An Introduction to Number Theory explores fundamental concepts like primes, divisibility, and modular arithmetic, building logical thinking skills and mathematical insight for beginners interested in pure mathematics and problem solving.
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Intermediate
9 Students 
8 hours, 31 minutes 
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An Introduction to Number Theory is a comprehensive course designed to introduce learners to the fascinating world of Number Theory, exploring the properties, patterns, and relationships found within numbers. Covering essential concepts such as integer properties, prime numbers, divisibility rules, and number bases, this course builds a strong foundation in discrete mathematics and mathematical reasoning.
Through engaging lessons on factorials, divisibility, primes, and modular arithmetic, learners will develop the ability to analyse number patterns and understand the logic behind mathematical proofs. The course introduces key techniques used in problem-solving, helping students strengthen their analytical skills and gain confidence in applying Number Theory concepts across various mathematical applications.
This course also explores advanced topics such as continued fractions and cryptography basics, demonstrating how Number Theory supports modern technologies and secure communication systems. Ideal for learners interested in mathematics, computer science, and logical problem-solving, this course provides valuable knowledge of mathematical structures, proof methods, and the principles behind cryptographic systems.
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Learners complete an assignment designed to evaluate their understanding of the course content. The assignment is reviewed by qualified tutors who provide personalised feedback, allowing learners to demonstrate their applied knowledge and skills.
After completing the An Introduction to Number Theory course assessment, you will be eligible to receive a CPD-accredited certificate worth £9 from One Education to demonstrate your achievement.
The certificate is also available as a printed hard copy delivered by post for £15.
An Introduction to Number Theory introduces learners to the fascinating study of integers, prime numbers, divisibility, and mathematical patterns. This course explores key concepts such as number properties, divisibility rules, modular arithmetic, mathematical proofs, and the foundations of number theory used in areas including cryptography and discrete mathematics.
Studying An Introduction to Number Theory develops logical reasoning, problem-solving abilities, and mathematical thinking. The course supports learners interested in mathematics, computer science, and related fields by building a strong understanding of integer relationships, proof techniques, number patterns, and the fundamental ideas behind modern mathematical applications.
The An Introduction to Number Theory course has a total study time of 8 hours, 31 minutes. This comprehensive programme is designed for flexible learning, allowing learners to progress at their own pace while exploring number theory concepts, including prime numbers, divisibility rules, integer properties, mathematical proofs, modular arithmetic, number patterns, cryptography basics, discrete mathematics, mathematical reasoning, and fundamental principles of numbers.
The An Introduction to Number Theory course requirements are simple and suitable for beginners. Learners should have a basic understanding of mathematics, an interest in numbers, logical reasoning, problem-solving, and mathematical patterns, and a willingness to explore concepts such as prime numbers, divisibility, integers, and mathematical proofs. Access to an internet-enabled device and commitment to regular study are recommended for effective learning and successful course completion.
This course introduces the fundamental concepts of number theory, covering prime numbers, divisibility rules, integer properties, mathematical proofs, modular arithmetic, number patterns, cryptography basics, discrete mathematics, and logical mathematical reasoning.
No. It is suitable for beginners, students, mathematics learners, computer science enthusiasts, and anyone interested in developing analytical thinking and problem-solving skills through number theory.
The course is delivered online, allowing you to learn at your own pace and develop essential knowledge of mathematical structures, patterns, and number-based concepts conveniently.
Yes. Number theory exercises, proof-based activities, problem-solving tasks, mathematical examples, practice questions, and quizzes may be included to reinforce learning.
You will receive a certificate of completion after successfully finishing the course.
This course supports further development in mathematics, computer science, cryptography, data analysis, cybersecurity, research, education, and other fields requiring strong logical and analytical skills.
| Introduction | |||
| What is Number Theory | 00:08:00 | ||
| Basics of Number Theory | |||
| Number Theory | 00:07:00 | ||
| Number Sets | 00:09:00 | ||
| Number Patterns | 00:10:00 | ||
| Even & Odd Numbers | 00:11:00 | ||
| Number Properties | 00:10:00 | ||
| Proofs | 00:11:00 | ||
| Number Bases | |||
| Number Bases | 00:12:00 | ||
| Binary Base | 00:12:00 | ||
| Binary Arithmetics | 00:15:00 | ||
| Hexadecimal Base | 00:13:00 | ||
| Hexadecimal Arithmetics | 00:14:00 | ||
| Factorials | |||
| Factorial | 00:05:00 | ||
| Double Factorial | 00:09:00 | ||
| Super Factorial | 00:03:00 | ||
| Exponential Factorial | 00:03:00 | ||
| Factorion | 00:05:00 | ||
| Stirling’s Formula | 00:03:00 | ||
| Number of Digits | 00:03:00 | ||
| Divisibility | |||
| Divisibility | 00:07:00 | ||
| Divisibility Rules | 00:04:00 | ||
| Euclidean Division Theorem | 00:08:00 | ||
| GCD & LCM | 00:11:00 | ||
| Bézout’s Identity | 00:08:00 | ||
| Perfect Numbers | 00:04:00 | ||
| Practical Numbers | 00:05:00 | ||
| Amicable Numbers | 00:04:00 | ||
| Fibonacci Sequence | 00:09:00 | ||
| Tribonacci Sequence | 00:05:00 | ||
| Golden Ratio | 00:11:00 | ||
| Primes | |||
| Prime Numbers | 00:09:00 | ||
| Fundamental Theorem of Arithmetics (FTA) | 00:10:00 | ||
| Almost Primes | 00:07:00 | ||
| Prime Powers | 00:02:00 | ||
| Factorial Prime | 00:03:00 | ||
| Euclid’s Theorems | 00:09:00 | ||
| The Prime Number Theorem | 00:04:00 | ||
| Unsolved Problems | 00:06:00 | ||
| Number Empire | 00:07:00 | ||
| Modular Arithmetic | |||
| Modular Arithmetics | 00:09:00 | ||
| Congruence | 00:13:00 | ||
| Congruence Class | 00:12:00 | ||
| Residue Systems | 00:04:00 | ||
| Quadratic Residues | 00:04:00 | ||
| Modular Operations | 00:06:00 | ||
| Inverses | 00:07:00 | ||
| Modular Exponentiation | 00:10:00 | ||
| Wilson’s Theorem | 00:05:00 | ||
| Chinese Remainder Theorem | 00:09:00 | ||
| Fermat’s Little Theorem | 00:05:00 | ||
| Euler’s Totient Function | 00:07:00 | ||
| Euler-Fermat Theorem | 00:04:00 | ||
| Continued Fractions | |||
| Continued Fractions | 00:08:00 | ||
| Negative Continued Fractions | 00:11:00 | ||
| Finite Continued Fractions | 00:14:00 | ||
| Infinite Continued Fractions | 00:17:00 | ||
| Periodic Continued Fractions | 00:10:00 | ||
| Convergent | 00:12:00 | ||
| Cryptography | |||
| Cryptography | 00:09:00 | ||
| Early Ciphers | 00:11:00 | ||
| Public Key Cryptography | 00:13:00 | ||
| RSA Encryption | 00:11:00 | ||
| Diffie-Hellman Protocol | 00:04:00 | ||
| Resources | |||
| Resource – An Introduction to Number Theory | 00:00:00 | ||
| Assignment | |||
| Assignment – An Introduction to Number Theory | 00:00:00 | ||
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