Federico CORBERI | ADVANCED COMPUTATIONAL PHYSICS

cod. 0522600059

ADVANCED COMPUTATIONAL PHYSICS

	0522600059
	DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
	EQF7
	PHYSICS
	2024/2025

PERCORSO SHARED STUDY PATHWAY

	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2021
	SPRING SEMESTER

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
FIS/03	4	32	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS
FIS/03	2	24	LAB	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	ADOLFO AVELLA T Curriculum
	-
	FEDERICO CORBERI Curriculum

EXAMS

	Exam	Date	Session
	APPELLO DI GENNAIO 2025	23/01/2025 - 15:00	SESSIONE DI RECUPERO
	APPELLO DI FEBBRAIO 2025	17/02/2025 - 15:00	SESSIONE DI RECUPERO

	Objectives
	THE COURSE HAS THE OBJECTIVE OF CONSOLIDATING STUDENTS' TRAINING IN THE USE OF BASIC AND ADVANCED COMPUTATIONAL TOOLS NECESSARY TO STUDY PHYSICAL SYSTEMS, BUT ALSO STATISTICAL AND BIOLOGICAL ONES, FROM THE MOST SIMPLE TO THE MOST COMPLEX. KNOWLEDGE AND UNDERSTANDING ABILITY THE COURSE IS INTENDED TO PROVIDE THE STUDENT WITH ADVANCED KNOWLEDGE CONCERNING THE FUNDAMENTAL NUMERICAL METHODS FOR THE RESOLUTION OF DIFFERENT TYPES OF PROBLEMS IN PHYSICS AND THE ABILITY TO UNDERSTAND / LEARN BY ONESELF ADDITIONAL ADVANCEMENTS. IN PARTICULAR, THE STUDY OF ALGORITHMS FOR THE FINDING PRIME NUMBERS, FOR THE FUNCTION INTEGRATION, FOR THE STUDY OF STATISTICAL SYSTEMS WITH RANDOM AND HAMILTONIAN EVOLUTION, FOR NUMERICAL DATA ANALYSIS, FOR THE DIAGONALIZATION OF MATRICES, FOR THE DEFINITION AND SOLUTION OF HAMILTONIAN FUNCTIONS, FOR PSEUDO-RANDOM NUMBER GENERATION, FOR MONTE CARLO METHOD IMPLEMENTATION, FOR THE DEVELOPMENT OF ARTIFICIAL INTELLIGENCE SYSTEMS AND SUPERVISED LEARNING EVEN VIA THE USE OF DEEP NEURAL NETWORK FOR THE SIMULATION OF REAL AND COMPLEX SYSTEMS (VIA INDEPENDENT CODE AND/OR BY USING PRECOMPILED PACKAGES). THE COURSE FORESEES THE USE OF PYTHON AND C++ AS ADVANCED PROGRAMMING LANGUAGES AND THE LEARNING OF THE LANGUAGE SYNTAX AND OF THE DIFFERENT PARADIGMS OF PROGRAMMING (PROCEDURAL, MODULAR, OBJECT-ORIENTED) THAT THEY SUPPORT, SO THAT THE STUDENT CAN UNDERSTAND / LEARN BY ONESELF OTHER HIGH-LEVEL LANGUAGES. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE COURSE IS INTENDED TO CONSOLIDATE STUDENT'S ABILITY TO SOLVE, AT A PROFESSIONAL LEVEL, PROBLEMS IN PHYSICS, BUT ALSO IN OTHER FIELDS OF SCIENCE, THROUGH THE USE OF NUMERICAL METHODS AND ALGORITHMS AND THEIR CODING IN TERMS OF COMPUTER PROGRAMS. IN PARTICULAR, THE STUDENT WILL HAVE TO RESTORE THE ABILITY TO DEAL WITH FUNCTIONS AND NUMERICAL DATA THROUGH INTEGRATION, SPLINE INTERPOLATION AND LEAST SQUARES, TO STUDY THE DYNAMICS OF INTERACTING QUANTUM SYSTEMS VIA THE LANCZOS METHOD, TO USE THE MONTE CARLO METHOD TO CALCULATE MULTI-DIMENTIONAL INTEGRALS, TO SIMULATE COMPLEX SYSTEMS AND EXPERIMENTAL APPARATUS, TO PROPAGATE THE EXPERIMENTAL UNCERTAINTIES EVEN IN VERY COMPLEX MEASUREMENTS AND TO DEVELOP AND MANAGE ARTIFICIAL INTELLIGENCE SYSTEMS FOR THE CONTROL AND PREDICTION OF THE BEHAVIOR OF SYSTEMS OF INTEREST IN MANY FIELDS, I.E. PHYSICAL, BIOLOGICAL, SOCIAL AND OTHERS. HE MUST ALSO ACQUIRE AN ADVANCED KNOWLEDGE OF THE LANGUAGES PYTHON AND C++ FOR THE CONCRETE APPLICATION OF THE NOTIONS ACQUIRED.

