Lecture 2 - About Counting public
Lecture 3 - The Natural Integers Set public
Lecture 4 - Proof by recursion public
Lecture 5 - Compare Natural Integers public
Lecture 6 - The Totally Ordered Set (N,≤) public
Lecture 7 - Construct and Compare the Natural Integers public
Lecture 8 - Addition Exploration
Lecture 9 - Properties of the Addition
Lecture 10 - Mastering Addition
Lecture 11 - The indexed sums Sigma
Lecture 13 - Subtraction Exploration
Lecture 14 - Addition and Subtraction Mutual Properties
Lecture 15 - Parentheses handling with addition and subtraction
Lecture 16 - Our First Equations
Lecture 17 - Master addition and subtraction together
Lecture 18 - Project - Balance Computation
Lecture 19 - The subtraction in the commutative monoid (N,+)
Lecture 20 - Multiplication Exploration
Lecture 21 - The monoids (N,x) and (N*,x)
Lecture 22 - Mastering multiplication
Lecture 23 - The indexed products Pi
Lecture 25 - Project - The Grocer's Bill
Lecture 26 - The Semi Ring (N, +, x)
Lecture 27 - Parenthesis handling with Addition, Subtraction and Multiplication
Lecture 28 - Linear and Affine function drawing
Lecture 30 - Decimal Numeration exploration
Lecture 31- Manual addition and subtraction
Lecture 32 - Manual Multiplication
Lecture 33 - Orders of magnitude and scientific notation
Lecture 35 - Exponentiation Exploration
Lecture 36 - Properties of the Exponentiation
Lecture 37 - Remarkable Identities
Lecture 38 - Draw our first polynomials
Lecture 40 - Order and addition
Lecture 41 - Order and subtraction
Lecture 42 - Our first inequations
Lecture 44 - Order and multiplication
Lecture 45 - Order and exponentiation
Lecture 46 - Comparison scheme in decimal notation
Lecture 2 - The negative Numbers Exploration
Lecture 3 - Construction of the integers set Z
Lecture 4 - Compare two integers of any signs
Lecture 5 - The totally ordered set (Z,≤)
Lecture 7 - Exploration of the addition in Z
Lecture 8 - Exploration of the subtraction in Z
Lecture 9 - Addition and subtraction mutual ptoperties
Lecture 10 - The Properties of the Addition of Integers
Lecture 11 - Solving additive and subtractive equations in Z
Lecture 13 - Exploration of the multiplication in Z
Lecture 14 - The commutative monoids (Z,x) and (Z*,x)
Lecture 15 - The commutative ring (Z,+,x)
Lecture 16 - Exponentiation of an integer of any sign
Lecture 17 - Master Computation with addition, subtraction, multiplication and exponentiation
Lecture 19 - Order and addition and subtraction in Z
Lecture 20 - Solve additive inequations
Lecture 21 - Solve subtractive inequations of type 1
Lecture 22 - Solve subtractive inequations of type 2
Lecture 24 - Order and multiplication of an integer of any sign
Lecture 25 - Order and exponentiation of an integer of any sign 1
Lecture 26 - Order and exponentiation of an integer of any sign 2
Lecture 2 - Division and Fractions
Lecture 3 - The example of the decimal numbers
Lecture 4 - Equality of fractions
Lecture 5 - Simplify fractions
Lecture 6 - Simplify fractions in Python
Lecture 8 - The rational numbers as equivalence classes of fractions
Lecture 9 - Compare two fractions
Lecture 10 - Compare two rational numbers
Lecture 11 - The totally ordered set (Q,≤)
Lecture 12 - Construction and comparison of the rational numbers
Lecture 13 -Exploration of the addition of fractions
Lecture 14 - Addition of rational numbers
Lecture 15 - Exploration of the subtraction of fractions
Lecture 16 - Subtraction of Rational numbers
Lecture 17 - Fractions and Rational Numbers Addition and Subtraction
Lecture 18 - Addition and subtraction mutual reciprocity in Q
Lecture 19 - Solving additive and subtractive equations in Q
Lecture 20 - Properties of the Addition in Q
Lecture 21 - The Indexed Sums in Q
Lecture 23 - Multiply Fractions and Integers
Lecture 24 - Multiply Rational Numbers
Lecture 25 - The Signs Rules for the Multiplication of Rationals
