Modern economic theory is based on mathematical models. Thus, a thorough understanding of the economic content of such models is not possible without a clear understanding of the mathematical concepts that underpin the modeling. This course introduces students to a range of optimisation concepts and techniques for economics and financial economics that form the basis of advanced economic theory courses. The introduced optimisation concepts and techniques will be derived from basic principles and assumptions as thoroughly as possible, and will be illustrated using standard applications from economics.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Demonstrate an understanding of the basic mathematical methods that are most widely used in economics, both from a formal, abstract perspective and an intuitive perspective.
2. Demonstrate an understanding of and ability to construct mathematical proofs, and appreciate their role in the derivation of mathematical concepts and structures.
3. Apply mathematical methods and techniques that are formulated in abstract settings to concrete economic applications.

Research-Led Teaching

The material taught in this course is directly relevant to various applied microeconomic research topics that have been considered by economists in academia, various public sector agencies, and various private sector organisations.

Field Trips

n.a

Additional Course Costs

n.a

Examination Material or equipment

Exams and quizzes will be closed-book, with a non-programmable calculator permitted.

Recommended Resources

The books recommended for this course are:

• Simon, C. and L. Blume (1994) Mathematics for Economists. Norton 
• A First Course in Optimization (1996) Theory by Rangarajan Sundaram 
• A Primer in Econometric Theory (2016) by John Stachurski

Additional media resources will be recommended to the students during the semester.

Staff Feedback

Students will be given feedback in the following forms in this course:

• Graded exams and answers.
• Verbal feedback in tutorials.
• Verbal feedback upon request during consultation hours and tutorials.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

Work-Load Expectations

The amount of work required for successful completion of this class may vary between students. As a rough guide, students should expect to devote at least 10 hours a week to this class. This should include all of the following.

• 3-4 hours a week: lectures
• 1 hour a week: tutorials.
• At least 5-6 hours a week: reading, research, writing, lecture and tutorial preparation.

Attendance Expectations

As a general rule, students should aim to attend all lectures and tutorials for this class unless they have a very good reason for not doing so. Recognising that occasional absences are often unavoidable, students are expected to attend at least 80 per cent of all lectures and tutorials (combined) for this class. The main exceptions to this are absences for medical or other reasons that can be supported by an appropriate form of official documentation.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Introduction: economics as an exercise in optimization
2	Mathematical foundation: elements of set theory, mappings and cardinality
3	Mathematical foundation: sequences, limits and continuity	Big Quiz #1
4	Mathematical foundation: matrices and matrix arithmetic, multivariate calculus	Big Quiz #1 Review
5	Mathematical foundation: vector spaces and linear operators	Big Quiz #2
6	Fundamentals of optimization: eigenpairs and diagonalization, quadratic forms	Big Quiz #2 Review
7	Unconstrained optimization: necessary and sufficient conditions	Big Quiz #3
8	Convexity and uniqueness	Big Quiz #3 Review
9	Optimization with equality constraints	Big Quiz #4
10	Karush-Kuhn-Tucker conditions	Big Quiz #4 Review
11	Envelope theorem	Big Quiz #5
12	Revision	Big Quiz #5 Review; Major Project due

Tutorial Registration

Tutorials this semester will be delivered in person on campus. You are expected to attend one tutorial each week from Week 2 onwards. Use MyTimetable to enroll in a tutorial. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage. https://www.anu.edu.au/students/program-administration/timetabling]

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Big Quizzes	25 %	*	*	1,2,3
In-class mini-quiz	10 %	*	*	1,2,3
Individual Project	15 %	29/05/2026	12/06/2026	1,2,3
Final Exam	50 %	04/06/2026	02/07/2026	1,2,3

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Canvas’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Lectures, tutorials, and consultations will be face to face. The face to face lectures will be recorded on Echo 360 and available soon after the lectures on the course Canvas page, though quality of any recording cannot be guaranteed.

Live tutorials (face to face and online) will occur from week 2. Tutorials for this course are a learning activity and include a significant discussion-based component. Worked solutions are not provided because they would not effectively compensate for missing a tutorial. Worked solutions imply that there is a unique correct solution and are therefore in opposition to the development of professional judgement, which is a key part of this course. Students who, through unavoidable and unplanned occurrences, are unable to attend a tutorial one week are encouraged to work through the problems and attend a consultation session to discuss any questions they have about their solutions.

Details on the delivery of this course and expectations of student participation are outlined in further detail on the Canvas course site in O-week. Attendance at lectures and tutorials, while not compulsory, is expected in line with “Code of Practice for Teaching and Learning”, clause 2 paragraph (b).

Examination(s)

Examinations will be held in-person and invigilated by the ANU Examinations department.

Assessment Task 1

Big Quizzes

A big quiz will be held in the Assessment block (Thursday 2pm) of Weeks 3, 5, 7, 9, and 11. Each quiz will consist of multiple choice, numerical, and short answer questions. The quiz is in-person, closed-book, and administered on paper. You will have 30 minutes to complete the quiz, with time starting at approximately 5 past the hour. The quiz will primarily assess material up to that covered in the preceding week's tutorial, but may also assess any material covered in lectures up to the time of the quiz.

Each quiz will count for 5% of the course grade, for a total of 25% of the course grade. In the case where a student misses one quiz for any reason, then the weighting from that quiz will go to the final exam. If a student misses more than one quiz for good reason (e.g. illness), then alternative re-weightings can be discussed.

Quizzes will be returned during the Assessment block the following week, and the material from the quiz will be reviewed at that time.

Assessment Task 2

In-class mini-quiz

Each week during lecture, a very short quiz will be held over Canvas (or similar). Each quiz will take approximately 5 minutes, and consist of a very small number of multiple choice/numerical questions. It will cover material from that lecture or previous work. The overall in-class quiz mark, which makes up 10% of the overall course grade, will be the arithmetic average of the 10 highest marks obtained in the 12 quizzes.

If students miss up to two quizzes for any reason, these will be the quizzes which do not count towards the final grade. If a student misses three or more quizzes with good reason (e.g. illness), then an appropriate re-weighting will be made.

Assessment Task 3

Individual Project

Each student will be assigned an optimization problem to solve.

The problem will be of a similar type to those covered in the course and tutorials.

The project will have to submitted as an explanatory video for the given problem, with an upper limit on its length.

The time for completion the project will be constrained to a few days.

Assessment Task 4

Final Exam

A final exam will be held during the ANU final exam period. The exam will cover material presented throughout the entire course. The final exam is compulsory to attempt and will count for 50% of your final grade. The exam will be approximately three hours, and run on-campus by the Examinations division during the exam period. The exam will contain a mix of multiple choice, numerical, and short answer question. Further details will be given on Canvas in week 10.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

Please refer to the information on this that was provided above in the discussion of the various assessment tasks. 

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No resubmission of any assignment after the due date and time for its submission will be permitted in this class.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Accessibility for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students