## MATH103 Supplementary Algebra 2

First Semester | Also available: Second Semester |

### ***** Not available in 2019! *****

This 9-point half-paper covers methods and applications of algebra, building on MATH 160/101. It consists of the algebra component of MATH 170. However, it is not by itself a sufficient foundation for second-year algebra (MATH 241, MATH 242, MATH 272) - for these papers, MATH 170 is required.

### Paper details

This paper first expands on the material on vectors and matrices begun in MATH 160/101. (Note, however, that sufficient background is provided on these topics to enable MATH 170 to be taken directly from school.) The course goes on to consider the determinant (a number associated with a matrix) and linear transformations (special mappings associated with computer graphics). The final section considers numbers and factorization, induction (used to prove sequential statements involving integers) and various counting techniques.

### Potential students

MATH 103 is taken only by students who need the algebra component (but not the calculus) of MATH 170. This situation may arise when a student has transferred from another university, or has previously taken the calculus half.

### Prerequisites

MATH 160 or MATH 101 or high achievement (mostly Excellences and Merits) in NCEA Level 3 Mathematics with Calculus

### Main topics

- Algebra and geometry of 3 dimensional vectors
- Manipulation of matrices and matrix equations
- Introduction to linear transformations
- Eigenvalues and eigenvectors
- Discrete mathematics, including mathematical induction, Diophantine equations and basic counting techniques

### Text

Course materials will be available on the resource page. The book *MATH 170 Algebra Outline Notes* is available for purchase from the Print Shop.

### Useful references

Several standard texts are suitable for reference. For example:

*Elementary Vector Algebra*by A.M. MacBeath*Algebra, Geometry and Trigonometry*by M.V. Sweet*Elementary Linear Algebra (Applications version)*by H. Anton and C. Rorres (7th edition)*Introductory Linear Algebra (with applications)*by B. Kolman (6th edition)

### Lecturer (Semester 1)

Professor Robert Aldred (room 221A)

### Lectures (Semester 1)

Monday, Wednesday and alternate Fridays at 12 noon

### Tutorials

Attendance at tutorials is voluntary. An open system operates: tutorial classes run for up to 10 hours per week (depending on demand), and students may attend as many as they need to and are able to.

### Internal Assessment

Five computer Skills Tests make up 20% of your final mark. The other 80% comes from a mix of your final exam mark and the assignment mark which is based solely on the ten marked weekly assignments.

You can check your marks by clicking on the Resources link at the top of this page.

### Terms Requirement

**You have to fulfil the terms requirement in order to be allowed to sit the final exam.**

In this paper, to pass “terms” you need to:

- achieve an overall mark of at least 40% on the 10 assignments

### Exam format

The 90-minute final exam is answered in spaces provided on the question booklet. All questions should be attempted and the number of marks available for each question is indicated on the paper. There are usually about 12 to 15 questions.

### Final mark

So your internal assessment counts at 1/5 weighting if that helps you.

### Linear transformations

Multiplication by a 2x2 matrix can be used to transform points in the x-y plane — such

**transformations**are called

**linear**since they map straight lines to straight lines.

Apply each of these matrices to the image and see what happens to the kiwi:

Which of these do you think is reversible?

### Sample problem

After an evening’s competition the six couples from the “Twirling Dervishes” Ballroom Dancing team headed off to the local pub for a drink. A fairly simple tavern, their local offers 6 different beers and 4 types of wine. Having crammed themselves around a table their captain, Fred, volunteered to get in the first round. Armed with the numbers of each type of drink required he set off for the bar. Being a bit of a wag, Fred decided to perform a pirouette on the way and became dizzy. When he reached the bar he had completely forgotten the order. Too embarrased to go back and ask for the order again, he just made up a selection of twelve drinks from those on offer. What is the probability that he got the order right?