This page is for the academic year 2021-22. The current handbook year is 2022-23
Department: Mathematical Sciences
NUMBER THEORY III
||Available in 2021/22
Excluded Combination of Modules
- To provide an introduction to Algebraic Number Theory (Diophantine
Equations and Ideal Theory).
- Diophantine equations using elementary methods.
- Unique factorization.
- Euclidean rings.
- Number fields.
- Algebraic integers.
- Quadratic fields and integers.
- The discriminant and integral bases.
- Factorization of ideals.
- The ideal class group.
- Dirichlet's Unit Theorem.
- Class number formula for quadratic fields.
- By the end of the module students will: be able to solve
novel and/or complex problems in Number Theory.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Number Theory.
- have acquired a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
- Euclidean rings, principal ideal domains, uniqueness of factorization.
- Algebraic number fields (especially Quadratic fields).
- Applications to Diophantine equations.
- In addition students will have specialised mathematical
skills in the following areas which can be used with minimal guidance:
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for
the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
||2 per week for 20 weeks and 2 in term 3
||Four in each of terms 1 and 2
|Preparation and Reading
||Component Weighting: 100%
||Length / duration
Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University