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The Natural Integers
Section 1: Introduction
Lecture 1: Introduction (5:10)
Section 2: Construct and Compare the Natural Integers
Lecture 2 : About Counting (6:17)
Lecture 3 : The Natural Integers Set (2:33)
Lecture 4: The Proof by Recursion (4:05)
Lecture 5 : Compare Natural Integers (9:16)
Lecture 6:: The Totally Ordered Set (N,≤) (11:46)
Lecture 7 : Construct and Compare the Natural Integers (PDF)
Section 2 test
Section 3: Add Natural Integers
Lecture 8: Addition Exploration (1:57)
Lecture 9: Properties of the Addition (12:40)
Lecture 10: Mastering Addition (17:39)
Lecture 11: The indexed sums Sigma (21:27)
Lecture 12 - The Natural Integers Additive Monoid (pdf)
Section 3 test
Section 4 - Subtract Natural Integers
Lecture 13 - Subtraction Exploration (2:53)
Lecture 14 - Addition and Subtraction Mutual Properties (3:06)
Lecture 15 - Parenthesis Handling with Additions and Subtractions (11:27)
Lecture 16 - Our First Equations (14:58)
Lecture 17 - Master Addition and Subtraction Together (9:35)
Lecture 18 - MS Excel Project : Balance Computation (4:40)
Lecture 19 - The Subtraction in the Commutative Monoid (N,+) (pdf)
Section 4 test
Section 5 - Multiply Natural Integers
Lecture 20 - Multiplication Exploration (3:38)
Lecture 21 - The Monoids (N,x) and (N*,x) (4:30)
Lecture 22 - Mastering Multiplication (7:32)
Lecture 23 - The Indexed Products PI (6:43)
Lecture 24 - The Commutative Monoids (N,x) and (N*,x) (pdf)
Section 5 test
Section 6 - Master computation in the natural integers
Lecture 25 - Project - The Grocer's Bill (4:35)
Lecture 26 - The Semi Ring (N,+,x) (6:18)
Lecture 27 - Parenthesis handling with +, - and x (4:43)
Lecture 28 - Linear functions drawing (13:08)
Lecture 29 - Computation in the Semi-Ring (N,+,x) (pdf)
Section 6 test
Section 7 - Powers of 10 and Decimal Numeration
Lecture 30 - Decimal Numeration exploration (8:47)
Lecture 31- Manual Addition and Subtraction (9:19)
Lecture 32 - Manual Multiplication (8:26)
Lecture 33 - Orders of Magnitude and Scientific Notation (8:40)
Lecture 34 - The Powers of 10 and the Decimal Notation (pdf)
Section 7 test
Section 8 - Exponentiation in N
Lecture 35 - Exponentiation Exploration (5:00)
Lecture 36 - Properties of the Exponentiation (3:04)
Lecture 37 - Remarkable Identities (4:20)
Lecture 38 - Draw our first Polynomials (11:34)
Lecture 39 - Exponentiation and Polynomials in N (pdf)
Section 8 test
Section 9 - The Ordered Monoid (N,+,≤)
Lecture 40 - Order and Addition (2:59)
Lecture 41 - Order and Subtraction (3:10)
Lecture 42 - Our First Inequations (16:40)
Lecture 43 - Solve Inequations in the Ordered Monoid (N,+,≤)
Section 9 test
Section 10 - The Ordered Semi-Ring (N,+,x,≤)
Lecture 44 - Order and Multiplication (3:26)
Lecture 45 - Order and Exponentiation (3:47)
Lecture 46 - Comparison Scheme in Decimal Notation (10:44)
Lecture 47 - The Ordered Semi-Ring (N,+,x,≤) (pdf)
Section 10 test
Section 11 - Final Assessment - The sum of the n first positive integers
Lecture 48 - The assessment subject
Section 12 - Conclusion
Lecture 49 - Conclusion (1:56)
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Lecture 45 - Order and Exponentiation
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