Lecture 26 - Divide Fractions and Integers
Lecture 27 - Divide Rational Numbers
Lecture 28 - The Signs Rules for the Division of Rationals
Lecture 29 - Fractions and Rational Numbers Multiplication and Division
Lecture 30 - The Division and Multiplication Mutual Reciprocity in Q*
Lecture 31 - Solve Linear Equations in Q
Lecture 32 - Properties of the Multiplication in Q
Lecture 33 - Solve Proportionality Problems
Lecture 34 - The Multiplicative Group of non-zero Rational Numbers
Lecture 35 - The Commutative Field (Q,+,x)
Lecture 36 - The Percentages Definition and Manipulation
Lecture 37 - More Properties of the Four Operations in Q
Lecture 38 - Solve Affine Equations in Q
Lecture 40 - Exponentiation of a Rational Number by a non-negative Integer
Lecture 41 - Exponentiation of a non-zero Rational Number by a negative Integer
Lecture 42 - Exponentiation of a Product and a Quotient
Lecture 43 -Homomorphism of the Group (Z,+) on the Group (Q*,x)
Lecture 44 - Exponentiation of Rational Numbers by Signed Integers
Lecture 49 - Order with Addition and Subtraction
Lecture 50 - Order with Multiplication and Division
Lecture 51 - Solve Linear and Affine Inequations
Lecture 52 - The Density of the Rational Numbers Set
Lecture 53 - Direction of Variation of Affine Functions and Hyperbolas
Lecture 54 - Comparison between two Positive Powers of a Positive Rational Number
Lecture 55 - Direction of Variation and Convexity of a Parabola
Lecture 56 - The Rational Numbers Ordered Field (Q,+,x,≤) (pdf)
Lecture 57 - About the Real Numbers
Lecture 58 - The Square Roots of Non Negative Real Numbers
Lecture 59 - The Quadratic Equations
Lecture 60 - Discover the Trigonometric Functions
Lecture 61 - The Sine and Cosine in the Unit Circle
Lecture 62 - Properties of the Cosine and Sine Functions
Lecture 63 - Draw the Cosine and Sine Functions
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Lecture 2 - About Counting public
Lecture 3 - The Natural Integers Set public
Lecture 4 - Proof by recursion public
Lecture 5 - Compare Natural Integers public
Lecture 6 - The Totally Ordered Set (N,≤) public
Lecture 7 - Construct and Compare the Natural Integers public
Lecture 8 - Addition Exploration
Lecture 9 - Properties of the Addition
Lecture 10 - Mastering Addition
Lecture 11 - The indexed sums Sigma
Lecture 13 - Subtraction Exploration
Lecture 14 - Addition and Subtraction Mutual Properties
Lecture 15 - Parentheses handling with addition and subtraction
Lecture 16 - Our First Equations
Lecture 17 - Master addition and subtraction together
Lecture 18 - Project - Balance Computation
Lecture 19 - The subtraction in the commutative monoid (N,+)
Lecture 20 - Multiplication Exploration
Lecture 21 - The monoids (N,x) and (N*,x)
Lecture 22 - Mastering multiplication
Lecture 23 - The indexed products Pi
Lecture 25 - Project - The Grocer's Bill
Lecture 26 - The Semi Ring (N, +, x)
Lecture 27 - Parenthesis handling with Addition, Subtraction and Multiplication
Lecture 28 - Linear and Affine function drawing
Lecture 30 - Decimal Numeration exploration
Lecture 31- Manual addition and subtraction
Lecture 32 - Manual Multiplication
Lecture 33 - Orders of magnitude and scientific notation
Lecture 35 - Exponentiation Exploration
Lecture 36 - Properties of the Exponentiation
Lecture 37 - Remarkable Identities
Lecture 38 - Draw our first polynomials
Lecture 40 - Order and addition
Lecture 41 - Order and subtraction
Lecture 42 - Our first inequations
Lecture 44 - Order and multiplication
Lecture 45 - Order and exponentiation
Lecture 46 - Comparison scheme in decimal notation
Lecture 2 - The negative Numbers Exploration
Lecture 3 - Construction of the integers set Z
Lecture 4 - Compare two integers of any signs
Lecture 5 - The totally ordered set (Z,≤)
Lecture 7 - Exploration of the addition in Z
Lecture 8 - Exploration of the subtraction in Z
Lecture 9 - Addition and subtraction mutual ptoperties
