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
|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.
Primes, Fundamental Theorem of Arithmetic, congruences, Chinese Remainder Theorem, solving linear equations in integers.
Quadratic fields, their ideals, class group, Euclidean domains, unique factorisation.
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)
|| Students MUST have passed:
Fundamentals of Pure Mathematics (MATH08064)
||Other requirements|| Students must not have taken MATH10036 Number Theory
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 5%, Examination 95%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Introduction to Number Theory (MATH10071)||2:00|
On completion of this course, the student will be able to:
- Solve linear and quadratic congruences.
- Work with continued fractions.
- Demonstrate familiarity with methods for writing an integer as a sum of two squares.
- Appreciate 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
|Course organiser||Dr Agata Smoktunowicz
|Course secretary||Miss Sarah McDonald
Tel: (0131 6)50 5043