## 15 Points

Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

### Staff

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#### Librarian(s)

: alistair.lamb@waikato.ac.nz

You can contact staff by:

• Calling +64 7 838 4466 select option 1, then enter the extension.
• Extensions starting with 4, 5, 9 or 3 can also be direct dialled:
• For extensions starting with 4: dial +64 7 838 extension.
• For extensions starting with 5: dial +64 7 858 extension.
• For extensions starting with 9: dial +64 7 837 extension.
• For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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### Paper Description

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This paper provides a formal approach to linear algebra, with applications. Topics include: Linear independence. Spanning sets and bases. Subspaces. Linear transformations. Kernels and Images. The Gram-Schmidt process. Eigenvectors and eigenspaces. Applications of linear algebra to science. Group theory via matrices including isomorphisms, group actions and permutation groups.
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### Paper Structure

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There are 4 contact hours per week. My teaching style is a mixture of lecturing and in-class tutorial work, so each contact hour will typically a mix of tutorial and lecture, rather than formal tutorials being assigned. Lectures will be Panopto recorded, however as lectures are interactive, they involve essential preparation for assessments.
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### Learning Outcomes

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Students who successfully complete the paper should be able to:

• 1. Solve systems of linear equations via the Gauss Jordan method.
• 2. Find matrix inverses where these exist.
• 3. Compute determinants by either cofactor expansion or Gaussian Elimination.
• 4. Determine whether a set of vectors is linear independent, forms a subspace or a basis and determine the dimension of the span of a set of vectors.
• 5. Determine the row space, column space and nullspace of a matrix.
• 6. Apply the Gram-Schmidt process to the Euclidean dot product.
• 7. Compute the eigenvalues, eigenvectors and (where possible) the diagonalisation of a matrix.
• 8. Demonstrate an understanding of the applicability of linear algebra to the applied sciences.
• 9. Demonstrate understaning of a group including isomorphisms, permutation groups and the group action of a symmetry.
• 10. Understand the theory of linear transformations including the kernel and image.
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### Assessment

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There will be three tests and four assignments. The tests are each forty-five minutes and will occur during the lecture times.

Please note the dates and times for the three tests and notify the lecturer as soon as possible if these are problematic - work or holiday are not valid excuses for missing a test.

• Test 1: Friday 26 March, 12-12:50pm, S.1.03
• Test 2: Friday 7 May, 12-12:50pm, S1.03
• Test 3: Friday 28 May, 12-12:50pm, S1.03

In order to pass this paper with an unrestricted grade (Grade C- or better) you must get an overall total of 50% or greater, and ALSO at least 40% in the final exam. If your overall grade is greater than 50% but you get less than 40% in the final examination you will be awarded the grade of RP(restricted pass) which cannot be used as a prerequisite to other papers.

The time, date and place of the FINAL examination will be arranged by the Examinations Office: the exam period is from

#### Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 50:50 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Test 1
26 Mar 2021
12:00 PM
10
2. Test 2
7 May 2021
12:00 PM
10
3. Test 3
28 May 2021
12:00 PM
10
4. Assignments
20
5. Exam
50
 Assessment Total: 100
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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You are not required to purchase a textbook for this paper. Below are some recommended readings for students looking for more worked problems, etc.

• Elementary linear algebra by Anton (any edition)
• Advanced Linear algebra by Roman (third edition)

### Online Support

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All course information will be on Moodle.
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It is a 15 point paper so we'll aim for 150 hours of work. That equates to roughly 10 hours per week, so you should expect to put in 6 hours per week of work for this paper in addition to the 4 hours of lectures.