The Master’s degree course in Mathematics is organized into four curricula:

  • Advanced Mathematics
  • Mathematics for Life and Data Sciences
  • Coding Theory and Cryptography
  • Teaching and Scientific Communication.

Curriculum: Advanced Mathematics

"Orientamento" General Advanced Mathematics

"Caratterizzanti" courses:

39 CFU (24 CFU in sectors MAT/01 – MAT/05 e 15 CFU in sectors MAT/06-MAT/09)

  • Advanced Analysis (9 CFU)
  • Advanced Geometry (9 CFU)
  • Computational Algebra (6 CFU)
  • Mathematical Logic (6 CFU)
  • Algebraic Geometry I (6 CFU)
  • Coding Theory and Applications (6 CFU)
  • Partial Differential Equations (9 CFU)
  • Stochastic Processes (9 CFU)
  • Mathematical Physics (9 CFU)
  • Numerical Methods for PDE (6 CFU)

"Affini" courses:

36 credits (24 in sectors MAT/* and FIS/*)

  • Algebraic Geometry II (6 CFU)
  • Geometric measure theory (6 CFU)
  • Algebraic Topology (6 CFU)
  • Advanced Topics in Analysis (6 CFU)
  • Model Theory (6 CFU)
  • Set Theory (6 CFU)
  • Type Theory (6 CFU)
  • Cryptography (6 CFU)
  • Topics in Mathematical Physics of Quantum Theories (6 CFU)
  • Geometric analysis (6 CFU)

Other credits:

  • Free choice (12 CFU)
  • Language skills (3 CFU)
  • Thesis (30 CFU)

"Orientamento": Advanced Algebra and Geometry

"Caratterizzanti" courses:

42 CFU

  • Computational Algebra (6 CFU)
  • Advanced Geometry (9 CFU)
  • Advanced Analysis (9 CFU)
  • Stochastic Processes (9 CFU)
  • Mathematical Physics (9 CFU)

"Affini" courses:

36 CFU, 12 in courses

  • Advanced Commutative Algebra (6 CFU)
  • Algebraic Geometry I (6 CFU)

and 4 courses from the following list:

  • Algebraic Geometry II (6 CFU)
  • Homological Algebra (6 CFU)
  • Discrete Fourier Analysis (6 CFU)
  • Advanced Group Theory (6 CFU)
  • Finite Fields and symmetric cryptography (6 CFU)
  • Hodge Theory (6 CFU)
  • Algebraic Topology (6 CFU)
  • Real Algebraic Geometry (6 CFU) 
  • Set Theory (6 CFU)
  • Model Theory (6 CFU)
  • Advanced Topics in Analysis (6 CFU)

Other credits:

  • Free choice (12 CFU)
  • Language skills (3 CFU)
  • Thesis (30 CFU)

"Orientamento": Calculus of Variations, Partial Differential Equations and Dynamical Systems

"Caratterizzanti" courses:

42 CFU

  • Advanced Analysis (9 CFU)
  • Advanced Geometry (9 CFU)
  • Partial Differential Equations (9 CFU)
  • Stochastic Processes (9 CFU)
  • Numerical Methods for PDE (6 CFU)

"Affini" courses:

36 CFU, 6 CFU in one of the courses

  • Advanced Topics in Analysis (6 CFU)
  • Geometric Measure Theory (6 CFU)

and 30 CFU from the list:

  • Advanced Topics in Analysis (6 CFU)
  • Geometric Measure Theory (6 CFU)
  • Fourier Analysis (6 CFU)
  • Stochastic Differential Equations (6 CFU)
  • Foundations of Analysis (6 CFU)
  • Hodge Theory (6 CFU)
  • Mathemathical Physics (9 CFU)
  • Topics in Mathematical Physics of Quantum Theories (6 CFU)
  • Geometric analysis (6 CFU)
  • Mathematical Control Theory (6 CFU)
  • Advanced Functional Analysis (6 CFU)
  • Dynamical Systems (6 CFU)
  • Advanced Calculus of Variations (6 CFU)

Other credits:

  • Free choice (12 CFU)
  • Language skills (3 CFU)
  • Thesis (30 CFU)

Curriculum: Mathematics for Life and Data Sciences

"Orientamento": Mathematics for Data Science

"Caratterizzanti" courses:

39 CFU

  • Fourier Analysis (6 CFU)
  • Mathematical Biology (9 CFU)
  • Scientific Computing (9 CFU)
  • Stochastic Processes  (9 CFU)
  • Stochastic Differential Equations (6 CFU)

"Affini" courses:

21 CFU

  • Data analysis and exploration (6 CFU)
  • Computational Algebra (6 CFU)
  • Bayesian statistics (6 CFU)
  • Statistical models (3 CFU)

Other "affini" courses and free courses:

    • Genomics (12 CFU)
    • Statistics of Stochastic Processes (6 CFU)
    • Laboratory of biological data mining (6 CFU)
    • Stochastic Differential Equations (6 CFU)
    • Big data and social networks (6 CFU)
    • Machine learning (6 CFU)

    Other credits:

    • Language skills (3 CFU)
    • Thesis (30 CFU)

    "Orientamento": Modelling, Statistics and Analysis of Biosystems

    "Caratterizzanti" courses:

    30 CFU 

    • Fourier Analysis (6 CFU)
    • Mathematical Biology (9 CFU)
    • Statistics of Stochastic Processes (6 CFU)
    • Stochastic Processes  (9 CFU)

    and one of the following courses:

