Program Overview
The Master's degree in Applied Mathematics for Engineering and Computing equips students with analytical and simulation skills for careers in aerospace, automotive, and energy industries. Combining numerical methods, computational techniques, and hands-on experience, the program prepares graduates for leadership roles in computational engineering, high-performance computing, and research.
Program Outline
Máster Universitario en Matemática Aplicada a la Ingeniería y Computación
Degree Overview:
The Máster Universitario en Matemática Aplicada a la Ingeniería y Computación is a unique and differentiating program designed to prepare students for careers in the international market of large companies. The program focuses on developing analytical and simulation interpretation skills, highly sought after in industries like aerospace, automotive, and energy. The program's objectives include:
- Providing a comprehensive understanding of simulation in various disciplines: aerodynamics, fluids, thermal analysis, structural calculation, HPC, with a strong transversal focus on aerospace, automotive, and energy engineering.
- Equipping students with the knowledge and skills to solve real-world problems in the industry using the most widely used software.
- Offering a learning experience guided by a faculty with extensive experience in leading companies within the sectors and a strong research background.
- Providing access to valuable resources like White papers, O'Reilly for Higher Education, and Steam Essentials, enhancing the learning experience.
Outline:
The Máster Universitario en Matemática Aplicada a la Ingeniería y Computación is a multidisciplinary program with a unique structure, offering a broad perspective valuable for future professionals and researchers. The program's strong connection to real-world industry problems, through its content and faculty (90% of whom come from the industry and are actively involved in computational development), provides students with practical knowledge essential for navigating the learning curve in companies and differentiating themselves as desirable candidates. The program is structured as follows:
FIRST YEAR
| Subject | ECTS | Type | Language |
|---|---|---|---|
| MODULE 1.
Numerical Methods in Differential Equations | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 2.
Computational Fluid Dynamics (CFD) | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 3.
Meshing Techniques | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 4.
Computational Structural Calculation and FEM | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 5.
Advanced Digital Modeling and CAD | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 6.
Simulation and Thermal Analysis | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 7.
Optimization | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 8.
Advanced High-Performance Computing (HPC) | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 9.
Research Methodology | 6 | OBLIGATORY | SPANISH (ES) |
| MODULE 10.
Master's Thesis | 6 | OBLIGATORY | SPANISH (ES) |
Module Descriptions:
- Covers numerical methods for ODEs and dynamic systems, finite difference methods for PDEs, integral methods for PDEs (finite elements, finite volumes), advanced discretization methods (discontinuous Galerkin, X-FEM), iterative methods for solving linear systems of equations, and iterative methods for non-linear systems of equations.
Computational Fluid Dynamics (CFD):
- CFD simulation is essential in the aerospace, automotive, and energy industries.
- Covers computational fluid dynamics, numerical methods in CFD, iterative methods for solving equations, turbulent flow modeling, turbulence models, direct simulation (DNS) and large-scale simulation (LES), stationary and non-stationary problems.
Meshing Techniques:
- Efficient meshing is crucial for handling increasingly complex simulations.
- Covers structured meshes, unstructured meshes, Cartesian meshes, adaptive meshes, data structures and their impact on equation solving, mesh requirements in structural and fluid problems.
Computational Structural Calculation and FEM:
- Structural calculation is fundamental in all industries.
- Covers linear and non-linear structures, finite element method (FEM) theory, FEM calculation, computational vibration calculation, modal analysis, computational structural load calculation, computational requirements for FEM calculations and numerical methods.
Advanced Digital Modeling and CAD:
- Modeling complex geometries is essential for advanced simulation.
Simulation and Thermal Analysis:
- Simulating heat transfer processes in aeronautics and the energy sector is complex and requires advanced knowledge.
- Covers heat transfer, radiation, conduction, and convection, thermal structure design, numerical simulation of thermal problems, thermo-mechanical analysis, numerical methods for solving thermal problems.
Optimization:
- Optimization is crucial for reducing product delivery times in the aerospace and energy industries.
- Covers mathematical optimization, optimization in engineering, genetic algorithms, gradient-based optimization, adjoint problem, optimization in the aerospace and industrial sectors, frontiers of optimization.
Advanced High-Performance Computing (HPC):
- HPC is the answer to the high demand for simulation in today's industry.
- Covers principles of advanced high-performance computing, design and analysis of applications for advanced computing, parallel programming, programming on graphics cards (GPUs), Big Data techniques, advanced high-performance computing in the industry.
Research Methodology:
- Research is highly valued in both industry and academia.
- Covers research questions, state of the art, formulation of objectives and/or research hypotheses, study design and methodology: quantitative studies, qualitative studies, and mixed studies, data analysis and interpretation, and conclusions, communication of research results in applied mathematics for computational engineering.
Master's Thesis:
- The Master's Thesis involves applying the acquired concepts to a chosen topic.
Teaching:
The program's teaching methods are described as flexible and engaging, with live virtual classes accessible from any location and device. The program emphasizes a personalized learning experience with expert faculty and dedicated tutors providing guidance and support. The faculty consists of professionals with extensive experience in leading companies within the sectors and a strong research background. Some notable faculty members include:
- Dr. Almudena Vega: Director of the Master's program, with experience in aerospace engineering, aeroelasticity, and turbomachinery.
- D. Yago Blando: Professor of Numerical Methods, with experience in developing CFD "mesh-less" codes in the aeronautical industry.
