Mathematics and the Search for Knowledge by Morris Kline

By Morris Kline

This used to be Morris Kline's final e-book, and was once released in 1985. He lived from 1908 to 1992.

Its significant topic is "how arithmetic unearths and determines our wisdom of the actual global" (86), and so its significant problem is "to describe what's recognized in regards to the realities of our actual international *only* throughout the medium of mathematics". (preface)

The publication he wrote ahead of this [Mathematics: The lack of walk in the park] (see my assessment) was once curious about the heritage of the rational justification of arithmetic, and during this ebook his difficulty is with using arithmetic as an tool or approach to wisdom (or clinical wisdom, in case you are prone to make a distinction). those are either epistemological issues, and you will ask: what conclusions did Kline settle upon?

"Nature neither prescribes nor proscribes any mathematical theory." (201)

"Our mathematical thought of the actual global isn't an outline of the phenomena as we understand them yet a daring symbolic building. arithmetic, published from the bondage of sensory event, now not describes truth yet makes types of truth that serve the needs of clarification, calculation, and prediction." (202-03)

"We have a technology of nature as humanity thinks approximately and describes it. technology stands among humanity and nature." (203)

"We needs to face the truth that there is not any universally approved correspondence among arithmetic and actual reality." (210)

"[M]athematics is a human job and is topic to the entire foibles and frailties of people. Any formal, logical account is pseudo-mathematics, a fiction, even a legend, regardless of the portion of cause. [...] [M]athematics is not any greater than the summary, and in simple terms approximate, formula of experience." (222)

He summarizes those options on web page 226:

"Because arithmetic is a human production, and since via arithmetic we find completely new actual phenomena, people create components in their universe, gravity, electromagnetic waves, quanta of strength, etc. in fact, perceptions and experimentation supply results in the mathematician. there's a substratum of actual truth, yet even if there's a few actual fact, the entire association, of completion, correction, and realizing come via mathematics.

"What we all know includes the human brain a minimum of up to what exists within the exterior international or even within the perceptions the human brain enters. To understand a tree with no spotting the "treeness" is incomprehensible. additionally, a set of perceptions in step with se is incomprehensible. people and their minds are a part of fact. technology can not confront nature as aim and humanity because the describer. they can't be separated.

"The dividing line among mathematical wisdom and empirical wisdom isn't really absolute. We continually regulate the documents of our observations and whilst regulate our theories to fulfill new observations and experimental effects. the target in either efforts is a finished and coherent account of the actual international. arithmetic mediates among guy and nature, among man's internal and outer worlds.

"We come eventually to the indisputable and impossible to resist end that our arithmetic and actual truth are inseparable." (226)

Thus Kline ends with the conflation of epistemology and ontology.

It should be illuminating to notice that Kline calls Ludwig Wittgenstein "one of the main profound philosophers of the topic" of arithmetic and the actual international, and feedback that he "declared that arithmetic is not just a human construction however it is especially a lot stimulated through the cultures within which it was once constructed. Its "truths" are as depending on humans as is the notion of colour or the English language." (222)

Nowhere within the booklet does Kline speak about the proposal of mathematical constructions. He in brief mentions Nicolas Bourbaki with no supplying any statement on what he reviews. He tells us this "distinguished workforce of mathematicians [...] say that there's an intimate connection among experimental phenomena and mathematical buildings. but we're thoroughly ignorant concerning the underlying purposes for this, and we will probably consistently stay blind to them. [...] we will ponder arithmetic as a storehouse of mathematical buildings, and sure points of actual or empirical fact healthy into those constructions, as though via one of those preadaptation." (224)

I stumbled on the 1st 8 chapters attractive, and as much as that time was once able to supply the booklet most sensible score. those chapters have been interested by real arithmetic on the subject of technological know-how. as soon as Kline reached the twentieth century the booklet became clear of its past concentration and have become a math-free popularization of relativity and quantum thought, with the addition of an undemanding examine a number of issues within the philosophy of technological know-how.

