# The Natural Integers

## Become an efficient calculator, from basics practice to deeply understood theory

The aim of that course is to give you the mastery of the construction and manipulation of the natural integers, the numbers we count with.

Starting with practical animated graphics, and Python manipulations, you will become by the end of that course a master in:

• Counting and constructing the natural integers set, from zero to infinity
• Comparing natural integers, and ordering the natural integers set
• Adding, subtracting and multiplying the natural integers, including doing all these operations in a unique formula.
• Understanding the powers of 10 and the exponential notation
• Exponentiating the natural integers, and manipulating polynomials
• Comparing the results of additions and/or subtraction
• Comparing the results of multiplications and/or exponentiation

At the top of all that, you will master the powerful proof by recursion, a tremendously useful method of proving theorems, based on the natural integers set construction.

That course includes 39 high quality video lectures, plus 9 downloadable recapitulative documents, one per section, with all the proofs.

Fabienne Chaplais

Fabienne holds the Agregation in Mathematics, the highest French diploma to teach mathematics in secondary schools. After a 26-year career as an R&D engineer in applied mathematics, she founded Mathedu (Mathematics Re-engineering) with her husband and collaborator Francois, to teach mathematics from a practical point of view, based on Python programming. She is both an expert in mathematics education and a passionate woman who will help you experience the joy of improving your mastery of mathematics.

## Course Curriculum

Section 1: Introduction
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Section 2: Construct and Compare the Natural Integers
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Section 4 - Subtract Natural Integers
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Section 5 - Multiply Natural Integers
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Section 6 - Master computation in the natural integers
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Section 7 - Powers of 10 and Decimal Numeration
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Section 8 - Exponentiation in N
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Section 9 - The Ordered Monoid (N,+,≤)
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Section 10 - The Ordered Semi-Ring (N,+,x,≤)
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Section 11 - Final Assessment - The sum of the n first positive integers
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Section 12 - Conclusion
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When does the course start and finish?
The course starts now and never ends! It is a completely self-paced online course - you decide when you start and when you finish.