Mathematics

Number Theory I(MAT365)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT365 Number Theory I 5 3 0 0 3 6
Prerequisites
Admission Requirements
Language of Instruction French
Course Type Elective
Course Level Bachelor Degree
Course Instructor(s) Alexis Michel apgmichel@gmail.com (Email)
Assistant
Objective This is an introduction to some key concepts of number theory, trying to show the diversity and richness of the approaches (algebraic, analyrtic, combinatorial or geometric) around a detailed presentation of classical results (ex. law of quadratic reciprocity) or quick evocation of unresolved problems (e.g. Goldbach's conjecture, twin primes).
Content Prime numbers, gcd, lcm, Euclidian algorithm, Bezout's identity, Fermat's little theorem, Gauss's lemma, Wilson's theorem
Ring of integers modulo N, primitive roots of unity, Euler indicator,Chinese remainder theroem, RSA algorithm (justification only)
Legendre symbol, Jacobi symbol, law of quadratic reciprocity (elementary proof, without of Gauss' sums), sum of two squares
Course Learning Outcomes To develop an intuition of certain arithmetic situations. as well as a broad vision of the diversity of available tools and a mistrust of simple statements. To know how to organize a proof. To master the elementary concepts of arithmetic with some detours through group theory (e.g. order of elements, Lagrange theorem) as well as set theory (e.g. diagram chase)
Teaching and Learning Methods Class, face-to-face, handouts, examples sheets
References - 104 Number theory problems, Titu Andreescu, Dorin Andrica, Zuming Feng, Birkhäuser (2007) : Exercices
- Elementary Number Theory: Primes, Congruences and Secrets, William Stein, Springer (2009) : Cours
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Practice Topics
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Contribution to Overall Grade
  Number Contribution
Contribution of in-term studies to overall grade 0 0
Contribution of final exam to overall grade 0 0
Toplam 0 0
In-Term Studies
  Number Contribution
Assignments 0 0
Presentation 0 0
Midterm Examinations (including preparation) 0 0
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 0 0
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
Toplam 0 0
No Program Learning Outcomes Contribution
1 2 3 4 5
1 understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; X
2 can properly state and use concepts and results of major mathematical interest; X
3 masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; X
4 is able to express one’s mathematical ideas in an organised way both in written and oral forms; X
5 understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); X
6 has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; X
7 has a theoretical and practical knowledge in computer science well adapted for learning a programming language;
8 has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;
9 has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;
10 masters French language as well as other foreign languages, to a level sufficient to study or work abroad. X
Activities Number Period Total Workload
Total Workload 0
Total Workload / 25 0,00
Credits ECTS 0
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