School of Mathematics Honours Handbook

Applying for Honours

Entry Requirements and Enrolment

The normal minimum requirement for honours (fourth year) in mathematics is:

  1. an average of at least 70 in 24 points of relevant third year units, or equivalent
  2. a willing supervisor for your honours project before the end of the first week of December of the year before commencing your honours degree.

How to apply

  1. Read the list of potential honours projects and supervisors: School of Mathematics Honours Projects.
  2. During late August-mid-November, contact potential supervisors and arrange to discuss the projects that they are offering. Ensure that you come prepared (i.e. an idea of your research interests and what you want from honours, a print out of your academic transcript from WES) to the meeting. Develop a project title and outline with your project supervisor. Do not hesitate to contact a potential supervisor even if they have nothing offered officially. Oftentimes, academics have other unlisted projects available.
  3. Make an appointment with the Honours Coordinator. Bring your academic transcript and your project form to your appointment.
  4. Complete the Faculty of Science Online Honours Application.

Honours Structure

Honours students are enrolled in two 24-point units: MTH4100 Mathematics Research Studies, and MTH4200 Advanced studies in Mathematics

MTH4100 Mathematics research studies (24 points)

M40110 - Writing and Presenting for Honours (3 points)

Research project (15 points)

  • Intermediate report (2 points)
  • Oral presentation (3 points)
  • Final report (10 points)
One honours lecture unit (6 points)

MTH4200 Advanced studies in mathematics (24 points)

A combination of lecture units that make up to 24 points. This can include a number of 4-point units* with permission from the Honours Coordinator and project supervisor.

Note: It is the student’s responsibility to ensure that sufficient units are taken to meet the points requirement.

Students must have permission from the Honours Coordinator before enrolling in 4-point units*. If students take more than 24 points, the best weighted 24 points will be used as the final mark

*see below for information about 4-point units

Honours Research Project

The form of the research project is decided by the supervisor depending on whether the project requires any extra reading or new skills. The focus of each research project will vary. Some research projects will have a higher computational focus, while other projects may be more reading and/or proof based. The research project should have a research objective that has not already been developed in the literature. This does not mean that the research project needs to result in publishable material. It can consist of a minor variation of a known result that has not been published before. For example, a generalization/extension of a result that an expert could establish on their own, but instead leaves as an exercise for the readers of a paper to complete. The research project can also be in terms of new insights into a possibly well-established area, rather than a novel result

Assessment of research projects

  1. Intermediate report (for students commencing S1 or S2 2024, this is 2 points). The due date is at the end of your first semester’s exam period, with exact date to be posted on Moodle.
    Comprising of a literature survey, and discussion of any new mathematical techniques that you needed to complete the project.
    Recommended length: 10-20 pages.
    Assessed by supervisor(s).
  2. Final report: (10 points). Due 4pm the last Friday of your second semester.
    Recommended length: 25-40 pages.  
    Assessed by two staff members of the School (other than the supervisor). The rubric for the report is available on the Honours Moodle page.
  3. Oral presentation: (3 points). During swotvac, second semester.
    Assessed by all staff who attend the Honours presentations.

Notes about the research project

The time you spend on the intermediate report and the project should be similar to the time spent on the equivalent (credit points-wise) number of lecture topics. You should start your intermediate report and project at the beginning of your first semester. You should meet with your supervisor regularly as soon as the teaching semester begins, ideally weekly.

Late submissions for Assignments and Reports will be penalised by 10% per day (or part thereof) late, including weekends. Work submitted more than 1 week late without special consideration will not be marked except in exceptional circumstances. This is in accordance with the Faculty of Science policy. Students who cannot submit work by the due date because of illness or other special circumstances are covered by the special consideration policy.

Keep copies of all your submissions for your own records.

Honours Lecture Topics

You can select lecture units from any group, as long as the requirements of your enrolled honours units are met. You can add units until the end of week 2. You can discontinue units until the end of week 8.

Semester 1

Writing and Presenting for Honours (3 points)    Compulsory for all MTH4100 students

MTH4089 - Computational statistical inference (same as MTH5540)
MTH5099 - Measure theory

Pure mathematics topics
MTH5141 - Computational group theory (odd years)
MTH5143 - Representation theory (even years)
MTH5151 - Advanced graph theory (odd years)
MTH5153 - Combinatorics (even years)

Stochastic lecture topics
MTH5210 - Stochastic calculus and mathematical finance  
MTH5220 - The theory of martingales in discrete time

Applied mathematics topics
MTH5311 - Methods of applied mathematics  
MTH5323 - Advanced numerical analysis of partial differential equations
MTH5333 - Discrete optimisation (odd years)
MTH5343 - Magnetohydrodynamics and visualisation of scientific data (even years)

