Advanced Calculus & Linear Algebra I (MATH1071)

Course overview

1. Elementary linear algebra: Vectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, Gaussian elimination, eigenvalues, eigenvectors, applications. Equation of straight line & plane.

2. Introduction to proof-based calculus: Fields, sequences, limits, continuity, intermediate and extreme value theorems, maxima & minima.

3. Techniques of calculus: Series, differentiation, integration, numerical methods, Taylor series, L'Hopital's rule.

This course differs from MATH1051 by treating material in more depth and with greater rigour.

MATH1071 provides an important foundation in analysis and linear algebra that will prove useful for further studies in pure and applied mathematics, sciences, engineering and finance.

We develop the theory of limits of sequences and functions of one real variable, as well as continuity. The students receive an introduction to rigorous mathematical reasoning and learn the concept of a proof. We then investigate differentiation, optimisation and standard integration techniques. Another topic is the study of series (infinite sums).

Our study of linear algebra begins with vectors and matrices. These topics are extensively utilised throughout the sciences, e.g., in modellingﾠ of systems of interacting elements. Matrix methods are common in structural engineering, and matrix algebra is necessary for computer graphics. The course covers linear independence, scalar product, simultaneous equations, Gaussian elimination and determinants. An important component of the study concerns eigenvalues and eigenvectors. These notions are fundamental to numerous problems in mathematics, physics and other areas, including modelling resonant frequencies in dynamical systems.

Any questions relating to administrative matters should be sent to math1071@uq.edu.au.

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 ﾠUQ Policy,ﾠ and will not be tolerated. We have developed aﾠ suite of resourcesﾠ 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

Students should be familiar with the following: factoring polynomials, expansion and simplification of algebraic expressions, trigonometric functions and identities, logarithms and the exponential function, solving systems of linear equations, vectors in 2D & 3D space, addition of vectors, angles between vectors.

Students who have trouble because of gaps in their background should work through exercises from the early chapters in the textbooks and discuss their difficulties in the First-Year Learning Centre or Science Learning Centre.

Prerequisites

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

A grade of 6 or above in MATH1050; or A grade of B or higher in Queensland Year 12 Specialist Mathematics (Units 3 & 4) (or equivalent).

Incompatible

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

MATH1051, MATH7051, MATH7501

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.ﾠ Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness). Alternative arrangements will be advised on Blackboard should the campus be closed for any reason. Important: Please refrain from attending classes in person if you are unwell. Alternative arrangements can be organised – consult Blackboard for details.

Aims and outcomes

The aim of this course is to provide students with an introduction to and a solid basis for further study in mathematics, in particular mathematical analysis. Students will be introduced toﾠ a number of new mathematical concepts, and will be presented both with theory and practical examples. The course also aims to help students develop a sense for the appropriate level of mathematical rigour needed in presenting mathematical arguments and solutions.

Learning outcomes

After successfully completing this course you should be able to:

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

Final exam

• Hurdle
• In-person

Mode

Written

Category

Examination

Weight

60%

Due date

End of Semester Exam Period

7/06/2025 - 21/06/2025

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.

Assignments

• Hurdle

Mode

Written

Category

Tutorial/ Problem Set

Weight

40%

Due date

Assignment 1 - 17 March 2025, 5pm.

Assignment 2 - 31 March 2025, 5pm.

Assignment 3 - 14 April 2025, 5pm.

Assignment 4 - 2 May 2025, 5pm.

Assignment 5 - 16 May 2025, 5pm.

Assignment 6 - 30 May 2025, 5pm.

Task description

Hurdle requirements

Submission guidelines

Assignment should be submitted through Blackboard.

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.

Due to the high frequency of assignments and the need to provide solutions swiftly (one week after the due date), the maximal possible extension for each of the six assignments is one week. See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.

Late submission

A penalty of 1 grade for each 24 hour period from time submission is due will apply for up to 7 days. After 7 days you will receive a mark of 0.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission 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

The maximal grade for students obtaining less than 40% of the available marks on the final exam or less than 40% of the available marks for the combined assignments is 2.

The maximal grade for students obtaining less than 45% of the available marks on the final exam or less than 45% of the available marks for the combined assignments is 3.

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 a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.  

Additional assessment information

Artificial Intelligence

Assessment tasks in this course evaluate students' abilities, skills and knowledge without the aid of generative Artificial Intelligence (AI) or Machine Translation (MT). Students are advised that the use of AI or MT technologies to develop responses is strictly prohibited and 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 date 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.
• 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.
• 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.
• 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

Additional learning materials, such as assignments and tutorial sheets, will be posted on the course Blackboard page.

Learning activities

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

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 - Students Policy and Procedure

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