution

   

Quantum mechanics

 

Quantization of the energy of a particle in a magnetic field

 


Show that the energy of a particle in a constant magnetic field oriented along the z axis can be written as

H = `ℏ`*`ω__c`*(`#msup(mi("a",mathcolor = "olive"),mo("†"))`*a+1/2)

where `#msup(mi("a",mathcolor = "olive"),mo("†"))`and a are creation and anihilation operators.

Solution

   

The quantum operator components of `#mover(mi("L",mathcolor = "olive"),mo("→",fontstyle = "italic"))` satisfy "[L[j],L[k]][-]=i `ε`[j,k,m] L[m]"

   

Unitary Operators in Quantum Mechanics

 

(with Pascal Szriftgiser, from Laboratoire PhLAM, Université Lille 1, France)

A linear operator U is unitary if 1/U = `#msup(mi("U"),mo("†"))`, in which case, U*`#msup(mi("U"),mo("†"))` = U*`#msup(mi("U"),mo("†"))` and U*`#msup(mi("U"),mo("†"))` = 1.Unitary operators are used to change the basis inside an Hilbert space, which physically means changing the point of view of the considered problem, but not the underlying physics. Examples: translations, rotations and the parity operator.

1) Eigenvalues of an unitary operator and exponential of Hermitian operators

   

2) Properties of unitary operators

   

3) Schrödinger equation and unitary transform

   

4) Translation operators

   

Classical Field Theory

 

The field equations for a quantum system of identical particles

 

 

Problem: derive the field equation describing the ground state of a quantum system of identical particles (bosons), that is, the Gross-Pitaevskii equation (GPE). This equation is particularly useful to describe Bose-Einstein condensates (BEC).

Solution

   

The field equations for the lambda*Phi^4 model

   

Maxwell equations departing from the 4-dimensional Action for Electrodynamics

   

General Relativity

 

Given the spacetime metric,

g[mu, nu] = (Matrix(4, 4, {(1, 1) = -exp(lambda(r)), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = -r^2, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -r^2*sin(theta)^2, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = exp(nu(r))}))

a) Compute the trace of

"Z[alpha]^(beta)=Phi R[alpha]^(beta)+`𝒟`[alpha]`𝒟`[]^(beta) Phi+T[alpha]^(beta)"

where `≡`(Phi, Phi(r)) is some function of the radial coordinate, R[alpha, `~beta`] is the Ricci tensor, `𝒟`[alpha] is the covariant derivative operator and T[alpha, `~beta`] is the stress-energy tensor

T[alpha, beta] = (Matrix(4, 4, {(1, 1) = 8*exp(lambda(r))*Pi, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 8*r^2*Pi, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 8*r^2*sin(theta)^2*Pi, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 8*exp(nu(r))*Pi*epsilon}))

b) Compute the components of "W[alpha]^(beta)"" ≡"the traceless part of  "Z[alpha]^(beta)" of item a)

c) Compute an exact solution to the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)" obtained in b)

Background: paper from February/2013, "Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories", by P. Fiziev.

a) The trace of "  Z[alpha]^(beta)=Phi R[alpha]^(beta)+`𝒟`[alpha]`𝒟`[]^(beta) Phi+T[alpha]^(beta)"

   

b) The components of "W[alpha]^(beta)"" ≡"the traceless part of " Z[alpha]^(beta)"

   

c) An exact solution for the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)"

   

The Physics Project

 

 

"Physics" is a software project at Maplesoft that started in 2006. The idea is to develop a computational symbolic/numeric environment specifically for Physics, targeting educational and research needs in equal footing, and resembling as much as possible the flexible style of computations used with paper and pencil. The main reference for the project is the Landau and Lifshitz Course of Theoretical Physics.

 

A first version of "Physics" with basic functionality appeared in 2007. Since then the package has been growing every year, including now, among other things, a searcheable database of solutions to Einstein equations and a new dedicated programming language for Physics.

 

Since August/2013, weekly updates of the Physics package are distributed on the web, including the new developments related to our plan as well as related to people's feedback.

 

 

Presentation_at_PI_and_UW.pdf     Presentation_at_PI_and_UW.mw

 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

After lots of hard work, vast amounts of testing, and enormous anticipation, Maple T.A. 10 is now available! Maple T.A. 10 is by far our biggest release to date - and we’re not just saying that. When we compare the list of new features and improvements in Maple T.A. 10 with that of previous releases, it’s clear that Maple T.A. 10 has the largest feature set and improvements to date.


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