# MATH130 Fundamentals of Modern Mathematics 1

Core mathematical skills and background for applications across the quantitative sciences.

The aim of this paper is to develop confidence and capability in the concepts and techniques of modern mathematics and its applications.

The paper delivers a standard syllabus combining calculus and linear algebra, but does so in a way that demonstrates how different concepts link together and why they are important. Calculus has been described as one of the most important tools in science. It allows us to think mathematically about continuous change, area and volumes. Linear algebra is invaluable for working with processes and models in high dimensions, linking both with calculus as well as geometry and data science.

The calculus and linear algebra covered in this paper provide the foundation for future study in mathematics and also the application of mathematics in other disciplines.

Paper title Fundamentals of Modern Mathematics 1 MATH130 Mathematics 0.1500 18 points Semester 1 (On campus) Semester 2 (On campus) \$929.55 Tuition Fees for international students are elsewhere on this website.
Restriction
MATH 101, MATH 102, MATH 160, MATH 170
Schedule C
Arts and Music, Science
Notes
It is strongly recommended that students enrolling in MATH 130 have a background in NCEA Level 2 Mathematics with Calculus or equivalent.
Eligibility

The paper assumes a mathematics background of a level equivalent to NCEA level two, though mathematics equivalent to NCEA level three is recommended.

Contact

Math130@maths.otago.ac.nz

Teaching staff

TBA

Paper Structure

The paper brings together ideas from calculus, algebra and geometry, teaching foundational skills for study in mathematics and for the application of mathematics in multiple disciplines.
Calculus is all about how to think mathematically about phenomena which change continuously in time, with examples drawn from mechanics, physiology, physics, mathematical biology, physical geography, surveying, and a wide range of other disciplines.
In linear algebra we introduce matrices and matrix algebra, demonstrating links with geometry and data analysis.
We look at how combining these strands allows us to deal with high dimensional models and problems.

Textbooks

No textbook required

Information literacy, Interdisciplinary perspective, Critical thinking, Lifelong learning

Learning Outcomes

Students who successfully complete the paper will:

• Realise how mathematical formalism is used for solving real-world problems
• Use notation, algebra and the language of mathematics with increasing fluency and confidence
• Apply mathematics within multiple disciplines
• Work with mathematical expressions and develop skills for communicating mathematics

## Timetable

### Semester 1

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

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 13:00-13:50 9-15, 18-22
Tuesday 15:00-15:50 9-15, 17-22
Wednesday 12:00-12:50 9-15, 17-22
Thursday 14:00-14:50 9-15, 17-22

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Wednesday 10:00-10:50 9-15, 17-21
A2 Wednesday 11:00-11:50 9-15, 17-21
A4 Thursday 10:00-10:50 9-15, 17-21
A5 Thursday 11:00-11:50 9-15, 17-21
A6 Thursday 12:00-12:50 9-15, 17-21
A7 Thursday 15:00-15:50 9-15, 17-21
A8 Wednesday 09:00-09:50 9-15, 17-22
A9 Thursday 09:00-09:50 9-15, 17-22

### Semester 2

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

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 13:00-13:50 28-34, 36-38, 40-41
Tuesday 13:00-13:50 28-34, 36-41
Wednesday 13:00-13:50 28-34, 36-41
Thursday 13:00-13:50 28-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Wednesday 10:00-10:50 28-34, 36-40
A2 Wednesday 11:00-11:50 28-34, 36-40
A3 Thursday 10:00-10:50 28-34, 36-40
A4 Thursday 11:00-11:50 28-34, 36-40

Core mathematical skills and background for applications across the quantitative sciences.

The aim of this paper is to develop confidence and capability in the concepts and techniques of modern mathematics and its applications.

The paper delivers a standard syllabus combining calculus and linear algebra, but does so in a way that demonstrates how different concepts link together and why they are important. Calculus has been described as one of the most important tools in science. It allows us to think mathematically about continuous change, area and volumes. Linear algebra is invaluable for working with processes and models in high dimensions, linking both with calculus as well as geometry and data science.

The calculus and linear algebra covered in this paper provide the foundation for future study in mathematics and also the application of mathematics in other disciplines.

Paper title Fundamentals of Modern Mathematics 1 MATH130 Mathematics 0.1500 18 points Semester 1 (On campus) Semester 2 (On campus) Tuition Fees for 2023 have not yet been set Tuition Fees for international students are elsewhere on this website.
Restriction
MATH 101, MATH 102, MATH 160, MATH 170
Schedule C
Arts and Music, Science
Notes
It is strongly recommended that students enrolling in MATH 130 have a background in NCEA Level 2 Mathematics with Calculus or equivalent.
Eligibility

The paper assumes a mathematics background of a level equivalent to NCEA level two, though mathematics equivalent to NCEA level three is recommended.

Contact

math130@otago.ac.nz

Teaching staff

Paper Structure

The paper brings together ideas from calculus, algebra and geometry, teaching foundational skills for study in mathematics and for the application of mathematics in multiple disciplines.
Calculus is all about how to think mathematically about phenomena which change continuously in time, with examples drawn from mechanics, physiology, physics, mathematical biology, physical geography, surveying, and a wide range of other disciplines.
In linear algebra we introduce matrices and matrix algebra, demonstrating links with geometry and data analysis.
We look at how combining these strands allows us to deal with high dimensional models and problems.

Textbooks

No textbook required.

Information literacy, Interdisciplinary perspective, Critical thinking, Lifelong learning

Learning Outcomes

Students who successfully complete the paper will:

• Realise how mathematical formalism is used for solving real-world problems
• Use notation, algebra and the language of mathematics with increasing fluency and confidence
• Apply mathematics within multiple disciplines
• Work with mathematical expressions and develop skills for communicating mathematics

## Timetable

### Semester 1

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

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 13:00-13:50 9-14, 16-22
Tuesday 13:00-13:50 9-14, 16, 18-22
Wednesday 10:00-10:50 9-14, 16-22
Thursday 10:00-10:50 9-14, 16-22

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Friday 09:00-09:50 9-14, 16-21
A2 Wednesday 11:00-11:50 9-14, 16-21
A4 Friday 10:00-10:50 9-14, 16-21
A5 Thursday 11:00-11:50 9-14, 16-21
A6 Thursday 12:00-12:50 9-14, 16-21
A7 Thursday 15:00-15:50 9-14, 16-21
A8 Wednesday 09:00-09:50 9-14, 16-22
A9 Thursday 09:00-09:50 9-14, 16-22

### Semester 2

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

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 13:00-13:50 28-34, 36-41
Tuesday 13:00-13:50 28-34, 36-41
Wednesday 13:00-13:50 28-34, 36-41
Thursday 13:00-13:50 28-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Wednesday 10:00-10:50 29-34, 36-40
A2 Wednesday 11:00-11:50 29-34, 36-40
A3 Thursday 10:00-10:50 29-34, 36-40
A4 Thursday 11:00-11:50 29-34, 36-40
A6 Friday 11:00-11:50 29-34, 36-40
AND
T5 Friday 10:00-10:50 29-34, 36-40