ALGEBRA with GEOMETRY
STUDENT INFO for MISS
| About the course
| Course contents
| Test scores
You may download my lecture notes on
fields and complex numbers
matrices and linear mappings
Jordan block matrices.
and problem sheets for
Tutorial 1 - complex numbers
Tutorial 2 - complex numbers ctd.
Tutorial 3 - polynomials, residues mod n
Tutorial 4 - groups and fields
Tutorial 5 - vector spaces
Tutorial 6 - linear independence
Tutorial 7 - basis and dimension
Tutorial 8 - matrices
Tutorial 9 - systems of linear equations
Tutorial 10 - determinant, inverse matrix
Tutorial 11 - linear mappings, their matrices
Tutorial 12 - change of basis matrix
Tutorial 13 - eigenvalues, eigenvectors, diagonal matrices
Midterm 1 problems from recent years.
Hints and typical solutions can be found here.
Midterm 2 problems with hints.
Some other midterm 2 problems.
Sample Jordan-block problems with detailed solutions.
Sample 12 Jordan-block problems with answers (not solutions!). I only included Jordan matrix, since there are infinitely many correct change-of-basis matrices. When you find your own change of basis matrix you can easily verify your solution by matrix multiplication.
You will find here, here,
here, here, here and also here solutions to some old final exams.
There are also sample exam-level sets of problems (some from old exams): set 1, set 2, set 3, set 4.
Final exams from recent years0 )
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Below you will find some extra problems on:
Bases and dimension
Matrices and systems of equations
The sets are not necessarily disjoint with tutorial problem sheets, but I have noticed that the symmetric difference between corresponding sets is usually nonempty.