July 21

Saturday July 21, 2007 7:40 am Lethbridge

It is +19 C with a high forecast of +30 C. Sunrise 5:47 Sunset 21:29 Hours of daylight: 15:42

A. Morning Musings

7:40 am

I slept in this morning, likely because the air is much cooler. I feel much more refreshed on waking than during many of the days during the last couple of weeks when it was too hot to be pleasant. And having a cup of coffee beside me is also good.

My mathematics hobby is finally progressing, slowly and steadily. I have completed all of the problems in chapter 1 of "The Humungous Book of Calculus Problems". These were all on "Linear Equations and Inequalities". The first eight chapters are all preparatory to the chapters on limits and differention and integration. I am not expecting too much difficulty with any of the 28 chapters in the book since I once took courses more advanced than any of this, but that was 40 years ago, and there has not been any real exposure to this material in that time. Chapter 2 is on "Polynomials".

The Herstein book, "Abstract Algebra", is another story. The notation is a bit daunting, and there appears to be a greater emphasis on proofs, which is fine once one gets a sense of how to do these, but the very first problem in the book is making me think. I think the Schaums Outline on the same topic will be a valuable resource. I think I will begin with it and work through the material on chapter 1 "Sets". My original idea was to alternate one hour sessions between calculus and abstract algebra. I will now see how that works in practice.

I will leave the two discussion boards on Fountain Pens and Model Trains until later in the day.

Immediate	Description	Time
Technology	Continue creating a tutorial web site: general sequence	1 hr
Literature	Continue reading "Kafka on the Shore" by Haruki Murakami	1 hr
Mathematics	Begin ch. 1 "Sets" of "Modern Abstract Algebra"	1 hr
Mathematics	Complete problems 2.1 - 2.? of "The Humongous Book of Calculus Problems"	1 hr

C. Actual Learning Activities

8:00 am

Mathematics 22

July 21, 2007

8:00 am

I am about to begin looking at the Schaum's Outline book, "Modern Abstract Algebra", by Frank Ayres.

Modern Abstract Algebra (1965) Frank Ayres, Jr.

Chapter 1 Sets

I am going to continue using handwritten notes and then scanning the session's work onto these web pages.

Here are my scans (original at color - magazine, 200 dpi, export at width of 600 pixels) of the problems I completed in a one hour session this morning.

algebra

2:50 PM

My approach to these notes is quite different than the approach I am using with calculus. With calculus, I am simply working my way, slowly and carefully, with annotations applied in red ink when I compare my answer with that provided in the book.

With abstract algebra, most of the terms and notational conventions are sufficiently new to me that I want to make some notes that capture the essential terms, definitions, and notational conventions as well. I also expect to move back and forth between the Hernstein textbook and the Schaum's outline.

I have begun with the Schaum's outline and have made notes for the first 3 pages. I have yet to tackle any problems. I had no difficulty understanding the elementary terms for set theory involving intersection and union, but the idea (and notation) of two complementary sets was new to me.

The one example, of the roots of a complicated algebraic expression expressed as a subset of a specified universal set was also new to me, but this is something I encountered a few months ago when reading a book about symmetry, so I already appreciate that the approach will eventually turn out to be very powerful. It is exciting to begin this topic. It is one that I hope to become proficient with.

3.15 PM

Now that I have the math books that I feel I need, it is important that I set aside a minimum of 2 hours/day to work on some topic within either calculus or abstract algebra.