# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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# Undergraduate Course: Introduction to Number Theory (MATH10071)

 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.
 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
 Pre-requisites None High Demand Course? Yes
 Academic year 2017/18, 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
 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.
 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.
 Graduate Attributes and Skills Not entered Study Abroad Not Applicable. Keywords INT
 Course organiser Dr Milena Hering Tel: Email: M.Hering@ed.ac.uk Course secretary Ms Hannah Burley Tel: (0131 6)50 4885 Email: Hannah.Burley@ed.ac.uk
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