Support the project
Applied mathematics
A look at mathematics from another side — practical rather than olympiad: how algorithms, modelling and plain intuition solve real modern problems.
One group, 14 lessons of 1.5 hours each, working in Python — no programming experience needed.
Who these classes are for
For students in grades 8-10 who want to see mathematics not as a set of olympiad problems but as a working tool — with code, real data and problems someone actually solves.
The minimum you need to know
- Confident work with fractions and algebraic manipulation
- An understanding of what a function is and what it is for
- The ability to read graphs of functions: zeros, intervals of constant sign, extrema and so on
- The ability to solve quadratic equations
- The ability to solve linear inequalities
Course program
In this new course Kvanta, together with Matematykotyky, invites you to look at the side of mathematics that established school practice treats as unconventional — its practical, experimental, applied side. We step away from the classic olympiad approaches and find out how algorithms, modelling, advanced mathematics and plain intuition solve real modern problems.
The autumn semester program covers two basic problems of computational mathematics in depth: finding roots and extrema of functions of one variable. On this course you get to learn the most modern methods, some of which have not even made it into university curricula yet.
Module I: Foundations
lessons 1-3- 1 Introduction to the Python language — the minimum a mathematician needs
- 2 Functions. Equations. Inequalities
- 3 School mathematics for solving real problems — elementary geometry, set theory, percentages, proportions, modelling, graphs and functions, equations and inequalities
Module II: Solving equations
lessons 4-8- 4 The bisection method. The method of chords
- 5 Even more methods! — the secant, Illinois, Pegasus, Ford and Anderson–Björck methods and others
- 6 Gaussian elimination for systems of linear equations
- 7 Algorithms built on Gaussian elimination
- 8 The Banach fixed-point theorem. The simple iteration method
Module III: Optimising
lessons 9-14- 9 The mathematical optimisation problem — its place in modern science and the main solution methods
- 10 Binary and ternary search
- 11 The golden-section and Fibonacci methods
- 12 Growth rates of functions
- 13 The derivative and its applications. The tangent line
- 14 Newton's methods and their descendants
Python — our working tool
Every method we cover is implemented in code straight away — Python here is not the point of the course but the instrument for it. The first lesson is devoted to exactly the amount of the language the rest of the program needs: no prior programming experience is required.