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 2015/16, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
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 S1 (December)  MATH10071 Introduction to Number Theory  2:00  

Academic year 2015/16, Partyear visiting students only (VV1)

Quota: None 
Course Start 
Semester 1 
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 S1 (December)  MATH10071 Introduction to Number Theory  2:00  
Learning Outcomes
1. Ability to solve linear and quadratic congruences.
2. Ability to work with continued fractions.
3. Familiarity with methods for writing an integer as a sum of two squares.
4. Appreciation of 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  Prof Andrew Ranicki
Tel: (0131 6)50 5073
Email: A.Ranicki@ed.ac.uk 
Course secretary  Mr Thomas Robinson
Tel: (0131 6)50 4885
Email: Thomas.Robinson@ed.ac.uk 

