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**Leibniz World of Math** is an *open textbook* free to use with an *open license* that grants usage rights to the public as long as this site as source is attributed. Note change of name from **Digimat Encyclopedia.**

**Gottfried Wilhelm von Leibniz (1646-1716) **invented both **Calculus** as the **mathematics of change** of the **scientific/industrial revolution** and the **Computer**, which together form the basis of todays **Digital World **as** Digital Calculus.**

**Leibniz** **World of Math **developed by leading academic competence offers (**Syllabus**):

**new reformed school mathematics education**as**Digital Calculus**- meeting
**new school syllabus**(TIMSS 2019 Encylopedia) with **programming part of mathematics.**

**Leibniz World of Math** combines** formal symbolic mathematics **with the **computer **by** programming (**using e.g.** p5.js JavaScript web editor**) into **Digital Calculus **where:

**programming gives mathematics a turbo,****mathematics gives programming meaning,**

with **new answers **to the** key questions of what, why and how** of mathematics education. Programming in general is difficult because notation and logic can be tricky, but Leibniz says that programming mathematics can be easy because logic is simple and tasks essentially boil down to repetition of +1.

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**More about Leibniz World of Math:**

**Leibniz WoM constructs all mathematical objects by computation** according to computer programs as mathematics expressed in symbolic form, with **object properties emerging from construction**.

**Leibniz WoM** is **learning-by-constructing **which gives the student an active role in what can be described as **construction of computer games** with **interaction man-machine, **which is** captive to the young mind. **

**Leibniz WoM** is **understandable,** because a principle of construction can be understood as well as properties emerging from construction, and **useful** by turning principle into output by powerful computing.

Mathematics is unique as science in that the most basic directly connects to the most advanced. This means that in Leibniz **the same basic constructive principles are used on all levels**, with only different depths and complexity, just like in learning to play a musical instrument.

**Leibniz WoM** carries** school mathematics far beyond traditional limits **with direct connection to **Leibniz Pro**, where the basic models/codes of Leibniz are automatically expanded using FEniCS into frontier research/professional simulation as FEniCS-HPC.

**Leibniz WoM** reflects a **practice-theory** approach (practice followed by theory) instead of traditional theory-practice, where practice is coding of a model in simple form and theory as analysis of accumulated experience develops from running the code. This is the way a child first learns to speak words and then through massive experience successively decodes the meaning of the words.

The student thus learns to understand the meaning of the **Fundamental Theorem of Calculus** expressing the connection between integral and derivative by writing simple codes for summation of little pieces into a total sum. The Fundamental Theorem so releases the power of Calculus to the young mind.

**Leibniz WoM** is secured to a **top academic/professional level** by a **top rope** connecting Pre to Pro through School making meaningful climb possible for anybody to any level:

**Leibniz WoM** may at first experience be viewed to primarily address the teacher, but in fact invites to direct exploration by students with the primary role of the teacher to open doors rather than detailed instruction. This because Leibniz is learning-by-constructing rather than doing-what-the-teacher-tells as an expression of Active Learning-Passive Teaching. History: Digital Mathematics 2018.

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