Category Archives: Number theory

Review of My Brain Is Open

It’s probably fair to say that a large majority of the general public in the U. S. could not name a single important mathematician who was active in the period 1933 to 1996 (the years of Paul Erdős’ adult life). … Continue reading

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Review of The Man Who Loved Only Numbers

When Paul Erdős died in 1996 Paul Hoffman had known him for about 10 years and interviewed him a number of times. Hoffman had also known and interviewed many of Erdős’ friends and associates. So it’s fair to say that … Continue reading

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Review of Mathematics without Apologies

Michael Harris’ book is definitely one that mathematicians shouldn’t miss. It’s also a must-read for people who aren’t professional mathematicians but do have a deep appreciation for the subject and have more than a passing interest in understanding what mathematics … Continue reading

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Algebraic number theory – index

This is a list of posts in the algebraic number theory series to date, oldest first. 1. A brief history of algebra 2. Numbers – rational and irrational, real and imaginary 3. Diophantine equations 4. Groups and rings 5. Fields … Continue reading

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Cyclotomic fields, part 2

In our previous article on cyclotomic fields we were talking about why the Galois group G of ℚ(μn)/ℚ is isomorphic to (ℤ/nℤ)×, where n∈ℤ and μn is the group of nth roots of unity, the roots of xn-1=0 in some … Continue reading

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Roots of unity and cyclotomic fields

In preparation for many good things that are to come, we need to have a talk about another important class of field extensions of ℚ – the cyclotomic extensions. (Check here for a list of previous articles on algebraic number … Continue reading

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Splitting of prime ideals in algebraic number fields

*.overline {text-decoration: overline;} Our series of articles on algebraic number theory is back again. Maybe this time it won’t be so sporadic. Stranger things have happened. The previous installment, of which this is a direct continuation, is here. All previous … Continue reading

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