MXB102 Abstract Mathematical Reasoning

Unit Outline: Semester 1 2024, Gardens Point, Internal

Overview

Mathematics is, at its heart, axiomatic: each new mathematical statement follows logically from previous statements and ultimately derives from the axiomatic foundations. This unit establishes the foundations of abstract mathematical reasoning, introducing the view of mathematics as axiomatic and emphasising the role of proof in mathematics. Fundamental concepts and tools including logic and sets, number systems, sequences and series, limits and continuity are covered. The tools established in this unit will serve as a foundation throughout your mathematics studies.

Learning Outcomes

On successful completion of this unit you will be able to:

1. Interpret and prove formal statements in mathematics using a variety of proof techniques.
2. Apply the concepts of abstract mathematical reasoning to reduce complex problems to simpler elements.
3. Use appropriate mathematical terminology and notation in communicating mathematical arguments in oral and written form.
4. Effectively work independently and collaboratively in groups to solve a range of problems.

Content

Learning Approaches

This unit involves lectures and workshops, in which you will engage in collaborative activity with peers, tutors and lecturers. Theory and concepts will be presented and discussed in lectures, and you will be exposed to the processes required to solve problems. The problems addressed in the workshop will help you build and consolidate these skills.
You will work with experts and peers to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information, and will learn how to work effectively within groups with consideration for cultural differences. You will work together to develop your skills in orally communicating mathematics.
At times you will be required to critically reflect on the feedback you are provided in order to identify and address gaps in your understanding.

Feedback on Learning and Assessment

Formative feedback will be provided for the in-semester assessment items by way of written comments, student perusal of marked assessment pieces and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.

Assessment

Overview

The assessment items in this unit are designed to determine your level of competency in meeting the unit learning outcomes while providing you with a range of tasks with varying levels of skill development and difficulty. 

QUT’s extension policy may not apply to all assessment items in this unit.  The extension policy pertaining to each assessment item can be found on the unit Canvas site.

Unit Grading Scheme

7- point scale

Assessment Tasks

Assessment: Workbook

You will be provided with mathematical problems to solve on a regular basis. Submission of your written solutions to these problems will be required at several points during the semester.

This assignment is eligible for the 48-hour late submission period and assignment extensions.

Assessment: Peer Review

You will be required to work in a group to provide a detailed constructive review of a proof presented by a tutor.

This assignment is eligible for the 48-hour late submission period and assignment extensions.

Assessment: Examination (invigilated)

This assessment will be based on unit material drawn from the full semester, and will allow you to demonstrate the theoretical knowledge and problem solving skills you have developed in this unit.

The examination will require attendance on QUT campus.

Academic Integrity

Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.

Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.

You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.

Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.

Resources

Risk Assessment Statement

There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp

Standards/Competencies

This unit is designed to support your development of the following standards\competencies.

Engineers Australia Stage 1 Competency Standard for Professional Engineer

1: Knowledge and Skill Base

1. 
   Relates to: Workbook, Peer Review, Examination (invigilated)

3: Professional and Personal Attributes

1. 
   Relates to: Workbook, Peer Review, Examination (invigilated)
2. 
   Relates to: Peer Review
3. 
   Relates to: Peer Review