MATHS 250 : Algebra and Calculus 2


2022 Semester One (1223) (15 POINTS)

Course Prescription

Designed for all students who plan to progress further in mathematics, this course follows directly from MATHS 120 and 130. Covering topics from multivariable calculus and linear algebra, which have many applications in science, engineering and commerce. Students will learn mathematical results and procedures as well as the underpinning ideas and mathematical proofs.

Course Overview

This course must be taken by all mathematics majors, and it serves as a prerequisite for MATHS 253, MATHS 254 and MATHS 260. It is suitable for all students who wish to deepen their mathematical rigour and covers topics from linear algebra and (multivariable) calculus that have many applications in science, engineering and commerce. 

Course Requirements

Prerequisite: MATHS 120 and 130, or 15 points from ENGGEN 150, ENGSCI 111, MATHS 150, 153

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
Capability 6: Social and Environmental Responsibilities
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Critically analyse logical arguments, and use advanced techniques in algebra and calculus to solve problems
  2. Demonstrate a command of fundamental techniques underpinning linear systems that evolve in time, including eigenvectors, eigenvalues and diagonalisation. (Capability 1 and 3)
  3. Identify and apply the acquired techniques from linear algebra to problems in further mathematics, the sciences and real-world settings (Capability 1, 3, 5 and 6)
  4. Demonstrate a command of the fundamentals underpinning calculus, including completeness of the real number system, sequences and (power) series; master the basics of multivariable calculus
  5. Identify and apply the acquired techniques from calculus to problems in further mathematics, the sciences and real-world settings (Capability 1, 3, 5 and 6)
  6. Appreciate and apply the intimate connection between linear algebra and geometry that highlights its applicability in other contexts including dynamical systems theory, graph theory and network (Capability 1, 5 and 6)
  7. Correctly express logical mathematical arguments, with sufficient detail, precision and structure (Capability 2)
  8. Gain experience in group work and communicating mathematical ideas to other (Capability 1, 4 and 6)


Assessment Type Percentage Classification
Final Exam 50% Individual Examination
Test 20% Individual Test
Assignments 24% Group & Individual Coursework
Tutorials 6% Group Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8
Final Exam

Key Topics

1. Vector spaces, linear independence, bases and dimension,
2. Linear transformations, kernel and image, matrix representation,
3. Inner product spaces and least squares,
4. Sequences and Cauchy sequences,
5. Series and power series, 
6. Multivariate functions, 
7. Taylor's theorem and optimisation.

Special Requirements

There are no special requirements, no compulsory attendance and no must-pass assessments.

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 [36] hours of lectures, a [12] hour tutorial, [28.5] hours of reading and thinking about the content and [40] hours of work on assignments and [30] hours test/exam preparation (plus [2] hours exam and [1.5] hours test.

Delivery Mode

Campus Experience

Attendance is expected at scheduled activities including tutorials to complete components of the course.

Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.

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.

MATHS 250 has its own course book that covers all of the content. It will be available online for free on Canvas; other online resources will also be pointed out/made available throughout the semester.

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.

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.

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.


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

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

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


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 09/11/2021 11:02 a.m.