# MATH160 Mathematics 1

This paper is divided between algebra and calculus. The algebra component introduces vectors and geometric constructions fundamental to applications in mechanics and computer graphics. Matrices, polynomials, and complex numbers are introduced. The calculus component covers ideas and methods of differential and integral calculus together with key applications and extensions.

If you want to know which of MATH 151, MATH 160 or MATH 170 is best for you, check out the information and placement tools at 'Which MATH 100-level paper should I take?'

Algebra and calculus provide 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 first create an algebraic structure in which to specify where our object is, and then we study how the position of the object changes with time using calculus. Many problems arising in areas such as economics or chemistry, for example, can be examined in a mathematical way using the same basic ideas. We may need to minimise a manufacturing cost, the time for a chemical reaction to take place or the effects of river pollution. In each case the techniques used for the minimisation require techniques from both algebra and calculus theories. This paper aims to develop these techniques for use in other subjects and for further study of mathematics.

This paper is a natural continuation of Year 13 mathematics and is divided between algebra and calculus. The algebra half of MATH 160 focuses 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 the algebra half of the paper. The calculus half of MATH 160 introduces the ideas and methods of differentiation and integration, using an intuitive approach. Applications include optimisation, related rates, finding areas, solving simple differential equations and an introduction to partial derivatives.

Paper title Mathematics 1 MATH160 Mathematics 0.15 18 points Summer School (On campus) \$913.95 Tuition Fees for international students are elsewhere on this website.
Restriction
FINC 102, FINQ 102, MATH 101, MATH 102, QUAN 102
Schedule C
Arts and Music, Science
Notes
(i)This paper is recommended for students with MATH151, NCEA Level 3 mathematics, or equivalent. (ii)MATH160 cannot be credited together with MATH103, MATH104, or MATH170 passed previously or concurrently.
Eligibility
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 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, differential and integral techniques is of benefit to all students exposed to the analysis of processes, whether involving one or several variables.
MATH 160 is aimed at students who have passed the externally assessed NCEA Calculus papers Apply differentiation methods in solving problems (AS91578) and Apply integration methods in solving problems (AS91579). Other students should see a maths adviser and consider taking MATH 151 first. Students with high achievement (mostly Excellences and Merits) in NCEA Level 3 Calculus should see a maths adviser for consideration of direct entry to MATH 170.
Contact
maths@otago.ac.nz
Teaching staff
Paper Structure
Algebra:
• Vectors; linear and planar geometry and applications
• Solving linear systems
• Matrices and applications
• Complex numbers
• Polynomials and their roots
Calculus:
• Functions
• Introduction to calculus
• Techniques of differentiation and integration
Textbooks

Algebra:

Calculus recommended text:
Calculus by James Stewart (Truncated edition) (available from the University Book Shop)
If you are planning on taking MATH 170, you should consider getting the full Calculus, metric edition.

Course outline
Critical thinking.
Learning Outcomes
Demonstrate in-depth understanding of the central concepts and theories.

## Timetable

### Summer School

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 10:00-10:50 2-5, 7
Monday 14:00-14:50 2-5, 7
Tuesday 10:00-10:50 2-7
Tuesday 14:00-14:50 2-7
Wednesday 10:00-10:50 2-7
Wednesday 14:00-14:50 2-7
Thursday 10:00-10:50 2-7
Thursday 14:00-14:50 2-7

#### Tutorial

Stream Days Times Weeks
Attend
A1 Monday 11:00-11:50 3-5, 7
Thursday 11:00-11:50 2-7