The 12 months after Kline's e-book was once released, Saunders Mac Lane released arithmetic: shape and serve as (currently out of print, to the shame of Springer-Verlag). Mac Lane's publication is written at a way more refined point, either mathematically and philosophically. Of Wittgenstein's philosophy of arithmetic, Mac Lane comments: "[T]he philosophy of arithmetic can't be a lot complicated through a few of the books entitled "Mathematical Knowledge", in view of the remark that this kind of identify often covers a ebook which appears to be like to contain little wisdom of arithmetic and lots more and plenty dialogue of ways Mathematicians can (or can't) understand the reality. This dismissal applies in particular to the later (posthumous) quantity of Wittgenstein [1964], the place the particular Mathematical content material hardly ever rises above 3rd grade mathematics, whereas the particular crisis is much less with arithmetic than with its use to demonstrate a few strictly philosophical issue." (Mac Lane: 444)

Related to Mac Lane's feedback: Kline usually disregards the philosophical underpinnings of the numerous authors he charges within the ultimate chapters of the publication the place he is discussing the relation of arithmetic to fact. up to I recognize Morris Kline, i will not see this ebook as totally profitable. The final 5 chapters weaken an another way attention-grabbing report.
___________

:: Contents ::
Historical evaluation: Is There an exterior World?
I. the flaws of the Senses and Intuition
II. the increase and position of Mathematics
III. The Astronomical global of the Greeks
IV. The Heliocentric conception of Copernicus and Kepler
V. arithmetic Dominates actual Science
VI. arithmetic and the secret of Gravitation
VII. arithmetic and the Imperceptible Electromagnetic World
VIII. A Prelude to the idea of Relativity
IX. The Relativistic World
X. The Dissolution of topic: Quantum Theory
XI. the truth of Mathematical Physics
XII. Why Does arithmetic Work?
XIII. arithmetic and Nature's Behavior
Bibliography
Index

Show description

By Morris Kline

This used to be Morris Kline's final e-book, and was once released in 1985. He lived from 1908 to 1992.

Its significant topic is "how arithmetic unearths and determines our wisdom of the actual global" (86), and so its significant problem is "to describe what's recognized in regards to the realities of our actual international *only* throughout the medium of mathematics". (preface)

The publication he wrote ahead of this [Mathematics: The lack of walk in the park] (see my assessment) was once curious about the heritage of the rational justification of arithmetic, and during this ebook his difficulty is with using arithmetic as an tool or approach to wisdom (or clinical wisdom, in case you are prone to make a distinction). those are either epistemological issues, and you will ask: what conclusions did Kline settle upon?

"Nature neither prescribes nor proscribes any mathematical theory." (201)

"Our mathematical thought of the actual global isn't an outline of the phenomena as we understand them yet a daring symbolic building. arithmetic, published from the bondage of sensory event, now not describes truth yet makes types of truth that serve the needs of clarification, calculation, and prediction." (202-03)

"We have a technology of nature as humanity thinks approximately and describes it. technology stands among humanity and nature." (203)

"We needs to face the truth that there is not any universally approved correspondence among arithmetic and actual reality." (210)

"[M]athematics is a human job and is topic to the entire foibles and frailties of people. Any formal, logical account is pseudo-mathematics, a fiction, even a legend, regardless of the portion of cause. [...] [M]athematics is not any greater than the summary, and in simple terms approximate, formula of experience." (222)

He summarizes those options on web page 226:

"Because arithmetic is a human production, and since via arithmetic we find completely new actual phenomena, people create components in their universe, gravity, electromagnetic waves, quanta of strength, etc. in fact, perceptions and experimentation supply results in the mathematician. there's a substratum of actual truth, yet even if there's a few actual fact, the entire association, of completion, correction, and realizing come via mathematics.

"What we all know includes the human brain a minimum of up to what exists within the exterior international or even within the perceptions the human brain enters. To understand a tree with no spotting the "treeness" is incomprehensible. additionally, a set of perceptions in step with se is incomprehensible. people and their minds are a part of fact. technology can not confront nature as aim and humanity because the describer. they can't be separated.

"The dividing line among mathematical wisdom and empirical wisdom isn't really absolute. We continually regulate the documents of our observations and whilst regulate our theories to fulfill new observations and experimental effects. the target in either efforts is a finished and coherent account of the actual international. arithmetic mediates among guy and nature, among man's internal and outer worlds.

