By C. R. Wylie Jr.
Clear up homicide difficulties and robberies, see which fishermen are liars and how a blind guy can determine colour — in simple terms by means of reasoning! Hours of mind-strengthening leisure.
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Additional info for 101 Puzzles in Thought and Logic
Tillers, eds. The Dynamics of Judicial Proof, Computation and Common Sense. Springer-Verlag, 2001. Jean Mawhin. ” Notices of the Amer. Math. , Oct. 2005, pp. 1041–1042. Kay L. O’Halloran. Mathematical Discourse: Language, Symbolisms and Visual Images. Continuum, 2005. indb 46 9/2/2010 2:31:12 PM 1 What Is Mathematics? As an elaboration of Q1–Q5 of “Letters to Christina,” it is time to say a few more words about what mathematics is. Strangely, this question is hardly discussed in any course of mathematics routinely taken by undergraduates or graduates.
While this paragraph could have been written entirely in mathematical symbols, it would have been both tedious and much more opaque, even to a professional reader. Mathematical language has developed over a long period of time. Many older symbolisms were actually abbreviations of natural language expressions. As new theories emerge, new symbolisms are born. Symbolisms can also die. The history of mathematics contains a graveyard of dead symbolisms. ” This is called the Sapir–Whorf Hypothesis in semiotics.
Indb 6 9/2/2010 2:31:15 PM What Is Mathematics? 7 One could describe the difference between pure and applied mathematics as follows: Pure mathematics is inward looking while applied mathematics is outward looking. That is to say, pure mathematics looks to the study and development of its own theories and interpretations while applied mathematics stresses the application of mathematical theories to the physical and social worlds. An example from pure mathematics is the theorem of Niels Henrik Abel that the roots of a polynomial of degree five or higher cannot, as a rule, be expressed in terms of integers subjected to the operations of elementary arithmetic and simple root extraction.
101 Puzzles in Thought and Logic by C. R. Wylie Jr.