## MATH101 Supplementary Algebra 1

Summer School | Also available: First Semester Second Semester |

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

This 9-point half-paper covers methods and applications of algebra. It consists of the algebra component of MATH 160. Note that to go on to MATH 170, you will need both MATH 101 and MATH 102 - or their equivalent, MATH 160.

### Paper details

This algebra paper is the natural continuation of 7th Form Mathematics.

After a review of basic trigonometry, the paper focusses on three-dimensional vectors and their many uses (such as in geometry, computer graphics, surveying and even calculus). The vector representation of lines, planes and projections leads naturally to the discussion of linear systems of equations. The basic properties of matrices are studied together with some applications. Complex numbers and polynomials complete this section of the course.

### Potential students

MATH 101 is taken only by students who need the algebra component (but not the calculus) of MATH 160. This situation may arise when a student has transferred from another university, or is looking for a 9-point paper, or has previously taken the calculus half.

### Prerequisites

None

### Main topics

- Vectors; linear and planar geometry and applications
- Solving linear systems
- Matrices and applications
- Complex numbers
- Polynomials and their roots

### Text

*MATH 160 Algebra Outline Notes* are available from the Print Shop.

### Useful references

*Elementary Vector Algebra* by A.M. MacBeath

*Algebra, Geometry and Trigonometry* by M.V. Sweet

### Lecturers (Summer School)

Ilija Tolich, email: itolich@maths.otago.ac.nz

### Lectures (Summer School)

Mon, Tue, Wed, Thu 10-11am

### Tutorials

11–12 and 3–4 Monday to Thursday

Attendance at tutorials is voluntary. An open tutorial system operates and students may attend as many as they need to and are able to.

### Internal Assessment

There are ten marked assignments which make up your assignment mark.

Five computer Skills Tests together make up 20% of your final mark.

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:

- gain at least 5/10 in each of the first four Skills Tests before the end of the 12th week
- achieve an overall mark of 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 from 15 to 20 questions.

### Final mark

Your internal assessment can boost your exam mark if that helps you. Note that the test component definitely counts and so the tests should be regarded as compulsory.

### Summer School details

### Sample problem

The aircraft’s flightpath goes through coordinates (1,2,0) and (23,-19,3). The top of the hill is at (18,-13,2).

How close does the aircraft get to the top of the hill? Vectors make this an easy calculation.

### J Willard Gibbs...

..., 1839-1903, was a pioneer in vector analysis. His family lived in Connecticut and Gibbs became Professor of Mathematical Physics at Yale in 1871 — rather surprisingly before he had published any work! He made major contributions to thermodynamics, the electromagnetic theory of light and statistical mechanics.

### Sample problem

In a certain city, commuters go to work by car or bus. A study shows that from each year to the next year 20% of car users change to travelling by bus, while 15% of bus users change to travelling by car. What percentage of commuters travel by car, once things have settled down?