• Class Number 8565
• Term Code 3060
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Griff Ware
• LECTURER
• Dr Griff Ware
• Dr Joan Licata
• Class Dates
• Class Start Date 27/07/2020
• Class End Date 30/10/2020
• Census Date 31/08/2020
• Last Date to Enrol 03/08/2020
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

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

## 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

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.

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 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 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 Matrices (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 Understanding of the content will be tested regularly and formatively via the weekly assignments and via the summative exams. All course activities will be accessible remotely.
2 Real analysis content to be covered: Improper Integrals Limits and Continuity in R^n Integral Calculus of Functions from R^n to R Differential and Integral Calculus of Functions from R to R^n Differential Calculus of Functions from R^n to R Infinite series of real numbers Understanding of the content will be tested regularly and formatively via the weekly assignments, and via the summative exams. All course activities will be accessible remotely.

## Tutorial Registration

Workshop registration will be via the course Wattle site. Workshops begin in Week 3.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Weekly Assignments 27 % 31/07/2020 06/11/2020 1,2,3,4
Mid-semester Examination 30 % 31/08/2020 26/09/2020 1,2,3,4
End of Semester Examination 40 % 05/11/2020 03/12/2020 1,2,3,4
Class Engagement 3 % 31/07/2020 30/10/2020 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.

## Examination(s)

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: 27 %
Due Date: 31/07/2020
Return of Assessment: 06/11/2020
Learning Outcomes: 1,2,3,4

Weekly Assignments

Weekly Assignments which involve both an online quiz component (using the WebAssign system) and a written component (submitted online via PDF upload to Wattle) will be due from Week 2 onwards. A student’s lowest Assignment score will be discounted, and the average of their remaining Assignment scores will constitute 27% 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 textbook and 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.

The date range for this task indicates the approximate due date for the first assignment, and the approximate return date for the last assignment. It is intended that the marked assignments will be returned within 14 days after submission. Further details can be found on the course Wattle site.

Value: 30 %
Due Date: 31/08/2020
Return of Assessment: 26/09/2020
Learning Outcomes: 1,2,3,4

Mid-semester Examination

A mid-semester examination is included in the assessment. The examination is likely to be held in Week 6 or Week 7, and details will be posted on Wattle when available. The dates specified for this task are the first and last days of Weeks 6 and 7, respectively.

Value: 40 %
Due Date: 05/11/2020
Return of Assessment: 03/12/2020
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 for both the linear algebra and analysis parts of the course. Specific details about the hurdle requirements are given via Wattle. The examination will be held during the university's official examination period for the semester (the date specified for this task is merely the first day of the exam period: the exam will probably be on a different day). Details will be posted on Wattle when available.

Value: 3 %
Due Date: 31/07/2020
Return of Assessment: 30/10/2020
Learning Outcomes: 1,4

Class Engagement

Due to the constraints of remote learning, there are fewer opportunities to engage in informal mathematical community building and discussion. 3% of the final mark in MATH1116 will be associated to active participation in online group discussions. These points will be readily available to students who engage in this activity throughout the semester.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignments. Please keep a copy of the assignments for your records. MATH1116 does not use Turnitin.

## Hardcopy Submission

All assignment submission is electronic, via Wattle.

## Late Submission

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

• Online Quizzes: Late submission is not permitted for the online quizzes. This also applies to any timed assessment that might be held during scheduled class times.
• Show Working: Late submission of the show working component 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 via Wattle.

## 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.

## 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

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

Banach Algebras

### Dr Griff Ware

 By Appointment

## Instructor

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

### Dr Griff Ware

 By Appointment

## Instructor

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