New Book by Dr. Vladimir Nodelman: Mathematical Research Through Technology

Mathematician Dr. Vladimir Nodelman, a lecturer at HIT's School of Computer Science, recently published a new book titled 'Mathematical Studies Through Technology' with the prestigious Scientific World publishing house.

'Mathematical Studies Through Technology', Dr. Vladimir Nodelman
Book Cover: World Scientific Publishing Co Pte Ltd

The book, released in January 2025, is Dr. Nodelman's third book on mathematics and mathematical visualization: about 11 years ago, in collaboration with Professor Gabriel Katz from MIT, he published a book on algebra with the same publisher; and in the 1980s, he published his first book in Russia about computers as an educational aids.

Dr. Nodelman's new book reflects a massive project he has been working on for 30 years: the development of VisuMatica - a unified software for learning, teaching, and researching mathematics at all levels, from high school and university students to mathematicians. VisuMatica has a user-friendly interface and allows users to define mathematical objects naturally, without requiring special syntax.

The new book presents methods for learning and researching mathematics from a functional perspective across various fields: calculus (“infi”), differential equations, linear algebra, complex functions, two-dimensional and three-dimensional geometry, and more. The book demonstrates how, based on mathematical material analysis, one can build and examine dynamic visual models for simulation, research, and visual expression of characteristic properties of the objects themselves. Such models go beyond the realm of simulation, even dynamic simulation: in some cases, they reveal characteristics hidden even from professional mathematicians and illustrate complex mathematical concepts that are difficult to approach in classical presentation, and therefore were omitted from standard textbooks. The book includes examples and counterexamples of concepts and theorems, along with questions, tasks, and exercises.

Dr. Nodelman has been researching and developing mathematics teaching and visualization since the beginning of his professional career, and his doctoral dissertation dealt with mathematics teaching tools. "In the 1970s, there were no computers in teaching," he recalls. "I invented electronic and other devices for teaching mathematics and patented them. After some time, I was invited to a secret institute in Moscow, where they showed me a computer with software that displayed on the screen a device I had developed. I was surprised; it was very impressive. I immediately understood this was the future: after all, the vast majority of mathematics teaching tools present information in a plane and can be replaced by a computer screen. At that time, as a senior research fellow at a research institute in Minsk, I switched to developing software implementing my ideas for teaching mathematics."

In 1990, Dr. Nodelman repatriated to Israel, and shortly afterward won an international award for software he developed for teaching several mathematics subjects. He joined HIT, initially as a visiting faculty member, and was the first to teach programming at the institute. Alongside his academic activities, he began developing VisuMatica, a unified mathematics software that became his life's mission. "I will never finish this software," says Dr. Nodelman. "It's a never-ending task, and I'm constantly adding support for new fields and deepening existing ones."

VisuMatica and ready-made models are available on the Scientific World publishing website

Posted: 24/02/2025