• Class Number 4030
• Term Code 3230
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Ivo Vekemans
• LECTURER
• Ivo Vekemans
• Dr Vigleik Angeltveit
• Class Dates
• Class Start Date 21/02/2022
• Class End Date 27/05/2022
• Census Date 31/03/2022
• Last Date to Enrol 28/02/2022
SELT Survey Results

Advanced Mathematics and Applications 1 (MATH1115)

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.
• Essential Calculus (2nd Edition) by James Stewart. Also available as an e-text from Cengage.

The first four chapters of the Linear Algebra textbook are followed quite closely in this course.

The first six chapters of the Calculus textbook are relevant for this course, but are mostly used as a reference for technical material that is assumed prerequisite knowledge. Only a small portion of the Calculus textbook is used as direct support for the Analysis lecture content. Lecture notes will be provided as a supplement. However, please note that later sections of the Stewart Essential Calculus textbook are used more extensively in MATH1116, and the same Calculus textbook is used very closely in MATH1013, MATH1014, and MATH2305.

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). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

## Other Information

Please note, that where there are multiple assessment tasks of the same type, e.g. weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Block - Linear Algebra 1 - Matrix operations 2 - Determinants 3 - Complex numbers 4 - Vector spaces and subspaces Feedback is given through written and online assignments as well as workshop worksheets.
2 Block - Analysis 1 - Integration Theory (Riemann-Darboux) 2 - Logic, Functions and Sets 3 - Limits of Sequences and Functions; Continuity (including epsilon-delta definitions and proofs) 4 - Differentiation (and related theorems) 5 - Real Number Axioms 6 - Key single variable real analysis theorems, culminating in the proof of the Fundamental Theorem of Calculus. 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 by following a process that will be detailed on the course Wattle page. Remote participation options will be provided for students who require them due to travel restrictions or COVID-safe guidelines. However, not all times will be available for both remote and in-person attendance. Please refer to the course Wattle site for more information.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Assignments 30 % * * 1, 2, 3, 4
Mid-semester examination 25 % * * 2, 3, 4
Final examination 45 % 02/06/2022 30/06/2022 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 Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

## 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 Integrity . 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 2022, this course is delivered on campus with adjustments for remote participants. Workshops will be available for in-person groups, and separately for online groups via Zoom. Exams are likely to be held remotely and require students to engage with a method of remote invigilation via Zoom, or Proctorio, or similar. The mode of examination will be confirmed closer to the time of the exams.

## 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.

Please note that, where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Value: 30 %
Learning Outcomes: 1, 2, 3, 4

Assignments

Assignments will be handed out weekly starting from Week 2. The assignments will usually consist of an online component (mostly delivered via the MATLAB Grader system, to which students will be given access) as well as a written show working component. There will be 10 assignments. The written show working components of assignments will be submitted through the Gradescope website.

The best 8 out 10 of these grades (given equal weight) will form the 30% assignment category contribution to a student's final grade.

Further details can be found on the course Wattle site.

Value: 25 %
Learning Outcomes: 2, 3, 4

Mid-semester examination

A mid-semester examination is included in the assessment. We aim 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.

Value: 45 %
Due Date: 02/06/2022
Return of Assessment: 30/06/2022
Learning Outcomes: 2, 3, 4

Final examination

A final examination is included in the assessment. 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 mid-semester exam.

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

## 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.

## Hardcopy Submission

Hardcopy submission is not utilised in MATH1115. All assignment submission is electronic, via Wattle 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

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

## 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.
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.

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).

## Convener

 Ivo Vekemans ivo.vekemans@anu.edu.au

### Research Interests

Algebraic Topology

### Ivo Vekemans

 By Appointment

## Instructor

 Ivo Vekemans 0261252908 ivo.vekemans@anu.edu.au

### Ivo Vekemans

 By Appointment

## Instructor

 Dr Vigleik Angeltveit 0261252908 vigleik.angeltveit@anu.edu.au