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HU Credits:
2
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof. Elon Lindenstrauss
Coordinator Office Hours:
by appointment
Teaching Staff:
Prof Elon Lindenstrauss
Course/Module description:
How well can one approximate a real number by a rational number? and what about algebraic numbers? This is the basic question in Diophantine inequalities.
The course will deal with this question and with applications to study integer solutions of polynomial systems of equations. Some central results on the topic will be presented by students including the thory of continued fractions, Khintchin theorem, multidimensional approximation, Roth and Thue's theorems.
Course/Module aims:
The course will deal with this question and with applications to study integer solutions of polynomial systems of equations. Some central results on the topic will be presented by students including the thory of continued fractions, Khintchin theorem, multidimensional approximation, Roth and Thue's theorems.
Learning outcomes - On successful completion of this module, students should be able to:
Students will be exposed to topics from the study of Diophantine inequalities, including open problems.
Students will learn how to present mathematical results in front of a peer group.
Attendance requirements(%):
93%
Teaching arrangement and method of instruction:
Seminar - introductory lecture by instructor, other lectures by students
Course/Module Content:
The course will deal with this question and with applications to study integer solutions of polynomial systems of equations. Some central results on the topic will be presented by students including the thory of continued fractions, Khintchin theorem, multidimensional approximation, Roth and Thue's theorems.
Required Reading:
list of papers and chapters to be read will given at the beginning of the course. The readin material will be in English.
Additional Reading Material:
Khintchin – Diophantine approximation
Zannier - Lecture Notes on Diophantine Analysis (Publications of the Scuola Normale Superiore)
Baker - Transcendental Number Theory
Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 75 %
Participation in Tutorials 25 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
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