Undergraduate Course: Introduction to Number Theory (MATH10071)
Course Outline
School | School of Mathematics |
College | College of Science and Engineering |
Course type | Standard |
Availability | Available to all students |
Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 10 |
Home subject area | Mathematics |
Other subject area | None |
Course website |
None |
Taught in Gaelic? | No |
Course description | 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. |
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 |
Additional Costs | None |
Information for Visiting Students
Pre-requisites | None |
Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
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Delivery period: 2014/15 Semester 1, Available to all students (SV1)
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Learn enabled: Yes |
Quota: None |
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Web Timetable |
Web Timetable |
Course Start Date |
15/09/2014 |
Breakdown of 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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Additional Notes |
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Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
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Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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Main Exam Diet S1 (December) | MATH10071 Introduction to Number Theory | 2:00 | |
Summary of Intended 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. |
Assessment Information
Coursework 5%, Examination 95% |
Special Arrangements
None |
Additional Information
Academic description |
Not entered |
Syllabus |
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. |
Transferable skills |
Not entered |
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. |
Study Abroad |
Not Applicable. |
Study Pattern |
See 'Breakdown of Learning and Teaching activities' above. |
Keywords | INT |
Contacts
Course organiser | Prof Chris Smyth
Tel: (0131 6)50 5054
Email: C.Smyth@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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© Copyright 2014 The University of Edinburgh - 29 August 2014 4:20 am
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