• Class Number 7011
• Term Code 3260
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• AsPr Joan Licata
• LECTURER
• Dr Griff Ware
• AsPr Joan Licata
• Class Dates
• Class Start Date 25/07/2022
• Class End Date 28/10/2022
• Census Date 31/08/2022
• Last Date to Enrol 01/08/2022
SELT Survey Results

Advanced Mathematics and Applications 2 (MATH1116)

This course continues on from MATH1115, providing an in-depth development of 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 - short introduction to metric spaces in the context of the calculus of functions of several variables, generalisation of the real analysis theory studied in MATH1115 to multivariable functions including limits and continuity, double integrals, Fubini's theorem, integrability of continuous functions, partial derivatives, gradients and directional derivatives, differentiation of multivariable functions, extreme values, vector functions, curves and parametrisations, infinite series, convergence tests, power series, Taylor series;

Linear Algebra – subspaces, span, linear independence, bases and dimension, linear maps, duality, eigenvalues and eigenvectors, inner product spaces, Gram-Schmidt orthogonalisation, operators on inner product spaces, the spectral theorem in finite dimensions, singular value decomposition.

Note: This is an Honours Pathway Course. It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.

## Learning Outcomes

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

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

## Required Resources

• Essential Calculus (2nd Edition) by James Stewart. Also available as an eBook from Cengage.
• Linear Algebra Done Right (3rd Edition) by Sheldon Axler. Also available as an eBook from Springer.

Whether you are on campus or studying remotely, there are a variety of online platforms you will use to participate in your study program. These could include videos for lectures and other instruction, two-way video conferencing for interactive learning, email and other messaging tools for communication, interactive web apps for formative and collaborative activities, print and/or photo/scan for handwritten work and drawings, and home-based assessment.

ANU outlines recommended student system requirements to ensure you are able to participate fully in your learning. Other information is also available about the various Learning Platforms you may use.

## Staff Feedback

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

• Automatic grading of the online quizzes.
• Verbal comments on group work in workshops.
• Lecturers and demonstrators may also give feedback to the whole class, to groups, to individuals, to focus groups.

## 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

Regarding collaboration when attempting assignments: you are encouraged to discuss the course material with your classmates as an aid to learning. However, every student is responsible for writing up their own solutions. Although you may work with others to understand the ingredients in a correct solution, producing the written solutions should be an individual effort. If you work with other students, please acknowledge this collaboration on the first page of your assignment. For example, write, “I discussed Problem 1 with Jane Doe and Problems 3 and 4 with John Doe.” When completing an assignment, you should consult only the textbooks, notes, lecturers, demonstrators, and classmates, as using other sources often compromises the learning goals of the assignment. However, if you do use any non-human resources (e.g., Wikipedia, other texts, online resources) besides the course textbooks and notes, you should cite these similarly.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Real analysis content to be covered: Limits and Continuity in R^n; Integral Calculus of Functions from R^n to R; Differential Calculus of Functions from R^n to R; Differential and Integral Calculus of Functions from R to R^n; Improper Integrals; Infinite Series of Real Numbers; Power Series and Taylor Series. Understanding of the content will be tested regularly and formatively via the weekly assignments and via the summative exams. Course activities will be in-person on campus (with remote adjustments only for participants with unavoidable travel restrictions/visa delays).
2 Linear algebra content to be covered (time permitting): Vector Spaces (mostly review from MATH1115: Definition of Vector Space, Subspaces, Span and Linear Independence, Bases, Dimension); Linear Maps (The Vector Space of Linear Maps, Null Spaces and Ranges, Representing a Linear Map by a Matrix, Invertibility and Isomorphic Vector Spaces, Duality); Eigenvalues, Eigenvectors, and Invariant Subspaces (Invariant Subspaces, Eigenvectors and Upper-Triangular Matrices, Eigenspaces and Diagonal Matrices); Inner Product Spaces (Inner Products and Norms, Orthonormal Bases, Orthogonal Complements and Minimization Problems); Operators on Inner Product Spaces (Self-Adjoint and Normal Operators, The Spectral Theorem, Positive Operators and Isometries, Polar Decomposition and Singular Value Decomposition). As above.

