This course begins an in-depth study of the fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas will allow students to develop analytical skills which will form a base for further study in fundamental mathematics, as well as providing a foundation for a wide range of quantitative areas such as actuarial studies, computer science, economics, engineering, physics and statistics.

Topics to be covered include:

Calculus/Analysis - suprema and infima of sets of real numbers, completeness, Riemann-Darboux definition of integration, introductory formal logic, axioms for the real numbers, sequences, convergence, limits, continuity, related real analysis theorems including the monotone convergence theorem for sequences of real numbers and the Bolzano-Weierstrass theorem, existence of extrema, differentiation, applications of derivatives, proof of the fundamental theorem of calculus, Taylor polynomials, l'Hospital's rules, inverse functions;

Linear Algebra - solving linear equations, matrix equations, linear independence, matrix transformations, matrix operations, matrix inverses, abstract vector spaces, subspaces, dimension and rank, determinants, Cramer's rule, complex numbers.

Note: This is an Honours Pathway Course (HPC).

It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1013.

Learning Outcomes

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

1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques.
3. Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from calculus and linear algebra.
4. Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.

Examination Material or equipment

Information about examination material will be made available through the Examinations timetable and/or the course Wattle page.

Required Resources

• Elementary Linear Algebra: Applications Version (10th, 11th, or 12th edition) by Howard Anton and Chris Rorres. Also available as an e-text from Wiley Direct.
• Calculus (3rd Edition) by Michael Spivak.

Recommended Resources

Recommended reading (not compulsory) is How to Study for a Mathematics Degree by Lara Alcock. Available for loan from the ANU library in electronic form.

Staff Feedback

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

• Automatic grading of the online quizzes.
• Written comments on the show working components of the assignments.
• Group work on the workshop exercises.
• Individual feedback may be given during the lecturer office hours.

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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Content Block: Linear Algebra Matrix Operations Determinants Complex Numbers Vector Spaces and Subspaces Eigenvectors and Eigenvalues	Feedback is given through written and online assignments as well as workshop worksheets.
2	Content Block: Analysis Limits and continuous functions Differentiation and related theorems Integration The Fundamental Theorem of Calculus Infinite sequences	Feedback is given through written and online assignments as well as workshop worksheets.

Tutorial Registration

Workshops begin in Week 2. Students are required to enrol in one of the available weekly workshop groups using the MyTimetable system. Remote participation options will be provided on a case by case basis, only for participants with unavoidable travel restrictions/visa delays or due to COVID-safe guidelines. However, not all times will be available for both remote and in-person attendance.

Assessment Summary

Assessment task	Value	Learning Outcomes
Assignments	30 %	1, 2, 3, 4
Mid-semester examination	25 %	2, 3, 4
Final examination	45 %	2, 3, 4

* 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
• Special Assessment Consideration Guideline and General Information 
• 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 ‘Wattle’ 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

In Semester 1 2023, this course is delivered on campus with adjustments for remote participants on a case by case basis. Workshops will be available for in-person groups, with one dedicated online workshop via Zoom if needed for students with unavoidable travel restrictions/visa delays or due to COVID-safe guidelines. Exams are likely to be held in person. The mode of examination will be confirmed closer to the time of the exams. Whilst lectures will be recorded, students are strongly encouraged to attend all class activities live.

Examination(s)

The course includes a mid-semester and final examination. More information is given in the assessment items. The details and mode of delivery for exams will be communicated through the course Wattle site. Students should consult the course Wattle site and the ANU examination timetables (when finalised) to confirm the date, time and venue of exams.

Assessment Task 1

Assignments

Assignments will be due weekly. The assignments will usually consist of a written show working component and an online component (mostly delivered via the MATLAB Grader system, to which students will be given access). The written show working components of assignments will be submitted through the Gradescope website.

The lowest two assignment scores will be dropped, and the remaining scores will form the 30% assignment category contribution to a student's final grade.

Further details can be found on the course Wattle site.

Assessment Task 2

Mid-semester examination

A mid-semester examination is included in the assessment. We intend for the examination to be held in Week 6 or Week 7. Details will be made available at the Examinations timetable.

Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and mode of the mid-semester exam.

Assessment Task 3

Final examination

A final examination is included in the assessment, to be held in the end of semester examination period. Students are required to satisfy a hurdle requirement for both the linear algebra and analysis parts of the course. Specific details about the hurdle requirements are given in Wattle. Details about the examination will be made available at the Examinations timetable.

Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and mode of the final exam.

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 agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. All assignment submissions will be electronic, via Gradescope and/or the MATLAB Grader platform. Please keep a copy of all your assignment submissions for your records. MATH1115 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

Hardcopy submission is not utilised in MATH1115. All assignment submission is electronic, via Wattle, Gradescope, and/or the MATLAB Grader platform

Late Submission

• Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after solutions are published.
• For assignment assessment tasks that include both an online quiz component and a written submission component, the above statement applies only to the written submission component. In contrast, the online quiz component may be set such that answers are available immediately after the due date, so that late submission of that component of the assignment will not be permitted, and a mark of 0 will be awarded for that component of the assessment task if not submitted by the due date.

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.

Returning Assignments

Assignments will be returned electronically through the Gradescope site, except for quiz components which will be delivered and returned through the online platform used; see the course Wattle site for more information.

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

Assignments may not be resubmitted.

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 Access and inclusion 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 and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students