DigiMat is a new education in mathematics + programming, which will be launched on this site. DigiMat is a continuation of NewMath: Mathematics-IT (English version) and Matematik-IT (Swedish version).

## What is Digital Mathematics

### Mathematics of the Digital Society

Th *digital society *is based on *digital mathematics* in the form of *digital computation* according to the methods and language of formal mathematics translated to computer code through *programming *and executed by the *microprocessor* of the *computer.*

*DigiMat* is new mathematics education in the form of

*digital mathematics = mathematics + programming + computer.*

DigiMat is developed by reserachers in digital mathematics at the Royal Institute of Technology in Stockholm (KTH) with world leading research presented at edX: High Performance Finite Element Modeling Part 1 and Part2.

DigiMat is freely available on the web connected to a web-editor för JavaScript.

DigiMat gives a thhematically unified mathematics education from basic school to university and research frontier, with successively increasing width and depth.

DigiMat meets the intentions behind new curricula with programming as part of mathematics education, reflecting the new role of mathematics in the digital society in the form of digital mathematics.

DigiMat teaches students to write computer codes constructing mathematics, starting with the most basic, which is then explored and used as building blocks for new constructions.

DigiMat is *learning-by-doing *and*creating-by-programming,* which makes mathematics understandable and useful.

DigiMat can be modified according to individual talents and interests.

DigiMat leads the student to independent work and liberates the teacher to individualised teaching and own development.

DigiMat can be compared with musical education where students are given a real instrumen (computer, iPad, mobile), such as a Bösendorfer grand piano or Stradivarius violin, and teaches how to play and create music together with others.

DigiMat teaches wider groups of students more relevant mathematics in shorter time and gives a boost to the digital .

DigiMat can give a developing country a short-cut to modernity.

### Digital Mathematics – Automated Computing

Digital mathematics is created through short computer codes which produce rich output upon repeated execution. A first code, which the student can write as soon as elementary reading and writing is mastered, is the following instructions which are repeatedTh

• n = n + 1

• print(n)

with n=0 as start. This short code, which has the form of *iteration* (repetition), creates and prints the sequence 1, 2, 3,…of *natural numbers*. A short code with rich output!

This is the principle of *automation *as the foundation of both the *industrial society *based on *automated material production,* och det digital society based on *automated digital computation: * Repetition of a single series of instructions can create rich output.

When so the student has created the natural numbers is next step to begin to explore their properties by construction, including representation in the binary form of the computer with zero and one as digits or the decimal form commonly used by humans, and their use in different settings.

The student will write short codes automating addition, subtraction, multiplication and division, including constructions of integers and rational numbers. The student can thus construct a calculator, in principle as soon as the student can read and write simple text, and with this tool start to *measure the world*, with better capacity than a grown up.

A student who has coded a calculator can be encouraged to use it to explore wide possibilities. This is the opposite to traditional mathematics education with computing by hand with pen and paper as the preferred tool with very limited possibilites.

As a next step the student constructs *Digital Calculus* as a digital version of *Newton’s Calculus* = mathematics for change = basis of the *industrial revolution*, through the code

• t = t + dt

• x = x + v(t)*dt

where t is *tid*, x can be* position in space*, v(t) is a given velocity as *function* of t, and dt is a (small) *time step,* med given *start values* för t och x. Genom repetition = *time stepping* the position x(t) is so constructed as function of t as *integral* av velocity v(t). Here x = x+v(t)*dt can be written as dx = v(t)*dt, vhich gives dx/dt = v(t), that is, v(t) as *derivate* of position x(t) as change dx of x per time unit dt.

So are *virtual worlds *of change created as a film, which picture after picture gives the illusion of continuous motion.

The young student thus creates/constructs both the numbers, computations with numbers, Descartes’ geometry Newton’s Calculus and mechanics through short computer programs and so builds a capacity beyond that carried by professors of mathematics.

This is a rationalisation of mathematics education by computation, where many more students can learn much more in shorter time. It is like giving the student the capability to steer an airplane, instead of forcing the student through a jungle where many get lost.

### Digital Mathematics: Automated Programmering = FEniCS

DigiMat carries the principle of automation one step further from automated computation to automated programming, where the computer code automatically is produced after specification in terms of formal mathematics by human hand and intelligence.

DigiMat thereby connects to the FEniCS Project as a open source software for automated programming of mathematical models in the form of differential equations, producing a wide range of virtual reality including in particular Unicorn/FEniCS covering solid/fluid mechanics.

The final step on the road of automation is to automate the formation of mathematical models as a form of *Artificial Intelligence* through which a given model automatically is modified (teaches itself), after comparison between reality and virtual reality produced by the model, by automated programming and computation.

DigiMat covers the whole chain from a start with construction of natural numbers to the research frontier and AI.