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The course comprises two very different subjects, analysis and groups, both fundamental to mathematics and requiring mathematically rigorous thinking. It gives a deeper understanding of the real number system and limits, and an introduction to the methods of abstract algebra via the study of symmetries and permutations.
This is a course in real analysis and group theory. These are fundamental topics and tools needed for a deeper understanding of almost all mathematics. The course comprises two somewhat different subjects, analysis and groups, both requiring mathematically rigorous thinking. It provides a deeper understanding of the real number system and limits, as well as an introduction to the methods of abstract algebra via the study of symmetries and permutations.Topics covered:Analysis: Properties of the real numbers; Convergence and divergence of sequences; Limits and continuity; The Intermediate and Extreme Value Theorems; Series and power series.Group theory: Groups and symmetry; Subgroups; Permutations; Cyclic, Dihedral and Matrix groups; Isomorphisms; Lagrange's Theorem; Fermat's Little Theorem.
By the end of the course, students will be able to:Understand a range of topics in real analysis and group theory.Formulate formal mathematical arguments and proofs.Work with both concrete examples and more abstract, axiomatic theory.Appreciate the wider relevance of the topics covered.
MATH103, MATH199 orEMTH119.
Students must attend one activity from each section.
General information for students
Domestic fee $788.00
International fee $4,438.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.