Algebra, Geometry and Number Theory

The Mathematics program at Leiden University offers an in-depth undergraduate and master’s education focused on algebra, geometry, and number theory, designed to develop a comprehensive understanding of fundamental mathematical concepts and their applications. Students will explore the structures and patterns that underlie modern algebra, including group theory, ring theory, and field theory, gaining a solid foundation in abstract algebra and its numerous applications in science and technology. The program emphasizes both theoretical mathematics and practical problem-solving skills, preparing students for research, industry, or academic careers.

Throughout the program, students are introduced to various branches of geometry, such as Euclidean, non-Euclidean, algebraic, and differential geometry. They will learn to analyze geometric structures, understand their properties, and apply geometrical methods to solve complex problems in multiple contexts. The curriculum includes coursework in topology, manifolds, and computational geometry, fostering a deep appreciation for the visual and structural aspects of mathematics.

Number theory constitutes a core component of the program, enabling students to explore the properties of integers, prime numbers, and their distributions. They will examine classical results, modern developments, and applications in cryptography, algorithms, and computer security. The program also emphasizes the interplay between algebra, geometry, and number theory, illustrating how these fields complement and enhance each other.

Leiden University’s Mathematics program offers a combination of rigorous coursework, research projects, and independent study, supported by experienced faculty and state-of-the-art facilities. Students have opportunities to participate in collaborative research, attend seminars, and engage with international mathematical communities. The program is designed to equip graduates with critical thinking, analytical skills, and mathematical literacy vital for a variety of careers or further academic pursuits.

In summary, the Mathematics program at Leiden University provides a thorough education in algebra, geometry, and number theory, balancing theoretical foundations with practical applications. It prepares students for a range of professional paths in academia, industry, or research, fostering the next generation of mathematicians, scientists, and innovators who will contribute to solving complex problems across multiple disciplines.

The Mathematics Bachelor's program at Leiden University offers a comprehensive foundation in core mathematical disciplines, with a particular emphasis on algebra, geometry, and number theory. Throughout the program, students will develop a strong understanding of fundamental mathematical principles, while also gaining advanced knowledge in specialized areas. The curriculum is designed to combine rigorous theoretical coursework with opportunities for practical application, fostering analytical thinking and problem-solving skills essential for both academic research and industry positions.

Students begin their studies with introductory courses in calculus, linear algebra, and discrete mathematics, establishing a solid base for more advanced topics. As they progress, they explore algebraic structures such as groups, rings, and fields, gaining insight into their properties and applications. The geometry component covers both classical and modern geometrical concepts, including Euclidean and non-Euclidean geometries, differential geometry, and topology, emphasizing how geometric ideas underpin many areas of mathematics and science.

Number theory is a central pillar of the program, where students investigate properties of integers, primes, and cryptographic algorithms, gaining both theoretical knowledge and practical skills. The coursework involves studying Diophantine equations, modular arithmetic, and algebraic number theory, preparing students for careers in research, cryptography, or data security.

Throughout the program, students have opportunities to participate in research projects, seminars, and workshops, enabling them to engage actively with current mathematical developments. Leiden University’s faculty are renowned for their expertise, providing mentorship and guidance to support students' academic and professional growth.

The program also emphasizes the importance of mathematical communication, cultivating students’ ability to articulate complex ideas clearly and effectively—an essential skill in academia and beyond. Graduates of this program are well-equipped for further study in master's and doctoral programs, or for careers in education, finance, technology, data analysis, and research institutions. With its balanced blend of theory and application, the Bachelor's in Mathematics at Leiden University prepares students not only to understand existing mathematical theories but also to contribute to future innovations in the field.

Admission requirements

See www.unileidenmasters.nl for details.

Other requirements

1. minimum kennis (ISPAC: overige vereisten) See www.unileidenmasters.nl for details.
2. minimum kennis (ISPAC: overige vereisten) See www.unileidenmasters.nl for details.
3. vooropleiding (ISPAC: vereiste vooropleiding) BSc degree in Mathematics or with a BSc major in Mathematics, or a relevant field (see website www.unileidenmasters.nl).
4. vooropleiding (ISPAC: vereiste vooropleiding) BSc degree in Mathematics or with a BSc major in Mathematics, or a relevant field (see website www.unileidenmasters.nl).

