100331 Introductory Number Theory

Course offering details

Instructors: Dr. Stefan Maubach

Type: Lecture

Org-unit:

Course Name Abbreviation: Intro Number Theo

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
This course gives a first introduction to number theory, first focusing on fairly elementary, but nonetheless interesting, aspects. Towards
the end of the course, some deeper result like the prime number theorem will be explained, though not proved fully. Number theory is about the properties of the integers. Typical questions that arise are:
How are the prime numbers distributed?
Which primes are sums of two squares?
When does an equation aX^2 + bY^2 = cZ^2 have a solution in integers, not all zero?

The answer to the first question is given by the prime number theorem, the answer to the second question is `all primes that are not of the form 4k-1', and the last one has a simple answer in terms of so-called quadratic residue or Legendre symbols. All these questions, and many more, will be answered in some detail in the course. Topics include congruences, Chinese Remainder Theorem, Fermat's little theorem and Euler's generalization, with applications to cryptography, multiplicative functions like the Euler phi function, Gaussian integers and the euclidean algorithm, sums of two, three and four squares, Mikowski's lattice point theorem, quadratic reciprocity, rational points on conics, more diophantine equations, e.g., Pell's Equation, the distribution of prime numbers, proofs of special cases of Dirichlet's theorem on primes in arithmetic progressions and its general statement.

Literature
Primary Text
Required Reading (To view a list click a category.)
Recommended Reading (To view a list click a category.)
Appointments
Date From To Room Instructors
1 Th, 2. Feb. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
2 Tue, 7. Feb. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
3 Th, 9. Feb. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
4 Tue, 14. Feb. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
5 Th, 16. Feb. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
6 Tue, 21. Feb. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
7 Th, 23. Feb. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
8 Tue, 28. Feb. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
9 Th, 1. Mar. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
10 Tue, 6. Mar. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
11 Th, 8. Mar. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
12 Tue, 13. Mar. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
13 Th, 15. Mar. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
14 Tue, 20. Mar. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
15 Th, 22. Mar. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
16 Tue, 27. Mar. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
17 Th, 29. Mar. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
18 Tue, 10. Apr. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
19 Th, 12. Apr. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
20 Tue, 17. Apr. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
21 Th, 19. Apr. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
22 Tue, 24. Apr. 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
23 Th, 26. Apr. 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
24 Th, 3. May 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
25 Tue, 8. May 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
26 Th, 10. May 2012 09:45 11:00 West Hall 8 Dr. Stefan Maubach
27 Tue, 15. May 2012 11:15 12:30 West Hall 8 Dr. Stefan Maubach
28 Th, 24. May 2012 09:00 11:00 East Hall 4 Dr. Stefan Maubach
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
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Instructors
Dr. Stefan Maubach