• Class Number 6042
• Term Code 3260
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Anand Deopurkar
• LECTURER
• Dr Anand Deopurkar
• 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 Algebra 1: Groups, Rings and Linear Algebra (MATH2322)

Algebra 1 is a foundational course in Mathematics, introducing some of the key concepts of modern algebra. The course leads on to other areas of algebra such as Galois Theory, Algebraic Topology and Algebraic Geometry. It also provides important tools for other areas such as theoretical computer science, physics and engineering.

Topics to be covered include the theory of groups and rings:

• Group Theory - permutation groups; abstract groups, subgroups, cyclic and dihedral groups; homomorphisms; cosets, Lagrange's theorem, quotient groups; group actions; Sylow theory.
• Ring Theory - rings and fields, polynomial rings, factorisation; homomorphisms, factor rings.

As well as additional topics selected from:

• Linear Algebra - unitary matrices, Hermitian matrices, canonical forms.
• Modules - free modules, presentations, classification of finitely generated abelian groups.

Note: This is an Honours Pathway Course. It emphasises mathematical rigour and proof and develops modern algebra from an abstract viewpoint.

## Learning Outcomes

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

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

Nil

## Examination Material or equipment

No materials are allowed for the exams.

## Required Resources

Artin's "Algebra" textbook. (Any edition is acceptable, although the 2nd edition and later are preferred.)

Recommended student system requirements

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, 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 photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

## Staff Feedback

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

• feedback to whole class, groups, individuals, focus group etc

## 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

This class has an add-on (ASE) which is optional for undergraduates. The add-on will count for 25% of the mark for enrolled students, and in this case the assessment noted above will be scaled by 75%.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Groups, subgroups, cyclic groups problem set
2 Cosets, Lagrange's theorem, homomorphisms, normal subgroups problem set
3 Groups of small order, Cayley's theorem, permutation groups problem set
4 Quotient groups, isomorphism theorems, correspondence theorems problem set
5 Free groups, generators and relations, symmetries of plane figures problem set
6 Dihedral groups, crystallographic groups, orthogonal groups, groups in physics problem set, mid-semester exam anticipated (week 6 or 7)
7 More group actions, Sylow theorems problem set, mid-semester exam anticipated (week 6 or 7)
8 Rings, examples, homomorphisms, ideals problem set
9 PIDs, quotient rings problem set
10 Prime ideals, maximal ideals, correspondence theorems problem set
11 Modules, linear algebra over a ring problem set
12 Applications to finite abelian groups problem set

## Tutorial Registration

Workshops will begin in week 2. Please see Wattle for more information, and note that workshop registration will be via MyTimetable. 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
Problem sets 30 % * * 1,2,3,4
Mid-semester exam 30 % 29/08/2022 23/09/2022 1,2,3
Final exam 40 % 03/11/2022 01/12/2022 1,2,3

* 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

Students are encouraged to discuss material with each other as an aid to learning. Collaboration in solving assigned problems must be acknowledged in writing on the submitted assignment. Remote participation will be possible for students who can't be in Canberra due to the pandemic. The exact details will be given on the first week of the semester according to the situation and will be adapted according to further developments.

## 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 mode of the exam.

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

Problem sets

Problem sets are the most important method for mastering the course material. Students will be assessed on both the correctness and clarity of their arguments.

Problem sets are due each week throughout the semester. It is intended that the sets will be returned within 1 week after submission. Further details can be found on the Course Wattle site.

Value: 30 %
Due Date: 29/08/2022
Return of Assessment: 23/09/2022
Learning Outcomes: 1,2,3

Mid-semester exam

The mid-semester exam is a hurdle for the course; students who do not take the exam will receive an NCN.

Please check the course Wattle site for exam details. The exam will be offered in week 6 or 7.

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

Final exam

The final exam is a hurdle for the course; students who do not take the exam will receive an NCN.

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please see posted details on Wattle.

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 electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. MATH2322 does not use Turnitin, having been granted an exemption.

## Hardcopy Submission

All problem sets must be submitted electronically. Students may use mathematical typesetting software or scan their handwritten assignments.

## Late Submission

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

• Late submission permitted. 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 more than 2 days past 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 generally be returned with feedback in a timely manner.

## 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

Students may not generally resubmit marked assignments. In the case that a marking error is suspected, students should write an explanation of what error they believe was made and submit it to the lecturer within three days.

## 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

 Dr Anand Deopurkar anand.deopurkar@anu.edu.au

### Research Interests

Algebraic geometry, algebra, representation theory, number theory

### Dr Anand Deopurkar

 By Appointment

## Instructor

 Dr Anand Deopurkar 61252908 anand.deopurkar@anu.edu.au

### Dr Anand Deopurkar

 By Appointment