By Carl B. Boyer, Uta C. Merzbach

ISBN-10: 0470630566

ISBN-13: 9780470630563

The up-to-date new version of the vintage and accomplished consultant to the historical past of arithmetic. (**Third Edition**)

For greater than 40 years, A historical past of arithmetic has been the reference of selection for these seeking to find out about the attention-grabbing heritage of humankind's dating with numbers, shapes, and styles. This revised version positive factors up to date insurance of issues reminiscent of Fermat's final Theorem and the Poincaré Conjecture, as well as contemporary advances in components comparable to finite staff conception and computer-aided proofs.

• Distills hundreds of thousands of years of arithmetic right into a unmarried, approachable volume

• Covers mathematical discoveries, thoughts, and thinkers, from historical Egypt to the present

• contains updated references and an intensive chronological desk of mathematical and common old developments.

Whether you're attracted to the age of Plato and Aristotle or Poincaré and Hilbert, even if you must recognize extra concerning the Pythagorean theorem or the golden suggest, A heritage of arithmetic is a necessary reference to help you discover the awesome heritage of arithmetic and the boys and ladies who created it.

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**Additional info for A History of Mathematics**

**Example text**

If the two numbers a and b are suitably chosen then xn should appear to be uniform. ) In fact, since there are only a ﬁnite number (albeit large) of possible numbers that can be represented on a digital computer, this algorithm must eventually repeat and hence xn must be a periodic sequence. The goal of designing a good pseudo-random number generater is to make the period as long as possible and to make the sequences produced look as much as possible like a random sequence in the sense that statistical tests for independence are fooled.

The ﬁrst is that probabilities must satisfy some consistency properties, we cannot arbitrarily deﬁne probabilities of distinct subsets of [0, 1) (or, more generally, ) without regards to the implications of probabilities for other sets; the probabilities must be consistent with each other in the sense that they do not contradict each other. 2. SPINNING POINTERS AND FLIPPING COINS 17 computing the probability of an interval, then both formulas must give the same numerical result — as they do in this example.

2(b). For example, the sequences of sets [1, 1 + 1/n) and (1−1/n, 1+1/n) are decreasing. Again we have a natural notion of the limit of this sequence: Both these sequences of sets collapse to the point of singleton set {1} — the point in common to all the sets. This suggests a formal deﬁnition based on the countably inﬁnite intersection of the sets. Given a decreasing sequence of sets Fn ; n = 1, 2, . . , we deﬁne the limit of the sequence by ∞ lim Fn = n→∞ Fn , n=1 34 CHAPTER 2. PROBABILITY that is, a point is in the limit of a decreasing sequence of sets if and only if it is contained in all the sets of the sequence.

### A History of Mathematics by Carl B. Boyer, Uta C. Merzbach

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