Thursday, May 3
5:50 am
It is -2 °C, with a high forecast of +13 °C.
From the Environment Canada website:
Today Mainly sunny. Increasing cloudiness early this afternoon. Wind becoming southeast 20 km/h near noon. High 13. UV index 6 or high.
Tonight Clearing late this evening. Low plus 2.
There is a good frost on the rooftops and vehicles this morning.
6:20 am Musings
I finally feel that I am back in the grove.
I have been following a regular diet and fitness routine for just over 2 weeks and am already feeling the difference in terms of well-being and energy levels. My 3 "free" sessions are now over. The next step is to join the club and make a longer term commitment. This is a no-brainer. Health is worth it.
Tracking information on some books I ordered from Amazon indicates they left Calgary this morning. I assume they will arrive today, although the estimated arrival date is tomorrow.
I want to visit a second photography shop in town and see if they have the Canon lens I am seriously considering purchasing. It never hurts to compare prices and subsidiary factors such as maintenance contracts. I am also looking for an Ontario wine that is highly recommended.
There are many books that I could begin reading.
7:00 am Life
This is too good. I have just searched the Web for information on an Ontario wine that I have heard is very good. The wine is a Reisling from Tawse Sketches of Niagara (2009). Here is one of the reviews:
"With an enticing nose, it is on the palate where this wine really delivers. It has a lot of bright fruit character with big notes of citrus, green apple and peach. The acidity is racy and mouthwatering with a hint of petrol sneaking in already. Enjoy now, this wine is patio ready!" Only a Canadian review would include "a hint of petrol sneaking in" as a plus.
8:10 am Mathematics
I have begun actually "doing" some mathematics using "A Book of Abstract Algebra" by Charles Pinter (1990).
Chapter 2 Operations [p. 19 - 24]
I have completed all 6 exercises in part A (Examples of Operations) and the first exercise in part B (Properties of Operations). However I am not sure that I am doing part B properly. I want to reread this before continuing. I feel that I have a good grasp of the idea of an operation on a set of elements but am not sure that I am manipulating the symbols properly when working with the identity and inverse elements.
It was a pleasure to be using a fountain pen again.
I recall reading something a while ago that said that we are no longer teaching cursive writing in elementary school. I can see this as not being overly problematic when considering the move to keyboards and screens, but it seems to me that it will have major repercussions for mathematics and by extension to other areas that use mathematical notation such as science and statistics. Creating a mathematical expression using current software is cumbersome at best and it definitely interferes with the flow of thinking.
I want to adopt a two-fold approach to my learning by alternating my activities between two books. The second book is the 2006 book, "Fearless Symmetry" by Ash & Gross. This book is 15 years newer and has a more modern flavor. I started this book a few years ago and then let it go. I want to try again. I will begin with a dialogue between me and the book and then move to cursive notes when the symbolism suggests that is a good idea.
Chapter 1 Representations
Ash: " ...the basic concept of representation ... is the key concept underlying the number-theoretic methods of Galois representations" [p. 3]
Me: representation is very similar in nature to the idea of an operation (Pinter). But I have no idea of what a Galois representation is.
Ash: "Representations ... explain one thing by means of another. The object we want to understand is the 'thing': ... The object that we know quite a bit about already, to which we compare the source via a representation, we call the standard object." [p. 5]
Ash: They then provide a series of definitions.
- A set is a collection of things, which are called the elements of the set.
- A one-to-one correspondence from a set A to a set B is a rule that associates to each element in A exactly one element in B, in such a way that each element in B gets used exactly once, and for exactly one element in A.
- A function from a set A to a set B is a rule that assigns to each element in A an element of B.
- A morphism is a function from A to B that captures at least part of the essential nature of the set A in its image in B.
- A representation is a morphism from a source object to a standard target object.
"When A and B have some additional 'structure' (e.g. they are finite sets, or ordered sets) and we restrict the possible morphisms from A to B to have something to do with that structure ... then the existence of a representation from A to B gives us some information about A in terms of the standard object B (e.g. how many elements are there in A)
Me: The setting up of these definition may seem a little pedantic, but it leads to clarity of thought within this restricted domain. The ideas of this chapter are almost identical to the ideas of an operation that Pinter describes. Slightly different terminology, and perhaps nuances of interpretation, but very, very similar. So far, so good. Each book reinforces the other.
2:00 PM Literature
I have selected a Canadian novel for my next read.
Here is a sentence from the first page: "Every beach has a particular acoustic signature ...".
Then a few pages on, while describing the contents of a closet, "numerous paperback novels, abundantly annotated". I thought I was the only one who yellow-highlighted novels and made notes in the margin." Dickner and I are kindred spirits. I am looking forward to the rest of this book.
The books I ordered from amazon.ca arrived this afternoon.
- "Sum" (2009) by David Eagleman
- "The Well at the World's End." (2011) by A. J. Mackinnon
- "No Trace" (2004) by Barry Maitland
- "All My Enemies" (1996) by Barry Maitland
- "The Reader" (1997) by Bernhard Schlink
9:00 PM Life
While shopping today I bought a package of Tazo Zen green tea for our Keurig coffee machine. It it really quite good for a late evening drink.