# MATH2922 Linear and Abstract Algebra (advanced)

## General Information

This unit is offered in Semester 1.

Lecturer(s): Andrew Mathas

For further information on Intermediate Mathematics and Statistics, refer to the Intermediate Handbook. In particular, see the MATH2922 handbook entry for further information relating to MATH2922.

You may also view the description of MATH2922 in the central units of study database.

• Credit point value: 6CP.
• Classes per week: Three lectures, one tutorial and practice class.

Email enquiries about MATH2922 may be sent to MATH2922@sydney.edu.au.

Students: Please give your name and SID when emailing us. Anonymous emails will not be replied to.

Students have the right to appeal any academic decision made by the School or Faculty. For further information, see the Science Faculty web site.

Consultation hour  Tuesdays 1-2pm, Carslaw 718

## Course Description

Linear and abstract algebra is one of the cornerstones of mathematics and it is at the heart of many applications of mathematics and statistics in the sciences and engineering. This unit is an advanced version of MATH2022, with more emphasis on the underlying concepts and on mathematical rigour. This unit investigates and explores properties of groups, fields, vector spaces, matrices and linear transformations, developing general principles relating to the solution sets of homogeneous and inhomogeneous linear equations, including differential equations. Linear independence is introduced as a way of understanding and solving linear systems of arbitrary dimension. Linear operators on real spaces are investigated, paying particular attention to the geometrical significance of eigenvalues and eigenvectors, extending ideas from first year linear algebra. To better understand symmetry, matrix and permutation groups are introduced and used to motivate the study of abstract group theory. The unit culminates in studying inner product spaces, quadratic forms and normal forms of matrices together with their applications to problems both in mathematics and in the sciences and engineering.

Assumed Knowledge: A working knowledge of the linear algebra components of advanced first year mathematics.

There are three lectures, one practice class and one tutorial each week. Tutorials start in week 2.

Please see the Unit Outline for detailed information about Math2922, including more detail on assessment and outcomes.

Questions about MATH2922 should be posted on the EdStem discussion board. Confidential questions can be emailed to MATH2922@sydney.edu.au. If your is of general interest then you will be asked to post it on EdStem so that everyone can benefit from it. We may not reply to anonymous emails so please always include your name and SID.

All on-line resources, including lecture sumaries and the questions solutions for the tutorials and assignments, will be available for download from the MATH2922 the on-line resources page.

## Tutorials

You should attend at the time and place given on your timetable. See the timetable for the tutorial times. Please always take your lecture notes to the tutorial, so you can look up what you need to solve the problems.

Tutorial sheets are available online as PDF files from the resources page on the Friday of the week before the tutorial takes place. No hard copies will be distributed.

Tutorials are an integral part of the course. You can only learn mathematics (or any other subject) by doing problems yourself, so attending tutorials is absolutely essential for performin well in the course.

## Assessment

The assessment tasks for MATH2922 are weekly on-line quizzes, two assignments and a final exam. The breakdown of marks is as follows:

Weekly on-line quizzes - 10%
Each week you should complete the weekly on-line quiz by 11 pm Sunday. The on-line quizzes start in week 2, so the first quiz should be completed by 11pm March 18.

The questions in the quiz are drawn from material covered in lectures that week. The questions are chosen from a random pool, so that everyone will receive slightly different questions. You can take the quiz as many times as you like. Your best quiz mark before the due date will be recorded. At the end of semester your ten best quiz marks will be used to give you a mark out of 10 that will contribute 10% towards your total assessment.

You have one hour to complete each quiz. If you start a quiz within an hour of the closing time, you will only get the remaining time to complete it (not the full hour). After the quiz has closed you will be able to review your answers and you will be given the solutions.

Assignments - 20%
There will be two assignments, each worth 10%. They are due on the following dates:
Assignment 1: Monday 23th April
Assignment 2: Monday 28th May

All assignments must be submitted electronically as PDF files using TurnItIn in Canvas. Late assignments, or assignments that illegible or poorly scanned, will not be marked.

If it is favourable to the majority of students the Better Mark Principle from first year may be used.
Final exam - 70%
There will be a two-hour final exam. Only material covered in lectures and tutorials will be tested using questions addressing the outcomes listed in the unit outline. The exam will also contain questions on the theory and proofs, and not just problems to solve.

Please do not post direct questions about the on-line quizzes or the assignment questions on the EdStem discussion forum. A mark of 0 for the assessment task may be awarded to any student who does this. You are encouraged to ask questions in the forum about the quizzes and the assignments one week after the due date for the assessment task.

The university rules for special consideration/arrangement apply to all assessments. There is no need to apply for special consideration if you miss a lecture, practice class or tutorial. Special consideration requests for not submitting an on-line quiz will be considered only in exceptional cases because the final quiz mark is calculated using your best 10 quiz results, out of a possible 13 quizzes. The maximal possible extension for an assignment is 7 days.

## Reference Books

There are some additional references on the MATH2922 SageMath web page. Finally, the Open Textbook Initiative of the American Institute of Mathematics is a very useful repository of (free) open source mathematics books. In particular, if you go to the approved textbook section you can download several books on linear and abstract algebra.