Numbers reveal patterns, structures and relationships that sit at the heart of modern mathematics. This number theory course provides a structured journey through essential concepts, beginning with number theory for beginners and gradually introducing more advanced ideas. First, learners explore elementary number theory, number sets, patterns, even and odd numbers, properties and mathematical proofs. In addition, number theory fundamentals introduce number bases, binary arithmetic, hexadecimal calculations and factorial concepts. Consequently, learners develop a stronger mathematical foundation.

Next, the programme examines divisibility, GCD, LCM, Bézout’s Identity, perfect numbers, Fibonacci sequences and the Golden Ratio. Moreover, prime numbers and factors are explored alongside Euclid’s theorems, the Fundamental Theorem of Arithmetic and the Prime Number Theorem. Learners also study divisibility rules, modular concepts and modular arithmetic basics, including congruence, inverses, residue systems and important theorems. These topics encourage structured mathematical problem-solving.

Finally, the course introduces continued fractions and their different forms before connecting number theory with cryptography. Learners explore early ciphers, public-key cryptography, RSA encryption and the Diffie-Hellman protocol. Therefore, this pure mathematics course provides valuable exposure to discrete mathematics fundamentals while showing how numerical principles contribute to modern computational security and mathematical reasoning.