### What is DigiMat?

DigiMat is mathematics education for the digital world from basic school level through top academic and professional, and teachers:

1. #### DigiMat-Basic

(playful learning of the key math algorithms with editable pedagogical games in JavaScript)
2. #### DigiMat-Pro

(advanced application - university and professional)
3. #### DigiMat BodyAndSoul

(basic/high school + teachers education). Please access the material in the current format, we are in the process of transferring the content to digimat.tech.

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.

Try the prototypes inetgrated in this page, and explore the wealth of material available in the entire program available below!

DigiMat is an innovative solution to widespread and well-documented problems in mathematics and programming education in Sweden and globally. With the help of computer games and physics simulation which unifies mathematics and programming, pre-school children as well as teachers and university students learn through a unique pedagogic concept. The method is based on world-leading mathematics research at KTH and Chalmers, together with didactic research at Stockholm University.

DigiMat will be exhibited as part of the World Expo 2020 together with Vinnova!

Kontakta oss (jjan@kth.se) så hjälper vi lärare och elever att komma igång! Konto är gratis under Corona-krisen.
Contact us (jjan@kth.se) and we will help teachers and students to get started! Accounts are free during the Corona crisis.

### Demo Learning Activity: Motion-Change: x = x + v*dt - Time stepping

Press the </> button to edit, modify and run again!

Motion is change of position x with a certain rate of change as velocity v according to the code

• x = x + v* dt;

where dt is a time step. Watch and play with the pedagogical game on the left, modify and run again!.

This code expresses mor generally any type of change of a quantity x with a certain rate of change v over a time step dt.

The code is interpreted as

• x_new = x_old + v*dt

### Demo Learning Activity: Time stepping - compute any mathematical model

Press the </> button to edit, modify and run again!

Watch and play with the adjacent Digital Math game containing the essence of Calculus in few lines.

We can express the Fundamental Theorem of Calculus as:

1. Time stepping of $\frac{dx}{dt} = f(t)$ constructs the integral $x=\int f(t)\, dt$ of the integrand $f(t)$.
2. Differentiation of the integral $x=\int f(t)\, dt$ produces the integrand $f(t)$.
• Study experimentally by computing the dependence of $\int_0^T f(t)\, dt$ on the time step $dt$.
• ### Learning goals

DigiMat contains the following fundamental learning goals, which are the basis for all of Digital Math:

1. Number representation [Basic] in first binary form making representation and arithmetic algorithms easy to understand.
2. Arithmetic algorithms [Basic] constructed by repetition of the basic operation of +1 according the basic prototype of all computer programs of DigiMat in the form n = n + 1
3. Time-stepping [Basic-Pro] automatically solving all (ordinary) mathematical models in the form x = x + v*dt
4. Text programing [Basic-Pro] enabling the students to understand, modify and extend the algorithms and computer realizatons themselves.
5. Finite Element Method (FEM) [Pro] automatically solving all continuum mathematical models in the form $r(u, v) = 0, \forall v \quad in V_h$
6. Real Simulation [Pro] directly predicting First Principles models $R(u)$ such as aerodynamics with FEM with adaptive error control, stability, and in a Best Possible sense in the form $(R(U), v) + h(R(U), R(v)) = 0, \forall v \quad \in V_h$