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)
Pre-requisites	Students MUST have passed: Fundamentals of Pure Mathematics (MATH08064)	Co-requisites
Prohibited Combinations		Other requirements	Students must not have taken MATH10036 Number Theory
Additional Costs	None

Information for Visiting Students
Pre-requisites	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, Part-year 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 Lo-keng Hua, Springer-Verlag, 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