THE COURSE HAS THE OBJECTIVE OF CONSOLIDATING STUDENTS' TRAINING IN THE USE OF BASIC AND ADVANCED COMPUTATIONAL TOOLS NECESSARY TO STUDY PHYSICAL SYSTEMS, BUT ALSO STATISTICAL AND BIOLOGICAL ONES, FROM THE MOST SIMPLE TO THE MOST COMPLEX.

KNOWLEDGE AND UNDERSTANDING ABILITY
THE COURSE IS INTENDED TO PROVIDE THE STUDENT WITH ADVANCED KNOWLEDGE CONCERNING THE FUNDAMENTAL NUMERICAL METHODS FOR THE RESOLUTION OF DIFFERENT TYPES OF PROBLEMS IN PHYSICS AND THE ABILITY TO UNDERSTAND / LEARN BY ONESELF ADDITIONAL ADVANCEMENTS. IN PARTICULAR, THE STUDY OF ALGORITHMS FOR THE FINDING PRIME NUMBERS, FOR THE FUNCTION INTEGRATION, FOR THE STUDY OF STATISTICAL SYSTEMS WITH RANDOM AND HAMILTONIAN EVOLUTION, FOR NUMERICAL DATA ANALYSIS, FOR THE DIAGONALIZATION OF MATRICES, FOR THE DEFINITION AND SOLUTION OF HAMILTONIAN FUNCTIONS, FOR PSEUDO-RANDOM NUMBER GENERATION, FOR MONTE CARLO METHOD IMPLEMENTATION, FOR THE DEVELOPMENT OF ARTIFICIAL INTELLIGENCE SYSTEMS AND SUPERVISED LEARNING EVEN VIA THE USE OF DEEP NEURAL NETWORK FOR THE SIMULATION OF REAL AND COMPLEX SYSTEMS (VIA INDEPENDENT CODE AND/OR BY USING PRECOMPILED PACKAGES).
THE COURSE FORESEES THE USE OF PYTHON AND C++ AS ADVANCED PROGRAMMING LANGUAGES AND THE LEARNING OF THE LANGUAGE SYNTAX AND OF THE DIFFERENT PARADIGMS OF PROGRAMMING (PROCEDURAL, MODULAR, OBJECT-ORIENTED) THAT THEY SUPPORT, SO THAT THE STUDENT CAN UNDERSTAND / LEARN BY ONESELF OTHER HIGH-LEVEL LANGUAGES.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE COURSE IS INTENDED TO CONSOLIDATE STUDENT'S ABILITY TO SOLVE, AT A PROFESSIONAL LEVEL, PROBLEMS IN PHYSICS, BUT ALSO IN OTHER FIELDS OF SCIENCE, THROUGH THE USE OF NUMERICAL METHODS AND ALGORITHMS AND THEIR CODING IN TERMS OF COMPUTER PROGRAMS. IN PARTICULAR, THE STUDENT WILL HAVE TO RESTORE THE ABILITY TO DEAL WITH FUNCTIONS AND NUMERICAL DATA THROUGH INTEGRATION, SPLINE INTERPOLATION AND LEAST SQUARES, TO STUDY THE DYNAMICS OF INTERACTING QUANTUM SYSTEMS VIA THE LANCZOS METHOD, TO USE THE MONTE CARLO METHOD TO CALCULATE MULTI-DIMENTIONAL INTEGRALS, TO SIMULATE COMPLEX SYSTEMS AND EXPERIMENTAL APPARATUS, TO PROPAGATE THE EXPERIMENTAL UNCERTAINTIES EVEN IN VERY COMPLEX MEASUREMENTS AND TO DEVELOP AND MANAGE ARTIFICIAL INTELLIGENCE SYSTEMS FOR THE CONTROL AND PREDICTION OF THE BEHAVIOR OF SYSTEMS OF INTEREST IN MANY FIELDS, I.E. PHYSICAL, BIOLOGICAL, SOCIAL AND OTHERS. HE MUST ALSO ACQUIRE AN ADVANCED KNOWLEDGE OF THE LANGUAGES PYTHON AND C++ FOR THE CONCRETE APPLICATION OF THE NOTIONS ACQUIRED.

