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Lectures 2004

MAS212 Linear Algebra I

Course Organiser Dr Francis J. Wright; click to contact me or report problems with this web site.

This page was last updated on 08 January 2007.

Contents: Lectures; Classes; Coursework; Test; Exam; Missed Assessments; Text Books; Documentation

Other main links are listed down the left side of this page.

Synopsis

Value: 1.0 cu
Level: 2
Semester: 3
Timetable: Lecture periods 43, 49, 57; exercise classes 44, 3*48
Overlap: None
Prerequisite: MAS114 Geometry I (or MAS106 Matrices and Geometry); a stapler!
Description: A rigorous first course in linear algebra.  The ideas introduced previously for 2- and 3-dimensional space are developed and extended in a more general setting.  Definitions and examples of fields and vector spaces.  Subspaces, spanning sets, linear independence, bases, dimension, direct sums.  Linear mappings, kernel and image.  Matrices and matrix algebra.  Determinants.  Echelon form.  Eigenvectors and diagonalization.  Orthogonal diagonalization of a real symmetric matrix.

Lectures

Lectures start on Thursday 28th September 2006.  The timetable is as follows:

Day Time Place
Thursday 11 am 12 noon Drapers Lecture Theatre
Thursday 5 pm 6 pm Drapers Lecture Theatre
Friday 3 pm 4 pm Drapers Lecture Theatre

Full lecture notes are available on the web.  We will cover one chapter of the lecture notes per week except for test week.  Students are expected to attend every lecture and a register of attendance will be taken in lectures on a random basis.

Exercise Classes

Exercise classes start on Thursday 5th October 2006.  The timetable is as follows (except during test week, when there are no exercise classes):

Day Time Place Who
Thursday 10 am 11 am Maths G2 GL11 and LG11 students
Thursday 12 noon 1 pm Engineering 324 Students not taking Probability II
Thursday 4 pm 5 pm Engineering 324 Other students, surname A G
Thursday 4 pm 5 pm Engineering 325 Other students, surname H Z
Thursday 4 pm 5 pm Computer Science 338 CANCELLED

If possible, please attend the exercise class for which the first letter of your surname (family name) is in the range indicated above.  However, my current intention is to treat all the classes the same and the above distribution is intended only to divide students reasonably uniformly among the three classes, so if you cannot attend the designated class then just go to one of the other classes.  You are encouraged to ask questions about any aspect of linear algebra and not only about the current exercises!

Coursework

Exercise sheets will be available both on paper at the Friday lecture and on the web (see below) as PDF files, which you will probably want to print before you attempt them.  The PDF files will be synchronized with chapters of the lecture notes using a consistent naming scheme, i.e. "Exercises 1.pdf" will correspond to "Chapter 1.pdf", which are respectively the exercises and lecture notes for the first week of the course.

Coursework will be set each week except for test week and is primarily intended to encourage you to think about the material and so help you to understand it.  However, the first 10 exercise sheets will be assessed and contribute 10% (1% each) to your overall assessment.  Assessed coursework must be submitted by 5pm on the Friday of the week after it is covered in lectures; the submission date will be stated on each exercise sheet.  I strongly recommend that you attempt each week's coursework as soon as possible after the corresponding lectures and before attending the exercise class, so that you can ask for help on questions that are causing you difficulty.  It is not my intention that you should attempt the coursework from scratch within the exercise class; there will not be enough time.  I will provide exercise solutions on the web as both PDF and Maple worksheet files shortly after the submission date for each assessed coursework.

I encourage you to make informal use of Maple, which is available on the College Teaching Network, to help you with this course, either to check your coursework solutions or to guide you towards a solution, but you must submit conventional written solutions on paper to all assessed coursework.  (It is much faster to write mathematics by hand than to use a computer!)  Note that you will not have access to a computer for the test or exam.

Coursework Collection and Return

Assessed coursework must be placed in the blue box (second from left) on the ground floor of the Mathematics Building by the deadline of 5pm on Friday.  Multiple sheets of paper must be stapled together and not joined in any other way.  Do not submit coursework in any kind of envelope, folder or binder.

To have the marks for your assessed coursework recorded you must:
  • print your full name and student number clearly at the top of the first sheet,
  • print the module title and exercise sheet number clearly at the top of the first sheet,
  • staple separate sheets together, and
  • put your coursework in the right collection box (see above) before the deadline.

No exceptions will be made to these rules!

Marked coursework will be returned in exercise classes.  Any uncollected coursework will be put into cabinets in the Maths Office (Maths room 101), from where students will be able to collect it at these times during the first semester: Tuesdays 10:0012:00; Fridays 2:003:00.  The cabinets will be emptied at the end of the semester and, if necessary, mid-semester.

