MTH5130 - Number Theory - 2023/24
Topic outline
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This forum is available for everyone to post messages to. If you have any questions about the module, please ask them here.
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This is the lecture note from Dr. Shu Sasaki. We will use this note as the main reference for this module.
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This book may be useful from time to time.
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80% for the final exam. It will be an on-campus written exam of duration 3 hours.
- No notes, formula sheets, or calculators are allowed in the exam.
- The exam will be of a similar format as the old exams. Look at the list of old exams below.
- You are expected to apply definitions, statements and proof ideas of the main theorems in the exam.
20% for the assessed coursework to be submitted twice (10% each) via QMplus at the end of Week 6 and Week 12, respectively.
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- Introduction
- Euclid's algorithm
- Prime factorization
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- Congruence arithmetic
- Fermat's little theorem
- Chinese remainder theorem
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- Euler's totient function
- Primitive roots
- Euler's totient function
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- Quadratic residues and non-residues
- The Legendre symbol
- The quadratic reciprocity
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Deadline 5th November 2023, 11:59 pm
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- Quadratic residues and non-residues
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- Finite continued fraction
- Algorithm for continued fraction
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- Infinite continued fraction
- Periodic continued fraction
- Infinite continued fraction
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- Diophantine approximation
- Periodic continued fraction revisited
- Diophantine approximation
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- Pell's equation
- Fundamental solution
- Pell's equation
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- Representations of primes as sums of squares
- Hermite's algorithm
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Deadline 17th of December 2023, 11:59 pm
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- Representations of primes as sums of squares
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- Introduction to algebraic number theory
- Quadratic number fields
- Units in the ring of integers
- Introduction to algebraic number theory
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Revision lecture and exam preparation
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This is an optional anonymous feedback form where you can let us know what you think works well and what can be improved about the module. Your feedback is very much appreciated and will be useful for further improving the student experience at QMUL.
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