Book Review: Introduction to number theory

Introduction to Number Theory

This seems simple enough, but let’s play with this definition. The Pythagoreans, an ancient sect of mathematical mystics, said that a number is perfect if it equals the sum of its positive integral divisors, excluding itself. For example, 6 = 1 + 2 + 3and 28 = 1 + 2 + 4 + 7 + 14are perfect numbers. On the other hand, 10 is not perfect because 1 + 2 + 5 = 8, and 12 is not perfect because 1+2+3+4...

Introduction to Algebraic Number Theory

6 CONTENTS Preface This book is based on notes I created for a one-semester undergraduate course on Algebraic Number Theory, which I taught at Harvard during Spring 2004 and Spring 2005. The textbook for the first course was chapter 1 of Swinnerton-Dyer's book [SD01]. The first draft of this book followed [SD01] closely, but the current version but adding substantial text and examples to make t...

Book Review: “Introduction to Artificial Life”

Despite the popularity of artificial life over the last 15 years or so, as witnessed by the establishment of several international conferences on the subject and the birth of the Artificial Life Journal and similar publications, there has been a conspicuous lack of decent introductory texts on the subject. Notable exceptions include “Artificial Life: An Introduction” (Langton 1995), an eclectic...

Solutions to Introduction to Analytic Number Theory

Algebraic Number Theory Introduction

Galois group, 222adeles, 149Artin’s conjecture, 293automorphic form, 292bar resolution, 172biquadratic reciprocity, 271Brauer group, 205Brauer-Hasse-Noether theorem, 252central simple algebra, 206centralizer, 206chain map, 163change of group, 184Chebotarev density theorem, 282class formation, 222class group, 33cohomological functor, 16...