Coursebooks

Rational quadratic forms

MATH-326

Lecturer(s) :

Schymura Matthias

Language:

English

Summary

Given a quadratic equation, e.g. x^2 + 2*y^2 = 81, how can we decide whether there is a rational solution (x,y)? This basic question is what the theory of Rational Quadratic Forms is all about. The course gives an introduction and highlights fundamental techniques and results.

Content

Keywords

quadratic forms, p-adic numbers, geometry of numbers, primes in arithmetic progressions

Learning Prerequisites

Required courses

Linear Algebra I + II

Analysis I + II

Recommended courses

Rings and Fields

Teaching methods

ex-cathedra lectures + discussion based exercise sessions

Assessment methods

Bonus system (up to 10% of final exam)

Exam (written)

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

Supervision

Office hours Yes
Assistants No
Forum No

Resources

Bibliography

"Rational Quadratic Forms" by J.W.S. Cassels

In the programs

  • Mathematics, 2019-2020, Bachelor semester 5
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Rational quadratic forms
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10 MAA112
10-11
11-12 MAA112
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German