##### Week 2: September 18-22, 2017.

** The quiz: ** On Tuesday we had a little `quiz', covering
some of the preliminaries for the course. The quiz was returned via
crowdmark. The median and mean scores were 11 and 10.9 out of 15,
respectively. I leave it up to you to draw conclusions. Just keep in
mind that last year, only 50 percent of initially enrolled students
managed to finish and pass the course. The `course change date' for changing from MAT240 to MAT223, is ** October 3 **. See this link for details.

** Tutorials: ** The tutorials started ** this **
week. Although the rooms are booked for two hours, the actual tutorial
won't go much over one hour. Following the `formal' part of the
tutorial, the TA will be available for additional questions. Please note that all our three TA's (Debanjana, Jeff and Ivan) also hold office hours, I
included the updated information (location, email addresses) on the course syllabus . (You may have to hit `refresh' if you downloaded this before.)

Required reading: Re-read Appendices A-D, and read Chapters 1.1 and 1.2.

In class, we covered: Meaning of the notation $P \Rightarrow Q$ and $P \Leftrightarrow Q$. More properties of fields, for example
$ab=0 \Rightarrow\ a=0 \mbox{ or } b=0$.
The field of complex numbers. Real and imaginary part, complex conjugate, absolute values, and their geometric interpretation in the complex plane. Basic properties (some of this will have to wait until next week): how to take the inverse of a complex number, geometry of multiplication of complex numbers, polar coordinates, triangle inequality $|z+w|\le |z|+|w|$, fundamental theorem of algebra (without proof).

Homework: ** Assignment #1 ** is due Friday 11:00pm. No late work is
accepted. ** Assignment #2 ** will be released before Friday 11:00 pm.

Additional homework (not to be handed in):
- Do examples with complex numbers! Problems with solutions can be found
on the web, for example
here
and many other places.
- Section 1.1: 3; Section 1.2: 1, 12, 18, 21; Section 1.3: 1, 19, 20, 22, 31

What's wrong with the calculation
$$ 1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}=i\cdot i=-1\ \ \ \ \ ??\ \ \ $$
Well, it assumes that $\sqrt{z w}=\sqrt{z}\sqrt{w}$ for complex numbers $z,w$, which is something one has to be careful about. It's true for positive real numbers, using the positive square root. The square root of a complex number is only given up to sign, and there's no consistent convention `fixing the sign' for which this formula would always be true.