### Follow at Google+

### Recent Comments

cgd02 on Review of Mathematics without… David on Review of Mathematics without… cgd02 on Review of Mathematics without… Michael Harris on Review of Mathematics without… -
### Recent Posts

### Archives

### Categories

### Blogroll

- A Neighborhood of Infinity
- Aleph Zero Categorical
- AMS Graduate Student Blog
- Annoying Precision
- Azimuth
- Betalog
- bit-player
- Blogderbeweise
- E. Kowalski's blog
- Geometry Bulletin Board
- God plays dice
- Gowers's Weblog
- Gyre&Gimble
- Hard Arithmetic
- Low Dimensional Topology
- Math ∩ Programming
- Math Drudge
- Matt Baker's Math Blog
- neverendingbooks
- Noncommutative Geometry
- Not Even Wrong
- Persiflage
- Power Overwhelming
- Secret Blogging Seminar
- Shtetl-Optimized
- sketches of topology
- The n-Category Café
- The polymath blog
- Theorem of the week
- Tom Lovering's Blog
- totallydisconnected
- urban maths
- What's new
- Wildon's Weblog
- with high probability

### Related sites

### Meta

# 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

Posted in Book reviews, Number theory
Tagged combinatorics, graph theory, Paul Erdős
Leave a comment

## 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

Posted in Book reviews, Number theory
Tagged combinatorics, graph theory, Paul Erdős
Leave a comment

## 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

## 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

Posted in Algebraic number theory, Number theory
Leave a comment

## 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

Posted in Algebraic number theory, Number theory
Leave a comment

## 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

Posted in Algebraic number theory, Number theory
Leave a comment

## 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

Posted in Algebraic number theory, Number theory
Leave a comment