Undergraduate Course: Introduction to Number Theory (MATH10071)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Credits  10 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  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. 
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 
Additional Costs  None 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information

Delivery period: 2013/14 Semester 1, Available to all students (SV1)

Learn enabled: Yes 
Quota: None 
Web Timetable 
Web Timetable 
Course Start Date 
16/09/2013 
Breakdown of 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 )

Additional Notes 

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

Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S2 (April/May)  MATH10071 Introduction to Number Theory  2:00   

Delivery period: 2013/14 Semester 1, Partyear visiting students only (VV1)

Learn enabled: Yes 
Quota: None 
Web Timetable 
Web Timetable 
Course Start Date 
16/09/2013 
Breakdown of 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 )

Additional Notes 

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

Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S1 (December)  MATH10071 Introduction to Number Theory (Semester 1 Visiting Students only)  2:00   
Summary of Intended 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. 
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
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. 
Transferable skills 
Not entered 
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. 
Study Abroad 
Not Applicable. 
Study Pattern 
See 'Breakdown of Learning and Teaching activities' above. 
Keywords  INT 
Contacts
Course organiser  Dr Chris Smyth
Tel: (0131 6)50 5054
Email: C.Smyth@ed.ac.uk 
Course secretary  Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk 

