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Read e-book online A Mathematical Bridge: An Intuitive Journey in Higher PDF

By Stephen Hewson

ISBN-10: 9812834079

ISBN-13: 9789812834072

Even if larger arithmetic is gorgeous, traditional and interconnected, to the uninitiated it may well suppose like an arbitrary mass of disconnected technical definitions, symbols, theorems and strategies. An highbrow gulf has to be crossed ahead of a real, deep appreciation of arithmetic can increase. This ebook bridges this mathematical hole. It specializes in the method of discovery up to the content material, prime the reader to a transparent, intuitive knowing of the way and why arithmetic exists within the approach it does. The narrative doesn't evolve alongside conventional topic strains: each one subject develops from its easiest, intuitive start line; complexity develops certainly through questions and extensions. all through, the publication contains degrees of rationalization, dialogue and keenness infrequently noticeable in conventional textbooks. the alternative of fabric is in a similar way wealthy, starting from quantity thought and the character of mathematical proposal to quantum mechanics and the historical past of arithmetic. It rounds off with a range of thought-provoking and stimulating routines for the reader.

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Additional resources for A Mathematical Bridge: An Intuitive Journey in Higher Mathematics

Example text

Creating subsets raises an interesting point: what if either of the two sets T and U were empty? We allow two special cases of subset: Any set is a subset of itself and the empty set is a subset of any set. Whilst the notion of a subset might seem to be quite straightforward, it can lead to the creation of very large, interesting sets in a very easy way. For example, consider the set T of subsets of the set S = {1,2 ,3}. T has 23 = 8 elements: {0},{1},{2},{3}, {1,2}, {1,3}, {2,3} {1,2,3} Now consider the set T' of subsets of T.

Therefore the suspect was present at the time of the crime. (3) If the Bank of England announces a rate cut then my mortgage pay­ ments will not go up. (4) Joseph grew up in London, so he is familiar with the tube system. (5) One thousand people took a test, scoring an average of 26%. Therefore some people scored more than 26%. (6 ) If either your mother or father is a British citizen then you are a British citizen. (7) The pass mark is 50%. You got 62 marks. Therefore, you won’t have failed. (8 ) There are two red balls and three green balls in a bag.

Now that we have a feel for the ideas involved, let us now explore the general ques­ tion of how we might combine simple mathematical statements to create compound mathematical statements. Of course, we will still need to com­ bine them in ways such that the combination is still either clearly true or false. The set of acceptable combinations forms the subject of propositional logic. Propositional logic allows us to combine mathematical statements 10 to produce other mathematical statements in particular ways so that the combination always forms a valid mathematical statement.

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A Mathematical Bridge: An Intuitive Journey in Higher Mathematics by Stephen Hewson

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