## MATH101 Supplementary Algebra 1

Summer School | Also available: First Semester Second Semester |

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 final mark F in the paper will be calculated according to this formula:

**F = 0.8max(E, 0.8E + 0.2A) + 0.2T**

where:

- E is the Exam mark
- A is the Assignments mark
- T is the Tests mark

and all quantities are expressed as percentages.

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.

### Students must abide by the University’s Academic Integrity Policy

**Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.**

The two most common forms of academic misconduct are *plagiarism* and *unauthorised collaboration*.

#### Academic misconduct: **Plagiarism**

Plagiarism is defined as:

- Copying or paraphrasing another person’s work and presenting it as your own.
- Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
- Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
- Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.

All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.

#### Academic misconduct: **Unauthorised Collaboration**

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.

### 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?