Student info

ALGEBRA with GEOMETRY

Remote Lectures

You may download my traditional lecture notes here:
fields and complex numbers
complex numbers
polynomials
groups
vector spaces
linear mappings
matrices
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 2019-20 solutions.
Midterm 2 2018-19 solutions.
Final Exam 1 2018-19 solutions.

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 years
final_2015_FEB_10.pdf
final_2015_SEP_11.pdf
final_2016_FEB_11.pdf
final_2016_FEB_4.pdf
final_2016_SEP_8.pdf
final_2017_FEB_7.pdf
final_2018_FEB_06.pdf
final_2018_JAN_30.pdf

Below you will find some extra problems on:
Groups
Fields
Vector spaces
Bases and dimension
Matrices and systems of equations
The sets are not necessarily disjoint with tutorial problem sheets, but the symmetric difference between corresponding sets is (usually) nonempty.