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:

• 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 - real symmetric matrices and quadratic forms, Hermitian matrices, canonical forms.
• Set Theory - cardinality.

Note: This is an HPC. 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:

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

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.)

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). 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 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	problem set
2	Examples, Homomorphisms	problem set
3	Equivalence Relations, Cosets, Modular Arithmetic	problem set
4	Correspondence Theorem, Product Groups, Quotient Groups	problem set
5	Free Groups, Generators and Relations	problem set
6	Group Actions	problem set
7	Rings, Homomorphisms, Ideals	problem set, mid-semester exam anticipated
8	Quotient Rings	problem set
9	Product Rings, Maximal Ideals	problem set
10	Modules, Free Modules	problem set
11	Diagonalising Integer Matrices	problem set
12	Generators and Relations, Structure of Abelian Groups	problem set

Tutorial Registration

Please see Wattle. Workshops are optional and will begin in Week 3.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Problem sets	40 %	29/07/2019	31/10/2019	1,2,3,4
Mid-semester exam	20 %	16/09/2019	25/09/2019	1,2,3
Final exam	40 %	31/10/2019	28/11/2019	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:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

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. 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.

Examination(s)

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 indicate the approximate timeframe in which the exam will be held and results returned to the student (official end of Semester results 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

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.

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 1week after submission. Further details can be found on the Course Wattle site.

Assessment Task 2

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 and the ANU Examination Timetable to confirm the date, time and location of the mid semester exam.

Assessment Task 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 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.

Academic Integrity

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.

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. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

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 within one week.

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

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.
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 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