Mathedu - Reengineering Mathematics

Mathedu Reengineering Mathematics

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Schedule

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

2021-2023

More Numerical Analysis

2023/2024 and beyond…

  • Natural Integers Masterclass

    Mastering 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 semi-ring (N,+,x,≤)

    Final Project: The Combinatory and the Binomial Coefficients

  • Elements of Number Theory

    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

    Mastering the computation with signed integers

    • Discover the negative numbers
    • Construct the two-sided 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 non-zeros 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

    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

    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

    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

    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