Learning outcomes

At the end of the cursus, students should be able to 

  • Use mathematical language in a correct manner, in order to make formal deductions and to establish proof, 
  • study the graph of a function, to compute its derivate or its integral and to understand their interest,
  • use set and relation theory to formally describe specified systems, and accordingly be able to establish their consistency, 
  • determine relation's properties, 
  • count the elements in any specified set,
  • use arithmetics and elliptic functions in a correct manner to ciffer any given message or to determine the content to any ciphered message, 
  • model system behavior equations by recurrent equations and to solve them. 

 

Content

 

The lecture's content is divided into four main parts, 

  1. first order logic and proof technics,
  2. Functional analysis
  3. Set theory and relation theory, with analysis of order relation. Combinatorial analysis. 
  4. Discrete mathematics continued,
    • recurrence equations
    • arithmetics
    • cryptography
    • elliptic function

 

Teaching methods

Academic lectures (30h), accompanied by exercise sessions (30h)

 

Assessment method

Written exam

Special care will be put on how  students explain their mathematical reasoning and deductions. Clarity and formalism are thus important.

 

Sources, references and any support material

Many books in this area exist. To cite but only two, there are - R.P. Grimaldi. Discrete and combinatorial mathematics. An applied introduction. Fifth Edition. Pearson Eduction, 2004 or  J. Hoffstein, J. Phiper et J.H. Silverman. An Introduction to Mathematical Cryptography, Springer, 2008.
 

 

 

Language of instruction

French