Lecture 10 - The Properties of the Addition of Integers
Lecture 11 - Solving additive and subtractive equations in Z
Lecture 13 - Exploration of the multiplication in Z
Lecture 14 - The commutative monoids (Z,x) and (Z*,x)
Lecture 15 - The commutative ring (Z,+,x)
Lecture 16 - Exponentiation of an integer of any sign
Lecture 17 - Master Computation with addition, subtraction, multiplication and exponentiation
Lecture 19 - Order and addition and subtraction in Z
Lecture 20 - Solve additive inequations
Lecture 21 - Solve subtractive inequations of type 1
Lecture 22 - Solve subtractive inequations of type 2
Lecture 24 - Order and multiplication of an integer of any sign
Lecture 25 - Order and exponentiation of an integer of any sign 1
Lecture 26 - Order and exponentiation of an integer of any sign 2
Lecture 2 - Division and Fractions
Lecture 3 - The example of the decimal numbers
Lecture 4 - Equality of fractions
Lecture 5 - Simplify fractions
Lecture 6 - Simplify fractions in Python
Lecture 8 - The rational numbers as equivalence classes of fractions
Lecture 9 - Compare two fractions
Lecture 10 - Compare two rational numbers
Lecture 11 - The totally ordered set (Q,≤)
Lecture 12 - Construction and comparison of the rational numbers
Lecture 13 -Exploration of the addition of fractions
Lecture 14 - Addition of rational numbers
Lecture 15 - Exploration of the subtraction of fractions
Lecture 16 - Subtraction of Rational numbers
Lecture 17 - Fractions and Rational Numbers Addition and Subtraction
Lecture 18 - Addition and subtraction mutual reciprocity in Q
Lecture 19 - Solving additive and subtractive equations in Q
Lecture 20 - Properties of the Addition in Q
Lecture 21 - The Indexed Sums in Q
Lecture 23 - Multiply Fractions and Integers
Lecture 24 - Multiply Rational Numbers
Lecture 25 - The Signs Rules for the Multiplication of Rationals
Lecture 26 - Divide Fractions and Integers
Lecture 27 - Divide Rational Numbers
Lecture 28 - The Signs Rules for the Division of Rationals
Lecture 29 - Fractions and Rational Numbers Multiplication and Division
Lecture 30 - The Division and Multiplication Mutual Reciprocity in Q*
Lecture 31 - Solve Linear Equations in Q
Lecture 32 - Properties of the Multiplication in Q
Lecture 33 - Solve Proportionality Problems
Lecture 34 - The Multiplicative Group of non-zero Rational Numbers
Lecture 35 - The Commutative Field (Q,+,x)
Lecture 36 - The Percentages Definition and Manipulation
Lecture 37 - More Properties of the Four Operations in Q
Lecture 38 - Solve Affine Equations in Q
Lecture 40 - Exponentiation of a Rational Number by a non-negative Integer
Lecture 41 - Exponentiation of a non-zero Rational Number by a negative Integer
Lecture 42 - Exponentiation of a Product and a Quotient
Lecture 43 -Homomorphism of the Group (Z,+) on the Group (Q*,x)
Lecture 44 - Exponentiation of Rational Numbers by Signed Integers
Lecture 49 - Order with Addition and Subtraction
Lecture 50 - Order with Multiplication and Division
Lecture 51 - Solve Linear and Affine Inequations
Lecture 52 - The Density of the Rational Numbers Set
Lecture 53 - Direction of Variation of Affine Functions and Hyperbolas
Lecture 54 - Comparison between two Positive Powers of a Positive Rational Number
Lecture 55 - Direction of Variation and Convexity of a Parabola
Lecture 56 - The Rational Numbers Ordered Field (Q,+,x,≤) (pdf)
Lecture 57 - About the Real Numbers
Lecture 58 - The Square Roots of Non Negative Real Numbers
Lecture 59 - The Quadratic Equations
Lecture 60 - Discover the Trigonometric Functions
Lecture 61 - The Sine and Cosine in the Unit Circle
Lecture 62 - Properties of the Cosine and Sine Functions
Lecture 63 - Draw the Cosine and Sine Functions
First published on Wednesday, Mar 11, 2026 and last modified on Saturday, Oct 10, 2026
Fabienne Chaplais Email
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