Degree in Mathematics
These studies lead to the degree of graduate in Mathematics. The curriculum consists of a total of 240 European ECTS credits(*) in accordance with article 12, point 2, of the Royal Decree 1393/2007, of October 29, and following the design included in the White Paper on the Degree in Mathematics. These credits are distributed over 4 academic years, at a rate of 60 credits per course, as stated in the Royal Decree 1125/2003, of September 5.
| Temporary programming of teachings starting in the 2020/21 academic year | |||||
|---|---|---|---|---|---|
| First course | |||||
| First quarter | ECTS | Character | Second quarter | ECTS | Character |
| Differential Calculus of a Real Variable | 9 | Basic | Linear Algebra | 7.5 | Basic |
| Statistics | 7.5 | Basic | Integral calculus of a real variable | 9 | Basic |
| Fundamentals of Mathematics | 6 | Basic | Advanced Computing | 6 | Mandatory |
| Introduction to Scientific Computing | 7.5 | Basic | Basic Geometry | 7.5 | Basic |
| Second course | |||||
| First quarter | ECTS | Character | Second quarter | ECTS | Character |
| Differential Calculus of several real variables | 6 | Mandatory | Algebra | 6 | Mandatory |
| Affine Geometry | 6 | Mandatory | Integral calculus of several real variables | 6 | Mandatory |
| Discrete Mathematics | 6 | Mandatory | Physics | 6 | Basic |
| Numerical Methods I | 6 | Mandatory | Optimization | 6 | Mandatory |
| General Topology | 6 | Mandatory | Odds | 6 | Mandatory |
| Third course | |||||
| First quarter | ECTS | Character | Second quarter | ECTS | Character |
| Differential Equations I | 6 | Mandatory | Differential Equations II | 6 | Mandatory |
| Differential Geometry of Curves and Surfaces | 6 | Mandatory | Introduction to Algebraic Topology | 6 | Mandatory |
| Statistical Inference | 6 | Mandatory | Measurement and Integration | 6 | Mandatory |
| Group Theory | 6 | Mandatory | Numerical Methods II | 6 | Mandatory |
| Complex Variable | 6 | Mandatory | Galois theory | 6 | Mandatory |
| Fourth course | |||||
| First quarter | ECTS | Character | Second quarter | ECTS | Character |
| Partial Differential Equations | 6 | Mandatory | Modeling | 6 | Mandatory |
| 2 elective subjects (see table below)*** | 12 | Electives | 2 elective subjects (see table below)*** | 12 | Electives |
| Internships (annual) | 6 | Internships (annual) | 6 | ||
| Final Degree Project (annual) | 6 | Final Degree Project (annual) | 6 | ||
***3 mentions are introduced: Statistics and Operations Research, Mathematics and Applications, and Pure Mathematics, curricular intensifications that each group together 4 of the 12 electives offered:
| Mention | Subject | Four-month period | ECTS |
|---|---|---|---|
| Statistics and Operations Research | Operational Research Models | 7th | 6 |
| Sampling and Surveys | 7th | 6 | |
| Multivariate Analysis | 8th | 6 | |
| Combinatorial Programming | 8th | 6 | |
| Mathematics and Applications | Differential Geometry and Applications | 7th | 6 |
| Mathematics for Teaching | 7th | 6 | |
| Spectral Data Analysis | 8th | 6 | |
| Numerical Methods in Partial Differential Equations | 8th | 6 | |
| Pure Mathematics | Commutative Algebra | 7th | 6 |
| Functional Analysis | 7th | 6 | |
| Algebraic Curves | 8th | 6 | |
| Algebraic Topology | 8th | 6 |
Students are deemed to have taken one of these curricular intensifications if the following circumstances are met:
- Mention in Statistics and Operational Research, if you pass the 4 subjects: Operational Research Models, Sampling and Surveys, Multivariate Analysis and Combinatorial Programming, that is, the electives are considered mandatory for mention.
- Mathematics and Applications Mention, if at least 3 of the 4 subjects of the corresponding curricular intensification are passed, being able to choose an elective from the other two a priori not taken mentions (Statistics and Operational Research or Pure Mathematics).
- Pure Mathematics Mention, if at least 3 of the 4 subjects of the corresponding curricular intensification are passed, being able to choose an elective from the other two a priori not taken mentions (Statistics and Operational Research or Mathematics and Applications).