	Prerequisites
	THE KNOWLEDGE OF THE BASIC CONCEPTS OF CLASSICAL AND MODERN PHYSICS, CLASSICAL AND QUANTUM STATISTICAL MECHANICS, AND MATHEMATICAL ANALYSIS AND PHYSICS.

	Contents
	1. ADVANCED FUNDAMENTAL METHODS: PRIME NUMBERS FACTORIZATION, GAUSSIAN INTEGRATION, SPLINES, LEAST SQUARES. APPLICATION TO PHYSICAL PROBLEMS. (6 HOURS). 2. PROBLEMS OF MATHEMATICAL PHYSICS AND STATISTICAL MECHANICS: RANDOM WALKER, ISING (2 HOURS). 3. DIAGONALIZATION OF MATRICES: LANCZOS ALGORITHM FOR QUANTUM INTERACTING SYSTEMS AND DENSITY MATRIX. APPLICATION TO PHYSICAL PROBLEMS (2 HOURS). 4. MACHINE LEARNING: BASIC NOTIONS. EXAMPLES ON POLYNOMIAL REGRESSION AND AUTONOMOUS DEVELOPMENT OF THE ASSOCIATED NUMERICAL CODES. COST FUNCTION. BIAS-VARIANCE DECOMPOSITION. GRADIENT DESCENT AND ITS GENERALISATIONS TO SEARCH MINIMA OF A COST FUNCTION. INTRODUCTION TO BAYESIAN INFERENCE. LINEAR REGRESSION AND ITS BAYESIAN FORMULATION. REGULARISATION. APPLICATIONS: LEARNING THE COUPLING CONSTANTS OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. CLASSIFICATION TASKS. PERCEPTRON. LOGISTIC REGRESSION. CROSS-ENTROPY AND SOFT-MAX REGRESSION. APPLICATIONS: DETECTION OF THE PHASE OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. NEURAL NETWORKS: ARCHITECTURE AND TRAINING. FEEDFORWARD AND BACKPROPAGATION ALGORITHM. APPLICATIONS: AUTONOMOUS DEVELOPMENT OF NUMERICAL CODES FOR THE PROBLEMS ASSOCIATED TO POLYNOMIAL REGRESSION AND TO THE ISING MODEL. EXAMPLES USING PRE-BUILT PACKAGES (MATHLAB) ENFORCING CONVOLUTIONAL NEURAL NETWORKS. (20 HOURS). 5. MONTE CARLO METHOD: BACKGROUND. GENERATION OF PSEUDO-RANDOM NUMBERS. EXAMPLES (3 HOURS) 6. SIMULATION OF PHYSICAL OBSERVABLE MEASUREMENTS (EXPERIMENTAL UNCERTAINTIES) AND OF SIMPLE EXPERIMENTAL APPARATUS. ERROR PROPAGATION IN PARAMETER ESTIMATES: SIMPLE CASES (FOR EXAMPLE SPEED ESTIMATE VIA TIME AND SPACE SIMULATED MEASUREMENTS, ETC.) (5 HOURS). 7. SIMULATION OF PHYSICAL OBSERVABLE MEASUREMENTS (EXPERIMENTAL UNCERTAINTIES) AND OF COMPLEX EXPERIMENTAL APPARATUS (EFFICIENCY, NOISE, ETC.). SIMULATION OF RADIATION-MATTER INTERACTION. ESTIMATES OF COMPLEX PARAMETERS (FOR EXAMPLE SIGNAL-TO-BACKGROUND SEPARATION IN INVARIANT MASS PLOTS, ETC.) (7 HOURS). 8. C++ LANGUAGE (5 HOURS). 9. PYTHON LANGUAGE (6 HOURS).

