G11LMA: LINEAR MATHEMATICS

For Spring Semester material see Dr Tew's web page http://www.maths.nott.ac.uk/personal/rht/g11lma/

See below for

• Module Information
• Handouts and additional documents
• Coursework and solutions
• Miscellaneous links of interest

Module information for 2003 to 2004

• Credits: 20
• Duration: approximately 40 lectures, two lectures a week plus a share in the Core problem classes and tutorials throughout the year, starting Tuesday September 30 2003.
• Lecturers
  • Autumn Semester: Dr J. F. Feinstein, room C301 Maths/Physics, email Joel.Feinstein@nottingham.ac.uk
  • Spring Semester: Dr R.H. Tew, room B22 Pope, email Richard.Tew@nottingham.ac.uk
• Lecture times (Autumn Semester): Tuesday 14:00 Chemistry X1 (LLT) and Thursday 15:00 Pope C16.
• Office hours: Dr J.F. Feinstein, room C301 M&P: See the web page http://www.maths.nott.ac.uk/personal/jff/ttnow.html for details of Dr Feinstein's timetable and office hours.
• Brief content description: The module introduces students to many concepts and techniques of mathematics that will be used in subsequent modules. Firstly the basic concepts of complex numbers, vector algebra and matrix algebra are established. Then these ideas are extended to vector spaces, inner product spaces and quadratic forms. Throughout the emphasis is on developing the theory to provide techniques that are widely applicable.
• Prerequisites: A-level Mathematics (normally grade B or above) or equivalent.
• Corequisites: G11ACF: Analytical and Computational Foundations, G11CAL: Calculus.
• Books:
  • Category 1: Almost ideal for the whole module, we strongly recommend students to buy this book.
    • H. Anton and C. Rorres, Elementary Linear Algebra, applications version, Wiley, ISBN 0471170526.
  • Category 2: Extremely useful references which the students may well find worth buying
    • W. Keith Nicholson, Elementary Linear Algebra, McGraw-Hill, ISBN: 0070911428
    • J. Bowers, Matrices and Quadratic Forms, (mainly for Spring Semester), Butterworth-Heinemann, ISBN: 0340691387
  • Category 3: Other useful references
    
    1. R B Allenby, Linear Algebra, Modular Mathematics, Arnold paperback.
    2. T S Blyth and E F Robertson, Matrices and vector spaces, Essential Student Algebra, Volume 2, Chapman and Hall, 1986.
    3. T S Blyth and E F Robertson, Linear Algebra, Essential Student Algebra, Volume 4, Chapman and Hall, 1986.
    4. C W Curtis, Linear Algebra, an Introductory Approach, Springer-Verlag.
    5. P R Halmos, Finite-dimensional vector spaces, Springer-Verlag.
    6. I N Herstein and D J Winter, A primer on Linear Algebra, Macmillan 1988.
    7. S. Lang, Introduction to Linear Algebra, 2nd edition, Springer-Verlag 1989.
    8. S. Lang, Linear Algebra, 3rd edition, Springer-Verlag 1987.
    9. David C. Lay, Linear algebra and its applications, (paperback + CD ROM) Pearson Higher Education
    10. S MacLane and G Birkhoff, Algebra, 2nd edition (more advanced and abstract), American Mathematical Society 1999.
    11. Larry E. Smith, Linear Algebra, Springer-Verlag.
• Further information: Further details, including details of assessment and a brief module syllabus, are included in the Core Mathematics Booklet.

Handouts and additional documents

The following documents are currently available from the module web page. It appears that, for printing diagrams, the postscript version prints better on many PCs. On a PC you can view and print postscript using the shareware program GSview, available from http://www.cs.wisc.edu/~ghost/gsview/

• Module information sheet  (this document).
• Autumn Semester Documents
  • Provisional blow-by-blow account for Autumn Semester: ps, pdf
  • Actual blow-by-blow account for Autumn Semester (now complete): ps, pdf
  • Numerical solutions to selected problems from lecture notes: ps, pdf
  • Chapter 1, Complex Numbers, full lecture notes: ps, pdf
  • Chapter 1 slides (4 slides per page, 29 slides): ps, pdf
  • Formulae for cos(3t) and sin(3t) obtained using complex numbers: ps, pdf
  • Chapter 2, Vector Algebra and Geometry, full lecture notes: ps, pdf
  • Chapter 2 slides (4 slides per page, 58 slides): ps, pdf
  • Chapter 3, Matrix Algebra, full lecture notes (including a correction to a misprint in Rule 3.55): ps, pdf
  • Chapter 3 slides (4 slides per page, 87 slides, including the correction to Rule 3.55): ps, pdf
  • Chapter 4, Linear Systems, full lecture notes: ps, pdf
  • Chapter 4 slides (4 slides per page, 38 slides): ps, pdf
  • Chapter 5, Eigenvalues and Eigenvectors, full lecture notes (heavily based on R.H. Tew's 2002-3 Spring Semester lecture notes, with very minor modifications by J.F. Feinstein. Note that there will be more differences than in the earlier chapters between these notes and the slides): ps, pdf
  • Chapter 5 slides (4 slides per page, 7 slides): ps, pdf

Coursework (problems/exercises)

• Numerical solutions to selected problems from lecture notes: ps, pdf
• Problems on Chapters 1-5 (Autumn Semester) for use in Core problem classes and tutorials: ps, pdf
• Solutions to problems on Chapters 1-5 (Autumn Semester): ps, pdf
• Assessed Coursework 1: this question sheet is not available online.
• Solutions to Assessed Coursework 1: ps, pdf
• Sample questions on Autumn Semester Chapters 1-4 (of similar style, length and difficulty to typical exam questions which could be set on this material): ps, pdf
• Solutions to sample questions on Autumn Semester Chapters 1-4: ps, pdf
• Solutions to 2002-3 G11LMA examination paper: ps, pdf

Miscellaneous links which may be of interest:

• Catalogue of Modules, entry for G11LMA: Linear Mathematics
• Spring Semester material (Dr Tew's web page)
• Core home page [an error occurred while processing this directive]

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