Number theory courses can help you learn prime numbers, divisibility rules, modular arithmetic, and integer properties. You can build skills in problem-solving, logical reasoning, and algorithmic thinking, that support tackling complex mathematical challenges. Many courses introduce tools like Python for implementing algorithms and mathematical software for exploring number patterns, enabling you to apply your knowledge in practical situations such as cryptography and coding theory.

University of California San Diego
Skills you'll gain: Cryptography, Encryption, Public Key Cryptography Standards (PKCS), Cybersecurity, Arithmetic, Algorithms, Theoretical Computer Science, Computational Thinking, Algebra, Python Programming
Beginner · Course · 1 - 4 Weeks

University of California San Diego
Skills you'll gain: Graph Theory, Logical Reasoning, Combinatorics, Computational Logic, Deductive Reasoning, Cryptography, Probability, Computational Thinking, Encryption, Probability Distribution, Network Analysis, Public Key Cryptography Standards (PKCS), Theoretical Computer Science, Bayesian Statistics, Python Programming, Data Structures, Cybersecurity, Algorithms, Arithmetic, Visualization (Computer Graphics)
Beginner · Specialization · 3 - 6 Months

Johns Hopkins University
Skills you'll gain: Linear Algebra, Algebra, Applied Mathematics, Advanced Mathematics, Artificial Intelligence and Machine Learning (AI/ML), Mathematical Modeling, Engineering Analysis, Mathematical Theory & Analysis, Numerical Analysis, Geometry, Data Transformation, Applied Machine Learning, Dimensionality Reduction, Markov Model, Probability
Beginner · Specialization · 3 - 6 Months
Stanford University
Skills you'll gain: Mathematical Theory & Analysis, Mathematics and Mathematical Modeling, Calculus, Deductive Reasoning, Logical Reasoning
Intermediate · Course · 1 - 3 Months

University of Colorado Boulder
Skills you'll gain: Probability, Statistical Inference, Estimation, Probability & Statistics, Probability Distribution, Statistical Methods, Statistics, Markov Model, Bayesian Statistics, Data Literacy, Statistical Analysis, Sampling (Statistics), Applied Mathematics, Artificial Intelligence, Generative AI, Data Analysis, Data Science, Theoretical Computer Science, Machine Learning Algorithms, Mathematical Theory & Analysis
Build toward a degree
Intermediate · Specialization · 3 - 6 Months

University of Maryland, College Park
Skills you'll gain: Cryptography, Encryption, Key Management, Public Key Cryptography Standards (PKCS), Cybersecurity, Communication Systems, Digital Communications, Authentications, Data Integrity, Algorithms
Mixed · Course · 1 - 3 Months

Universitat Politècnica de València
Skills you'll gain: Taxonomy, Deductive Reasoning, Applied Mathematics
Beginner · Course · 1 - 4 Weeks

University of California San Diego
Skills you'll gain: Graph Theory, Combinatorics, Network Analysis, Data Structures, Visualization (Computer Graphics), Algorithms, Mathematical Theory & Analysis, Theoretical Computer Science, Program Development
Beginner · Course · 1 - 3 Months

University of California San Diego
Skills you'll gain: Combinatorics, Probability, Probability Distribution, Algorithms, Bayesian Statistics, Mathematical Modeling, Statistics, Arithmetic, Python Programming, Simulations
Beginner · Course · 1 - 3 Months

The Chinese University of Hong Kong
Skills you'll gain: Communication Systems, Digital Communications, Theoretical Computer Science, Telecommunications, Information Management, Probability, Probability Distribution, Linear Algebra, Digital Signal Processing, Algorithms
Mixed · Course · 3 - 6 Months

Stanford University
Skills you'll gain: Game Theory, Mathematical Modeling, Graph Theory, Bayesian Statistics, Behavioral Economics, Probability, Economics, Problem Solving, Algorithms, Probability Distribution
Beginner · Course · 1 - 3 Months

Princeton University
Skills you'll gain: Combinatorics, Mathematical Theory & Analysis, Advanced Mathematics, Graph Theory, Theoretical Computer Science, Calculus, Probability, Computational Thinking
Intermediate · Course · 1 - 3 Months
Number theory is a branch of mathematics that deals with the properties and relationships of numbers, particularly integers. It is important because it forms the foundation for various fields, including cryptography, computer science, and algebra. Understanding number theory can enhance problem-solving skills and logical reasoning, which are essential in many scientific and technological applications.‎
Careers related to number theory often involve roles in data analysis, cryptography, and algorithm development. Positions such as data scientist, cryptographer, and mathematician are common. Additionally, industries like finance, cybersecurity, and academia value expertise in number theory, making it a versatile skill set for various job opportunities.‎
To learn number theory effectively, you should focus on developing strong analytical skills, mathematical reasoning, and problem-solving abilities. Familiarity with algebra and basic calculus can also be beneficial. Additionally, programming skills, particularly in languages like Python, can enhance your ability to apply number theory concepts in practical scenarios.‎
Some of the best online courses for number theory include Number Theory and Cryptography, which explores the connections between number theory and cryptographic applications. These courses often provide a mix of theoretical knowledge and practical exercises to help learners grasp complex concepts.‎
Yes. You can start learning number theory on Coursera for free in two ways:
If you want to keep learning, earn a certificate in number theory, or unlock full course access after the preview or trial, you can upgrade or apply for financial aid.‎
To learn number theory, start by exploring introductory courses that cover basic concepts and gradually progress to more advanced topics. Engage with practice problems and real-world applications to reinforce your understanding. Joining study groups or online forums can also provide support and enhance your learning experience.‎
Typical topics covered in number theory courses include prime numbers, divisibility, modular arithmetic, and theorems such as the Fundamental Theorem of Arithmetic. Advanced courses may also explore topics like Diophantine equations, number patterns, and applications in cryptography and computer science.‎
For training and upskilling employees, courses like Number Theory and Cryptography are particularly beneficial. They provide practical applications of number theory in fields such as cybersecurity and data protection, making them valuable for professionals looking to enhance their skills in a technology-driven environment.‎