MATH 42 is a symbolic CAS (Computer Algebra System) package which was self-developed by Cogeon. It is neither based on other Open Source CAS-Systems, nor is it derived or influenced by another system. MATH 42 is a completely new and self-developed proprietary technology.

Description of the mathematical coverage

## MATH 42 Characteristics

MATH 42 is an intelligent CAS system, that permanently observes itself:

- MATH 42 notes everything that it does, and explains each step of its reasoning.
- MATH annotates the reasons, why it does something — e.g. a special substitution etc. in its notes.
- MATH 42 comments errors or problems, where they originate, etc. in its notes, e.g. when a division by zero is the result of a transformation. (‚1/(5-5)’ => ‘1/0 … division by zero‘)
- MATH 42 draws conclusion from the occurred absurdities. If for example a wrong equation of the form ‘6=7’ is yielded, MATH 42 draws the conclusion that the corresponding x-value cannot be the answer to the equation.

## MATH 42 Components

MATH 42 consists of 3 components:

### (1) Interface, Entry / Keyboard and graphical visualization

- HTML-5, SVG, Java Script
- React Framework
- TeX Darstellung

### (2) Authentication and User Management

- AWS
- AWS Cognito

### (3) Mathematics Core

- Swift 2.0
- Runs on an AWS Backend under Linux, respectively as a local component on iOS
- The mathematics of MATH 42 are not based on, derived from or influenced by any other (open source) system. MATH 42 is a proprietary development.

The components communicate with each other via HTTPS.

## iOS App

On iOS the Swift mathematics core does not run on a ‘distant’ server, but runs locally on the device.

## Android App

The Android app encapsulates the interface-components — the authentication and the mathematics core run on the AWS Backend. These are accessed by the Android app via HTTPS requests.

MATH 42 requires a working internet connection on Android.

## Services

The MATH 42 Services provide the MATH 42 functionality or aspects of it via integrable widgets.

### Requirements:

- The widgets run on either a Safari- or a Chrome-Browser.
- Before a user can use a widget, he has to be authenticated. The authentication can be done transparently for the user by the publisher, via a ‘shared secret‘ on the server side, which can be implemented in 1 line of code.

### Integration of the widget:

- The widget encapsulates the slightly changed interface components.
- The widget can be integrated with 1 line of code.
- The widget — just like the Android app — communicates with the AWS backend via HTTPS requests to address the mathematics core.

### Customizable sub-parts of the widget:

- Full MATH 42 functionality
- Only step-by-step solutions (with explanations)
- Only the interactive graphs
- Only the a assessment