Marks

All available coursework and test marks will be sent automatically by SID, our departmental marks system, to the College Computer Services email address of each student taking the course.  Marks will be posted to students weekly on Saturdays and the first posting will be at the end of week 4.  Please check your marks regularly and report any errors or omissions to me immediately.

Complaints about coursework marks must be brought to my attention within two weeks of the submission deadline, i.e. approximately one week after the marked coursework is returned to you.  I will not consider complaints brought to my attention later than this unless there are extenuating circumstances.

Test Week

Test week is week 7, which is used as a reading week by some departments but not by Maths.  The timetable is different from the rest of the semester and is as follows:

Day Time Function Place
Thursday 9th November 2006 5 pm 6 pm Revision Lecture Drapers Lecture Theatre
Friday 10th November 2006 11:00 am 12 noon Test Great Hall
Test for Special Arrangement Students Maths B11

The test contributes 10% to the overall assessment.  It will be on the material covered in the first 5 weeks of the course, i.e. Chapters 15.  The rubric and style of the test will probably be similar to previous years (see below); calculators will not be allowed.  I will mark the test as quickly as my other commitments permit but it may take a few weeks.  Once I have marked your test you will receive your mark in the same way you receive other marks; some of you may receive your mark before others.

Final Examination

The final written examination in May contributes the remaining 80% to the overall assessment.  The rubric and style of examination paper will be the same as previous years (see below); calculators will not be allowed.

Missed Coursework, Test or Final Examination

The procedure to follow if you miss an assessment for a good reason is explained in the School of Mathematical Sciences Undergraduate Handbook, which is issued to all Mathematics students at the start of each year and can be accessed online.  You should either photocopy from the back of the handbook or print from below the appropriate form and submit it to the Pastoral Tutor for Mathematics, Prof. R. A. Bailey; see the instructions on the form for further details.

If your reason for missing the coursework or test is accepted by the Pastoral Tutor then you will be excused from the assessment, which means (for this course) that a missed coursework mark will be replaced by your average coursework mark and a missed test mark will be replaced by your final examination mark.

Text Books

No specific reference will be made to any text book during the course, but it can be very useful to have a text book for reference purposes and to provide a "second opinion".  The main text book that I use for this course, which I recommend, is Linear Algebra by Seymour Lipshutz, Schaum Outline Series (ISBN: 0071362002).  It normally costs about £10 and should be available from the College bookshop, although Amazon.co.uk may sell it (considerably) cheaper!  Other text books may be equally suitable.  Beware that text books may use different definitions from mine; if in doubt then use my definitions for this course.

Documentation

Course documentation is available on the web only.  Documents dated earlier than June 2003 are provided courtesy of Prof. David Arrowsmith, who taught this course for several years before I took it over from the academic year 20034.  If you have problems opening document files then here are some suggestions.

  • Lecture notes are available as both PDF (.pdf) and Standard Maple 10 worksheet (.mw) files.
  • Lecture notes for 2004 are still available as both PDF (.pdf) and Classic Maple worksheet (.mws) files.
  • Exercise questions will be available roughly weekly as PDF files.
  • Exercise solutions will be available after each submission deadline as both PDF and Maple worksheet (.mw) files.
  • Past examination papers since 2000 and model solutions since 2003 only are available separately as PDF files.  Please also read these brief notes about exam papers and solutions.
  • Past in-term test papers are available as PDF files.  From 2003 onwards they include model solutions, but model solutions from before 2003 are not available.  Note that before 2002 there were two tests per year held in weeks 5 and 10 but from 2002 onwards there has been only one test per year held in week 7.
  • Learning outcomes constitute the key objectives; a student who has mastered them all should be able to achieve at least a bare pass, but to achieve an A grade will require competence in most of the material covered in the published lecture notes (see above).
  • This eigenvector animation was generated from this Maple worksheet (.mws) file.
  • The 2004, 2005 and 2006 course questionnaire summaries are available as (partly scanned) PDF files.

I recommend Adobe Reader to read and/or print the Portable Document Format (.pdf) files.  If you experience any problems with the PDF files then please let me know.  (I currently generate PDF versions of Maple worksheets using the excellent free (GPL) PDFCreator printer driver, which provides a convenient interface to the excellent free tool Ghostscript.)

You need a reasonably recent version of Maple on your computer to read the Maple worksheets directly.  The .mws files were updated for 2004 using Classic Maple 9.5 on Windows XP and some of the worksheets contain a few embedded Microsoft Equation Editor objects.  If your software is not sufficiently compatible with mine then you may experience some problems, such as missing information.  If so then please use the PDF files.  The .mw files were updated for 2005 using Standard Maple 10 and are reliably readable only using Standard Maple 10.01 or later, but they do not contain any embedded objects and should be more portable.  See also this additional Maple Information.