By Stephen Hewson
Even supposing better arithmetic is gorgeous, common and interconnected, to the uninitiated it could actually think like an arbitrary mass of disconnected technical definitions, symbols, theorems and strategies. An highbrow gulf should be crossed earlier than a real, deep appreciation of arithmetic can advance. This e-book bridges this mathematical hole. It makes a speciality of the method of discovery up to the content material, top the reader to a transparent, intuitive knowing of the way and why arithmetic exists within the method it does. The narrative doesn't evolve alongside conventional topic traces: each one subject develops from its easiest, intuitive place to begin; complexity develops obviously through questions and extensions. all through, the publication contains degrees of clarification, dialogue and fervour hardly ever visible in conventional textbooks. the alternative of fabric is in a similar fashion wealthy, starting from quantity idea and the character of mathematical idea to quantum mechanics and the background of arithmetic. It rounds off with a variety of thought-provoking and stimulating workouts for the reader.
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Extra info for A Mathematical Bridge: An Intuitive Journey in Higher Mathematics
Nothing more, nothing less. Such statements A Mathematical Bridge 36 implicitly bundle up mathematics into a single, indivisible whole, which does not happen in other disciplines: Whereas it would be unsurprising to hear that a talented sportsman might be said to be ‘a good all-rounder and an excellent soccer player’, or a gifted writer might be ‘a good novel ist who writes outstanding poetry’ it would perhaps be more surprising to hear that Jane was a ‘talented algebraist with particularly exceptional skills of visualisation’.
It is natural to allow the existence of a set corresponding to such a sack: • The empty set 0 is the set containing no elements. The empty set also raises questions, such as: is the set of words with both exactly three and exactly two letters simultaneously the same as the set of positive numbers which are simultaneously both even and odd? Both are empty sets, but are they the same empty set? Mathematicians, who like to be minimal in their definitions, agree that the empty set is unique. Next imagine that instead of merging the contents of two sacks S and T to create the union of S and T we place the entire unopened sacks S and T into a larger sack U.
At high school, students who are ‘good’ at mathematics tend to be good at all of the mathemat ics that high school can throw at them. More so than experts at other subjects, a student who is very talented at mathematics tends to be able to perform in their strongest area with ease and without apparent effort. All problems suitable for whole class teaching will be solved with mini mal working and effort of thought, regardless of the particular piece of the syllabus being studied. At the other end of the spectrum, in high school there are very large numbers of students, many of whom will be perfectly intelligent and may excel in all manner of other fields, for whom algebra is almost totally impenetrable.
A Mathematical Bridge: An Intuitive Journey in Higher Mathematics by Stephen Hewson