skip to content
Easy as [pi]? : an introduction to higher mathematics Preview this item
ClosePreview this item
Checking...

Easy as [pi]? : an introduction to higher mathematics

Author: O A Ivanov
Publisher: New York ; Berlin ; Heidelberg : Springer, cop. 1999.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

Aimed at the reader possessing some high school mathematics, this book introduces the fundamental developments of the basic themes of elementary mathematics.

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: O A Ivanov
ISBN: 0387985212 9780387985213
OCLC Number: 490417239
Notes: Le symbole mathématique PI apparait sur la première page.
Description: 1 vol. (xviii-187 p.) : ill. ; 24 cm.
Contents: 1 Induction.- 1.1 Principle or method?.- 1.2 The set of integers.- 1.3 Peano's axioms.- 1.4 Addition, order, and multiplication.- 1.5 The method of mathematical induction.- 2 Combinatorics.- 2.1 Elementary problems.- 2.2 Combinations and recurrence relations.- 2.3 Recurrence relations and power series.- 2.4 Generating functions.- 2.5 The numbers ?e, and n-factorial.- 3 Geometric Transformations.- 3.1 Translations, rotations, and other symmetries, in the context of problem-solving.- 3.2 Problems involving composition of transformations.- 3.3 The group of Euclidean motions of the plane.- 3.4 Ornaments.- 3.5 Mosaics and discrete groups of motions.- 4 Inequalities.- 4.1 The means of a pair of numbers.- 4.2 Cauchy's inequality and the a.m.-g.m. inequality.- 4.3 Classical inequalities and geometry.- 4.4 Integral variants of the classical inequalities.- 4.5 Wirtinger's inequality and the isoperimetric problem.- 5 Sets, Equations, and Polynomials.- 5.1 Figures and their equations.- 5.2 Pythagorean triples and Fermat's last theorem.- 5.3 Numbers and polynomials.- 5.4 Symmetric polynomials.- 5.5 Discriminants and resultants.- 5.6 The method of elimination and Bezout's theorem.- 5.7 The factor theorem and finite fields.- 6 Graphs.- 6.1 Graphical reformulations.- 6.2 Graphs and parity.- 6.3 Trees.- 6.4 Euler's formula and the Euler characteristic.- 6.5 The Jordan curve theorem.- 6.6 Pairings.- 6.7 Eulerian graphs and a little more.- 7 The Pigeonhole Principle.- 7.1 Pigeonholes and pigeons.- 7.2 Poincare's recurrence theorem.- 7.3 Liouville's theorem.- 7.4 Minkowski's lemma.- 7.5 Sums of two squares.- 7.6 Sums of four squares. Euler's identity.- 8 The Quaternions.- 8.1 The skew-field of quaternions, and Euler's identity.- 8.2 Division algebras. Frobenius's theorem.- 8.3 Matrix algebras.- 8.4 Quaternions and rotations.- 9 The Derivative.- 9.1 Geometry and mechanics.- 9.2 Functional equations.- 9.3 The motion of a point-particle.- 9.4 On the number e.- 9.5 Contracting maps.- 9.6 Linearization.- 9.7 The Morse-Sard theorem.- 9.8 The law of conservation of energy.- 9.9 Small oscillations.- 10 The Foundations of Analysis.- 10.1 The rational and real number fields.- 10.2 Nonstandard number lines.- 10.3 "Nonstandard" statements and proofs.- 10.4 The reals numbers via Dedekind cuts.- 10.5 Construction of the reals via Cauchy sequences.- 10.6 Construction of a model of a nonstandard real line.- 10.7 Norms on the rationals.- References.
Responsibility: O.A. Ivanov ; translated by Robert G. Burns.
More information:

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(2)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


<http://www.worldcat.org/oclc/490417239>
library:oclcnum"490417239"
library:placeOfPublication
library:placeOfPublication
library:placeOfPublication
library:placeOfPublication
owl:sameAs<info:oclcnum/490417239>
rdf:typeschema:Book
schema:about
schema:about
schema:about
schema:copyrightYear"1999"
schema:copyrightYear"op."
schema:creator
schema:datePublished"1999"
schema:exampleOfWork<http://worldcat.org/entity/work/id/365795569>
schema:inLanguage"en"
schema:name"Easy as [pi]? an introduction to higher mathematics"
schema:publisher
schema:url
schema:workExample

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.