- DigiMat Pre: Ada’s World : pre/early school.
- DigiMat School (this site): from school to university.
- DigiMat Pro: top professional level: FEniCS-HPC.
DigiMat is a 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 The World as +1).
DigiMat 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.
DigiMat combines formal mathematics with programming into a synthesis, which in different forms can serve many different students.
DigiMat meets new school curricula asking programming to be part of mathematics education.
DigiMat is understandable because a principle of construction can be understood, and useful by turning principle into output by powerful computing.
DigiMat is learning-by-constructing. DigMat offers a rich program unified over levels to a wide variety of students (and teachers) with different interests and capacities.
DigiMat is an expansion of the BodyandSoul program.
DigiMat Pro is launched as MOOC on edX as High Performance Finite Element Modeling Part 1 and 2.
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.
DigiMat Pro at top offers a 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.
The menu items Introduction – Basics – Model Workshop and Game Workshops show a path from the most simple over less simple to more complex. If you follow the path, you will with satisfaction discover that you have learned to master powerful mathematics, which in traditional teaching is viewed far too advanced to serve as school mathematics. It is the computational-constructive aspects of DigiMat which allows you to take this leap even if you are not a math freak. Be confident that the path is open to you!
Books gives the foundation of the path and lead into a wider world as computational mathematics.
Continue to explore DigiMat School by watching Introduction and then proceed to Basics, which will take you step by step from the simple to more advanced following a basic principle to construct-simulate-understand-control the world by computation (combine with Perspective on Math Education):
- First the natural numbers are constructed by repetition of the basic operation of +1 according to a basic prototype of all computer programs of DigiMat of the form n = n + 1, which starting with n = 1 generates 2 = 1 + 1, 3 = 2 + 1, 4 = 3 + 1, and so on. Similarly the negative integers are constructed with repetition of the operation -1.
- Once the integers have been constructed, representation in binary or decimal form is specified and the basic algorithms of addition, subtraction, multiplication and division are defined and then expressed as computer programs taking the form of a pocket calculator programmed by the student, which in a next step is extended to rational numbers in binary or decimal form.
- With rational numbers at hand Newton/Leibniz’ world of Calculus and Linear Algebra, can be constructed as spatial and temporal variation expressed by numbers. The prototype program then takes the form x = x + v*dt and v = v+a*dt, where x is spatial position, v is velocity and a is acceleration, which can depend on x and v, and dt is a time step. This is the time stepping version of Newton’s Laws dx =v*dt, dv=a*dt and a=f/m.
- The next step is to extend to cover all aspects of the world as solid/fluid/quantum mechanics, thermodynamics, electromagnetics, biology, geoscience, economy, and more, all in constructive form based on computer programs of the prototype form.
Here you find more material in the form of earlier versions of DigiMat: