Universitat Politècnica de Catalunya · BarcelonaTech

Bachelor's degree in Mathematics

School of Mathematics and Statistics (FME)

The bachelor’s degree in Mathematics is a rigorous course that will provide you with comprehensive training in the core disciplines of mathematics and their applications. If your goal is to do research, you will be well equipped to join leading groups conducting research in mathematics, engineering and technology, natural and health sciences, or the social sciences. You will be able to pursue a career in business or industry, or in banking and finance, consulting, health or services – all sectors in which mathematicians are increasingly valued for their training and ability to learn. If you are interested in teaching, after completing a master’s level teacher-training course, you will be able to teach mathematics at secondary schools.

Duration
4 years
Study load
240 ECTS credits (including the bachelor's thesis). One credit is equivalent to a study load of 25-30 hours.
Delivery
Face-to-face
Language of instruction

Check the language of instruction for each subject (and timetable) in the course guide in the curriculum.

Information on language use in the classroom and students’ language rights.

Fees and grants
Approximate fees per academic year: €1,107 (€2,553 for non-EU residents). Consult the public fees system based on income (grants and payment options).
Location
School of Mathematics and Statistics (FME)
Official degree
Recorded in the Ministry of Education's degree register
Places
75
Registration and enrolment
What are the requirements to enrol in a bachelor's degree course?
Legalisation of foreign documents
All documents issued in non-EU countries must be legalised and bear the corresponding apostille.

Fourth semester

Seventh semester

Eighth semester

  • CompulsoryECTS
  • OptionalECTS
  • ProjectECTS
Professional opportunities
  • Strategic consulting, technology consulting, management of projects and educational programmes.
  • Business, industry and services: data analysis, programming and software engineering, market research, planning and management, cryptography and security.
  • Research in mathematics: teaching and research at universities and research centres.
  • Research in other sciences and in engineering and technology: research centres and laboratories in the public and private sector: computing, communications, robotics, mechanics, biology and medicine.
  • Banking, finance, insurance: risk analysis and control, portfolio and fund management, investment management, design and evaluation of financial products, cryptography and security.
  • Teaching positions with public and private secondary schools, publishers, and companies in the education sector.
With universities around the world
  • Bachelor’s degree in Mathematics + Master's degree in Advanced Mathematics and Mathematical Engineering and Ingénieur INP from the École Nationale Supérieure d'Informatique et de Mathématiques Appliquées de Grenoble (ENSIMAG)
Within the framework of the courses offered by the Interdisciplinary Higher Education Centre (CFIS)
You can also take an interdisciplinary double degree coordinated by the CFIS at two UPC schools.
Further information on the CFIS website

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