Language:
English
繁體中文
Help
圖資館首頁
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
A journey through the realm of numbe...
~
Aka, Menny.
A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /
Record Type:
Electronic resources : Monograph/item
Title/Author:
A journey through the realm of numbersby Menny Aka, Manfred Einsiedler, Thomas Ward.
Reminder of title:
from quadratic equations to quadratic reciprocity /
Author:
Aka, Menny.
other author:
Einsiedler, Manfred.
Published:
Cham :Springer International Publishing :2020.
Description:
xix, 344 p. :ill., digital ;24 cm.
Contained By:
Springer Nature eBook
Subject:
Number theory.
Online resource:
https://doi.org/10.1007/978-3-030-55233-6
ISBN:
9783030552336$q(electronic bk.)
A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /
Aka, Menny.
A journey through the realm of numbers
from quadratic equations to quadratic reciprocity /[electronic resource] :by Menny Aka, Manfred Einsiedler, Thomas Ward. - Cham :Springer International Publishing :2020. - xix, 344 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series: SUMS Readings. - Springer undergraduate mathematics series..
1 Introduction: Polynomial Equations -- 2 Cantor's Paradise -- 3 Sums of Squares -- 4 Sums of Two Squares -- 5 Abstract Algebra: Ring Theory -- 6 Cubic and Quartic Diophantine Equations -- 7 The Structure of the Group Fp⨯ -- 8 Studying Squares Again -- Hints to Selected Exercises -- References and further reading -- Index.
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.
ISBN: 9783030552336$q(electronic bk.)
Standard No.: 10.1007/978-3-030-55233-6doiSubjects--Topical Terms:
189521
Number theory.
LC Class. No.: QA241 / .A336 2020
Dewey Class. No.: 512.7
A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /
LDR
:03140nmm a2200337 a 4500
001
586267
003
DE-He213
005
20210128141544.0
006
m d
007
cr nn 008maaau
008
210323s2020 sz s 0 eng d
020
$a
9783030552336$q(electronic bk.)
020
$a
9783030552329$q(paper)
024
7
$a
10.1007/978-3-030-55233-6
$2
doi
035
$a
978-3-030-55233-6
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA241
$b
.A336 2020
072
7
$a
PBH
$2
bicssc
072
7
$a
MAT022000
$2
bisacsh
072
7
$a
PBH
$2
thema
082
0 4
$a
512.7
$2
23
090
$a
QA241
$b
.A313 2020
100
1
$a
Aka, Menny.
$3
877646
245
1 2
$a
A journey through the realm of numbers
$h
[electronic resource] :
$b
from quadratic equations to quadratic reciprocity /
$c
by Menny Aka, Manfred Einsiedler, Thomas Ward.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2020.
300
$a
xix, 344 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
Springer undergraduate mathematics series: SUMS Readings
505
0
$a
1 Introduction: Polynomial Equations -- 2 Cantor's Paradise -- 3 Sums of Squares -- 4 Sums of Two Squares -- 5 Abstract Algebra: Ring Theory -- 6 Cubic and Quartic Diophantine Equations -- 7 The Structure of the Group Fp⨯ -- 8 Studying Squares Again -- Hints to Selected Exercises -- References and further reading -- Index.
520
$a
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.
650
0
$a
Number theory.
$3
189521
650
0
$a
Algebra.
$3
188312
650
1 4
$a
Number Theory.
$3
274059
700
1
$a
Einsiedler, Manfred.
$3
509078
700
1
$a
Ward, Thomas.
$3
255456
710
2
$a
SpringerLink (Online service)
$3
273601
773
0
$t
Springer Nature eBook
830
0
$a
Springer undergraduate mathematics series.
$3
544774
856
4 0
$u
https://doi.org/10.1007/978-3-030-55233-6
950
$a
Mathematics and Statistics (SpringerNature-11649)
based on 0 review(s)
ALL
電子館藏
Items
1 records • Pages 1 •
1
Inventory Number
Location Name
Item Class
Material type
Call number
Usage Class
Loan Status
No. of reservations
Opac note
Attachments
000000190087
電子館藏
1圖書
電子書
EB QA241 .A313 2020 2020
一般使用(Normal)
On shelf
0
1 records • Pages 1 •
1
Multimedia
Multimedia file
https://doi.org/10.1007/978-3-030-55233-6
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login