The subjects must be effectively taken, that is, none of them can be obtained as recognition, except if it is because it adapts precisely that optional subject, existing in the 2013 Plan. In any of the intensifications it would be advisable for the Final Degree Project (TFG) subject to maintain the profile of the chosen mention.
Students who have completed any of the above-mentioned courses will see the corresponding curricular intensification reflected in the issuance of their Official Degree as a Graduate in Mathematics. Students who do not opt for any of the above-mentioned courses must complete 24 ECTS credits by choosing any 4 of the optional subjects offered, without any restriction on the recognition of any of these optional subjects. When their degree is issued, only Graduate in Mathematics will appear.
Description of the module structure
The modules are listed below, specifying subjects, nature, time location and number of ECTS in the curriculum programming:
| Level 1: Module | Character (Matter) | Level 2: Subjects | Four-month period | ECTS |
|---|---|---|---|---|
| Algebra | Basic (Mathematics) | Fundamentals of Mathematics | 1st | 6 |
| Linear Algebra | 2nd | 7.5 | ||
| Mandatory | Algebra | 4th | 6 | |
| Group Theory | 5th | 6 | ||
| Galois theory | 6th | 6 | ||
| Electives | Commutative Algebra | 7th | 6 | |
| Algebraic Curves | 8th | 6 | ||
| Mathematical Analysis | Basic (Mathematics) | Differential Calculus of a Real Variable | 1st | 9 |
| Integral calculus of a real variable | 2nd | 9 | ||
| Mandatory | Differential Calculus of several real variables | 3rd | 6 | |
| Integral calculus of several real variables | 4th | 6 | ||
| Complex Variable | 5th | 6 | ||
| Measurement and Integration | 6th | 6 | ||
| Elective | Functional Analysis | 7th | 6 | |
| Computing | Basic (Mathematics) | Introduction to Scientific Computing | 1st | 7.5 |
| Mandatory | Advanced Computing | 2nd | 6 | |
| Differential Equations and Numerical Methods | Mandatory | Differential Equations I | 5th | 6 |
| Differential Equations II | 6th | 6 | ||
| Numerical Methods I | 3rd | 6 | ||
| Numerical Methods II | 6th | 6 | ||
| Partial Differential Equations | 7th | 6 | ||
| Modeling | 8th | 6 | ||
| Elective | Numerical Methods in Partial Differential Equations | 8th | 6 | |
| Statistics and Operations Research | Basic (Mathematics) | Statistics | 1st | 7.5 |
| Mandatory | Discrete Mathematics | 3rd | 6 | |
| Optimization | 4th | 6 | ||
| Odds | 4th | 6 | ||
| Statistical Inference | 5th | 6 | ||
| Electives | Operational Research Models | 7th | 6 | |
| Sampling and Surveys | 7th | 6 | ||
| Multivariate Analysis | 8th | 6 | ||
| Combinatorial Programming | 8th | 6 | ||
| Physics | Basic (Physics) | Physics | 4th | 6 |
| Elective | Spectral Data Analysis | 8th | 6 | |
| Geometry and Topology | Basic (Mathematics) | Basic Geometry | 2nd | 7.5 |
| Mandatory | Affine Geometry | 3rd | 6 | |
| General Topology | 3rd | 6 | ||
| Differential Geometry of Curves and Surfaces | 5th | 6 | ||
| Introduction to Algebraic Topology | 6th | 6 | ||
| Electives | Differential Geometry and Applications | 7th | 6 | |
| Algebraic Topology | 8th | 6 | ||
| Mathematics for Teaching | Elective | Mathematics for Teaching | 7th | 6 |
| Internships | Internships | Internships | Annual | 12 |
| Final Degree Project | Final Degree Project | Final Degree Project | Annual | 12 |
(*) In compliance with Royal Decree 1125/2003, each ECTS credit is computed as 25 hours of student work, which include hours of lectures (theory and problem solving), seminars, supervised practical work or projects, preparation and presentation of work, preparation and completion of exams, study of theoretical concepts and independent problem solving. Additionally, the General Guidelines for the Design of Bachelor's Degrees of the University of La Laguna, based on Royal Decree 1393/2007 of October 29, consider that they are divided into 10 hours of face-to-face activities and 15 hours of independent work.