MATHS 332 : Real Analysis
Science
2020 Semester Two (1205) (15 POINTS)
Course Prescription
Course Overview
An introduction to the basic theory of analysis in one real variable. Students will have seen the topics covered in the prerequisite courses, such as Maths250 and Maths130 (or equivalent), but in this course you understand how to actually develop and prove this theory.
Apart from enabling a thorough understanding of the results treated, this course lays the foundations of this type of mathematical thinking, reasoning, and arguing. In this sense it is important for development of a rounded mathematical student and essential for those wishing to advance in pure mathematics or any part of mathematics that uses mathematical analysis or its understanding. This includes many parts of applied mathematics, mathematical physics, and statistics. It is a prerequisite for Maths333, and then many of the 700 level mathematics courses.
Course Requirements
Capabilities Developed in this Course
| Capability 1: | Disciplinary Knowledge and Practice |
| Capability 2: | Critical Thinking |
| Capability 3: | Solution Seeking |
| Capability 4: | Communication and Engagement |
| Capability 5: | Independence and Integrity |
Learning Outcomes
- Demonstrate how analysts use the real numbers and their properties (Capability 1, 2, 3 and 4)
- Develop and apply the theory of convergent and divergent sequences (Capability 1, 2, 3, 4 and 5)
- Develop and apply the theory of (power) series and convergence tests. (Capability 1, 2, 3, 4 and 5)
- Develop and apply the theory of continuous functions and the associated classical theorems. (Capability 1, 2, 3, 4 and 5)
- Develop and apply the theory of differentiable functions and the associated classical theorems (Capability 1, 2, 3, 4 and 5)
- Develop and apply the theory of Riemann integrals and the associated classical theorems (Capability 1, 2, 3 and 4)
- Develop and apply the theory of uniform convergence and the associated classical theorems (Capability 1, 2, 3 and 5)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Assignments | 20% | Individual Coursework |
| Test | 20% | Individual Coursework |
| Final Exam | 60% | Individual Coursework |
| 3 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||
| Assignments | ||||||||||
| Test | ||||||||||
| Final Exam | ||||||||||
Key Topics
functions; differentiation; the Riemann integral; sequences of functions; and infinite series.
Learning Resources
Workload Expectations
This course is a standard [15] point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For this course, you can expect [3] hours of lectures, a [1] hour tutorial, [2] hours of reading and thinking about the content and [4] hours of work on assignments and/or test preparation.
Digital Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
Copyright
The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.
You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website at http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Student Feedback
During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.
Your feedback helps to improve the course and its delivery for all students.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.