MTH3137 Number theory and cryptography (Advanced)
Faculty of Science
MTH3137 Number theory and cryptography (Advanced) is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2026 in Semester 2 at Clayton. It has no prerequisites and unlocks 1 unit, leading on to 3 units in all.
- Credit points
- 6
- Offered in 2026
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2026 handbook entry. See the 2027 entry.
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Requisites
Before MTH3137
No prerequisites or corequisites besides the enrolment rules below.
After MTH3137
1 unit list MTH3137 as a prerequisite or corequisite.
Enrolment rules
PROHIBITION: MTH2121, MTH2137, MTH3121
PREREQUISITE: You must have least a Distinction in one unit from MTH2025 or MTH2141 or MTH3141 or by approval of the unit coordinator or be enrolled in the Master of Mathematics.
You must enrol in this unit manually via the online Enrolment Amendment form.
Equivalent units
The same content under another code. Only one of them counts.
Overview
Prime numbers; Euclidean algorithm; congruences; the Euler totient function; the theorems of Fermat, Euler and Wilson; RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; primitive roots; factorisation and primality testing algorithms; secure key exchange; elliptic curve cryptography.
Offerings in 2026
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
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
Apply the classification of numbers and analyse their relationships, such as divisibility and primality;
- 2
Illustrate the power of pure mathematics and appreciate its beauty;
- 3
Demonstrate a deep understanding of the fundamental concepts of number theory;
- 4
Develop proofs involving number theoretic insights and techniques;
- 5
Demonstrate advanced problem solving and theorem proving skills;
- 6
Explain how thousands of years of pure mathematical developments have enabled secure electronic communication and commerce;
- 7
Analyse fundamental number theoretic algorithms for a range of tasks including exchanging information securely and testing whether numbers are prime.
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Teaching approachActive learning
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week
Where it fits
MTH3137 is part of 6 areas of study in the 2026 handbook.
- APPLMTH07Additional elective unitApplied mathematicsNo reviews yet
- MTHSTAT07Additional elective unitsMathematical statisticsNo reviews yet
- MATHS09Mathematics elective unitsMathematicsNo reviews yet
- MATHS11Mathematics elective unitsMathematicsNo reviews yet
- MATPURE09Pure mathematics elective unitsPure mathematicsNo reviews yet
- MATPURE11Pure mathematics elective unitsPure mathematicsNo reviews yet
Contacts
- Unit Coordinators
- Professor Ian Wanless
- Chief Examiners
- Professor Ian Wanless
Common questions
What are the prerequisites for MTH3137?
MTH3137 has no prerequisites, but enrolment rules apply.
What can I take after MTH3137?
MTH3137 is a prerequisite or corequisite for 1 unit, including MTH3170. Those lead on to 3 units in all.
When is MTH3137 offered?
In 2026, MTH3137 runs in Semester 2 at Clayton.
Does MTH3137 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.
Which majors and minors include MTH3137?
MTH3137 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.