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

Additional Course Costs

Nil

Examination Material or equipment

No materials are allowed for the final exam.

Recommended Resources

Recommended textbooks

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

I. Herstein, Abstract algebra.

J. Rotman, Advanced Modern Algebra (Graduate Studies in Math 114)  

There are a variety of online platforms you will use to participate in your study program as a whole. 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:

• written comments
• verbal comments
• 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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

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
7	More group actions, Sylow theorems	problem set
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	Learning Outcomes
Weekly Assignments	30 %	1,2,3,4
Quizzes	20 %	1,2,3,4
Final exam	50 %	1,2,3,4

* 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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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-person lectures and workshops are held on the main Acton campus of ANU. Students are expected to attend in-person; recordings of lectures will be made available through the Echo360 system where possible. Students are encouraged to discuss material with each other as an aid to learning, however the write-up of assignment solutions must be a student's own individual work. Collaboration in solving assigned problems must be acknowledged in writing on the submitted assignment.

Examination(s)

Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.

Assessment Task 1

Weekly Assignments

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. Assignments are to be submitted via the Gradescope platform. It is intended that the sets will be returned within 2 weeks after submission. The assignment with the lowest grade will be dropped from the average. Further details can be found on the Course Wattle site.

Assessment Task 2

Quizzes

There will be at least 8 quizzes throughout the semester, during workshops. Each quiz will be marked out of 4 marks. A student's total marks from their quizzes will be added together, and the lesser of that total or the maximum cap of 20, will be be the mark (out of 20) that contributes 20% towards their overall course grade.

Assessment Task 3

Final exam

An end of semester examination is included in the assessment. The examination will be held during the university's official examination period for the semester. Details will be posted on Wattle when available. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode/venue for the exam.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

Assignments will be submitted online, through a system to be explained on Wattle. 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

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

It is intended that assignments will be returned with feedback within two weeks of submission.

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 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.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
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.

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 Access 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 all ANU students