Program Overview

Introduction to MATH107 - Introduction to Logic and Algebra

MATH107 is a unit that provides students with foundational knowledge of logic, algebra, and mathematical reasoning to support further study in Mathematics and Computer Sciences. The unit covers various topics, including matrices, graphs, vectors, sets, functions, and complex numbers.

Unit Rationale, Description, and Aim

The aim of this unit is to provide students with a solid foundation in several aspects of Mathematics, including logic and algebra, which are requirements for various career-oriented degrees. The unit introduces students to foundational concepts and structures of mathematics, exploring numerous important real-world applications of mathematics.

Learning Outcomes

Upon completing this unit, students will be able to:

• Solve systems of linear equations using matrices and related algebraic techniques.
• Apply the theory of matrices, graphs, vectors, and complex numbers in solving problems.
• Construct and verify mathematical arguments using logic, including proof by induction.

Unit Content

The unit covers the following topics:

1. Matrices definitions and arithmetic
2. Systems of linear equations and the use of matrices in their solution
3. Other matrix operations (determinant and inverse) and transformations of the plane
4. Logic and the basic techniques of proof
5. Proof, including mathematical induction
6. Introduction to vectors, arithmetic, and basic properties
7. Scalar product, equation of lines and planes, vector geometry, cross product
8. Introduction to graphs (networks) and their applications
9. Solving polynomial equations introduction to complex numbers and their arithmetic
10. Complex numbers Argand plane, polar representation

Assessment Strategy and Rationale

The assessment strategy includes:

• A take-home assignment that allows students to develop problem-solving skills
• Two invigilated tests that ensure students have fully integrated the learning and can independently apply various strategies to solve problems

Learning and Teaching Strategy and Rationale

The teaching approach puts the student at the center of their learning, integrating asynchronous interactive online elements with learning experiences and practical exercises that facilitate problem-solving and peer collaboration.

Representative Texts and References

Recommended references include:

• Anton, H. & Kaul, A (2019). Elementary Linear Algebra
• Croft, A., & Davison, R. (2016). Foundation Maths
• Eccles, P. (1997). An Introduction to Mathematical Reasoning: Numbers, Sets and Functions
• Lay, D.C. & Lay, S.R. (2014). Linear Algebra and Its Applications
• Levin, O. (2025). Discrete Mathematics: An Open Introduction
• Liebeck, M. (2010). A Concise Introduction to Pure Mathematics
• Lisle, J. (2018). Introduction to Logic
• Smullyen, R.M. (2011) What Is the Name of This Book?
• Strang, G. (2016) Introduction to Linear Algebra
• Wilson, R. (2015) Introduction to Graph Theory

Locations and Credit Points

The unit is offered in:

• Brisbane
• Melbourne
• North Sydney
• Strathfield The unit is worth 10 credit points.