MATHS 332 : Real Analysis
2021 Semester Two (1215) (15 POINTS)
This paper aims to give a broad introduction to the theory of Real Analysis in one variable.
It will cover properties of the real numbers, sequences and series, limits, continuous functions, differentiation, the Riemann integral, sequences of functions and infinite series.
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|
- Demonstrate ability to construct rigorous mathematical proofs. (Capability 1)
- Demonstrate and apply the theory to solve problems. (Capability 3)
- Evaluate mathematical proof for correctness. (Capability 2)
- Communicate mathematical ideas in written form. (Capability 4)
- Independently develop approaches to unfamiliar mathematical problems. (Capability 5)
|Final Exam||50%||Individual Examination|
|Assessment Type||Learning Outcome Addressed|
Māori and Pasifika students are encouraged to participate in the Maths Tuākana Programme and use their free drop-in tutorial sessions.
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 36 hours of lectures, a one hour tutorial per week, 3 hours of reading and thinking about the content and 3 hours of work on assignments and/or test preparation per week.
Attendance is expected at scheduled activities including lectures and tutorials to complete credit for components of the course.
Lectures will be available as recordings, but the students should be aware that the whiteboard can not always be captured. Other learning activities including tutorials will not be available as recordings.
The course will not include live online events.
Attendance on campus is required for the test and exam.
The activities for the course are scheduled as a standard weekly timetable.
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.
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.
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.
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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.
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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 http://disability.auckland.ac.nz
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.
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
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.
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.