Undergraduate Course: Introduction to Number Theory (MATH10071)
Course Outline
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.
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites |
Students MUST have passed:
Fundamentals of Pure Mathematics (MATH08064)
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Co-requisites | |
Prohibited Combinations | |
Other requirements | Students must not have taken MATH10036 Number Theory |
Information for Visiting Students
Pre-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2018/19, Available to all students (SV1)
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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 )
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Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Coursework 5%, Examination 95% |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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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:
- 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.
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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. |
Keywords | INT |
Contacts
Course organiser | Dr Agata Smoktunowicz
Tel:
Email: A.Smoktunowicz@ed.ac.uk |
Course secretary | Miss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk |
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