Mathematics Chronology

8:30 am

I have had a quick look at most of the mathematics books on my shelves near my computer. It was relatively easy to place the titles into a table in my Project Mathematics web page where I monitor my progress in learning mathematics. However that page is more a place where I keep track of what I have done than a map for what I should be doing in the future. Calculus     Calculus (1998) Roland Larson, Robert Hostetler & Bruce Edwards   Calculus (1994) Michael Spivak   What is Mathematics? (1996) Richard Courant & Herbert Robbins   Calculus: An Intuitive and Physical Approach (1977) Morris Kline   The Calculus Tutoring Book (1986) Carol Ash & Robert B. Ash All five book take a different approach to the topic. The Larson book is the most "modern" in terms of comprehensiveness and use of graphics and imagery. It is also a traditional approach with a large number of problems that provide a high amount of drill and repetition in order for the skill of being able to "do" various types of problems to become automatic. It makes extensive use of technology to obtain graphs of complex situations. The Spivak book is much more theoretical and abstract with an emphasis on the ideas rather than the skill of applying different algorithms to different situations. One noticeable feature of this book is the large preliminary treatment of ideas that are necessary before discussing the concepts of differentiation and integration. The first 150 pages discuss the nature of numbers, functions , graphs, limits and continuity. There is a lot of basic mathematics here, but treated at a very sophisticated level. The Ash book is more like an abbeviated Larson book, much less sophisticated from a publishing perspective. The emphasis is not on the formalism of the topic but the general ideas and makes extensive use of hand-drawn sketches. Kline takes a number of practical problems as the starting point for a discussion of the ideas of calculus. Courant & Robbins describe mathematics in terms of its basic ideas and procedures. Overall strategy: I will try to read and do the exercises from both the Larson and the Spivak books in parallel. That is, I will cover the same topic in both books before moving on. The Larson book has an initial chapter on graphs and functions followed by a chapter on limits and continuity. Spivak begins with a chapter on numbers and then has separate chapters on functions, graphs, limits and continuity. For each chapter I will create a concept map (using Inspiration) as well as a mind map (using Mindmanager). I will then try to combine these two maps into a diagram that is a synthesis of both images. Technology continues to be problematic. Most of my mathematics software is specific to windows operating systems whereas I am now using a Mac for my core web authoring (using Dreamweaver). I need to get my windows version on the Mac up-dated for Word so I can use the notation. I also want to install Mathematica on this machine. There is nothing for it but to see what happens when I try this.

9:20 am Begin installing MathType for windows. That was easy. It was already there!

9:35 am Now to see if I can get Mathematica installed. This has turned out to be an adventure. After I installed the software, it asked for my password. Fortunately I had this written down, but when I tried it, it said it was invalid. After trying my license number, my MathID, and my password, and not having any success, I tried registering it on the web. This appeared to work but it was cumbersome as I was switching back and forth between operating systems and trying to keep track of what was going on. I finally realized that Mathematica had allocated a new MathID to my installation on the Mac and the password was only valid for the MathID that had been assigned for the PC. I went back to the web site and managed to get a new password but it is only valid for 4 days. I then needed to print out a form and fax it to Wolfram. I took it into the university only to find that the key person is away this week. Hopefully this will all resolve itself, but it is annoying (and time consuming).