Linear algebra part 2, Spring 2019

Lectures (hoorcolleges) will be on Wednesdays. Werkcolleges (and hence tests) will be on Mondays. The first werkcollege on Monday (1 April) is cancelled, since there would be no lecture before it.

Weekly tests

Please note that there will be weekly tests in the Werkcolleges, which will count towards your final grade.

Teacher: David Holmes.

Organisation

For the course "Linear algebra 2" (Lineaire Algebra 2) there are lectures ("Hoorcolleges") and exercise classes ("Werkcolleges"). In each werkcollege the last 20 minutes will be a test on the material from the course up to that point. This will count towards your final grade.

Where and when?

See timetable here. Rooms are not the same each week; the room schedule is here.

Required Literature

We will follow closely parts of the book "Linear algebra and its applications" by David Lay. Every student will need a copy of the book; for example, weekly exercises will be set from the book, and the tests will contain similar questions.

Assessment

Weekly tests

As noted above, there will be a short test held every week during the Werkcollege.

Examinations

There is one exam for the course, after the end of the course (see the timetable above). The exam will last 3 hours. It will cover material from the whole course, including that already covered in the weekly tests, and in LA1.

Past exam papers

A good number of past exam papers are available here. Most have solutions, some not. Please be aware that the course content has evolved, so there may be questions you cannot reasonably answer, and some topics may not be covered. But this should give you plenty of questions to practise on.

There will be 6 tests in total. Each test will count towards your grade if and only if it increases your grade compared to your exam grade. This means that it makes sense to attempt every test, and if a test goes badly it will not decrease your final grade.

The exact formula is as follows. Write E for your grade (0-10) on the final exam, and T1, ..., T6 for your test grades (0-10). Let Ti' = max(Ti, E). Then your final grade is

1 + 0.9*(0.75*E + 0.25*(T1' + ... + T6')/6)

This is different from the formula for LA1, with practical consequenes including:

- even if you get a 10 on the first 4 tests, it's still worth trying the last two;

Homework and classes

Each week, some problems from the book will be suggested. These will not be graded, and will not count towards the final grade. However, you are extremely strongly recommended to attempt all the problems - the problems in the short tests and the final exam will be similar, and past experience suggests that ability to do he homework problems is a very strong predictor of success in the course. The problems will be discussed during the classes, and you will have the opportunity to obtain help on problems you found difficult.

Office hours

Office hours by appointment in room 233 in Snellius.

Content and detailed timetable

The first column is the date of the monday of the week (note the lectures and the exercise classes are on thursdays). The second column refers to chapters of the course book "Linear algebra and its applications" [Lay]. The final column contains the reccomended exercises from [loc.cit]; `H1.1:4,8' means exercises 4 and 8 from the end of chapter 1.1 of the book.
 Week begins Lecture Homework 01/04/2019 4.1, 4.2 Homework sheet Solutions 8/04/2019 4.3, 4.4, 4.5, 4.6 Read the section `Subspaces of a finite dimensional space' in the textbook. Read briefly chapter 4.6, in particular the Rank Theorem. Homework sheet Solutions 15/04/2019 5.1, 5.2, beginning of 5.3 Homework sheet 3. Solutions 29/04/2019 5.3, 6.1 Homework sheet. Solutions. 6/05/2019 6.2 6.3, (not Properties of Orthogonal Projections), 6.4 (not QR factorisation) Homework sheet. Solutions. 14/05/2018 6.5 (not Alternative Calculations of Least-Squares Solutions), 6.6 Homework sheet. Solutions. Start revising for exam. Attempt the LA2 2018 retake exam ready for next lecture.
--> At present this timetable is only approximate, and will be updated during the semester.
David Holmes <holmesdst@math.leidenuniv.nl>