# arrow_back What is algorithm addiction?

9 views

Many students have the attitude that a problem must be solved or a proof constructed by an algorithm. They become quite uncomfortable when faced with problem solutions that involve guessing or conceptual proofs that involve little or no calculation.

Example

Recently I gave a problem in my Theoretical Computer Science class that in order to solve it required finding the largest integer $n$ for which $n !<10^{9} .$ Most students solved it correctly, but several wrote apologies on their paper for doing it by trial and error. Of course, trial and error is a method.

Example 2 Students at a more advanced level may feel insecure in the case where they are faced with solving a problem for which they know there is no known feasible algorithm, a situation that occurs mostly in senior and graduate level classes. For example, there are no known feasible general algorithms for determining if two finite groups given by their multiplication tables are isomorphic, and there is no algorithm at all to determine if two presentations (generators and relations) give the same group. Even so, the question, "Are the dihedral group of order 8 and the quaternion group isomorphic?" is not hard. (Answer: No, they have different numbers of elements of order 2 and 4.) I have even known graduate students who reacted badly to questions like this, but none of them got through qualifiers!

by SIlver Status
(18,311 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is an algorithm?
What is an algorithm?What is an algorithm? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the algorithm for credit score?
What is the algorithm for credit score?What is the algorithm for credit score? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is an algorithm?
What is an algorithm?What is an algorithm? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the 5-step Machine Learning (ML) meta algorithm?
What is the 5-step Machine Learning (ML) meta algorithm?What is the 5-step Machine Learning (ML) meta algorithm? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is a machine learning algorithm?
What is a machine learning algorithm?What is a machine learning algorithm? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is parameter tuning when using k-nearest-neighbour algorithm?