Office hours: by appointment. I will be in Friday 6 January 10:30 - 12:30, in S125 (Malostranské nám. 25, 1st floor).
Lectures for the course Linear Algebra I in the winter semester of 2016
are given by Jiri Fiala
. Exam topics list
The online collection of exercises
provides further practice problems supplementary to those given in
may be helpful in tackling some of the exercises (just a few basic
commands are needed to perform the calculations needed for this course - you will be able to register for a Sage account
at the beginning of the semester).
Weekly exercises will be given as homework. These are not formally
graded, but students may be asked to
present solutions in the tutorial class the week after
the exercise sheet. Short tests on routine aspects of the
course will occasionally be given in class to check that all is going well.
Performance on homework exercises will not directly affect
your grade for the main course. However, if you intend to be graded for
the main course, you require a "pass" for the exercises. A pass/fail
grade for the exercises will be decided based on regular attendence and
participation in class, and
satisfactory performance on the
during the semester and the longer test at the end.
Exercise classes are
held at 14:00 on Tuesdays in semester
(except for Dean's Day on 8.11.2016) in
Room S6 in the MFF building in Mala Strana (lectures are in the same room at 9:00 on
Robert Beezer, A First Course in Linear Algebra
- a free online textbook.
includes video lectures and supplementary material to Gilbert
Strang's Introduction to Linear Algebra. Strang's own sample material etc.
Jiri Matousek's preliminary version of the recommended book Thirty-three miniatures: mathematical
and algorithmic applications of linear algebra.
M. Anderson and T. Feil, A First Course in Abstract Algebra: Rings, Groups, and Fields, CRC, 2015 (chapters 17-19 for groups).
F. Goodman, Algebra: Abstract and Concrete, edition 2.6
Answers to some excercises may take the
form of Sage worksheets posted online. Handwritten work on exercises
please hand in at the beginning of the following class for marking.
(Questions 1 and 2 for handing in 17
October; Question 3 collaboratively. In addition, if you do not know
Sage, please be sure to register for a Sage account
, and as a warm-up work through the worksheet entitled "Sage GS: Getting Started" which is at the bottom of this page
of the section on Solving Systems of Linear Equations in the online book A First Course in Linear Algebra
Elementary row operations
: supplement to
exercise class - includes proofs that elementary row operations
preserve solution sets of systems of linear equations.
. Gaussian Elimination Sage worksheet
Rank uniqueness numerical example (JF)
Computer package problem
(for practicing using Sage - guess pattern, check with calculation for larger matrices)
. No class due to Matriculation Day.
to Exercise Sheet 3 (Sage worksheet)
to computer package problem (Sage worksheet
Matrix properties exercise
. No class (Dean's Day).
Solution to problem 2 on exercise sheet 4
(Gauss elimination for matrix with variable entries).
K. Conrad, The 15-puzzle (and Rubik's cube)
. (In question 4, there was a missing cardinality sign around I(p) in the exponent of
(-1) which has now been corrected.)
TEST on basic definitions and examples on the following topics: Elementary row operations, Row echelon form, Systems of linear equations, Matrices, Groups, Permutations, Fields, Matrices over finite fields, Vector spaces, Linear independence, Bases.