Week 1: September 11-15, 2017.

  • Required Reading: Appendices C and D, including things that were not covered in class. Some comments:
  • My office hours are set for Thursdays, 1:30-2:30 or by email appointment. (Not Tuesdays as originally announced.) I'm also available right after Thursday lectures -- Tuesdays are not so good since I need to teach another class.
  • There will be a Putnam orientation session, with free pizza , on Friday, September 15, 4-6 in WB 116. For details, see here
  • This coming Tuesday (Sept 18) there will be a written quiz during the second half of class. This quiz does not count towards the course mark in any way, so it won't be written under formal `exam conditions'. However, the quiz will be graded by out TA's, scanned, and returned via email. The quiz will be about preliminaries (sets, functions), and possibly a question or two from high school level calculus/algebra. The purpose of this quiz is to give you an idea where you stand in comparison to your peers. You'll get the statistics of class performance, and it's up to you to draw your conclusions from the result.
  • Homework: Assessment #1.
  • Some do's and dont's when writing proofs: We are ok with simple logic symbols such us $\forall,\ \exists, \Leftarrow, \Rightarrow, \Leftrightarrow$ provided that you use them properly . In case of doubt, plain words are often better. Please do not use the $\therefore$ symbol since this is very uncommon in mathematical writing. Also, some other logic symbols such as $\land$ and $\lor$ are not commonly used in math texts (outside of mathematical logic), it's better to use words. Finally, avoid the use of $\times $ for multiplications (of numbers etc) since there are too many other meanings attached to this symbol -- the cross product of vectors, the variable $x$, and so on. (Use $\cdot$ instead.)
  • Additional Homework (not to be handed in):
  • Let $R$ be the set of rational functions on a real variable $x$. The elements are thus functions $f$ that can be written as quotients of polynomials, e.g. $$ f(x)=\frac{1+x^2}{1-2x-x^4}.$$ The domain of definition of $f$ is the set of all $x$ for which the denominator is non-zero. We identify two such functions if they coincide on their domain of definition, for example, $\frac{x}{x}=1$. Is this $R$ a field?
  • Tutorials will start this coming week. If you couldn't get into the tutorial of your choice, please note that neither me or our TA's deal with enrolment into tutorials, and we cannot help to `get you in'! Typically, in a couple of weeks once some students migrate to MAT223, space in tutorials will free up. The assignments and tests for this course are independent of tutorials.