online digital math education
— from school to pro

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What is DigiMat?

DigiMat unifies math and programming in a unique way. Creativity, motivation and industrial impact are key elements. The program spans all levels, from pre-school to top academic and professional.

The method is based on world-leading mathematics research at KTH and Chalmers, together with didactic research at Stockholm University. Computation is the leading principle and music and visual art is part of the pedagogical concept.

By learning a few basic algorithms anyone can understand and carry out advances programming and physics simulations. No prior knowledge is needed. See the learning goals for details, and get started with ”Ada's World”!

Try our DigiMat learning activities!

Pedagogical Editable App [Basic]

Enter Ada's World! Our pedagogical app is inspired by Ada Lovelace (1815-1852), mathematician and one of the first programmers in history. Here you learn the binary addition algorithm and
time-stepping for simulation, by organizing a party.

Ada's World Intro and Tutorial!

"Time-stepping" activity in DigiMat Ada's World, allowing you to solve all mathematical models!

advanced application - university and professional.

DigiMat-Basic

The headings below show a path from the most simple over less simple
to more complex. Ada's World makes the fundamental algorithms and text
programming accessible, integrating a narrative, art and music with
games representing visualizations of the algorithms.

Learning goals

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

Number representation in first binary form making representation and arithmetic algorithms easy to understand.

Arithmetic algorithms 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

Time-stepping automatically solving all (ordinary) mathematical models in the form x = x + v*dt

Text programing enabling the students to understand, modify and extend the algorithms and computer realizatons themselves.

Real Simulation experiencing directly predicting First Principles models such as aerodynamics with time-stepping.

Ada's World

Enter Ada's World! Our pedagogical app is inspired by Ada Lovelace (1815-1852), mathematician and one of the first programmers in history. Here you learn the binary addition algorithm and
time-stepping for simulation, by organizing a party.

Ada's World Intro and Tutorial!

"Time-stepping" activity in DigiMat Ada's World, allowing you to solve all mathematical models!

DigiMat Basic Sessions

See code to read explanation if not given explicitly. Run code by clicking arrow.

“One mathematical model can say more than 1 million words.” (Leibniz)

“Mathematical models reveal the essence of existence.” (Einstein)

Model Workshop opens to a problem based approach to learning, where tools and methods are collected as they are needed to handle specific cases of significance, rather than teaching generalities first. For the young mind particularities can be more captivating than generalities and generalisation can come at a later stage by discovering similarities of particularities.

Model Workshop invites to an answer – question form of learning, where the student after having explored a simulation gets incentive to answer the questions: How is it done? What elements are included? What does the code express? How can I expand the simulation? It is like watching a magician showing a trick and then seeking to find out how it was done and how to repeat/modify it. This gives the student an active role in an open search for information on the web, to be compared with a the passive role in the traditional form of question – answer directed by teacher and book.

Explanation is thus kept sparse to give incentive to explore models by trial and error computation with inspiration from reality and web in learning-by-computing. Watch out: Can be Addictive!

Check code to find explanation of model if not given directly. The models are carefully selected to be as simple as possible yet open windows to a complex world of many phenomena. Be confident that in retrospect you will see the scientific wealth buried in these (seemingly simple) models.

Add to Game Workshop using the physics of Model Workshop.

Run code by clicking arrow on upper left corner. Modify code, test and have fun!

Games represent interaction of one or more players with a symbolic or real model, such as a game of cards or a ball game. Games serve a basic role in DigiMat to express interaction between human mind and mathematical model in computational form, where mind reacts to output from computation to give input to new computation in a feed back loop. In Angry Birds the player chooses initial data for sling shot aiming to hit a chosen target and the corresponding trajectory is computed by time stepping Newton’s laws of motion which gives feed back to the player to change initial data until hit.

Interaction with a mathematical model in symbolic form typically is difficult, while interaction with a mathematical model in computational form typically is direct and informative.

Role of Simulators

Simulators are interactive computer games used for training to meet challenges in real life, including flight simulators and surgery simulators.

Real Flight Simulator is DigiMat software which captures the true action of an airplane by computational solution of Euler’s equations expressing first principle physics, as the first simulator with this capability.

List of Games

Play game to discover the math behind the game. You may need to initialise game by clicking game name and pressing start arrow.

There is an extensive list of books supporting
DigiMat.

Books
gives the foundation of the path and lead into a wider world as
computational mathematics.

DigiMat is an expansion of
the BodyandSoul program,
which contains supporting material, some of the software material may not be supported
anymore.

DigiMat unifies math and programming in a unique way. Creativity, motivation and industrial impact are key elements. The program spans all levels, from pre-school to top academic and professional.

The method is based on world-leading mathematics research at KTH and Chalmers, together with didactic research at Stockholm University. Computation is the leading principle and music and visual art is part of the pedagogical concept.
By learning a few basic algorithms anyone can understand and carry out advances programming and physics simulations. No prior knowledge is needed. See the learning goals for details, and get started with ”Ada's World”!

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: 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:

Time stepping of constructs the integral of the integrand .

Differentiation of the integral produces the integrand .

Study experimentally by computing the dependence of on the time step .

Observe that the differential equations express that the velocity vector and the position vector satisfies

, (velocity is orthogonal to position)

which means that the point moves around a circle with radius 1, which give and a geometric meaning with t appearing as an angle. Find out the details of the geometry.

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

Number representation [Basic] in first binary form making representation and arithmetic algorithms easy to understand.

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

Time-stepping [Basic-Pro] automatically solving all (ordinary) mathematical models in the form x = x + v*dt

Text programing [Basic-Pro] enabling the students to understand, modify and extend the algorithms and computer realizatons themselves.

Finite Element Method (FEM) [Pro] automatically solving all continuum mathematical models in the form $r(u, v) = 0, \forall v \quad in V_h$

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 $(R(U), v) + h(R(U), R(v)) = 0, \forall v \quad \in V_h$