100331 Introductory Number Theory

Course offering details

Instructors: Prof. Dr. Dierk Schleicher

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 Mon, 1. Feb. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
2 Wed, 3. Feb. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
3 Mon, 8. Feb. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
4 Wed, 10. Feb. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
5 Mon, 15. Feb. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
6 Wed, 17. Feb. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
7 Mon, 22. Feb. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
8 Wed, 24. Feb. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
9 Fri, 26. Feb. 2010 11:15 12:30 West Hall 8 Prof. Dr. Dierk Schleicher
10 Mon, 1. Mar. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
11 Wed, 3. Mar. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
12 Mon, 8. Mar. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
13 Wed, 10. Mar. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
14 Mon, 15. Mar. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
15 Wed, 17. Mar. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
16 Mon, 22. Mar. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
17 Wed, 24. Mar. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
18 Wed, 7. Apr. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
19 Mon, 12. Apr. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
20 Wed, 14. Apr. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
21 Mon, 19. Apr. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
22 Wed, 21. Apr. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
23 Fri, 23. Apr. 2010 11:15 12:30 West Hall 8 Prof. Dr. Dierk Schleicher
24 Mon, 26. Apr. 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
25 Wed, 28. Apr. 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
26 Fri, 30. Apr. 2010 11:15 12:30 West Hall 8 Prof. Dr. Dierk Schleicher
27 Mon, 3. May 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
28 Wed, 5. May 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
29 Fri, 7. May 2010 11:15 12:30 West Hall 8 Prof. Dr. Dierk Schleicher
30 Mon, 10. May 2010 09:45 11:00 West Hall 4 Prof. Dr. Dierk Schleicher
31 Wed, 12. May 2010 08:15 09:30 West Hall 4 Prof. Dr. Dierk Schleicher
32 Tue, 25. May 2010 16:00 18:00 East Hall 4 Prof. Dr. Dierk Schleicher
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
Prof. Dr. Dierk Schleicher