MATHS 333 : Analysis in Higher Dimensions

Science

2024 Semester One (1243) (15 POINTS)

Course Prescription

By selecting the important properties of distance many different mathematical contexts are studied simultaneously in the framework of metric and normed spaces. This course examines carefully the ways in which the derivative generalises to higher dimensional situations. These concepts lead to precise studies of continuity, fixed points and the solution of differential equations. A recommended course for all students planning to advance in pure mathematics.

Course Overview

This course is intended for students who have enjoyed the introduction to real analysis. An essential course for every student intending to advance in mathematics. It develops the foundational mathematics underlying calculus, it introduces a rigorous approach to continuous mathematics and fosters an understanding of the special thinking and arguments involved in this area.

Course Requirements

Prerequisite: MATHS 332 or a B or higher in MATHS 254

Capabilities Developed in this Course

Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking
Capability 6: Communication
Capability 7: Collaboration
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Display a high level of knowledge of mathematical concepts. (Capability 3 and 4)
  2. Demonstrate an understanding of potential applications and connections with other disciplines. (Capability 3, 4 and 7)
  3. Demonstrate an understanding a range of methods used in pure mathematics. (Capability 3 and 4)
  4. Demonstrate an understanding of the nature of precision and proof in mathematics, and be able to present valid arguments in verbal and written form. (Capability 3, 4, 5, 6 and 7)

Assessments

Assessment Type Percentage Classification
Final Exam 50% Individual Examination
Test 20% Individual Coursework
Assignments 30% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4
Final Exam
Test
Assignments
The total grade for this course is determined by the higher of either 50% Exam, 20% Test, and 30% Assignments or 100% Exam.
A minimum of 35% in the exam is required to pass the course.
The use of calculators in the test and exam is not permitted.

Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

Whanaungatanga and manaakitanga are fundamental principles of our Tuākana Mathematics programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Maths programme consists of workshops and drop-in times, and provides a space where Māori and Pasifika students are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

Special Requirements

The mid-semester test will run in the evening outside of normal hours. This is usually in the seventh or eighth week of semester and for 90 minutes between 18:15 and 20:00.

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 a total of 36 hours of lectures, 12 hours of tutorials, 40 hours of reading and thinking about the content and 62 hours of work on assignments and/or test preparation.

Delivery Mode

Campus Experience

  • Attendance is expected at scheduled activities.
  • Lectures will be available as recordings, when the lecture rooms have recording facilities. The course will not include live online events.
  • The activities for the course are scheduled as a standard weekly timetable.

Learning 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.

The course will follow the content of the MATHS 333 Coursebook.

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.

The student feedback has taken into consideration.

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 for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

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.

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 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.

Learning Continuity

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 course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 06/11/2023 08:40 a.m.