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The Natural Integers Masterclass
Section 1: Introduction
Preliminary survey
Lecture 1: Introduction (7:20)
Section 2 : Construct and Compare the Natural Integers set
Lecture 2 : About Counting (6:17)
Lecture 3 : The Natural Integers Set (2:33)
Lecture 4: The Proof by Recursion (3:51)
Lecture 5 : Compare Natural Integers (9:21)
Lecture 6:: The Totally Ordered Set (N,≤) (13:03)
Lecture 7 : Construct and Compare the Natural Integers (PDF)
Section 2 test
Section 3: Add Natural Integers
Lecture 8: Addition Exploration (2:08)
Lecture 9: Properties of the Addition (13:19)
Lecture 10: Mastering Addition (18:13)
Lecture 11: The indexed sums Sigma (22:49)
Lecture 12 - The Natural Integers Additive Monoid (pdf)
Section 3 test
Section 4 - Subtract Natural Integers
Lecture 13 - Subtraction Exploration (3:08)
Lecture 14 - Addition and Subtraction Mutual Properties (3:19)
Lecture 15 - Parenthesis handling with additions and subtractions (12:45)
Lecture 16 - Our First Equations (18:47)
Lecture 17 - Master addition and subtraction together (10:33)
Lecture 18 - MS Excel Project : Balance Computation (5:43)
Lecture 19 - The subtraction in the commutative monoid (N,+) (pdf)
Section 4 test
Section 5 - Multiply Natural Integers
Lecture 20 - Multiplication Exploration (3:51)
Lecture 21 - The monoids (N,x) and (N*,x) (4:37)
Lecture 22 - Mastering multiplication (8:32)
Lecture 23 - The indexed products PI (7:49)
Lecture 24 - The commutative monoids (N,x) and and (N*,x) (pdf)
Section 5 test
Section 6 - Mastering computation in the natural integers
Lecture 25 - Project - The Grocer's Bill (4:45)
Lecture 26 - The Distributivity Law (6:20)
Lecture 27 - Parenthesis handling with +, - and x (5:18)
Lecture 28 - Linear function drawing (16:19)
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 (9:10)
Lecture 31- Manual addition and subtraction (10:15)
Lecture 32 - Manual Multiplication (10:10)
Lecture 33 - Orders of magnitude and scientific notation (10:22)
Lecture 34 - The powers of 10 and the decimal notation (pdf)
Section 7 test
Section 8 - Exponentiation in N
Lecture 35 - Exponentiation Exploration
Lecture 36 - Draw our first polynoms
Lecture 37 - Remarkable Identities
Lecture 38 - Project -The sum of the n first positive integers
Lecture 39 - Exponentiation and Polynomials in N (pdf)
Section 8 test
Section 9 - The ordered monoid (N,+,≤)
Lecture 40 - Order and addition
New LectureLecture 41 - Order and subtraction
Lecture 42 - Our first inequations
Lecture 43 - Inequations in the ordered monoid (N,+,≤)
Section 9 test
Section 10 - The ordered semi-ring (N,+,x,≤)
Lecture 44 - Order and multiplication
Lecture 45 - Comparison scheme in decimal notation
Lecture 46 - Order and exponentiation
Lecture 47 - Comparison scheme in scientific notation
Lecture 48 - Polynomials Values Comparison
Lecture 49 - The ordered semi-ring (N,+,≤,x) (pdf)
Section 10 test
Section 11 - Final Project - Binomial coefficients and combinatory
Lecture 50 - The binomial coefficients
Lecture 51 - The triangle of Pascal
Lecture 52 - The binomial theorem for (a+b) to the power n
Lecture 53 - Expanding (a+b) to the power n pdf)
Section 11 test
Section 12 - Conclusion
Lecture 54 - Conclusion
Final assessment
Final Survey
Lecture 20 - Multiplication Exploration
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