Introduction to Number Theory (MAT364) | GSÜ

Content

Objective

In this course, we will go over some introductory topics in number theory.

Course Content

Divisibility, Prime Numbers, Modular Arithmetics, Multiplicative Functions, Diaphontine Equations, Rational Approximations, Continued Fractions

Course Learning Outcomes

Understanding basic number theoretic structures and proof methods.

Teaching and Learning Methods

Lectures and problem solving in class, homework, exams

References

An Introduction to the Theory of Numbers-Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Divisibility, Euclidean Algorithm, Greatest Common Divisor Function
2	Primes, Fundamental Theory of Arithmetics
3	Binomial Theorem, Pascal Triangle
4	Modular Arithmetics
5	Solutions of modular equations, Chinese Remainder Theorem
6	Primitive Roots
7	Midterm
8	Greatest Integer Function
9	Multiplicative Functions
10	Möbius Inversion
11	Diophantine Equations
12	Markov Equation, Vieta Jumps
13	Farey Tree, Rational Approximations
14	Continued Fractions

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	15	60
Contribution of final exam to overall grade	1	40
Total	16	100

In-Term Studies
Activities	Number	Contribution
Assignments	13	30
Presentation	0	0
Midterm Examinations (including preparation)	1	25
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	1	5
Make-up	0	0
Total	15	60

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways;					X
2	can properly state and use concepts and results of major mathematical interest;					X
3	masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools;					X
4	is able to express one’s mathematical ideas in an organised way both in written and oral forms;					X
5	understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...);				X
6	has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;				X
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;		X
8	has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;		X
9	has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;		X
10	masters French language as well as other foreign languages, to a level sufficient to study or work abroad.		X

ECTS

Activities	Number	Period	Total Workload
Class Hours	13	3	39
Working Hours out of Class	13	1	13
Assignments	13	3	39
Presentation	0	0	0
Midterm Examinations (including preparation)	1	10	10
Project	0	0	0
Laboratory	0	0	0
Other Applications	0	0	0
Final Examinations (including preparation)	1	20	20
Quiz	0	0	0
Term Paper/ Project	0	0	0
Portfolio Study	0	0	0
Reports	0	0	0
Learning Diary	0	0	0
Thesis/ Project	0	0	0
Seminar	0	0	0
Other	0	0	0
Make-up	0	0	0
Total Workload			121
Total Workload / 25			4.84
Credits ECTS			5