語系:
繁體中文
English
說明(常見問題)
圖資館首頁
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Number theory and geometry :an intro...
~
Lozano-Robledo, Álvaro, (1978-)
Number theory and geometry :an introduction to arithmetic geometry /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Number theory and geometry :Alvaro Lozano-Robledo.
其他題名:
an introduction to arithmetic geometry /
作者:
Lozano-Robledo, Álvaro,
面頁冊數:
xv, 488 pages ;27 cm.
標題:
Arithmetical algebraic geometryCongresses.
ISBN:
9781470450168
Number theory and geometry :an introduction to arithmetic geometry /
Lozano-Robledo, Álvaro,1978-
Number theory and geometry :
an introduction to arithmetic geometry /Alvaro Lozano-Robledo. - xv, 488 pages ;27 cm. - Pure and applied undergraduate texts ;35. - Pure and applied undergraduate texts ;6..
Includes bibliographical references and index.
Introduction -- Part 1. Integers, Polynomials, Lines, and Congruences: The Integers -- The Prime Numbers Congruences -- Groups, Rings, and Fields -- Finite Fields -- The Theorems of Wilson, Fermat, and Euler -- Primitive Roots -- Part 2. Quadratic Congruences and Quadratic Equations: An Introduction to Quadratic Equations -- Quadratic Congruences -- The Hasse-Minkowski Theorem -- Circles, Ellipses, and the Sum of Two Squares Problem -- Continued Fractions -- Hyperbolas and Pell's Equation -- Part 3. Cubic Equations and Elliptic Curves: An Introduction to Cubic Equations -- Elliptic Curves
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level. -- Provided by publisher.
ISBN: 9781470450168$109.00
LCCN: 2018056079
Nat. Bib. No.: GBB989128bnb
Nat. Bib. Agency Control No.: 019400922UkSubjects--Topical Terms:
509349
Arithmetical algebraic geometry
--Congresses.Index Terms--Genre/Form:
708244
Textbooks.
LC Class. No.: QA242.5 / L925 2019
Dewey Class. No.: 512.7/4
Number theory and geometry :an introduction to arithmetic geometry /
LDR
:03432nam a2200385 a 4500
001
548487
003
OCoLC
005
20190801023751.0
008
190801s2019 riua b 001 0 eng
010
$a
2018056079
015
$a
GBB989128
$2
bnb
016
7
$a
019400922
$2
Uk
020
$a
9781470450168
$q
hardcover
$q
alkaline paper
$c
$109.00
020
$a
147045016X
$q
hardcover
$q
alkaline paper
029
1
$a
AU@
$b
000065224208
029
1
$a
UKMGB
$b
019400922
034
3 3
$a
cam 2200385 i 4500
035
$a
(OCoLC)1080247853
035
$a
on1080247853
040
$a
DLC
$b
eng
$e
rda
$c
DLC
$d
OCLCO
$d
OCLCF
$d
YDX
$d
HF9
$d
UKMGB
042
$a
pcc
049
$a
NUKM
050
0 0
$a
QA242.5
$b
L925 2019
082
0 0
$a
512.7/4
$2
23
100
1
$a
Lozano-Robledo, Álvaro,
$d
1978-
$e
author.
$3
827896
245
1 0
$a
Number theory and geometry :
$b
an introduction to arithmetic geometry /
$c
Alvaro Lozano-Robledo.
264
1
$a
Providence, Rhode Island :
$b
American Mathematical Society,
$c
[2019]
300
$a
xv, 488 pages ;
$c
27 cm.
336
$a
text
$b
txt
$2
rdacontent
337
$a
unmediated
$b
n
$2
rdamedia
338
$a
volume
$b
nc
$2
rdacarrier
490
1
$a
Pure and applied undergraduate texts ;
$v
35
504
$a
Includes bibliographical references and index.
505
0
$a
Introduction -- Part 1. Integers, Polynomials, Lines, and Congruences: The Integers -- The Prime Numbers Congruences -- Groups, Rings, and Fields -- Finite Fields -- The Theorems of Wilson, Fermat, and Euler -- Primitive Roots -- Part 2. Quadratic Congruences and Quadratic Equations: An Introduction to Quadratic Equations -- Quadratic Congruences -- The Hasse-Minkowski Theorem -- Circles, Ellipses, and the Sum of Two Squares Problem -- Continued Fractions -- Hyperbolas and Pell's Equation -- Part 3. Cubic Equations and Elliptic Curves: An Introduction to Cubic Equations -- Elliptic Curves
520
$a
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level. -- Provided by publisher.
650
0
$a
Arithmetical algebraic geometry
$v
Congresses.
$3
509349
650
0
$a
Number theory
$3
254084
650
7
$a
Arithmetical algebraic geometry.
$3
347677
650
7
$a
Number theory.
$3
189521
650
7
$a
Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Arithmetic algebraic geometry (Diophantine geometry).
$2
msc
$3
827897
650
7
$a
Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic problems. Diophantine geometry.
$2
msc
$3
827898
655
7
$a
Textbooks.
$2
fast
$3
708244
830
0
$a
Pure and applied undergraduate texts ;
$v
6.
$3
603576
938
$a
YBP Library Services
$b
YANK
$n
16048888
994
$a
C0
$b
TWNUK
筆 0 讀者評論
全部
西方語文圖書區(四樓)
館藏
1 筆 • 頁數 1 •
1
條碼號
館藏地
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
320000721680
西方語文圖書區(四樓)
1圖書
一般圖書
QA242.5 L925 2019
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼
登入