## Tutorial Registration

Workshops begin in Week 2. If you are overseas and thus a remote student, your workshop will be the 4:00pm-6:00pm session (Canberra time) on Wednesdays, via Zoom. Overseas students need to nominate themselves as a remote student using the tool on Wattle, and then MyTimetable will be updated to reserve a spot for them in that single online session. For most students (on-campus), Workshop registration is via MyTimetable opening on 11 July, 2022. 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.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Weekly Assignments 30 % * * 1,2,3,4
Mid-semester Exam 28 % * * 1,2,3,4
End of Semester Examination 40 % 03/11/2022 01/12/2022 1,2,3,4
Small Group Discussion Forum 2 % * * 1,4

* 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 ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

## 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-person lectures and workshops are held on the main Acton campus of ANU. In 2022, MATH1116 is on campus with remote adjustments only for participants with unavoidable travel restrictions/visa delays.

## Examination(s)

Please note that the due date and return date for the end of semester exam indicates the first day of the ANU end of semester exam period, and the the date official end of semester results are released on ISIS, respectively. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode/venue for the exam.

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

Weekly Assignments

Weekly assignments, which can involve both an online quiz component (using the MATLAB Grader system) and a written component (submitted online via PDF upload to the Gradescope system) will be due from the end of Week 2 onwards, most Friday afternoons at 6pm Canberra time. A student’s lowest Assignment score will be discounted, and the average of their remaining Assignment scores will constitute 30% of their overall grade for MATH1116. This is an advanced stream course, so most of your written work will be formal proofs. Writing clear, concise, and compelling arguments is a skill that takes time to master, and there are a variety of resources posted on Wattle to help you. The proofs in the textbooks / notes, and in the posted solutions also provide excellent examples to study. Language is a mathematician’s primary tool; we don’t generally get to run experiments or do fieldwork, so in the absence of data to support our hypotheses, our arguments need to be sufficiently convincing.

It is intended that the marked assignments will be returned within 12 days after submission. Further details can be found on the course Wattle site.

Value: 28 %
Learning Outcomes: 1,2,3,4

Mid-semester Exam

A mid-semester examination is included in the assessment. We will request that the ANU Examinations Department schedule the mid semester exam for Monday of Week 7 (19 September, 2022). However, it is possible that the exam could be held at any point in Week 6 or Week 7. Details will be posted on Wattle when available, including information about the mode of delivery of the exam.

Value: 40 %
Due Date: 03/11/2022
Return of Assessment: 01/12/2022
Learning Outcomes: 1,2,3,4

End of Semester Examination

An end of semester examination is included in the assessment. Students are required to satisfy a hurdle requirement on the end of semester exam, for both the linear algebra and analysis parts of the course: to pass the course, as well as scoring at least 50 out of 100 as an overall course mark, students must both score at least 35% of the marks available on the analysis portion of the final exam and also score at least 35% of the marks available on the linear algebra portion of the final exam. The examination will be held during the university's official examination period for the semester. Details will be posted on Wattle when available. Please note that the due date and return date for the end of semester exam indicate the first day of the end of semester exam period, and the the date official end of semester results are released on ISIS, respectively. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode/venue for the exam.

Value: 2 %
Learning Outcomes: 1,4

Small Group Discussion Forum

Due to the constraints of remote learning, which some students require, there are fewer opportunities to engage in informal mathematical community building and discussion. For all students, 2% of the final mark in MATH1116 will be associated with active participation in online group discussions conducted via a special Small Group Discussion forum on Wattle. These points will be readily available to students who engage in this activity throughout the semester.

## Online Submission

You will be required to electronically make a declaration concerning academic integrity, as part of the submission of your assignments. Please keep a copy of the assignments for your records. MATH1116 does not use Turnitin, having been granted an exemption: submission of assignments is via Gradescope and/or MATLAB Grader.

## Hardcopy Submission

All assignment submission is electronic.

## Late Submission

Individual assessment tasks may or may not allow for late submission. The policy regarding late submission is detailed below:

• Online Quiz Questions: Late submission is not permitted for MATLAB Grader questions. This also applies to any timed assessment that might be held during scheduled class times.
• Show Working: Late submission of the show working component (i.e., the portion submitted via Gradescope) of the assignments without an extension is 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 the release of solutions.

## 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.

## Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions 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

Resubmission of assignments is not permitted in MATH1116, except that it is possible to update an early submission of an assignment up until its due date and time.

## Privacy Notice

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

 AsPr Joan Licata 61252903 joan.licata@anu.edu.au

### Research Interests

Low-dimensional topology and contact geometry.

### AsPr Joan Licata

 By Appointment

## Instructor

 Dr Griff Ware 61252431 griffith.ware@anu.edu.au

## Instructor

 AsPr Joan Licata 61252903 joan.licata@anu.edu.au

### AsPr Joan Licata

 By Appointment