eLearning

As the power of desktop computers increases, it is becoming more feasible to provide interactive software to aid students in better understanding the various mathematical theories and principles. Visualization applications have been widely adopted in the academic community to help make technical education more authentic and tangible. More than 3,500 universities around the world use such products for teaching and research in a broad range of technical disciplines.

There are numerous math software available worldwide, with more being developed each day. Let us briefly take a look at three popular visualization software products and how lecturers in NUS are using them.

Maple screenshotsMaple is a powerful mathematical problem-solving and visualization system which is used in education, research, and industry. Its principal strength is its symbolic problem solving algorithms. Unlike conventional math software, which can only work with floating-point numbers, Maple can solve problems involving formal mathematical definitions and return answers as mathematical objects.

Its mathematical engine has an extensive library which covers:

  • Calculus, precalculus
  • Differential equations (ODEs, PDEs)
  • Linear algebra and high performance matrix computation
  • Engineering mathematics including transforms
    (Laplace, Fourier, Z, FFT)
  • Pure mathematics including discrete mathematics, number theory and group theory
  • Over 3,500 functions

Dr. Victor Tan, from the Department of Mathematics, uses Maple in Advanced Calculus modules where multivariable concepts are introduced. His students attend computer laboratory sessions where all the PCs are installed with the Maple software. Students learn how to use Maple commands to plot a variety of module-related graphs. Particularly, students construct three dimensional objects such as “surfaces” and “space curves” which are difficult to visualize and plot by hand.

Maple also enables students to rotate the 3D graphics and view the plotted objects from different angles. Two or more graphs can be plotted on the same axes for comparison, with different colours distinguishing the graphs. These functions assist the students in performing calculations and in interactively visualizing concepts. Maple usage helps students to understand and internalize mathematical theories.

MATLAB screenshotMATLAB is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis and numerical computation. Using MATLAB, users can solve technical computing problems faster than traditional programming languages, such as C, C++, and Fortran. It can be used in a wide range of applications, including signal and image processing, communications, control design, test and measurement, financial modeling and analysis, and computational biology.

Some of the key features of MATLAB are:

  • High-level language for technical computing
  • Development environment for managing code, files, and data
  • Interactive tools for iterative exploration, design, and problem solving
  • Mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration
  • 2-D and 3-D graphics functions for visualizing data
  • Tools for building custom graphical user interfaces
  • Functions for integrating MATLAB-based algorithms with external applications and languages, such as C, C++, Fortran, Java, COM, and Microsoft Excel

In the Department of Chemical and Biomolecular Engineering, Dr. Lakshminarayanan Samavedham’'s students use MATLAB to solve nonlinear ordinary differential equations and partial differential equations. The software is useful for solving linear and nonlinear algebraic equations. These mathematical concepts are applied in process simulation, control and process data analysis.

With the 2-D and 3-D plotting capabilities of MATLAB, students are able to see the response surfaces, contour plots, etc. They use FEMLAB, an application built on MATLAB, to understand problems involving multiphysics such as chemical or biological reactions plus electrokinetic flow. Dr. Laksh and his students also simulate 3-D models of systems, visualizing 2-D or 3-D graphical results, including the systems’ evolution over time.

LiveMath exampleAnother interesting product is LiveMath. This is a computer algebra system that allows interactive and graphical experimentation via the web browser by using a free plugin. The product suite comprises of LiveMath Maker, LiveMath Plugin, LiveMath Viewer and MathEQ Equation Editor. Using the LiveMath Maker, the lecturer can create “notebooks” which can then be embedded in any web page. Students can access these LiveMath notebooks through the LiveMath Plugin.

Beyond seeing static math symbols on a screen, the plugin enables the student to interact with algebra, investigate graphs, and explore live mathematics. They can modify the input expressions and watch the computations change without the need for any math engine running on the server side.

The key features of this product are:

  • Looks like Math - WYSIWYG - What You See Is What You Get
  • "Drag and Drop" intuitive actions to complete math operations
  • "Show Steps" feature that allows you to see and work through intermediate steps
  • Not programming language-based
  • Convenient symbol entry using a mouse click palette or the keyboard
  • Object-oriented, powerful 2-D and 3-D graphing with easy-to-use investigatory tools
  • Publish to the web for free, interactive viewing with most web browsers

There are many other useful tools and utilities listed in the references below which are available either as Shareware or Freeware. We hope that the usage of mathematical visualization software will enhance your teaching.

References
1. List of Mathematical Software
2. Guide to Available Mathematical Software
3. Maple
4. MATLAB
5. LiveMath

For more information on Mathematics software and other courseware, contact Mr .

What is RSS?

RSS is defined by some as Rich Site Summary, others as RDF (Resource Description Framework) Site Summary, while a few call it Really Simple Syndication. Whatever it may be called, RSS is a means of delivering content directly from the author to its recipient automatically, instantaneously and without viruses, spam and other electronic nuisance.

