Math 281: Introduction to Mathematical Reasoning



Renzo's class



MWF 11– 11:50 am



ENG E 202








Office Hours







A concise Introduction to Pure Mathematics

M. Liebeck

Chapman &  Hall



PDF output

LaTeX source





1)      On various types of numbers

2)      On Rings and Fields




Worksheet on Cayley's Theorem

Worksheet on Linear Independence

Worksheet on Algebraic Numbers

Worksheet on Symmetric Polynomials




Exam 1 (take home due friday 10/10)

Checklist for Final



Office hours : official office hours are

·        Monday, 10-11 am

·        Wednesday, 12-1 pm

If you can't make it at those times, most of the time I should be able to arrange a meeting by appointment. Please use the office hours, come discuss problems, confusions , ideas, or simply to chat about math or to have a cup of tea.

The tables of the law for this class are contained in the following document:

Once you get settled, you are warmly invited to tell me what you
do and don't like about me and this class. I try my best to take criticism very well.

Click here to fill up the (anonymous)evaluation form!

Homework: here is the suggested homework (blue) and the due to be graded homework(red) . Remember that homework is due every Friday.

However, remember to do as much homework as you need. Each and everyone of us learns at his/her own very personal pace, and needs his/her own very personal amount of exercise!



Aug 29th

Given 6 square tiles of unit side-length, what are the possible perimeters of plane tilings?

PROVE your answer. If you come up with more than one proof, that’s even better.

MEDITATE on the process:

·        How did you get to the answer?

·        What strategies did you use for your proof?

TURN in one write-up per group. If you didn’t get to a proof, just write whatever you found, ideas, conjectures, possible strategies.

Sep 5th

Homework 1

Sep 12th

No-homework…projects in progress.

Sep 19th

Projects writeups due.

Sep 26th

Homework 2

Oct 13th

Homework 3

Oct 17th

Homework 4

Oct 20th

Recovery Homework 1 (This homework is REQUIRED for anybody who got less than 60% in the midterm)

Oct 24th

Homework 5

Oct 27th

Recovery Homework 2 (This homework is REQUIRED for anybody who got less than 60% in the midterm)

Oct 31st

Homework 6

Nov 14th

Homework 7

Dec 5th

Homework 8

Dec 12th

Write your own account of the proof of the theorem about algebraic numbers being a field.


NOTE: the account must NOT include all that we have done in class over the last two weeks. What I would like is a nice, condensed, streamlined product. You are allowed to state certain things without proving them, but you have to make clear what you prove and what you don’t.


This is an important homework (and I am considering possibly incorporating the evaluation of it into the final evaluation). Do it well, please!


Midterm exams.