# NUMBER SYSTEMS AND LINEAR ALGEBRA

MAT1NLA

2017

Credit points: 15

## Subject outline

In this subject, students learn and apply mathematical concepts and develop skills that provide a foundation for all studies in mathematical sciences. Students review and extend their knowledge of algebra, functions, sets and number systems with significant coverage of complex numbers adding to their repertoire. After consideration of sequences and series, students proceed to a module on Logic and Proof. Students also explore a coherent treatment of vectors and vector geometry that includes matrices and solutions of systems of linear equations via the Gauss-Jordan algorithm, and brief treatment of eigenvalues and eigenvectors. An emphasis is placed on students improving their understanding of mathematical concepts and results so they can be appropriately applied, and development of their reasoning skills and ability to clearly present written arguments, essential in both study and employment.  (Engineering students will work to achieve the stage one competencies 1.2 (conceptual understanding of the underpinning mathematics, numerical analysis and statistics), 3.2 (effective written communication) and 3.4 (management of self).)

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorKatherine Seaton

Subject year levelYear Level 1 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites VCE Mathematical Methods 3/4 or equivalent

Co-requisitesN/A

Incompatible subjects MAT1CNS, MAT1CPE, MAT1CLA, MAT1CA, MAT1CB

Equivalent subjectsN/A

Special conditions May not be taken by students who are currently enrolled in MAT1ICA.

## Graduate capabilities & intended learning outcomes

01. Manipulate and find solution sets to equalities and inequalities involving algebraic expressions.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)

02. Calculate limits of sequences and sums of infinite series.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Discipline-specific GCs (Discipline-specific GCs)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Creative Problem-solving (Creative Problem-solving)
Critical Thinking (Critical Thinking)

03. Solve algebraic problems involving complex numbers, including the use of geometric interpretations to find and describe solutions.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)
Critical Thinking (Critical Thinking)

04. Apply vector techniques and matrix operations to find and describe objects in three dimensional space, and find eigenvalues and eigenvectors in two dimensions.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Critical Thinking (Critical Thinking)
Discipline-specific GCs (Discipline-specific GCs)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)

05. Use Gaussian elimination to solve systems of linear equations and interpret the solutions geometrically.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Critical Thinking (Critical Thinking)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)

06. Explore and creatively apply the ideas and techniques of a specified area of mathematics (either Probability or Logic and Proof) and effectively communicate the processes and outcomes.

Activities:
Students are introduced to fundamental concepts in lectures and practice using ideas and techniques covered, under staff supervision, in Practice Classes. Reinforcement practice, feedback and assessment are provided through assignments and online activities.
Creative Problem-solving (Creative Problem-solving)
Writing (Writing)
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)

07. Present mathematical thinking in written form in a meaningful and succinct way using both words and mathematical notation.

Activities:
Emphasis is placed on this in lectures and practice classes and assignments have specifically allocated marks for, and feedback on improvements to, written mathematical communication.
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)
Writing (Writing)

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Bendigo, 2017, Semester 1, Blended

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorSimon Smith

### Class requirements

Lecture Week: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Practical Week: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

### Assessments

3 hour exam65 01, 02, 03, 04, 05, 06, 07
5 assignments (typically 3-4 pages each) (1000 word equiv)20 01, 02, 03, 04, 05, 06, 07
5 online diagnostic tasks (500 word equiv)Hurdle requirement: Students will be required to achieve a mark of at least 40% on the exam, as well as an overall mark of at least 50%, in order to pass this subject.15 01, 02, 03, 04, 05, 06

## Melbourne, 2017, Semester 1, Blended

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorKatherine Seaton

### Class requirements

Lecture Week: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Practical Week: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.