Welcome to our course where you will learn everything you need to know about the natural integers.

The course is integrated with Python and it is highly recommended that you attend our free course Scientific Computing with Python: The Basics.

You will learn to count and construct the natural integer set N, that is equal to 0, 1, 2, and so on.

You will discover and understand the proof by recursion, also called the mathematical induction.

And you will compare the numbers and construct the natural integers totally ordered set N with less or equal.

You will also learn to master natural integers addition and subtraction.

and to construct the commutative monoid (N,+).

In particular, you will learn addition and subtraction mutual property.

They are mutually reciprocal.

You will learn to solve additive and subtractive equations in the natural integers N. And you will learn how to move parentheses with additions alone and with additions and subtractions together.

What more? You will also learn to master natural integers multiplication and construct the commutative monoids, N, multiplication, of natural integers, and N*, multiplication, of positive integers.

You will learn to master the computation with expressions that mix addition, subtraction and multiplication, and construct the commutative semi-ring N, plus, multiplication.

In particular, you will learn the distributivity laws of the multiplication on the addition and the subtraction.

And then you will study the powers of 10 and how it is related to the decimal numeration.

It will be applied to the proof of the manual addition, abstraction and multiplication processes with carries, and it will be used to explore the scientific notation and the orders of magnitude that are related to it.

And then you will study the exponentiation in N, n to the power k.

It is an iterated multiplication of n by itself.

You will study the multiplication and exponentiation mutual properties.

And you will learn the remarkable identities a plus b to the square, a minus b to the square, and a to the square minus b to the square.

And you will draw your first polynomials, and then you will study the ordered semi ring N with the addition, the multiplication and the order relationship less or equal.

You will study the properties of inequalities under addition, subtraction, multiplication and exponentiation.

And this will be applied to the proof of the comparison schemes in decimal notation and scientific notation.

And you will end the course with a final project.

It will be a travel around the sum of the n positive integers, and it will be up to you to do it because it will be your final assessment.

What is the learning process? The course includes 12 sections containing 42 video lectures for progressive learning, and one recapitulative document at the end of each of the sections 2 to 10, with rigorously proved theorems.

And each section starts from the practice with Python to end with the theory with rigorously proved theorems.

So are you ready for the course? The Natural Integers.