Contents

1. ADVANCED FUNDAMENTAL METHODS: PRIME NUMBERS FACTORIZATION, GAUSSIAN INTEGRATION, SPLINES, LEAST SQUARES. APPLICATION TO PHYSICAL PROBLEMS. (6 HOURS).
2. PROBLEMS OF MATHEMATICAL PHYSICS AND STATISTICAL MECHANICS: RANDOM WALKER, ISING (2 HOURS).
3. DIAGONALIZATION OF MATRICES: LANCZOS ALGORITHM FOR QUANTUM INTERACTING SYSTEMS AND DENSITY MATRIX. APPLICATION TO PHYSICAL PROBLEMS (2 HOURS).
4. MACHINE LEARNING: BASIC NOTIONS. EXAMPLES ON POLYNOMIAL REGRESSION AND AUTONOMOUS DEVELOPMENT OF THE ASSOCIATED NUMERICAL CODES. COST FUNCTION. BIAS-VARIANCE DECOMPOSITION. GRADIENT DESCENT AND ITS GENERALISATIONS TO SEARCH MINIMA OF A COST FUNCTION. INTRODUCTION TO BAYESIAN INFERENCE. LINEAR REGRESSION AND ITS BAYESIAN FORMULATION. REGULARISATION. APPLICATIONS: LEARNING THE COUPLING CONSTANTS OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. CLASSIFICATION TASKS. PERCEPTRON. LOGISTIC REGRESSION. CROSS-ENTROPY AND SOFT-MAX REGRESSION. APPLICATIONS: DETECTION OF THE PHASE OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. NEURAL NETWORKS: ARCHITECTURE AND TRAINING. FEEDFORWARD AND BACKPROPAGATION ALGORITHM. APPLICATIONS: AUTONOMOUS DEVELOPMENT OF NUMERICAL CODES FOR THE PROBLEMS ASSOCIATED TO POLYNOMIAL REGRESSION AND TO THE ISING MODEL. EXAMPLES USING PRE-BUILT PACKAGES (MATHLAB) ENFORCING CONVOLUTIONAL NEURAL NETWORKS. (20 HOURS).
5. MONTE CARLO METHOD: BACKGROUND. GENERATION OF PSEUDO-RANDOM NUMBERS. EXAMPLES (3 HOURS)
6. SIMULATION OF PHYSICAL OBSERVABLE MEASUREMENTS (EXPERIMENTAL UNCERTAINTIES) AND OF SIMPLE EXPERIMENTAL APPARATUS. ERROR PROPAGATION IN PARAMETER ESTIMATES: SIMPLE CASES (FOR EXAMPLE SPEED ESTIMATE VIA TIME AND SPACE SIMULATED MEASUREMENTS, ETC.) (5 HOURS).
7. SIMULATION OF PHYSICAL OBSERVABLE MEASUREMENTS (EXPERIMENTAL UNCERTAINTIES) AND OF COMPLEX EXPERIMENTAL APPARATUS (EFFICIENCY, NOISE, ETC.). SIMULATION OF RADIATION-MATTER INTERACTION. ESTIMATES OF COMPLEX PARAMETERS (FOR EXAMPLE SIGNAL-TO-BACKGROUND SEPARATION IN INVARIANT MASS PLOTS, ETC.) (7 HOURS).
8. C++ LANGUAGE (5 HOURS).
9. PYTHON LANGUAGE (6 HOURS).