    • Numerical Methods for PDE (6 CFU)
    • Scientific Computing (9 CFU)

    "Affini" and free courses:

    One of the following courses:

    • Statistical models (3 CFU)
    • Data analysis and exploration (6 CFU)
    • Modelling and simulation of biological systems (9 CFU)
    • Introduction to Cell Biology (9 CFU)

    One of the following courses:

    • Advanced Topics in biomathematics (6 CFU)
    • Laboratory of biological data mining (6 CFU)

    One of the following courses (or among those not chosen above):

    • Partial Differential Equations (9 CFU)
    • Stochastic Differential Equations (6 CFU)
    • Mathematical aspects of bioelectromagnetism and imaging (6 CFU)
    • Machine learning (6 CFU)

    Other credits:

    • Language skills (3 CFU)
    • Thesis (30 CFU)

    "Orientamento": Modelling and Simulation for Biomedical Applications

    "Caratterizzanti" courses:

    36 CFU

    • Fourier Analysis (6 CFU)
    • Mathematical Biology (9 CFU)
    • Numerical Methods for PDE (6 CFU)
    • Scientific Computing (9 CFU)
    • Mathematical aspectcs of bioelectromagnetism and imaging (6 CFU)

    "Affini" courses:

    at least 36 CFU:

    • Statistical models (3 CFU)
    • Theoretical biomechanics (9 CFU)
    • Physiological flow and transport in porous tissues (6 CFU)
    • Bio-Medical Imaging (6 CFU)
    • Computational haemodynamics (9 CFU)
    • Partial Differential Equations (9 CFU)
    • Molecular and Cllular Biophysics (6 CFU)

    Other credits:

    • Language skills (3 CFU)
    • Thesis (30 CFU)

    Curriculum: Coding Theory and Cryptography

    "Orientamento": Stage-oriented

    "Caratterizzanti" courses:

    39 CFU

    • Computational Algebra (6 CFU)
    • Coding Theory and Applications (6 CFU)
    • Algebraic Cryptography (12 CFU)
    • Stochastic Processes (I module) (6 CFU)
    • Scientific computing (9 CFU)

    "Affini" courses:

    36 CFU, 6 CFU from the course

    • Advanced Programming of Cryptographic Methods (6 CFU)

    and 30 CFU from the list:

    • Advanced Coding Theory and Cryptography (12 CFU)
    • Formal Technique for Cryptographic Protocol Analysis (6 CFU)
    • Discrete Fourier Analysis (6 CFU)
    • Statistics of Stochastic Processes (6 CFU)
    • Network Security (6 CFU)
    • Computability and computational complexity (6 CFU)
    • Security Engineering (6 CFU)
    • Digital signal processing (6 CFU)
    • Data Hiding (6 CFU)
    • Formal methods (12 CFU)
    • Advanced  Natural  Language Processing  and  Information Retrival (6 CFU)

    Other credits:

    • Free choice (12 CFU);
    • Language skills (3 CFU);
    • Tirocinio (12 crediti)
    • Thesis (30 CFU)

    "Orientamento": Research-oriented

    "Caratterizzanti" courses:

    39 CFU:

    • Computational Algebra (6 CFU)
    • Coding Theory and Applications (6 CFU)
    • Algebraic Cryptography (12 CFU)
    • Stochastic Processes (9 CFU)
    • Statistics of Stochastic Processes (6 CFU)

    "Affini" courses:

    36 CFU, 30 CFU from the courses:

    • Advanced Coding Theory and Cryptography (12 CFU)
    • Discrete Fourier Analysis (6 CFU)
    • Algebraic Geometry I (6 CFU)
    • Formal Technique for Cryptographic Protocol Analysis (6 CFU)

    Other credits:

    • Free choice (12 CFU);
    • Language skills (3 CFU);
    • Tirocinio (12 crediti)
    • Thesis (30 CFU)

    Curriculum: Teaching and Scientific Communication

    "Caratterizzanti" courses:

    30 CFU in the sectors MAT/01-05, at least 18 CFU from the list:

    • Foundations of Analysis (6 CFU)
    • Foundations of Geometry (6 CFU)
    • Elementary Mathematics from a higher Viewpoint I (6 CFU)
    • Elementary Mathematics from a higher Viewpoint II (6 CFU)
    • Laboratory of Didactics of Mathematics (6 CFU)
    • Experimental Mathematics Laboratory at High School Level (6 CFU)

    The remaining CFU from the list:

    • Advanced Analysis (9 CFU)
    • Advanced Geometry (9 CFU)
    • Algebraic Geometry I (6 CFU)
    • Computational Algebra (6 CFU)
    • Mathematical Logic (6 CFU)
    • Mathematical Biology (9 CFU)
    • Mathematical models for the Physical, Natural and Social Sciences (6 CFU)

    "Affini" courses: 

    36 CFU: 6 CFU from the course

    • Modern Physics (12 CFU)

    and at least 12 CFU from the courses

    • Experimental Physics Laboratory at High School Level I (6 CFU)
    • Experimental Physics Laboratory at High School Level II (6 CFU)
    • Didactics of Computer Science (6 CFU)

    Other credits:

    • Free choice (15 CFU);
    • Language skills (3 CFU);
    • Thesis (30 CFU)
    Aggiornato il
    9 April 2018