The study of mathematics can have various effects on the body, both physical and psychological.

Improving Brain Function: Learning math requires active use of different areas of the brain such as the frontal cortex, hippocampus, and temporal lobes. Regular practice of mathematics can lead to improved memory, concentration, logical thinking, and problem solving.

Reducing Stress: Many people feel anxious and stressed at the thought of math. However, with regular practice of math exercises, this can change. Learning math requires logic and consistency, which can help reduce stress and anxiety levels.

Improving Problem Solving: Mathematics is the science of problem solving. Studying mathematics helps develop the skills to analyze a problem, break it down into simpler parts, and apply logical strategies to find a solution.

Main course (M5G)
Lesson 1.4: Common fractions

In this lesson you will find out about common fractions, numerator, denominator, how to compare, add, multiply fractions etc.

Write your questions in the comments, I will be happy to answer 🤓

Interesting fact

Charles Lutwidge Dodgson is a little-known British mathematician who devoted a fair amount of his life to the study of logic. However, he became famous under a different name - Lewis Carroll, author of Alice in Wonderland.

Interesting fact

Banach-Tarski paradox: There is a strange paradox in mathematics known as the Banach-Tarski paradox. He claims that one can take a sphere, break it into several pieces, and with only rotations and shifts, assemble two complete spheres of the same size. This is contrary to common sense, but in mathematics it is possible!

Main course (M6G)
Lesson 1.1: Relations between numbers and quantities

In this lesson you will get acquainted with such concepts as the ratio of numbers, scale. The very important concepts of percentage, direct and inverse proportionality are also clarified. At the end is an interesting comment by Isaac Newton.

Remember, each lesson builds on the previous ones, so I recommend studying them sequentially.

Write your questions in the comments, I will be happy to answer 🤓

Interesting fact

The number zero (0) was not recognized as a number in many ancient civilizations. It was introduced to the Western world by the Italian mathematician Fibonacci in the 13th century.

By the way, The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. This sequence appears in various natural phenomena, such as the arrangement of leaves on a stem or the spiral pattern of a seashell.

The Four Color Theorem states that any map can be colored using only four colors in such a way that no two adjacent regions have the same color. Although it was first conjectured in the 19th century, it wasn't proven until 1976 with the help of computers.

The four color theorem has been notorious for attracting a large number of false proofs and disproofs in its long history. At first, The New York Times refused, as a matter of policy, to report on the Appel–Haken proof, fearing that the proof would be shown false like the ones before it (Wilson 2014). Some alleged proofs, stood under public scrutiny for over a decade before they were refuted. But many more, authored by amateurs, were never published at all.

Pi (π) is an irrational number: Pi is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It is an irrational number, which means it cannot be expressed as a fraction or a finite decimal. Its decimal representation goes on infinitely without repeating.

It's important to understand the origin of this number. This is why: L = 2πR, L – length of the circle and so formulas.

Task

Complexity: ⭐️⭐️⭐️

The last digit in a natural number is 2016 times less than the number itself. Find all tick numbers.

Task

Complexity – ⭐️⭐️⭐️⭐️

A natural number n is called good if each of the numbers n, n + 1, n + 2 and n + 3 is divisible by the sum of its digits. (For example, n = 60398 is good.)
Does a good number ending in 8 necessarily have a 9 as the penultimate digit?

By the way, a number that is divisible by the sum of its digits is called a Harshad number.

Source: Vseross., 2001.

Task

Difficulty – ⭐️⭐️⭐️⭐️

Three digits were written to the right of the natural number A. The resulting number turned out to be equal to the sum of all natural numbers from 1 to A. Find A.

Source: Vseross., 1999.

Main course (M6G)
Lesson 1.2: Whole numbers

In this lesson you will find out about some essential integer properties like: commutative, associative. Also, we represent integers on the coordinate axis here.

Remember, each lesson builds on the previous ones, so I recommend studying them sequentially.

Write your questions in the comments, I will be happy to answer 🤓

Use of math

Structural Analysis - the prediction of the response of structures to specified arbitrary external loads. Engineers use mathematical concepts to analyze the strength and stability of structures. They apply principles of statics, mechanics of materials, and structural analysis to calculate forces, stresses, and deformations in buildings, bridges, and other infrastructure.

During the preliminary structural design stage, a structure's potential external load is estimated, and the size of the structure's interconnected members are determined based on the estimated loads.

Interesting facts (Integers)

1. Zero (0) is the only integer that is neither positive nor negative. It is an essential concept in mathematics and plays a crucial role in many operations.

2. Every integer greater than 0 can be expressed as the sum of consecutive positive integers. For example, 15 can be expressed as 1 + 2 + 3 + 4 + 5.

3. The sum of any two even numbers is always even, and the sum of any two odd numbers is always even. However, the sum of an even number and an odd number is always odd. (If we speak about whole numbers)

4. Integers are closed under addition and multiplication. This means that if you add or multiply two integers, the result will always be an integer.

Quote

"Do not worry too much about your difficulty in mathematics, I can assure you that mine are still greater." — Albert Einstein

Mathematics has a wide range of applications across various fields. Some notable areas where math is extensively applied include:

Science and Engineering: Mathematics plays a fundamental role in physics, chemistry, biology, and engineering disciplines. It provides the language and tools for modeling and understanding natural phenomena, analyzing data, and solving complex problems.

Finance and Economics: Math is crucial in the fields of finance, economics, and accounting. It is used for financial modeling, risk analysis, optimization, portfolio management, and economic forecasting.

Computer Science: Mathematics forms the foundation of computer science and is essential for algorithms, cryptography, data structures, artificial intelligence, computer graphics, and computational modeling.

Statistics: Statistics relies heavily on mathematical concepts and methods for data analysis, hypothesis testing, probability theory, regression analysis, sampling techniques, and experimental design.

Cryptography and Information Security: Mathematical principles are vital in cryptography and information security to ensure secure communication, encryption algorithms, digital signatures, and data protection.

Operations Research: Mathematics is extensively used in operations research to optimize complex systems and decision-making processes. It helps find optimal solutions to problems in logistics, supply chain management, resource allocation, and transportation.

Physical and Social Sciences: Mathematics provides quantitative tools for analyzing and modeling phenomena in various scientific disciplines, including astronomy, geophysics, psychology, sociology, and environmental science.

Medicine and Healthcare: Math is applied in medical imaging, biomedical research, epidemiology, medical statistics, pharmacokinetics, and medical modeling for diagnostic and treatment purposes.

Architecture and Design: Mathematical principles, such as geometry and calculus, are utilized in architectural design, structural engineering, computer-aided design, and three-dimensional modeling.

Communication and Signal Processing: Mathematics is crucial in signal processing, telecommunications, data compression, image processing, and information theory for efficient transmission and storage of digital data.

I recommend that you familiarize yourself with a very exciting video: https://youtu.be/OmJ-4B-mS-Y

Main course (M6G)
Lesson 1.3: Rational numbers

In this lesson you will find out about some rational numbers. Comparison of them, laws of addition and multiplication. We'll find out image of a rational number on the coordinate axis. And a few words about equations.

Remember, each lesson builds on the previous ones, so I recommend studying them sequentially.

Write your questions in the comments, I will be happy to answer 🤓