"We come eventually to the indisputable and impossible to resist end that our arithmetic and actual truth are inseparable." (226)

Thus Kline ends with the conflation of epistemology and ontology.

It should be illuminating to notice that Kline calls Ludwig Wittgenstein "one of the main profound philosophers of the topic" of arithmetic and the actual international, and feedback that he "declared that arithmetic is not just a human construction however it is especially a lot stimulated through the cultures within which it was once constructed. Its "truths" are as depending on humans as is the notion of colour or the English language." (222)

Nowhere within the booklet does Kline speak about the proposal of mathematical constructions. He in brief mentions Nicolas Bourbaki with no supplying any statement on what he reviews. He tells us this "distinguished workforce of mathematicians [...] say that there's an intimate connection among experimental phenomena and mathematical buildings. but we're thoroughly ignorant concerning the underlying purposes for this, and we will probably consistently stay blind to them. [...] we will ponder arithmetic as a storehouse of mathematical buildings, and sure points of actual or empirical fact healthy into those constructions, as though via one of those preadaptation." (224)

I stumbled on the 1st 8 chapters attractive, and as much as that time was once able to supply the booklet most sensible score. those chapters have been interested by real arithmetic on the subject of technological know-how. as soon as Kline reached the twentieth century the booklet became clear of its past concentration and have become a math-free popularization of relativity and quantum thought, with the addition of an undemanding examine a number of issues within the philosophy of technological know-how.

The 12 months after Kline's e-book was once released, Saunders Mac Lane released arithmetic: shape and serve as (currently out of print, to the shame of Springer-Verlag). Mac Lane's publication is written at a way more refined point, either mathematically and philosophically. Of Wittgenstein's philosophy of arithmetic, Mac Lane comments: "[T]he philosophy of arithmetic can't be a lot complicated through a few of the books entitled "Mathematical Knowledge", in view of the remark that this kind of identify often covers a ebook which appears to be like to contain little wisdom of arithmetic and lots more and plenty dialogue of ways Mathematicians can (or can't) understand the reality. This dismissal applies in particular to the later (posthumous) quantity of Wittgenstein [1964], the place the particular Mathematical content material hardly ever rises above 3rd grade mathematics, whereas the particular crisis is much less with arithmetic than with its use to demonstrate a few strictly philosophical issue." (Mac Lane: 444)

Related to Mac Lane's feedback: Kline usually disregards the philosophical underpinnings of the numerous authors he charges within the ultimate chapters of the publication the place he is discussing the relation of arithmetic to fact. up to I recognize Morris Kline, i will not see this ebook as totally profitable. The final 5 chapters weaken an another way attention-grabbing report.
___________

:: Contents ::
Historical evaluation: Is There an exterior World?
I. the flaws of the Senses and Intuition
II. the increase and position of Mathematics
III. The Astronomical global of the Greeks
IV. The Heliocentric conception of Copernicus and Kepler
V. arithmetic Dominates actual Science
VI. arithmetic and the secret of Gravitation
VII. arithmetic and the Imperceptible Electromagnetic World
VIII. A Prelude to the idea of Relativity
IX. The Relativistic World
X. The Dissolution of topic: Quantum Theory
XI. the truth of Mathematical Physics
XII. Why Does arithmetic Work?
XIII. arithmetic and Nature's Behavior
Bibliography
Index

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Applied Game Theory: Proceedings of a Conference at the by P. Levine, J.-P. Ponssard (auth.), S. J. Brams, A. Schotter,

By P. Levine, J.-P. Ponssard (auth.), S. J. Brams, A. Schotter, G. Schwödiauer (eds.)

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MEMS and Nanotechnology, Volume 5: Proceedings of the 2013 by Ningning Du, George F. Raiser, W. Carter Ralph (auth.),

By Ningning Du, George F. Raiser, W. Carter Ralph (auth.), Gordon Shaw III, Barton C. Prorok, LaVern Starman, Cosme Furlong (eds.)

