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Applied mathematics
A look at mathematics from the other side - not from the Olympic side, but from a practical side: how algorithms, simulations and intuition overcome the challenges of the modern world. We analyze use cases and optimization methods for tasks that technology and business face every day. We use Python as a tool - no previous experience is required.
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 programming language - minimum mathematics required
- 2 Functions. Equation. Inequalities
- 3 School mathematics for solving real problems
Module II: Solving equations
lessons 4-8- 4 Dichotomy method. Chord Method
- 5 Even more methods!
- 6 Gauss method of solving systems of linear equations
- 7 Algorithms based on the Gauss method
- 8 Banach's fixed point theorem. Simple iteration method
Module III: Optimising
lessons 9-14- 9 Mathematical optimization problem
- 10 Binary and ternary search
- 11 Golden section and Fibonacci methods
- 12 Growth rate of function
- 13 Derivative and its applications. Tangential
- 14 Newton's methods and their development
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.