Category: College Mathematics

Curve Sketching 3: Understanding Vertical and Horizontal Asymptotes

College Algebra, College Mathematics, High School Mathematics

This is the third part  of the Mathematics and Multimedia Curve Sketching Series. In the first part of this series, we have learned how to sketch linear functions, while in the second part, we have learned how to sketch quadratic functions.  In this post and the next post, we will discuss about another important property of some functions that can be used in curve sketching.

asymptote

In Curve Sketching 2, we have learned the different properties of quadratic functions that can help in sketching its graphs.  This property is called the asymptote. » Read more

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Guest Post: An Interesting Property of Prime Numbers

College Mathematics, High School Mathematics, High School Number Theory, Number Theory

Although I have already discussed modulo division, I believe that this proof is beyond the reach of average high school students. To explain further, I made additional notes on Patrick’s proof . I hope these explanations would be able to help students who want to delve on the proof. 

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I’ve got a prime number trick for you today.

  1. Choose any prime number p > 3.
  2. Square it.
  3. Add 5.
  4. Divide by 8.

Having no idea which prime number you chose, I can tell you this:

The remainder of your result is 6.  » Read more

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The Definition of Congruence in the Modular Systems

College Mathematics, Number Theory

This is the fourth part of the Introduction to the Modular Number Systems Series. In the previous parts, we have learned intuitively the modular systems using a 12-hour analog clock, performed operations with its numbers and introduce the symbol for congruence,  and discussed the different number bases.  In this post, we formally define congruence.

modular systems

image via Wikipedia

Recall that the statement 17 \equiv 5 (\mod 12) means that 17 gives a remainder of 5 when divided by 12, or that 17 and 5 give the same remainder when divided by 12. We have also learned that 17, 29, and 41 are congruent since all of them give the same remainder (that is 5) when divided by 12. Notice also that since all of them are congruent, » Read more

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