# Gentle Introduction to the Art of Mathematics by Joe Fields

By Joe Fields

GIAM (a mild advent to the artwork of arithmetic) is a unfastened, open-source textbook -- the present model is 3.1. GIAM covers a number of subject matters within the foundations of arithmetic (logic, units, relatives, services and cardinality) and introduces the reader to many options of mathematical facts (direct, oblique, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic).

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Additional info for Gentle Introduction to the Art of Mathematics

Sample text

No Yes Let r = r − d. Let q = q + 1. 4: The division algorithm in flowchart form. pseudocode a “Label” statement is required which indicates a spot where flow can be redirected via subsequent “Goto” statements. Because of the potential for confusion in complicated algorithms that involve multitudes of Goto statements and their corresponding Labels, this sort of redirection is now deprecated in virtually all popular programming environments.

Perhaps in the not-too-distant future machines will be capable of understanding instruction sets that currently require human interpreters. 5. SOME ALGORITHMS 39 • Assignment statements • If-then control statements • Goto statements • Return We take the view that an algorithm is something like a function, it takes for its input a list of parameters that describe a particular case of some general problem, and produces as its output a solution to that problem. ) The intermediary between input and output is the algorithm instructions themselves and a set of so-called local variables which are used much the way scrap paper is used in a hand calculation – intermediate calculations are written on them, but they are tossed aside once the final answer has been calculated.

1. Every dog has his day. 2. Some days it’s just not worth getting out of bed. 3. There’s a party in somebody’s dorm this Saturday. 4. There’s someone for everyone. A couple of the examples in the exercise above actually have two quantifiers in them. When there are two or more (different) quantifiers in a sentence you have to be careful about keeping their order straight. The following two sentences contain all the same elements except that the words that indicate quantification have been switched.