Want to improve your English level for admission?

Prepare for the program requirements with English Online by the British Council.

• ✔️ Flexible study schedule
• ✔️ Experienced teachers
• ✔️ Certificate upon completion

📘 Recommended for students with an IELTS level of 6.0 or below.

Enroll in the course

The financing options for the Mathematics program at Leiden University are designed to accommodate both domestic and international students, ensuring accessible education through various funding sources. Tuition fees vary depending on the student's nationality and study load. For EU/EEA students, the standard statutory tuition fee applies, which is approximately €2,350 per year. Non-EU/EEA students are generally required to pay institutional or institutional-plus tuition fees, which may range from €9,000 to €15,000 annually, depending on the specific program and study load.

Leiden University offers a range of scholarships and grants to support talented students financially. The Holland Scholarship, for example, provides funding for non-EU students to study in the Netherlands, including programs at Leiden University. Additionally, there are Talent Scholarships open to outstanding students demonstrating exceptional academic ability and motivation. International students can also explore external funding opportunities through government grants or private foundations in their home countries.

For EU students, financing strategies include applying for student loans or grants provided by the Dutch government, such as the Studiefinanciering, though eligibility criteria and application processes vary. Support services at Leiden University also advise students on financial planning, budgeting, and accessing part-time work opportunities within Dutch regulations, which can help offset living expenses.

Living costs in Leiden are estimated at approximately €1,000 to €1,200 per month, covering accommodation, food, transportation, insurance, and personal expenses. Students are encouraged to plan their finances accordingly, taking into account tuition fees and living costs. The university also has a fund to assist students facing unforeseen financial difficulties, providing emergency aid or loans.

Students are advised to start their financial planning early by reviewing the official Tuition Fee page, scholarship opportunities, and external funding sources, and to complete necessary application procedures by deadlines. Overall, Leiden University strives to make its Mathematics program accessible by providing comprehensive financial support options, enabling students from diverse backgrounds to pursue their academic goals without undue financial stress.

The Bachelor's degree program in Algebra, Geometry and Number Theory at Leiden University offers a comprehensive and rigorous curriculum designed to provide students with a solid foundation in pure mathematics. The program emphasizes the development of logical thinking, problem-solving skills, and abstract reasoning. Students will explore various fundamental areas, including algebraic structures, geometric concepts, and the properties of numbers, which are essential for understanding advanced mathematical theories and applications. The program is structured into introductory courses that cover basic concepts, progressing to more specialized topics such as abstract algebra, topology, algebraic geometry, and number theory. Leiden University is renowned for its strong emphasis on research-led education, and students are encouraged to participate in academic projects, seminars, and workshops that enhance their understanding and foster innovative thinking.

Throughout the programme, students benefit from excellent teaching staff who are active researchers in their respective fields, creating an inspiring learning environment. The curriculum is designed to not only impart theoretical knowledge but also to develop practical skills necessary for mathematical research and problem-solving in various scientific and industrial contexts. The program also emphasizes the interconnectedness of different areas of mathematics, enabling students to see the bigger picture and appreciate the beauty and utility of mathematics in real-world applications.

In addition to coursework, students have opportunities for internships, collaborative research projects, and attendance at international conferences, broadening their academic and professional horizons. The program prepares students for a range of careers in academia, industry, finance, and technology, among others. Graduates of the programme typically pursue further studies in mathematics through Master's programmes at Leiden University or other renowned institutions worldwide. The curriculum is designed to foster independent learning, critical thinking, and innovative problem-solving abilities—skills that are highly valued in today's data-driven and technologically advanced society. Overall, the Bachelor's in Algebra, Geometry and Number Theory at Leiden University offers a robust foundation for students passionate about exploring the depths of pure mathematics and its applications.