## ALGEBRA with GEOMETRY

### STUDENT INFO for MISS

Main page
| About the course
| Course contents
| Test scores

You may download my lecture notes on

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 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

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.