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.
|
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-requisites | None |
Course Delivery Information
|
| Academic year 2015/16, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
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 S1 (December) | MATH10071 Introduction to Number Theory | 2:00 | |
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.
|
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 | Prof Chris Smyth
Tel: (0131 6)50 5054
Email: |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)51 4351
Email: |
|
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