Mathematical Analysis & Advanced Topics (MATH2401)

Course overview

Sequences & series of real functions. Intermediate value theorem. Extreme value theorem. Taylor's theorem & error estimates. Criteria for integrability. Vector functions, continuity & differentials. Implicit & inverse function theorems & applications. Metric spaces: compactness, completeness, continuity, contraction mapping principle. Ascoli-Arzela theorem.

MATH2401 provides a rigorous introduction to key concepts from real mathematical analysis. There is some overlap between this course and MATH2400. However, MATH2401 will treat topics in a more in-depth fashion and covered more challenging material.

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and against UQ Policy, and will not be tolerated. We have developed a suite of resources to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.

Course requirements

Assumed background

This is an advanced course designed to challenge students. Those interested in MATH2401 should have received a grade of 6 or 7 inﾠMATH1071. If you do not meet these criteria, you are stronglyﾠadvised to takeﾠMATH2400. Although not a prerequisite, familiarity with the course material of MATH1061 is helpful.

Prerequisites

You'll need to complete the following courses before enrolling in this one:

MATH1071

Incompatible

You can't enrol in this course if you've already completed the following:

MATH2400, MATH7407 (co-taught).

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness).

Important: if you are ill, then do not attend any classes in person.

Aims and outcomes

The aim of this course is to provide students with solid grounding in mathematical analysis. Students will be introduced to a number of fundamentalﾠmathematical conceptsﾠand will be presentedﾠwith theory andﾠexamples. Furthemore it is expected thatﾠstudents willﾠdevelopﾠthe appropriate level of mathematical rigour requiredﾠin the presentation ofﾠmathematical arguments, proofs and solutions.

Assessment

Assessment summary

A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.

Assessment details

In class quizzes

• Hurdle
• In-person

Mode

Written

Category

Quiz

Weight

79.96% All quizzes are equally weighted

Due date

Quiz 1 22/08/2025 11:00 am

Quiz 2 12/09/2025 11:00 am

Quiz 3 10/10/2025 11:00 am

Quiz 4 31/10/2025 11:00 am

Task description

Hurdle requirements

Submission guidelines

Deferral or extension

You cannot defer or apply for an extension for this assessment.

If students miss one quiz, but not Quiz 4, the three remaining quizzes will be scaled to be worth 26.6533% each. No medical certificate is required.

If students miss Quiz 4 and no other quizzes, they will have to do a 50-minute oral exam during exam week, covering the material of Quiz 4. This exam will be worth 19.99%. No medical certificate is required.

If students miss two quizzes, they will have to do a 70-minute oral exam during exam week, covering the material of the two missed quizzes. This exam will be worth 39.98%. No medical certificate is required.

If students miss three quizzes, they will have to do a 90-minute oral exam during exam week covering the material of the three missed quizzes. This exam will be worth 59.97%. Medical certificates for each of the missed quizzes are required.

If students miss all quizzes, they will have to do 90-minute oral exam during exam week as well as a 45 minute quiz. Both will cover all of the course material. The oral exam will be worth 59.96% and the quiz 20%. Medical certificates for all of the missed quizzes are required.

Assignment 1

Mode

Written

Category

Tutorial/ Problem Set

Weight

10.02%

Due date

5/09/2025 5:00 pm

Task description

Submission guidelines

Assignment 1 should be submitted online using Gradescope.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

In order to be able to post assignment solutions in a timely manner, extensions beyond 7 days of the due date are not possible. See ADDITIONAL ASSESSMENT INFORMATION for extension and deferred examination information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

You are required to submit your assignment on time. If you fail to meet the submission deadline, the listed penalty will be deducted per day for up to 7 calendar days, at which point submissions will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.

Assignment 2

Mode

Written

Category

Tutorial/ Problem Set

Weight

10.02%

Due date

24/10/2025 5:00 pm

Task description

Submission guidelines

Assignment 2 should be submitted online using Gradescope.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

In order to be able to post assignment solutions in a timely manner, extensions beyond 7 days of the due date are not possible. See ADDITIONAL ASSESSMENT INFORMATION for extension and deferred examination information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

You are required to submit your assignment on time. If you fail to meet the submission deadline, the listed penalty will be deducted per day for up to 7 calendar days, at which point submissions will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Additional course grading information

If students miss Quiz 1 or Quiz 2 (but not both and not Quiz 3), the remaining two quizzes will be scaled to be worth 37.5% each. No medical certificate is required.

If students miss Quiz 3 (but not Quizzes 1 and 2), they will have to do an oral exam during exam week. This exam will cover the material of Quiz 3, last for 45 minutes and be worth 25%. No medical certificate is required. Note the hurdle requirement: Students who miss Quiz 3 and fail to do an oral exam cannot achieve a pass mark (or higher).

If students miss two quizzes, they will have to do an oral exam during exam week. This exam will cover the material of the entire course, last for 1 hour and be worth 50%. A medical certificate for one of the two missed quizzes is required. Note the hurdle requirement: Students who miss two quizzes and fail to do an oral exam cannot achieve a pass mark (or higher).

If students miss all three quizzes, they will have to sit one quiz during exam week as well as an oral exam, both covering the material of the entire course. Both will be 1 hour long and be worth 25% and 50%, respectively. A medical certificate for two of the three missed quizzes is required. Note the hurdle requirement: Students who miss all three quizzes and fail to do a quiz or oral exam in exam week cannot achieve a pass mark (or higher).

Supplementary assessment

Supplementary assessment is available for this course.

Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply. 

Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.  

If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.  

Supplementary assessment in this course will be an oral exam. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment. 

Additional assessment information

Students should check that all assessment marks are correctly recorded.

Artificial Intelligence

To pass this course, students will be required to demonstrate a detailed understanding of course material together with a range of associated skills independent of Artificial Intelligence (AI) and Machine Translation (MT) tools.

For assessment tasks that are completed in-person (including examinations) termed “secure assessment”, the use of generative Artificial Intelligence (AI) or Machine Translation (MT) tools will not be permitted unless otherwise advised. Any attempted use of AI or MT may constitute student misconduct under the Student Code of Conduct.

Other non-secure assessment tasks (such as assignments) are designed to help you develop your understanding and skills, and to prepare you for secure assessment. You are thus generally encouraged to complete such assessment without the use of AI/MT, unless explicitly advised to the contrary in the assessment item. In any event, if you choose to use such tools, then you must clearly reference any such use within your submitted work. A failure to reference AI or MT use may constitute student misconduct under the Student Code of Conduct. 

Applications for Extensions to Assessment Due Dates

Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.

Please note:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum timeframe applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• An extension for an assessment item due within the teaching period in which the course is offered, must not exceed four weeks in total. If you are incapacitated for a period exceeding four weeks of the teaching period, you are advised to apply for Removal of Course.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

Applications to defer an exam

In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.

Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.

Please note:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

Learning resources

You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.

Library resources

Find the required and recommended resources for this course on the UQ Library website.

Additional learning resources information

Relevant course material will be posted on the Blackboard page of the course at ﾠhttps://learn.uq.edu.au.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

Additional learning activity information

All students are expected to attend classes in person and lecture will be delivered in traditional Blackboard style in a lecture theatre that is not equipped with cameras. Students should attend their weekly tutorials.

Policies and procedures

University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:

• Student Code of Conduct Policy
• Student Integrity and Misconduct Policy and Procedure
• Assessment Procedure
• Examinations Procedure
• Reasonable Adjustments for Students Policy and Procedure

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.