December 2012 - Page 4 of 8 - Math and Multimedia

Book Review: How to Prove It

December 23, 2012 GB Book Review, High School Mathematics, Miscellaneous

If you are familiar with Polya’s How to Solve It, one of the most well-known classic books in mathematical problem solving, a similar book exists for learning mathematical proofs. Daniel Velleman’s How to Prove It: A Structured Approach is one of the good books available for learning the structure of proofs.

The books include topics onm Sentential logic, Quantification Logic, Proof Strategies, Relations, Functions, Mathematical Induction and Infinite Sets. It contains detailed explanation and numerous examples on different types of proofs and the logic behind them. It contains explanations on connectives, quantifiers, truth tables, countable and uncountable sets and more.

How to Prove It is a recommended book for undergraduate mathematics students as well as advanced high school students who plan to be mathematics majors.

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GeoGebra 4.2 Tutorials, Now Available

December 22, 2012 GB GeoGebra

It’s almost a month now since the release f GeoGebra 4.2 and since then I have updated tutorials to the said version. The update to version 4.2 of the GeoGebra Essentials Series and the GeoGebra Basic Geometric Construction Series are now complete.

I will be updating the GeoGebra Intermediate Tutorial Series and the GeoGebra Advanced Series after Christmas. Hopefully, I will be able to finish them before new year.

For now, let’s enjoy the holidays with our families. Have a blessed Christmas and a prosperous New Year to all.

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4 Common Errors in Calculating Expressions with Exponents

December 20, 2012 GB High School Algebra, High School Mathematics

The errors below are usually made by students in calculating algebraic expressions with integer exponents. These errors result from the misunderstanding of the law of exponents.

If you have seen errors like the following, please don’t hesitate to use the comment box below.

Common Error 1 : $-a^n = (-a)^n$

That equation is only true if $n$ is odd. If $n$ is even, the equation does not hold. For example, in the expression $-3^4$ , the exponent $4$ only applies to $3$ and not $-3$ . That means that $-3^4 = - 81$ . However, $(-3)^4 = 81$ . » Read more

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