The Resource Methods of Solving Number Theory Problems, by Ellina Grigorieva, (electronic resource)

# Methods of Solving Number Theory Problems, by Ellina Grigorieva, (electronic resource) Resource Information The item Methods of Solving Number Theory Problems, by Ellina Grigorieva, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.

Label
Methods of Solving Number Theory Problems
Title
Methods of Solving Number Theory Problems
Statement of responsibility
by Ellina Grigorieva
Creator
Subject
Language
eng
Summary
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter of the book covers topics like even and odd numbers, divisibility, prime, perfect, figurate numbers, and introduces congruence. The next chapter works with representations of natural numbers in different bases, as well as the theory of continued fractions, quadratic irrationalities, and also explores different methods of proofs. The third chapter is dedicated to solving unusual factorial and exponential equations, Diophantine equations, introduces Pell’s equations and how they connect algebra and geometry. Chapter 4 reviews Pythagorean triples and their relation to algebraic geometry, representation of a number as the sum of squares or cubes of other numbers, quadratic residuals, and interesting word problems. Appendices provide a historic overview of number theory and its main developments from ancient cultures to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.--
Assigning source
Provided by publisher
Grigorieva, Ellina
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
• 90 \0
• Springer eBooks.
• Springer eBooks
• Mathematics
• Mathematical logic
• Number theory
• Mathematics
Label
Methods of Solving Number Theory Problems, by Ellina Grigorieva, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
Preface -- Numbers: Problems Involving Integers -- Further Study of Integers -- Diophantine Equations and More -- Pythagorean Triples, Additive Problems, and More -- Homework
Control code
978-3-319-90915-8
Dimensions
unknown
Extent
1 online resource (XXI, 391 pages)
File format
multiple file formats
Form of item
• online
• electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319909158
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.1007/978-3-319-90915-8
Other physical details
16 illustrations, 12 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1043880624
Label
Methods of Solving Number Theory Problems, by Ellina Grigorieva, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
Preface -- Numbers: Problems Involving Integers -- Further Study of Integers -- Diophantine Equations and More -- Pythagorean Triples, Additive Problems, and More -- Homework
Control code
978-3-319-90915-8
Dimensions
unknown
Extent
1 online resource (XXI, 391 pages)
File format
multiple file formats
Form of item
• online
• electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319909158
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.1007/978-3-319-90915-8
Other physical details
16 illustrations, 12 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1043880624