Advanced computational physics

The main objective of this course is to introduce to the student to the
advanced computational skill which are required to to solve complex problems
in the different branches of physics, both theoretical and experimental,
including:

- Knowledge of operating systems and the languages ​​and programming techniques
commonly used in physics.

- The skill to solve equations using numerical methods,
differential and integral algebraic problems and minimization problems
and optimization.

- The ability to design physical models using computer simulation.

- The ability to manage IT applications to solve Physical problems through
symbolic manipulation techniques and advanced graphics.

- Fundamentals of UNIX. Introduction to programming languages. Compiled and
interpreted languages. Programming in Python. Advanced thecnics in
programming: Object-oriented programming and functional
programming. Programming in C + +.

- Numerical Methods. Resolution of ordinary differential equations and
equations in partial derivatives. Methods of differences. Finite
elements. Spectral methods.

- Simulation methods. Classical simulation problems: Ising model,
percolation. Monte-Carlo methods. Random numbers and
pseudorandom numbers. Generation of probability distributions.

- Advanced Statistical Methods. Multivariate Methods. Principal component
analysis. Discriminant analysis. Fischer analysis. Factor
Analysis. Neural networks.

- Symbolic computation: Introduction. Simpy. Solution of linear algebra
problems. Resolution and representation of partial differential
equations. Solution of integro-differential equations: Moments methods.

- M. Lutz, Learning Python, O'Reilly 2009.

- http://sympy.org/es/index.html

- B. Stroustrup: El lenguaje de programación C++, Addison-Wesley, 2009.

- S. Wolfram, Mathematica : a system for doing mathematics by computer,
Addison-Wesley 1993.

- E. Weinstein: Wolfram Mathworld, http://mathworld.wolfram.com

- W.H. Press et al.: Numerical recipes: the art of scientific computing,
Cambridge University Press, 2007.

- W. Cheney y D. Kincaid: Numerical mathematics and computing, T. Brooks/Cole,
2007

- D. W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer
1990.

- T. Pang, An introduction to computational physics, Cambridge 2006.

- M.M. Woolfson, G.J. Pert, An Introduction to Computer Simulation, Oxford
1999.

- H. Gould, J. Tobochnik, W. Christian, An introduction to computer
simulation methods. Applications to physical systems, Addison-Wesley.

- M.A. Kalos y P.A. Whitlock: Monte Carlo methods, Wiley, 2008

- I.T. Jolliffe Principal Component Analysis, second edition, Springer 2002.

- F. Husson, S. Le, J. Pages, Exploratory Multivariate Analysis by Example
Using R, Chapman & Hall 2010.

- T. Hastie et al., The elements of statistical learning, Springer 2008.

BASIC AND GENERAL

CG01 - Acquire the ability to carry out research work in a team.

CG02 - Have the capacity for analysis and synthesis.

CG03 - Acquire the ability to write scientific texts, articles or reports in accordance with publication standards.

CG04 - Become familiar with the different modalities used for the dissemination of results and dissemination of knowledge in scientific meetings.

CG05 - Apply knowledge to solve complex problems.

CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context.

CB7 - That students know how to apply the acquired knowledge and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of ​​study.

CB8 - That students are able to integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments.

CB9 - That students know how to communicate their conclusions and the knowledge and ultimate reasons that support them to specialized and non-specialized audiences in a clear and unambiguous way.

CB10 - That students possess the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous.

TRANSVERSAL

CT01 - Ability to interpret texts, documentation, reports and academic articles in English, the scientific language par excellence.

CT02 - Develop the ability to make responsible decisions in complex and / or responsible situations.

SPECIFIC

CE01 - Know the operating systems and relevant programming languages ​​in physics.

CE02 - Solve algebraic, equation solving and optimization problems using numerical methods.

CE03 - Model and simulate complex physical phenomena by computer.

CE04 - Manage computer applications of symbolic calculation.

CE05 - Acquire advanced training aimed at research and academic specialization, which will allow you to acquire the necessary knowledge to access the doctorate.

The course will have a fundamentally practical and applied nature. There will
be a small number of theory classes to introduce the required methods The rest
of the classes will be in a computer lab, where the students will work on the
proposed subjects, by programming, calculate and simulate applied to different
problems in physics. Specific assignments to each student will be
proposed. These may be related to other subjects related to the Master. The
student work will be complemented by tutorial sessions.

The evaluation will be a continuous evaluation taking into account the
following aspects.

- The student must attend lectures and interactive sessions and perform
the required assignments.

- Specific work will be proposed to each student to implement the methods and
techniques learned as a small project.

- The final grade will be an average of the two with the following weights:

Attending classes and assignments 60%
Presentation of papers or projects 40%

Exceptionally, for those students which do not choose for a continuous
evaluation, a final examination may be done, if the student has completed all the exercises proposed during the interactive sessions.

In cases of fraudulent completion of exercises or tests, the following will apply to the provisions of the "Regulations for evaluating students' academic performance and reviewing grades":

"Article 16. Fraudulent performance of exercises or tests.

The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failed in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among other things, the realization of plagiarized works or obtained from sources accessible to the public without re-elaboration or reinterpretation and without citations to the authors and the sources ”.

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