MEMS and Nanotechnology, quantity five: court cases of the 2013 Annual convention on Experimental and utilized Mechanics, the 5th quantity of 8 from the convention, brings jointly contributions to this significant quarter of analysis and engineering. the gathering offers early findings and case reports on quite a lot of parts, together with:

Microelectronics Packaging

Single Atom/Molecule Mechanical Testing

MEMS units & Fabrication

In-Situ Mechanical Testing

Nanoindentation

Experimental research of Low-Dimensional fabrics for Nanotechnology

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By Ningning Du, George F. Raiser, W. Carter Ralph (auth.), Gordon Shaw III, Barton C. Prorok, LaVern Starman, Cosme Furlong (eds.)

MEMS and Nanotechnology, quantity five: court cases of the 2013 Annual convention on Experimental and utilized Mechanics, the 5th quantity of 8 from the convention, brings jointly contributions to this significant quarter of analysis and engineering. the gathering offers early findings and case reports on quite a lot of parts, together with:

Microelectronics Packaging

Single Atom/Molecule Mechanical Testing

MEMS units & Fabrication

In-Situ Mechanical Testing

Nanoindentation

Experimental research of Low-Dimensional fabrics for Nanotechnology

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Continue reading "MEMS and Nanotechnology, Volume 5: Proceedings of the 2013 by Ningning Du, George F. Raiser, W. Carter Ralph (auth.),"

Insight into Theoretical and Applied Informatics. by Andrzej Yatsko, Walery Suslow

By Andrzej Yatsko, Walery Suslow

The publication is addressed to youngsters drawn to machine applied sciences and laptop technology. the target of this ebook is to supply the reader with all of the worthy parts to get her or him begun within the glossy box of informatics and to permit her or him to notice the connection among key components of machine technological know-how. The publication is addressed not just to destiny software program builders, but additionally to all who're drawn to computing in a extensively understood feel. The authors additionally count on that a few desktop pros may want to overview this publication to boost themselves above the day-by-day grind and to embody the distinction of the complete box of computing device technology. not like current books, this one bypasses concerns about the building of pcs and focuses purely on info processing. spotting the significance of the human consider info processing, the authors intend to give the theoretical foundations of laptop technology, software program improvement ideas, and a few company elements of informatics in non-technocratic, humanistic phrases.

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By Andrzej Yatsko, Walery Suslow

The publication is addressed to youngsters drawn to machine applied sciences and laptop technology. the target of this ebook is to supply the reader with all of the worthy parts to get her or him begun within the glossy box of informatics and to permit her or him to notice the connection among key components of machine technological know-how. The publication is addressed not just to destiny software program builders, but additionally to all who're drawn to computing in a extensively understood feel. The authors additionally count on that a few desktop pros may want to overview this publication to boost themselves above the day-by-day grind and to embody the distinction of the complete box of computing device technology. not like current books, this one bypasses concerns about the building of pcs and focuses purely on info processing. spotting the significance of the human consider info processing, the authors intend to give the theoretical foundations of laptop technology, software program improvement ideas, and a few company elements of informatics in non-technocratic, humanistic phrases.

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The Belousov-Zhabotinskii Reaction by John J. Tyson (auth.)

By John J. Tyson (auth.)

In 1958 B. P. Belousov chanced on that the oxidation of citric acid by means of bromate within the presence of cerium ions doesn't continue to equilibrium methodically and uniformly, like so much chemical reactions, yet particularly oscillates with clocklike precision among a yellow and colorless nation. See Fig. eleven. 1, p. 30. A. M. Zhabotinskii up on Belousov's unique remark and in 1964 his first investigations seemed within the Russian magazine Biofizika. notwithstanding H. Degn (in Copenhagen on the time) knew of Zhabotinskii's paintings and released his personal account of the mechanism of oscillation in Nature (1967), this fascinating response attracted little recognition between Western scientists until eventually 1968, whilst Zhabotinskii and his coworkers and Busse (from Braunschweig, W. Germany) stated on their paintings at a world convention on organic and biochemical oscillators held in Prague. almost immediately thereafter seemed· a flurry of papers on temporal oscillations and spatial styles during this response procedure. Vavilin and Zhabotinskii (1969) [and later Kasperek and Bruice (1971)] studied the kinetics of the oxidation three of Ce+ through Br0 and the oxidation of natural species through Ce+4. Busse (1969) three stated his commentary of coloured bands of chemical task propagating up and down in a protracted tube of unstirred resolution. Zaikin and Zhabotinskii (1970) saw round chemical waves in skinny layers of solution.

