Mathedu Series of Courses of Mathematics
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Natural Integers MasterClass
Available
Elements of Numbers Theory
August 30, 2020
The Signed Integers MasterClass
December 25, 2020
The Fractions and the Rational numbers MasterClass
April 30, 2021
The Real Numbers and Approximation MasterClass
August 30, 2021
The Calculus Classes
20212023
More Numerical Analysis
2023/2024 and beyond…

Natural Integers Masterclass
Enroll in The Natural Integers MasterClass, for $380, Lifetime subscription
OR
Subscribe to Practical Mathematics Premium Subscription for $10 a monthMastering the construction and manipulation of the Natural integers
 Count and construct the natural integers set
 Prove theorems by recusion, a powerful method of proof
 Order the natural integers set
 Add, subtract and multiply the natural integers
 Powers of 10 and scientific notation
 Exponentiation of the natural integers
 Comparison and addition/subtraction
 Comparison and multiplication/exponentiation
And the course includes a final project: the combinatory binomial coefficients and the binomiel theorem.
That course includes:
 54 high quality video lectures,
 10 downloadable recapitulative documents, one per section, with all the proofs.
 10 intermidiate tess, one per section, with a process to have them corrected
 One final assessment, to submit to correction and grading
And when the final assessment is successfully passed, the students will get a module cerificate.
Construct and Compare the Natural Integers set
Add natural integers
Subtract Natural Integers
Multiply natural integers
Mastering computation in the natural integers
Powers of 10 and decimal numeration
Exponentiation in N
The ordered monoid (N,+,≤)
The ordered semiring (N,+,x,≤)
Final Project: The Combinatory and the Binomial Coefficients
Enroll in The Natural Integers MasterClass, for $380, Lifetime subscription
OR
Subscribe to Practical Mathematics Premium Subscription for $10 a month 
Elements of Number Theory
Scheduled for August 30, 2020
Mastering the divisibility and the division of positive integers
 Divisibility, divisors and multiples
 The Eucidean division (long division)
 The prime numbers and the Sieve of Erathosthenes
 The decomposition of positive integers into prime factors
 Greater Common Divisor of two positive integers
 Least Common Multiple of two positive integers
And the course includes a final project: The Euclidean algorithm to calculate a Greater Common Divisor of two positive integers, with its implementation in Python, and its proof in a downloadable document.
That course includes:
 38 high quality video lectures,
 6 downloadable recapitulative documents, one per section, with all the proofs.
 6 intermidiate tess, one per section, with a process to have them corrected
 One final assessment, to submit to correction and grading
And when the final assessment is successfully passed, the students will get a module cerificate.
Multiples and Divisors in the positive integers set
Criteria of divisibility by specific positive integers
The Euclidean Division between positive integers
The long division manual and computurized process
The prime numbers and the fundamental theoem of arithmetics
Greater Common Divisors (GCD) and Lower Common Multiples (LCM)
Final Project: The Euclidean Algorith to compute a Greater Common Divisor

The Signed Integers MasterClass
Scheduled for December 25, 2020
Mastering the computation with signed integers
 Discover the negative numbers
 Construct the twosided integer line of integers Z
 Compare and order integers of any signs
 Add , subtract and multiply integers of any signs
 Discover integer polynomialls
 Exponentiate integers of any sign
 Divide nonzeros integers when integer division is possible
 Practice the signs rules for inequalities
 Discover calculation modulo a positive integer p, and the quotient set Z/pZ
And the course includes a final project: Final Project: The Bezout Identity to calculate the multiplicative inverses in the finite field Z/pZ, with its implementation in Python, and its proof in a downloadable document.
That course includes:
 58 high quality video lectures,
 10 downloadable recapitulative documents, one per section, with all the proofs.
 10 intermidiate tess, one per section, with a process to have them corrected
 One final assessment, to submit to correction and grading
And when the final assessment is successfully passed, the students will get a module cerificate.
Construct and order the Integers set Z
A free version of that section: Construct and compare the Signed Integers, is scheduled for June 2020
Add two integers of any sign
Subtract two integers of any sign
Multiply Integers of any signs
Mastering computation with the signed integers
Exponentiation in Z and polynomial functions
Integer division and multiplicative integer equations
The ordered commutative ring (Z,+,x,≤)
The calculation modulo p and the quotient set Z/p
Final Project: The Bezout Identity and the finite fields Z/pZ

The Fractions and the Rational numbers MasterClass
Scheduled for April 30, 2021
Mastering the Fractions and the Rational Numbers Construction and Manipulation
In that course, we will discover the fractions of integers, that are interesting by themselves, and the rational numbers, that are represented by fraction, but not reduced to fractions.
This is because many fractions (an infinity in fact) reprent the same rational number.
We willl learn to add, subtract, multiply, divide and exponentiate fractions, and also rational numbers, that are families of fractions.

The Real Numbers and Approximation MasterClass
Scheduled for August 30, 2021
Mastering the Real Numbers Construction and Manipulation
In that course, we will construct the real numbers set as famiies of sequences of rational numbers, the sort of sequences called Cauchy sequences.
(The Cauchy sequences areinteresting by themselves, because they give a rigorous frame to the approximation matter.)
The addition, subtraction, multiplication, division, and exponentiation of real numbers will be comprehensively taught.

The Calculus Classes
Scheduled for 20222023
Mastering Calculus, from a numerical analysis point of view
With the real numbers set and the approximation tools, we shall be ready for the Calculus Classes:
 The polynomial functions
 The systems of linear equations
 The continuity of functions
 The diffenrentiation of functions
 The integration of functions
The particularity of these Calculus classes is that they don't only start from a practical point of view, as all our courses, but it leads also to numerical analysis, the science of algorithms.
So that you will be able to practice immediatly in Python, and to use your mastery for any scientfic computing project you may havr to develop.

More Numerical Analysis
Scheduled for 2023/2024 and beyond
Mastering Numerical Analysis of any kind
By the end of the year 2024, you will get more classes of numerical analysis:
 Sequences and series of real numbers
 with the definition of exponential and logarithm functions
 Complex numbers with their exponential
 The polar coordinates in the plane
 The fourier transforms
 The multivariables functions with the optimisation problems
 Eigenvalues and Eigenvectors
 With the conditioning of a problem
 Differential equations of one real variable
 Two boundary values problems
 Sequences and series of real numbers
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