Leibniz WoM: From Pre to Pro

Leibniz World of Math is new reformed mathematics education for the digital world developed by leading academic competence based on the idea combining the language and methods of mathematics with the computer.

Leibniz WoM is a unique unified program with varying depth and scope over all levels with computation as leading principle, where all mathematical objects are constructed by computation according to computer programs as mathematics expressed  in symbolic form. See ScopeMethod and The World from +1 in the menu.

Leibniz Pre introduces counting in pre-school using binary numbers with different symbol systems some invented by the children themselves. Fun, easy, opening to constructive mathematics and computing.

Leibniz School meets new school curricula asking programming to be part of mathematics education.

Leibniz School invites to Continued Teacher Education.

Leibniz School gives new answers to the key questions of what?, why? and how? of school mathematics, with the traditional answers no longer convincing in the digital society.

Leibniz School combines formal mathematics with programming into a synthesis, which in different forms can serve many different students.

Leibniz School is understandable because a principle of construction can be understood, and useful by turning principle into output by powerful computing.

Leibniz School is learning-by-constructing in a rich program unified over levels to a wide variety of students (and teachers) with different interests and capacities.

Leibniz School opens to understanding of basics of the digital society and gives tools to meet possibilities and challenges. Read For Whom? and Comparison with Music!

Leibniz School is an expansion of the BodyandSoul program.

Leibniz Pro connects to  CMU-OLI course.

From School to University

Mathematics is unique as science in that the most basic directly connects to the most advanced. In DigiMat this comes to expression by the fact (which will become apparent as you proceed) that essentially the same things are done on all levels just with different depths and complexity, just like in cooking and music, from school to university to professional level.

Leibniz carries school mathematics far beyond traditional limits.

Top Rope

DigiMat Pro representing top academic/professional level offers a top rope securing meaningful possible climb for anybody to any level.

The fact that in mathematics top connects to base is illustrated in a proof of the statement 2 = 1 + 1 filling two full dense pages in the monumental three-volume treatise Principia Mathematica by Russell-Whitehead, something which is clear to any child. So DigiMat starts by constructing the natural numbers as 1, 2=1+1, 3=2+1, 4=3+1,…,simply by repetition of the basic operation of +1.

Video Introduction 2

Here is the first in a series of videos introducing basic concepts, methods, tools and visions of Mathematical Simulation Technology in a short presentation of constructive calculus:

Summary: Constructive calculus is classical calculus restricted by the limits of finite precision computation and augmented by the new capacities of automated computation by the computer. In constructive calculus, the elementary functions are computed solving differential equations by time stepping, which decodes the reality behind symbols like sin(1) and exp(2) and shows how these symbols are to be used. In constructive calculus the student actively constructs models of the world from scratch in the form of computer programs (like a composer writes a partiture), which is given life by a computer running the program (like an orchestra performing the composed music). Constructive calculus is today booming with the computer, while classical calculus was perfected in the 19th century.