Semester 2

MTH5118 - Dynamical systems (even years)

Pure mathematics topics
MTH5111 - Differential Geometry
MTH5113 - Low-dimensional topology (even years)
MTH5115 - Algebraic topology (odd years)
MTH5123 - Partial differential equations (odd years)

Stochastic lecture topics
MTH5230 - Markov chains and random walks  
MTH5240 - Mixing of finite Markov chains

Applied mathematics topics
MTH5331 - Nonlinear optimisation
MTH5341 - Fluid dynamics and turbulence (odd years)
MTH5351 - Mathematical biology (odd years)

Financial mathematics units

Requires approval of Honours Coordinator

Semester 1

MTH5530 - Computational methods in finance
MTH5550 - Quantitative trading and market microstructure
MTH5540 - please enrol in MTH4089 as these units are jointly taught

Semester 2

MTH5510 - Quantitative risk management
MTH5520 - Interest rate modelling
MTH5560 - Partial differential equations for finance

Other topics

Requires approval of Honours Coordinator

  • AMSI Summer School units can count as credit towards your honours degree. Either one 4-week course or two 2-week courses (6 points).
  • External honours units via AMSI Online: Honours and Masters https://rhed.amsi.org.au/honours-masters/  (4 or 6 points, depending on the unit).
  • Some third-year ASP3xxx, ATM3xxx or MTH3xxx mathematics lecture units (4 points each). An additional 2 points worth of extra assessment must be arranged.
  • Honours students may also enrol in one relevant non-shared 5th year unit for credit but must have the permission of both their supervisor and the Honours Coordinator (6 points).

For permission to enrol in any of these, contact the Honours Coordinator at least three weeks before the start of the unit.

Honours Prizes

All students enrolled in honours in the School of Mathematics are eligible for the following prizes:

  • Carl Moppert Prize in Mathematics: prize for the best all-round Mathematics honours student.
  • Leo Gleeson Prize: prize for the best honours student in Applied Mathematics.
  • Pure Mathematics Prize: prize for the best honours student in Pure Mathematics.
  • Statistics Prize: prize for the best honours student in Statistics.

Contacts

Honours Coordinator:  Dr Julie Clutterbuck
E: julie.clutterbuck@monash.edu

Deputy Honours Coordinator:  Dr Andy Hammerlindl
E: andy.hammerlindl@monash.edu

Administrative Officer (Honours): Ms Karen Hogeboom
E: karen.hogeboom@monash.edu

Appendix

Writing and Presenting for Honours

Lecturer(s):  Heiko Dietrich  
Contact details:  heiko.dietrich@monash.edu

M40110 is a compulsory topic for ALL honours students in Mathematical Sciences.  There will be an introductory lecture, but most of the work will be a study guide that needs to be read through, along with practical reports and presentations.

Objectives

Proposed topic is to give honours students guidance and feedback on presenting and writing mathematics, prior to their Intermediate report and presentation at the end of the first semester of study. Also to teach students LATEX, BibTEX and Beamer, however guidance on writing and presentation style will be hopefully be technology independent.

Syllabus

Technical Aspects:
1. LATEX and BIBTEX software.
2. Structure of BibTeX, LaTeX and Beamer documents.
3. Managing and citing references using BibTeX.
4. Writing mathematics in LaTeX.

Writing:
1. Structure of documents, e.g. reports, papers, theses, presentations.
2. What to include and referencing.
3. Writing Introductions, Conclusions and Abstracts.
4. Equations: formatting, e.g. spacing, inline vs display equations, multiple line equations and subequations, when to include equation numbers and referencing.
5. Tables and figures: guidelines, e.g. should always be discussed in text and captions.
6. Table of Contents.
7. Appendices.

Presenting Mathematics:
1. Audience awareness.
2. Timing.
3. Content: how much and what to include.
4. Know your audience.
5. Handling questions.

Mode of Delivery:
Self-paced Study Guide with good and bad initial presentations and examples.

Assessment:
-  Practical presentation (in Week 11/12), usually 10 mins (4 slides or less), with feedback
- 8 page report (in Week 10/11), usually on topic of honours project
- Pass/Fail: based on attendance of all lectures (usually 4), practical presentation, and report.

References:
1. Fowler's Modern English Usage.
2. Higham, N.J., Handbook of Writing for the Mathematical Sciences, SIAM, 1998.
3. Krantz, S.G., A Primer of Mathematical Writing, AMS, 1997.
4. LATEX tutorial material, http://www.ctan.org/topic/tut-latex