Number Theory - MAT00085H
Module summary
Number theory studies the properties of one of the most basic mathematical objects known to humankind. In doing so, it utilises an unusually wide variety of methods and proofs, many of which are surprisingly deep. This course will introduce some of the fundamental problems in this subject, ranging from determining whether a number is a square modulo p or not, to finding the most accurate approximation to real numbers with continued fractions.
Related modules
Module will run
Occurrence | Teaching period |
---|---|
A | Semester 2 2024-25 |
Module aims
Number theory studies the properties of one of the most basic mathematical objects known to humankind. In doing so, it utilises an unusually wide variety of methods and proofs, many of which are surprisingly deep. This course will introduce some of the fundamental problems in this subject, ranging from determining whether a number is a square modulo p or not, to finding the most accurate approximation to real numbers with continued fractions.
Module learning outcomes
By the end of the module, students should be able to:
1. Demonstrate facility with the unusually wide variety of methods and proofs which appear in number theory.
2. Apply algorithms taught in the course in specific calculations.
3. Demonstrate the ability to reason in a rigorous, precise and logical manner.
Module content
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Congruences and residues
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Primitive roots and quadratic reciprocity
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Sum of squares
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Multiplicative functions and average orders
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Continued fractions and Pell’s equations
Indicative assessment
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Indicative reassessment
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
Rose, A Course in Number Theory, Oxford University Press.