	Teaching Methods
	THE COURSE INCLUDES 24 HOURS OF FRONTAL LECTURES IN CLASSROOM FINALIZED TO THE LEARNING OF THE ADVANCED KNOWLEDGE ABOUT NUMERICAL METHODS AND PROGRAMMING AND 36 HOURS OF FRONTAL PRACTICAL LECTURES IN LABORATORY FOCUSED ON THE ILLUSTRATION OF THE PROCESS OF MODELING THE PHYSICAL PROBLEM UNDER CONSIDERATION, THE SELECTION AND DEVELOPMENT OF NUMERICAL METHODS AND ALGORITHMS NECESSARY FOR ITS NUMERICAL SOLUTION, THE DESIGN OF THE CODE ACCORDING TO THE CHOSEN PROGRAMMING PARADIGM, THE CONCRETE DRAFTING OF THE CODE IN C++ AND PYTHON (SYNTAX OF THE LANGUAGE), ITS COMPILATION, EXECUTION, AND RELATED COLLECTION AND GRAPHICAL REPRESENTATION OF THE RESULTS.

Teaching Methods

THE COURSE INCLUDES 24 HOURS OF FRONTAL LECTURES IN CLASSROOM FINALIZED TO THE LEARNING OF THE ADVANCED KNOWLEDGE ABOUT NUMERICAL METHODS AND PROGRAMMING AND 36 HOURS OF FRONTAL PRACTICAL LECTURES IN LABORATORY FOCUSED ON THE ILLUSTRATION OF THE PROCESS OF MODELING THE PHYSICAL PROBLEM UNDER CONSIDERATION, THE SELECTION AND DEVELOPMENT OF NUMERICAL METHODS AND ALGORITHMS NECESSARY FOR ITS NUMERICAL SOLUTION, THE DESIGN OF THE CODE ACCORDING TO THE CHOSEN PROGRAMMING PARADIGM, THE CONCRETE DRAFTING OF THE CODE IN C++ AND PYTHON (SYNTAX OF THE LANGUAGE), ITS COMPILATION, EXECUTION, AND RELATED COLLECTION AND GRAPHICAL REPRESENTATION OF THE RESULTS.

	Verification of learning
	THE ASSESSMENT AND EVALUATION OF THE STUDENT'S LEVEL OF LEARNING WILL TAKE PLACE THROUGH A FINAL TEST THAT WILL CONSIST IN THE ORAL DISCUSSION OF A RESEARCH PROJECT, ASSIGNED AT THE END OF THE COURSE TO A GROUP OF TWO/THREE STUDENTS, CONCERNING THE SOLUTION OF A PHYSICAL PROBLEM NOT MENTIONED IN THE COURSE, BUT SOLVED BY THE NUMERICAL METHODS COVERED DURING THE COURSE. THE ORAL DISCUSSION IS AIMED AT ASSESSING THE LEVEL OF THEORETICAL KNOWLEDGE, THE AUTONOMY OF ANALYSIS AND JUDGMENT, AS WELL AS THE STUDENT'S PRESENTATION SKILLS. THE EVALUATION LEVEL IS ASSIGNED TAKING INTO ACCOUNT THE EFFICIENCY OF THE METHODS USED, THE COMPLETENESS AND ACCURACY OF THE ANSWERS, AS WELL AS THE CLARITY IN THE PRESENTATION. THE MINIMUM LEVEL OF EVALUATION (18) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A BARELY SUFFICIENT ABILITY IN THE APPLICATION OF NUMERICAL METHODS AND IN THE IDENTIFICATION OF METHODS TO CONTROL NUMERICAL ERROR, AND HAS A LIMITED KNOWLEDGE OF THE MAIN ALGORITHMS. THE MAXIMUM LEVEL (30) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF NUMERICAL METHODS AND ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY AND MANAGE THE SOURCES OF NUMERICAL ERROR PRESENT IN THE SPECIFIC PROBLEM HE/SHE HAS CHOSEN TO DEAL WITH. PRAISE IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS HOW TO PRESENT THE TOPICS WITH CONSIDERABLE MASTERY OF THE SPECIFIC TECHNICAL LANGUAGE AND AUTONOMOUS PROCESSING SKILLS EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.

