MTH1110 Foundations of mathematics
Faculty of Science
MTH1110 Foundations of mathematics is a level 1, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 1 and Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 1, Semester 2
- Clayton
- Assessment
- Exam 50%
- and 2 other tasks
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Requisites
Before MTH1110
No prerequisites or corequisites besides the enrolment rules below.
After MTH1110
No unit lists MTH1110 as a prerequisite in the 2027 handbook.
Enrolment rules
PREREQUISITE: VCE Specialist Mathematics or Mathematical Methods units 3 and 4 with a raw study score of at least 25
PROHIBITION: MAT1830, FIT1058
Overview
This unit develops foundational concepts and techniques in discrete mathematics, with an emphasis on mathematical structures, proof and abstraction. Topics include logic and proof, sets, relations and functions, combinatorics, recurrence relations, graph theory and elementary probability. These topics provide the language and methods for reasoning about discrete structures that arise throughout modern mathematics and its applications, including computation, algorithms, data science, network analysis and discrete modelling. The unit provides a foundation for further study in mathematics and related quantitative disciplines.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | Flexible |
| Second semester | Clayton | Flexible |
Assessment
- Assessment 1Quiz / Test35%
- Assessment 2Exercise15%
- Assessment 3 - Final assessment (Exam): 3 hours and 10 minutesExamination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Construct, analyse and critique rigorous mathematical arguments, including direct proofs, proofs by contradiction and proofs by induction;
- 2
Use sets, relations and functions as foundational mathematical structures, and apply them to formulate and solve abstract problems;
- 3
Develop, solve and interpret recurrence relations as models for discrete and recursively defined processes;
- 4
Apply graph-theoretic concepts, including trees and graphs, to model discrete structures and prove structural properties;
- 5
Use combinatorial reasoning to solve enumeration problems, including problems that require constructing and justifying appropriate counting methods.
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
- One 3-hour seminar;
- One 2-hour applied class (in weeks 2–12) and
- Seven hours of independent study per week.
Learning resources
Required resources
Course notes booklet (available as a pdf from the course Moodle page).
Recommended resources
The following textbooks are available at the library and may prove useful if you want additional resources beyond the course notes. It is not recommended that you buy them unless you find that you need your own copy.
"Discrete Mathematics" (7th Ed) by Richard Johnsonbaugh. ISBN: 0131354302
"Discrete Mathematics for Computing" (3rd Ed) by Peter Grossman. ISBN: 9780230216112
Contacts
- Chief Examiners
- Associate Professor Daniel Horsley
- Unit Coordinators
- Associate Professor Daniel Horsley
Common questions
What are the prerequisites for MTH1110?
MTH1110 has no prerequisites, but enrolment rules apply.
When is MTH1110 offered?
In 2027, MTH1110 runs in Semester 1 and Semester 2 at Clayton.
Does MTH1110 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 2 other tasks.
More details
- Credit points
- 6
- Level
- 1
- Study level
- Undergraduate
- Faculty
- Faculty of Science
- Organisational unit
- School of Mathematics
- Type
- Coursework
- EFTSL
- 0.125
- Student contribution
- SCA Band 1
- Study abroad
- Available
- Handbook years
- 2027