## MATH101 Supplementary Algebra 1

Second Semester | Also available: First Semester Summer School |

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

### Introduction

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 year 13 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.

### Texts

MATH 160/101 Algebra Outline Notes~~ are available from the Print Shop (or as a pdf file from the resource webpage)

### 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*Calculus with Analytic Geometry*by Howard Anton (Wiley)*Calculus*by James Stewart (Full edition.)

### Lecturers (Semester 2)

Dr Jörg Hennig, room 215

### Lectures (Semester 2)

Mon, Wed and alternate Fri, 12 noon

### Office hours (Semester 2)

by arrangement (or just pop in if I am in my office)

### Tutorials

You are required to attend one tutorial per week, and they contribute to your final grade. You will be assigned a tutorial time before the beginning of the semester, and changes to these times can be arranged with your tutor.

### Quizzes

After most lectures there will be an online quiz, which must be completed before the beginning of the next lecture.

### Internal Assessment

There are five marked assignments which make up your assignment mark A.

The top 80% of your quiz grades will be used to determine your quiz mark Q.

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:

- attend at least 5 out of 10 tutorials, and
- achieve a quizzes mark of at least 40 out of 100.

### Exam format

The 90 min final exam consists of multiple-choice questions and long answer questions.

### Calculators

In the exam, you may use any calculator from List A (Scientific Calculators) of the University of Otago's approved calculators; these are Casio FX82, Casio FX100, Sharp EL531, Casio FX570 and Casio FX95.

### Final mark

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

**F = max(0.6E + 0.25A, 0.75E + 0.1A) + 0.1Q + 0.05T**

where:

- E is the Exam mark
- A is the Assignments mark
- Q is the Quizzes mark
- T is the Tutorials mark

and all quantities are expressed as percentages.

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

**Academic integrity** means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

**Academic misconduct** is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

**Plagiarism**

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

- Although not intended,
*unintentional plagiarism*is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided. *Intentional plagiarism*is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

**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 students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

**Impersonation**

Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

**Falsiﬁcation**

Falsiﬁcation is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

**Use of Unauthorised Materials**

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

**Assisting Others to Commit Academic Misconduct**

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

### 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?