# Mathematics 1

University of Otago

## Course Description

• ### Course Name

Mathematics 1

• ### Host University

University of Otago

• ### Location

Dunedin, New Zealand

• ### Area of Study

Algebra, Calculus, Mathematics

• ### Language Level

Taught In English

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

18
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

This paper is divided between algebra and calculus (which can be taken as separate 9 point papers). 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.

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 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 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

Learning Outcomes
Demonstrate in-depth understanding of the central concepts and theories.

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