Verification of learning

THE ASSESSMENT AND EVALUATION OF THE STUDENT'S LEVEL OF LEARNING WILL TAKE PLACE THROUGH A FINAL TEST THAT WILL CONSIST IN THE ORAL DISCUSSION OF A RESEARCH PROJECT, ASSIGNED AT THE END OF THE COURSE TO A GROUP OF TWO/THREE STUDENTS, CONCERNING THE SOLUTION OF A PHYSICAL PROBLEM NOT MENTIONED IN THE COURSE, BUT SOLVED BY THE NUMERICAL METHODS COVERED DURING THE COURSE. THE ORAL DISCUSSION IS AIMED AT ASSESSING THE LEVEL OF THEORETICAL KNOWLEDGE, THE AUTONOMY OF ANALYSIS AND JUDGMENT, AS WELL AS THE STUDENT'S PRESENTATION SKILLS.

THE EVALUATION LEVEL IS ASSIGNED TAKING INTO ACCOUNT THE EFFICIENCY OF THE METHODS USED, THE COMPLETENESS AND ACCURACY OF THE ANSWERS, AS WELL AS THE CLARITY IN THE PRESENTATION.

THE MINIMUM LEVEL OF EVALUATION (18) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A BARELY SUFFICIENT ABILITY IN THE APPLICATION OF NUMERICAL METHODS AND IN THE IDENTIFICATION OF METHODS TO CONTROL NUMERICAL ERROR, AND HAS A LIMITED KNOWLEDGE OF THE MAIN ALGORITHMS.

THE MAXIMUM LEVEL (30) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF NUMERICAL METHODS AND ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY AND MANAGE THE SOURCES OF NUMERICAL ERROR PRESENT IN THE SPECIFIC PROBLEM HE/SHE HAS CHOSEN TO DEAL WITH.

PRAISE IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS HOW TO PRESENT THE TOPICS WITH CONSIDERABLE MASTERY OF THE SPECIFIC TECHNICAL LANGUAGE AND AUTONOMOUS PROCESSING SKILLS EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.

