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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Introduction to Number Theory (MATH10071)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA 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)
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
Information for Visiting Students
Pre-requisitesNone
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:
  1. Solve linear and quadratic congruences.
  2. Work with continued fractions.
  3. Demonstrate familiarity with methods for writing an integer as a sum of two squares.
  4. 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 Lo-keng Hua, Springer-Verlag, 1982.
Additional Information
Graduate Attributes and Skills Not entered
Study Abroad Not Applicable.
KeywordsINT
Contacts
Course organiserDr Agata Smoktunowicz
Tel:
Email: A.Smoktunowicz@ed.ac.uk
Course secretaryMiss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk
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