- Dr. Elliott Bache: Professor of Computational Fluid Dynamics (CFD) and Thermal Analysis, with experience in CFD across various sectors.
- Dr. Jesús Pueblas: Professor of Computational Fluid Dynamics (CFD), with experience in developing CFD solvers.
- Álvaro Escudero: Professor of Meshing Techniques, with experience in aerodynamics and aeroelasticity of turbomachinery.
- Ramón Guadalupe: Professor of Computational Structural Calculation and FEM, with experience in structural calculation and FEM at Airbus.
- Carlos Avila: Professor of Advanced Modeling and CAD Techniques, with experience in designing aeronautical and space structures.
- Dr. Ricardo Puente: Professor of Optimization, with experience in developing optimization algorithms for CFD codes.
- Dr. Marc Bolinches: Professor of Advanced High-Performance Computing (HPC), with experience in high-order simulations.
Careers:
The Máster Universitario en Matemática Aplicada a la Ingeniería y Computación prepares students for careers in the international market of large companies, particularly in the aerospace, automotive, and energy sectors. Graduates can pursue roles such as:
- Director or Head of Computational Engineering
- Doctoral Studies
- Director or Head of High-Performance Computing
- Head of Department of Aerodynamics, Aeroelasticity, Thermal Analysis, or Structural Calculation
- White papers: Unlimited access to white papers written by professors, professionals, and doctoral specialists in each subject area.
- O'Reilly for Higher Education: Unlimited access to a learning platform with over 35,000 text resources and 30,000 hours of video content covering programming, web development, software architecture, cloud platforms, and more.
- Steam Essentials: Unlimited access to up-to-date readings on various engineering and technology topics, providing a transversal learning experience. The program also emphasizes the importance of research, with a dedicated module on research methodology and a Master's Thesis requirement.
Universidad Europea: A Comprehensive Overview
Overview:
Universidad Europea is a private university in Spain offering a wide range of academic programs, including undergraduate, postgraduate, doctorate, and technical degrees. It boasts a strong focus on practical learning, internationalization, and employability. The university has six campuses located in Madrid, Valencia, Alicante, and Canarias, as well as online programs for flexible learning.
Services Offered:
Universidad Europea provides a comprehensive range of services to its students, including:
Academic Support:
Educational counselling, internships, careers service, diplomas and certificates, management services, and financial information.Campus Life:
Active student clubs and associations, volunteering opportunities, and a vibrant campus experience.Internationalization:
Study abroad programs, international mobility opportunities, and tailor-made programs for international students.Research:
Extensive research opportunities, including collaborations with leading institutions and industry partners.Facilities:
Modern libraries, state-of-the-art classrooms, and specialized laboratories.Student Life and Campus Experience:
Students at Universidad Europea can expect a dynamic and engaging campus experience. The university fosters a strong sense of community with numerous student clubs and associations, providing opportunities for social interaction, extracurricular activities, and personal development. The university also encourages volunteering, promoting social responsibility and engagement.
Key Reasons to Study There:
Practical Learning:
Universidad Europea emphasizes a "learning by doing" approach, incorporating real-world projects, internships, and industry collaborations into its curriculum.Internationalization:
The university offers a diverse and international learning environment with a significant number of international students and faculty.Employability:
Universidad Europea boasts a high employability rate, with graduates finding employment within 18 months of graduation.Campus Locations:
The university's six campuses provide students with a choice of locations across Spain, offering diverse cultural experiences and opportunities.Online Programs:
The university's online programs provide flexibility and accessibility for students who prefer distance learning.Academic Programs:
Universidad Europea offers a wide range of academic programs across various disciplines, including:
Undergraduate Programs:
Degrees in Animation, Architecture, Biomedicine and Health, Business and Technology, Communication and Marketing, Criminology, Design, Fashion, Education, Engineering, Games Design, International Relations, Languages and Translation, Law, Sciences, Sports, and Tourism.Postgraduate Programs:
Master's degrees in various fields, including Business Administration, Big Data Analytics, Sustainability, Project Management, Construction Management, Sports Management, Esports Management, Sports Psychology, and Sports Nutrition.Doctorate and PhD Programs:
Programs in Biomedicine and Health, Engineering, and Sports.Higher-Level Technical Degrees:
Programs in Biomedicine and Health, Business and Technology, Communication and Marketing, Education, Engineering, and Gaming and Animation.Other:
Universidad Europea has a strong reputation for its commitment to quality education and innovation. The university is recognized by various rankings as one of the best private universities in Spain. It also has a strong partnership with Real Madrid Graduate School, offering specialized programs in sports management and communication.
Entry Requirements:
- For EU Home Students:
- Bachelor's Degree: Applicants must hold a bachelor's degree in a related field, such as engineering, mathematics, physics, or computer science.
- Work Experience: Applicants with a bachelor's degree in a non-related field may be considered if they have at least one year of relevant work experience in the field of mathematical engineering.
- For International Overseas Students Outside the EU:
- Bachelor's Degree: Applicants must hold a bachelor's degree equivalent to a Spanish bachelor's degree in a related field, such as engineering, mathematics, physics, or computer science.
- Work Experience: Applicants with a bachelor's degree in a non-related field may be considered if they have at least one year of relevant work experience in the field of mathematical engineering. The required level of proficiency will be determined by the university.
