- Class Number 6249
- Term Code 3160
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- AsPr Uri Onn
- AsPr Uri Onn
- Class Dates
- Class Start Date 26/07/2021
- Class End Date 29/10/2021
- Census Date 14/09/2021
- Last Date to Enrol 02/08/2021
This course introduces the basic concepts of modern algebra such as groups and rings. The philosophy of this course is that modern algebraic notions play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. This course emphasizes the application of techniques.
Topics to be covered include:
- 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.
- Linear algebra - unitary matrices, Hermitian matrices, canonical forms.
Note: Graduate students attend joint classes with undergraduates but are required to have a deeper understanding of the material, are expected to do extra work of a more theoretical nature and are assessed separately
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, 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
Additional Course Costs
Examination Material or equipment
No materials are allowed for the exams.
Artin's "Algebra" textbook. (Any edition is acceptable, although the 2nd edition and later are preferred.)
Herstein's "Abstract algebra" textbook.
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.
- 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
For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements
Students will be given feedback in the following forms in this course:
- written comments
- verbal comments
- feedback to whole class, groups, individuals, focus group etc
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.
|Week/Session||Summary of Activities||Assessment|
|1||Groups, Subgroups, Examples||problem set|
|2||Homomorphisms, Kernel, Image, Normal Subgroups, Isomorphism||problem set|
|3||Cosets, Lagrange's Theorem, Modular Arithmetic||problem set|
|4||Correspondence theorem, Products, Quotients, Homomorphism Theorems||problem set|
|5||Free Groups, Generators and Relations, Group Actions, Cayley's Theorem||problem set|
|6||Actions on Cosets, Class Equation, Cauchy's and Sylow's Theorems||problem set, mid-semester exam anticipated (week 6 or 7)|
|7||Rings, Examples, Homomorphisms, Ideals||problem set, mid-semester exam anticipated (week 6 or 7)|
|8||Quotient Rings, Homomorphism Theorems, Product Rings||problem set|
|9||Maximal and Prime Ideals, Fields and Domains, PID||problem set|
|11||Diagonalising Integer Matrices and Structure of Abelian Groups||problem set|
|12||Selected topics||problem set|
Please see Wattle. Workshops are optional and will begin in Week 3.
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Problem sets||30 %||*||*||1,2,3,4|
|Mid-semester exam||15 %||30/08/2021||24/09/2021||1,2,3|
|Final exam||30 %||04/11/2021||02/12/2021||1,2,3|
|Add-on module||25 %||*||*||1,2,3,4|
* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details
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:
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.
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.
There will be a mid-semester and a final exam. 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.
Assessment Task 1
Learning Outcomes: 1,2,3,4
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.
The date range for these tasks indicates the approximate due date for the first problem set, and the approximate return date for the last problem set. 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.
Assessment Task 2
Learning Outcomes: 1,2,3
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 and the ANU Examination Timetable to confirm the date, time and location of the mid semester exam.
Assessment Task 3
Learning Outcomes: 1,2,3
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 check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam.
Assessment Task 4
Learning Outcomes: 1,2,3,4
Students enrolling in the graduate version (MATH6118) of Algebra 1 are required to take the add-on module. This entails an additional lecture each week and has associated written and possibly oral assessment that will be announced on Wattle. The content of the add-on is not assumed in the regular lectures, but the add-on does assume that students are keeping up with the content of the main part of the course. Attendance and active engagement at the add-on lecture is expected each week.
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.
The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.
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. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.
For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.
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 after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.
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.
Assignments will generally be returned with feedback within one week.
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.
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 Diversity 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