Learning: The Journey of a Lifetime

Journals as an Aid to Learning

Nature of Mathematics

math8

An Example of a "Learning Process" Journal (using the 2 colored box format)
 
October 8 , 2003

Book: The Nature of Mathematics 10th ed by Karl Smith.

Source: Toronto Thomson Brooks/Cole, 2004.

It is 6:00 am (Wednesday). It has been a full two weeks since I opened this book. I must do better.


Chapter Summary (p. 47 - 52)

There are a number of sections:

  • Important Terms
  • Types of Problems
  • Chapter 1 Review Questions
  • Group Research Problems
  • Individual Research Problems

The chapter summary is very well organized. However the number of important terms is a bit overwhelming (N = 69). Still, it is worthwhile to go over them, at least subvocally, and see which terms are still unfamiliar.

It is a bit sobering to realize how many of these terms I stumble over. The ideas are clear (I think) but I am weak at being able to give clear statements for many of the terms. Perhaps I don't know this as well as I think I do.

Important Terms: (in bold in the list, and in highlighted green boxes in the text)

Term
Description
Exponential notation

where b is called the base, n is called the exponent and the left hand expression is called the exponential.
Extended order of operations First compute expressions in parentheses, then compute expressions involving exponents, then muliplication and division, and then compute expressions involving addition and subtraction, each category from left to right.
Fundamental counting principle If you have a rectangular array of objects of m rows and n columns, then there are mn objects
Infinite set A set that has cardinality aleph-null
Laws of exponents  
One-to-one correspondence  
Order of operations Same as Extended order, but without mention of exponents.
Scientific notation m p where m is between 1 and 9 and p is the number of factors of 10.
Substitution property If a=b, then a may be substituted for b in any mathematical expression without affecting the truth or falsity of the expression.

 

It is still quite frustrating to type an expression in conventional mathematical notation using Dreamweaver!

Review Questions

20. Suppose you could write out 7*1000. What is the last digit?

7*1000 = 7*10 x 7*10 x 7*10

7*10 = (7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7)

= (49 x 49) * 5

= (number ending in 1) *5

Therefore the last digit will be a 1.

Overall I found this summary to be not worth the time. The overall theme of the first chapter is Problem Solving.

I have skimmed the second chapter on the Nature of Logic and feel that there is nothing here that I am unfamiliar with. Next time I will begin Chapter 3 The Nature of Numeration Systems. This looks like it could be quite interesting.

7:30 am

Reminder: each "Learning" session has a new web page.

Mathematics Index