	Texts
	COMPUTATIONAL PHYSICS: T. PANG; AN INTRODUCTION TO COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 2ND ED. (2006), CODICI IN FORTRAN 90: 1ST ED. (1997). N.J. GIORDANO; COMPUTATIONAL PHYSICS; BENJAMIN CUMMINGS; 2ND ED. (2005). J. THIJSSEN; COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2007). R.H. LANDAU, J. PAEZ, C.C. BORDEIANU; A SURVEY OF COMPUTATIONAL PHYSICS: INTRODUCTORY COMPUTATIONAL SCIENCE; PRINCETON UNIVERSITY PRESS (2008). P.L. DEVRIES , J.E. HASBUN; A FIRST COURSE IN COMPUTATIONAL PHYSICS; JONES & BARTLETT PUBLISHERS; 2ND ED. (2010). A. KLEIN; INTRODUCTORY COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2010). R. FITZPATRICK; COMPUTATIONAL PHYSICS; LECTURE NOTES. MATHEMATICAL METHODS: K.F. RILEY, M.P. HOBSON, AND S.J. BENCE; MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING; CAMBRIDGE UNIVERSITY PRESS; 3RD ED. (2006). S. HASSANI; MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS; SPRINGER SCIENCE+BUSINESS MEDIA, LLC; 2ND ED. (2009). H. SHIMA, AND T. NAKAYAMA; HIGHER MATHEMATICS FOR PHYSICS AND ENGINEERING; SPRINGER-VERLAG (2010). NUMERICAL METHODS AND ALGORITHMS: W.H. PRESS, S.A. TEUKOLSKY, H.A. BETHE, W.T. VETTERLING, AND B.P. FLANNERY; NUMERICAL RECIPES - THE ART OF SCIENTIFIC COMPUTING; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 3RD ED. (2007). A HIGH-BIAS,LOW-VARIANCE INTRODUCTION TO MACHINE LEARNING FOR PHYSICISTS: P.METHA, M. BUKOV, C-H. WANG, A.G.R. DAY, C. RICHARDSON, C.K. FISHER, D.J. SCHWAB (HTTPS://ARXIV.ORG/ABS/1803.08823). NOTES OF THHE LECTURER ON MACHINE LEARNING.

Texts

COMPUTATIONAL PHYSICS: T. PANG; AN INTRODUCTION TO COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 2ND ED. (2006), CODICI IN FORTRAN 90: 1ST ED. (1997). N.J. GIORDANO; COMPUTATIONAL PHYSICS; BENJAMIN CUMMINGS; 2ND ED. (2005). J. THIJSSEN; COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2007). R.H. LANDAU, J. PAEZ, C.C. BORDEIANU; A SURVEY OF COMPUTATIONAL PHYSICS: INTRODUCTORY COMPUTATIONAL SCIENCE; PRINCETON UNIVERSITY PRESS (2008). P.L. DEVRIES , J.E. HASBUN; A FIRST COURSE IN COMPUTATIONAL PHYSICS; JONES & BARTLETT PUBLISHERS; 2ND ED. (2010). A. KLEIN; INTRODUCTORY COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2010). R. FITZPATRICK; COMPUTATIONAL PHYSICS; LECTURE NOTES.
MATHEMATICAL METHODS: K.F. RILEY, M.P. HOBSON, AND S.J. BENCE; MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING; CAMBRIDGE UNIVERSITY PRESS; 3RD ED. (2006). S. HASSANI; MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS; SPRINGER SCIENCE+BUSINESS MEDIA, LLC; 2ND ED. (2009). H. SHIMA, AND T. NAKAYAMA; HIGHER MATHEMATICS FOR PHYSICS AND ENGINEERING; SPRINGER-VERLAG (2010).
NUMERICAL METHODS AND ALGORITHMS: W.H. PRESS, S.A. TEUKOLSKY, H.A. BETHE, W.T. VETTERLING, AND B.P. FLANNERY; NUMERICAL RECIPES - THE ART OF SCIENTIFIC COMPUTING; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 3RD ED. (2007). A HIGH-BIAS,LOW-VARIANCE INTRODUCTION TO MACHINE LEARNING FOR PHYSICISTS: P.METHA, M. BUKOV, C-H. WANG, A.G.R. DAY, C. RICHARDSON, C.K. FISHER, D.J. SCHWAB (HTTPS://ARXIV.ORG/ABS/1803.08823). NOTES OF THHE LECTURER ON MACHINE LEARNING.

	More Information
	THE ATTENDANCE, ALTHOUGH NOT MANDATORY, IT IS STRONGLY RECOMMENDED. FOR A SATISFACTORY PREPARATION, IT IS REQUIRED, ON AVERAGE, TWO HOURS OF STUDY FOR EACH HOUR OF CLASS, BOTH FRONTAL AND LABORATORY ONES.

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Federico CORBERI | ADVANCED COMPUTATIONAL PHYSICS