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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.
We will begin with Analysis in Term 3 and follow with Group Theory in Term 4.While the contents of this course are drawn from Analysis and Algebra, the course goals are to develop mathematical thinking, rigour and the construction of clear and precise mathematical arguments that communicate your thinking to others. You will learn about the role that axiomatic, abstract theory plays in mathematics by working with the concepts and actually doing mathematics! We will help you to develop your mathematical thinking via• the concepts, explanations, examples and proofs in lectures; and • the problems that we ask you to do on your own; and • collaboration with peers; and• feedback on your work.Syllabus / topics coveredAnalysis: Properties of the real numbers; Convergence and divergence of sequences; Limits and continuity; The Intermediate and Extreme Value Theorems; Series and power series. Differentiation and Taylor’s Theorem (as time permits).Group theory: Groups and symmetry; Subgroups; Permutations; Cyclic, Dihedral and Matrix groups; Isomorphisms; Lagrange's Theorem; Fermat's Little Theorem.
Upon successful completion of the course, students will:understand a range of topics in real analysis and group theory;be able to formulate formal mathematical arguments and proofs;be able to work with both concrete examples and more abstract, axiomatic theory;appreciate the wider relevance of the topics covered.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
Employable, innovative and enterprising
Students will develop key skills and attributes sought by employers that can be used in a range of applications.
MATH103, MATH199 or EMTH119.
Students must attend one activity from each section.
General information for students
Domestic fee $824.00
International fee $4,750.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see
Mathematics and Statistics