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Course, academic year 2017/2018
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MSTR Elective 2 - NMAG499
Czech title: Výběrová přednáška z MSTR 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information: https://sites.google.com/site/vitakala/teaching/kvadraticke-formy
Note: you can enroll for the course repeatedly
Guarantor: doc. RNDr. Jiří Tůma, DrSc.
Class: M Mgr. MSTR
M Mgr. MSTR > Volitelné
Classification: Mathematics > Algebra
Annotation -
Last update: JUDr. Dana Macharová (24.08.2015)

The title of the topic in the academic year 2015/16 is Quadratic form Quadratic forms with integral coefficients form a central part of number theory - for example, investigation of which primes are of the form x^2+ny^2 led to the development of a number of crucial tools in algebraic number theory. The goal of the course is to cover some topics in arithmetic theory of quadratic forms, especially with focus on questions concerning representation of integers. The course is suitable for students of 3rd and higher years.
Literature -
Last update: JUDr. Dana Macharová (21.08.2015)

B.W. Jones, "The arithmetic theory of quadratic forms" , Math. Assoc. Amer.

(1950)

Bhargava, Manjul, "On the Conway???Schneeberger fifteen theorem", Contemp.

Math. 272. Providence, RI: Amer. Math. Soc. pp. 27???37.

David A. Cox, "Primes of the Form x^2+ny^2: Fermat, Class Field Theory, and

Complex Multiplication", Wiley; 2 edition, 2013.

Syllabus -
Last update: JUDr. Dana Macharová (21.08.2015)

1. Basic theory over fields

2. Classification of positive definite forms, genus

3. Binary forms and representation of primes

4. Indefinite forms

5. Universal forms and Conway-Schneeberger 15 Theorem

 
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