What makes RSS special is the way it is being used and delivered. Usually, a RSS is created by the content or news publisher (usually seen by many as content expert) and then delivered to people who have subscribed to the feed using a RSS “feed reader” application called an aggregator. When the aggregator is initialized, it would crawl out to the different content providers and download summarized information automatically. A subscriber can subscribe to multiple feeds and read these summarized news on one screen. If the subscriber is interested in any particular news, he/she can then click on the headline of an item and access the full article from the originating website

Beyond the Technology

RSS is useful as it keep users up-to-date with new content on websites and weblogs (blogs). It has the potential to replace email updates or even HTML newsletters.

With RSS, a subscriber is given the controls to subscribe to the contents he or she wants to view, thus eliminating possibility of unwanted emails and spam. RSS, being a read-only XML language, is not a possible means of transporting viruses and worms. Subscribing to a RSS feed is anonymous; no one can send you a message outside the channel you are subscribing to and if you are unhappy with the contents which you subscribed to, you can remove the link on your own. Another useful feature of RSS is it allows users to communicate without the exchanging of personal email addresses.

RSS usually comes pre-categorized. You can read your news and updates in an organized manner. This is unlike receiving an email, when you will first have to set filters and rules.

RSS also allows users to syndicate or republish others’ contents and provide the latest news to his own readers without composing it himself. There are no legal implications and copyright violations because the actual full content is residing on the originating site.

RSS and Learning

RSS has been used by instructors in many ways. Some ways you can use RSS include:
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  • Subscribing to current feeds on a certain subject you are interested in
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  • Republishing syndicated contents on your own module website or blogs

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  • Notifying readers about new contents, news & resources (both internal and external) made available for your modules.

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  • Having learners create their own web logs and then subscribing to the feeds of all these web logs to check on their new contents. This encourages learners to self-reflect on what they have learnt.

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  • Subscribing to feeds from learning object repositories to see the newest objects added to a topic of your interest (see Merlot below).

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  • A social networking tool which sends you information about others who have joined your network of research etc.

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  • Problem solving – you can subscribe to a feed that describes the topics related to your needs and get updates whenever someone writes on that topic. This is similar to discussion thread forums.

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  • Collaborative workspaces that aggregate different pieces of information to different individuals working on the same project.

Summary

RSSes and Weblogs allow the objective aggregation of contents in a world where spams and viruses are consistently annoying our users. The ability for RSS to gather accurate and selective information quickly makes it a useful educational tool. It is probably one of the few ways used to keep up to speed in a world wide web of information which changes daily. RSS enables users to effectively and efficiently gather and share knowledge across borders and boundaries.

RSS Tutorial
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Interesting Educational Sites using RSS to inform users
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RSS Aggregators
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A viewlet to show faculty on how to use the library e-Reserves through IVLE.

Viewlets are small animated programs that run within a web browser that can be used to demonstrate computer software and show screen simulations. Through viewlets, you can demonstrate in a step-by-step approach with mouse and cursor movements, cut-outs and dialog bubbles to show exactly what a user has to do to apply or navigate your website. It is like running a video to show you how things work.

No special software or plug-in is necessary to watch viewlets from a browser as it is Flash-based. The software is easy to use and comes with a wizard to help in the creation and anybody can build compelling content in a viewlet format.

The Office of Human Resources used viewlets to show NUS staff how to apply and use the new online leave applications. IVLE will also be using viewlets to demonstrate to faculty and students how to use the various resources and tools on IVLE. One such viewlet was created to show faculty how to use the library e-Reserves through IVLE.

For faculty who would like to use viewlets to create online simulation tutorials for their students, please contact Ms .

Macromedia Breeze is a new software solution that allows faculty to leverage on their Microsoft PowerPoint knowledge and expertise to create rich engaging and interactive contents from their desktop. From PowerPoint, faculty can re-purpose and upgrade their PowerPoint slides into interactive multimedia contents, incorporating audio narration, Flash animation and surveys. Easy editing features that allow faculty to do post-production, cut and change slides are also available.

If you are thinking of embarking on updating your PowerPoint slides or creating new content for the coming semester, why not try Macromedia Breeze.

Below two faculty give their comments on Breeze:

Innovative Retrofit Solutions for Structural Repair
By Associate Professor Gary Ong Khim Chye, Department of Civil Engineering

"Breeze provided me an opportunity to make available portions of my presentation which the students can access on-line at their own convenience. Some of the part timers could easily have missed some parts of my lectures due to their being unable to attend one or more of the lectures or being unable to come on time.

To make use of Breeze I used slides from a keynote address I delivered at an International Conference held in Bali in March 2002. Just some minor editing to meet copyright obligations and reorganization of the PowerPoint slides that are relevant to CE5610 was all that was needed. It took me about four days to record the narration.

Feedback from students was that it was very good. They could go to the relevant parts that they were interested in and could pick and choose the order of presentation of the three case studies presented."

Giving an Oral Presentation
By Dr Carissa Young, Centre for English Language Communication

"Overall, I found Breeze easy to use. It allowed me to deliver my presentation over the internet at low bandwidth, making it easier for my students to access the presentation. Breeze also enabled me to add interactive questions in order to engage and capture my students' attention."

For more information, contact Mr .