## MATH160 Mathematics 1

First Semester | Also available: Second Semester Summer School |

### Introduction

Algebra and calculus form the basic tools used to produce most mathematical frameworks for modelling quantifiable phenomena. For example, to model the movement of an object through space we need first to create an algebraic structure in which to specify where our object is, and then we can study how that position changes with time (i.e. its movement) using calculus.

Many other problems arising in areas such as Economics or Chemistry, can be examined in a mathematical way using the same basic ideas. For example, we may need to minimize a manufacturing cost, or the time for a chemical reaction to take place, or the effects of river pollution; in each case the techniques used for the minimization are based on a mixture of algebra and calculus theories.

This course aims to develop these tools and techniques both for use in other subjects and in preparation for further study of Mathematics.

### Paper details

This paper is the natural continuation of Year 13 Mathematics, and is divided between algebra and calculus.

In the algebra half, you will learn about 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 and matrices. The basic properties of matrices are studied together with some applications. An introduction to the algebra of complex numbers completes this section of the course.

In the calculus half, you will study the ideas and methods of differentiation and integration, using an approach that is intuitive and avoids excess formality. Applications will include optimization, related rates, solving simple differential equations, and the definition of area.

### Potential students

MATH 160 is intended both for those with a main interest in studying Mathematics and/or Statistics, and those whose interest in Mathematics is mainly to support other areas of study. These areas might include the physical, health and biological sciences, computer and information science, engineering, surveying, architecture, economics and finance, and philosophy of science. An understanding of basic algebraic and differential and integral techniques is of benefit to all students exposed to the analysis of processes, whether involving one or several variables.

### Prerequisites

Formally, MATH 160 has no prerequisites other than “sufficient achievement in NCEA Level 3 Calculus”. However, we strongly suggest that if you have not passed the externally assessed NCEA Calculus papers “Apply differentiation methods in solving problems” (AS91578) and “Apply integration methods in solving problems” (AS91579), then you should consider taking MATH 151 before attempting MATH 160. If you have high achievement (mostly Excellences and Merits) in NCEA Level 3 Calculus, please see a maths advisor for consideration of direct entry to MATH 170. The placement tool can help you decide which paper is appropriate for you.

### Main topics

Algebra:

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

Calculus:

- Introduction to functions of one variable
- Limits and continuity of functions
- Differentiation of functions and applications
- Integration of functions and applications

### Texts

Algebra and Calculus notes will be made available online during the semester.

**Recommended text for Calculus**: *Calculus* by James Stewart (Truncated edition) or the full *Calculus* (metric edition 8) by James Stewart are available from the University Book Shop; if you are planning on taking MATH 170, you should consider getting the full version.

### Lecturers (Semester 1)

- Algebra: Professor David Bryant david.bryant@otago.ac.nz
- Calculus: Martin Forbes martin.forbes@postgrad.otago.ac.nz

### Office Hours

These are hours where you can drop in to see us in our offices without making an appointment first.

David: Tuesday and Thursday, 11:30 - 12:15.

Martin: TBA

At other times, please make an appointment by talking to us in person, or by e-mail or phone.

### Class reps

Do you want to be a class rep for MATH 160? We will ask around for potential class reps in the first two weeks of the semester.

### 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. Tutorials begin in week 2 of the semester (4-5 March). The tutorials on 8-9 April (week before midterm break) and 27-28 May (last week of semester) do not contribute to your grade and are intended as revision sessions.

### Internal Assessment

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

Due dates for the assignments are

- Friday 13 March, 12pm
- Friday 3 April, 12pm
- Friday 8 May, 12pm
- Friday 22 May, 12pm

We will have online quizzes posted after each lecture (Monday to Thursday) which must be completed by 10am the following day. There will be no quizzes in the first and last week of the semester, and no quizzes on 9, 21, 22, 27 April because of holidays and the midterm test.

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.

### Midterm test

There is a midterm test taking 60 minutes which will cover the material in the Algebra section of the paper. The test will be held on Wednesday, 22 April at 10am, which is during the first week back after midterm break. The room will be announced shortly.

### Terms Requirement

There is no terms requirement for this paper.

### Exam format

The 2-hour final exam consists of multiple-choice and long-answer questions. The exam will be 1/4 algebra and 3/4 calculus.

### 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(0.2M + 0.4E + 0.25A, 0.25M + 0.5E + 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
- M is the Midterm 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.