Math Made Easy: ‘To understand a topic, its application in real-life is necessary’

Due to several reasons, Math is often seen as difficult by many learners. It is abstract in nature making it difficult for concrete learners. Weak background knowledge can make complex concepts appear overwhelming. Students may have developed a fear of mathematics because of anxiety and past unpleasant experiences they’ve had with the subject.

According to Abhishek Bajaj, PGT Math at Apeejay School, Rama Mandi, it is common for students to find the subject difficult, especially when it comes to certain chapters. “A common chapter that many students find tough is Number Theory. “There are a few reasons for the same. The main reason is that the topic is vast. Number Theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. There are different types of numbers: Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers, Real numbers, and Complex numbers. To understand each type, it is necessary to understand their application,” the educator stated and shared the following tips.

Natural numbers are the set of positive integers typically used for counting and ordering. The two predominant daily applications of natural numbers are ordering and counting.

·         Counting – in this application, we have to count the specific amount of objects by assigning the first object to the natural number 1…

·         Ordering – Ordering is also known as ranking the objects.

Whole numbers start from zero and include all natural numbers. They are important for counting and calculating quantities. They are used in everyday tasks like tracking student attendance, counting items in a store, and measuring ingredients for recipes.

 Integers are a set of numbers that include all whole numbers, both positive and negative, as well as zero.

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. They can be represented in the form: a/b, b≠0. These numbers can be expressed as terminating or repeating decimals.

“For any calculation of percentages like exam score, cooking, profit or loss, accounts, interest, banks, and taxes, we use rational numbers/fractions. For example: If we share a pizza or a bag of popcorn, chocolates, or even fruits with our friends, we each get a fraction of it. Knowledge of rational numbers is important,” Bajaj explained.

Irrational numbers are numbers that cannot be expressed as a fraction of two integers.

Real numbers are a set of numbers that include all rational and irrational numbers.

Complex numbers are numbers that consist of a real part and an imaginary part. They can be expressed in the form: a + ib (where a and b are real numbers, The real part is denoted by Re z = a, and the imaginary part is denoted by Im z = ib).  Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics. They’re useful for modelling periodic motions (such as water or light waves) as well as alternating currents.

Number Theory has several practical applications in real-life

·         Public Key Cryptography: Algorithms like RSA rely on the properties of prime numbers and modular arithmetic to secure communications.

·         Encryption: Used to protect sensitive information online, including banking and personal data.

·         Algorithms: Number Theory informs algorithms for tasks such as hashing, random number generation, and error detection.

·         Data Structures: Applications in hash tables and efficient data storage methods.

·         Error Detection and Correction: Techniques based on number theory help in designing codes that detect and correct errors in data transmission (Hamming codes).

·         Strategy Development: Number theory can help analyse games involving strategies and outcomes, particularly in competitive scenarios.

·         Fourier Transforms: Number theory aids in algorithms used in digital signal processing, including sound and image compression.

·         Algorithmic Trading: Number-theoretic concepts help in developing algorithms for trading strategies and risk assessment.

·         Combinatorial Designs: Applications in scheduling problems, such as round-robin tournaments and experimental design.

·         Art and Architecture: Concepts of symmetry and ratios derived from number theory influence design and aesthetics.

·         Pathfinding Algorithms: Used in programming robots and AI systems for efficient movement and decision-making.

·         Sampling Techniques: Number theory assists in methods for ensuring unbiased sampling in surveys and research.

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