Learning and Teaching Mathematics using Simulations

This is aunique, comprehensive and documented collection of simulations in mathematics and physics: More than 2000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the documentation to the simulations. This is a great way to learn mathematics and physics. Suitable for courses in Mathetmatics for Engineering and Sciences.

Auteur

Dieter Röss, Wilhelm and Else Heraeus Foundation, Hanau, Germany.

Texte du rabat

Readers are provided with hands-on access to mathematics. They work with numerous interactive Java simulations including examples of infinitesimal calculus, partial differential equations, fractals and much more. In the process, they become acquainted with the technique of simulation. The work also offers a collection of some 2000 physics simulations. In the electronic version, this unique, comprehensive and well documented collection can be accessed directly from the text and operated online or from the download package installed on a local hard disk. The modern interactive format is an ideal tool to help users visualize and understand mathematics and physics.

Résumé

• Mathematics course with 60 Java-based interactive mathematic simulations by the author
• Comprehensive and systematically organized collection of 2,000 Java-based physics simulations
• All simulations are runnable, and can be accessed both on- and offline
• Visualization of mathematic relationships
• Facilitates an experiment-based understanding of problems, including suggestions for your own mathematical experiments
• Calculation procedures can be adjusted in a variety of ways
• Introduction to simulation techniques with the EJS (Easy Java Simulation) tool
• Visual interface for simple and transparent modeling and programming
• Building block library for programming one's own simulations
• Quick access to simulations from links embedded in the digital text
  Mathematics is the language of physics and technology. Yet in the age of computers, mathematic skill is not based on mastery of arithmetic. Rather, it depends on understanding relationships in time and space, and expressing them with precise and clear formulas. In this regard, one cannot rely on the rote memorization of rules and formulas - insight and intuitive understanding are crucial. But how can this understanding be achieved in higher mathematics, which depends on abstract concepts such as complex numbers, real and complex infinite series, infinitesimal calculus, 2, 3, and 4 dimensional functions, conformal maps, vectors, and linear and nonlinear ordinary and partial differential equations?

The author takes a highly practical approach to facilitating the insight essential for true learning in mathematics. Students can work directly with the simulation programs, can visualize relationships, and creatively interact with the calculation procedures. Proceeding in textbook fashion, the work makes use of a broad palette of multimedia tools, and features numerous interactive calculation programs for mathematical experimentation. Students merely have to select one of the many predefined examples and set the relevant parameters - and in a flash the results are graphically displayed in 2 or 3 dimensions. In addition, the specific functions used can be changed or even newly formulated according to user preferences. For example, a procedure developed for a fourth degree power function for the numerical calculation of zero points can be adapted for use with another function. Each simulation is accompanied by a detailed description, instructions for use, and numerous suggestions for experimentation. The mathematical simulations are based on the Easy Java Simulation (EJS) programming tool. All of the files developed with EJS are completely open and transparent. The user can even draw on the examples as building blocks for the development his or her own calculation procedures. The appendix contains a short introduction to EJS.

The work is enriched by a comprehensive collection of cosmological simulations as well as models from the Open Source Physics project, organized by subject area. Intended as a systematic collection of methods and materials for upper-secondary school teachers and as a course for students of physics and mathematics, the work facilitates hands-on and experiment-driven learning in higher mathematics.

The print version contains the electronic text and simulations for offline use. For questions concerning download or online access to the simulations, please contact service@degruyter.com.