Undergraduate Course: Introduction to Number Theory (MATH10071)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  A first course in Number Theory: Primes, Remainder Theorem, Quadratic fields, Euclidean domains, Continued fractions, Primitive roots, pseudoprimes, Representation of integers as sums of squares, Fermat descent. 
Course description 
Primes, Fundamental Theorem of Arithmetic, congruences, Chinese Remainder Theorem, solving linear equations in integers.
Quadratic fields, their ideals, class group, Euclidean domains, unique factorisation.
Continued fractions.
Primitive roots, pseudoprimes, primality testing, quadratic residues and quadratic reciprocity.
Representation of integers as sums of squares, Fermat descent.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
Students MUST have passed:
Fundamentals of Pure Mathematics (MATH08064)

Corequisites  
Prohibited Combinations  
Other requirements  Students must not have taken MATH10036 Number Theory 
Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2018/19, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 5%, Examination 95% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Introduction to Number Theory (MATH10071)  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Solve linear and quadratic congruences.
 Work with continued fractions.
 Demonstrate familiarity with methods for writing an integer as a sum of two squares.
 Appreciate some algebraic techniques in number theory.

Reading List
Elementary Number Theory, by Kenneth H. Rosen, 6th Edition, 2010, Pearson.
 A friendly introduction to number theory by J. H. Silverman, Prentice Hall, 2001.
 Introduction to number theory by Lokeng Hua, SpringerVerlag, 1982. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Study Abroad 
Not Applicable. 
Keywords  INT 
Contacts
Course organiser  Dr Agata Smoktunowicz
Tel:
Email: A.Smoktunowicz@ed.ac.uk 
Course secretary  Miss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk 