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By John J. Tyson (auth.)

In 1958 B. P. Belousov chanced on that the oxidation of citric acid by means of bromate within the presence of cerium ions doesn't continue to equilibrium methodically and uniformly, like so much chemical reactions, yet particularly oscillates with clocklike precision among a yellow and colorless nation. See Fig. eleven. 1, p. 30. A. M. Zhabotinskii up on Belousov's unique remark and in 1964 his first investigations seemed within the Russian magazine Biofizika. notwithstanding H. Degn (in Copenhagen on the time) knew of Zhabotinskii's paintings and released his personal account of the mechanism of oscillation in Nature (1967), this fascinating response attracted little recognition between Western scientists until eventually 1968, whilst Zhabotinskii and his coworkers and Busse (from Braunschweig, W. Germany) stated on their paintings at a world convention on organic and biochemical oscillators held in Prague. almost immediately thereafter seemed· a flurry of papers on temporal oscillations and spatial styles during this response procedure. Vavilin and Zhabotinskii (1969) [and later Kasperek and Bruice (1971)] studied the kinetics of the oxidation three of Ce+ through Br0 and the oxidation of natural species through Ce+4. Busse (1969) three stated his commentary of coloured bands of chemical task propagating up and down in a protracted tube of unstirred resolution. Zaikin and Zhabotinskii (1970) saw round chemical waves in skinny layers of solution.

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Change and Language: Papers from the Annual Meeting of the by Lynne Cameron

By Lynne Cameron

This quantity is a set of papers from the yearly assembly of the British organization for utilized Linguistics (BAAL) held on the college of Leeds, September 1994. It investigates the connection among switch and language within the broadest feel.

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By Lynne Cameron

This quantity is a set of papers from the yearly assembly of the British organization for utilized Linguistics (BAAL) held on the college of Leeds, September 1994. It investigates the connection among switch and language within the broadest feel.

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An Introduction to Quantitative Finance by Stephen Blyth

By Stephen Blyth

The worlds of Wall highway and the town have constantly held a undeniable attract, yet lately have left an indelible mark at the wider public attention and there was a necessity to turn into extra financially literate. The quantitative nature of complicated monetary transactions makes them a desirable topic region for mathematicians of all kinds, even if for basic curiosity or as a result of huge, immense financial rewards on supply.

An advent to Quantitative Finance matters monetary derivatives - a spinoff being a freelance among entities whose price derives from the cost of an underlying monetary asset - and the probabilistic instruments that have been built to examine them. the idea within the textual content is influenced through a wish to supply a certainly rigorous but available beginning to take on difficulties the writer encountered when buying and selling derivatives on Wall road. The e-book combines an strange mix of real-world derivatives buying and selling event and rigorous educational historical past.

Probability offers the foremost instruments for analysing and valuing derivatives. the cost of a by-product is heavily associated with the predicted price of its pay-out, and definitely scaled spinoff costs are martingales, essentially vital items in chance conception.

The prerequisite for studying the fabric is an introductory undergraduate direction in chance. The e-book is in a different way self-contained and specifically calls for no extra instruction or publicity to finance. it really is compatible for a one-semester path, speedy exposing readers to robust conception and substantive difficulties. The e-book can also entice scholars who've loved chance and feature a wish to see the way it may be utilized. Signposts are given during the textual content to extra complex issues and to diverse methods for these seeking to take the topic additional.

Show description

By Stephen Blyth

The worlds of Wall highway and the town have constantly held a undeniable attract, yet lately have left an indelible mark at the wider public attention and there was a necessity to turn into extra financially literate. The quantitative nature of complicated monetary transactions makes them a desirable topic region for mathematicians of all kinds, even if for basic curiosity or as a result of huge, immense financial rewards on supply.

An advent to Quantitative Finance matters monetary derivatives - a spinoff being a freelance among entities whose price derives from the cost of an underlying monetary asset - and the probabilistic instruments that have been built to examine them. the idea within the textual content is influenced through a wish to supply a certainly rigorous but available beginning to take on difficulties the writer encountered when buying and selling derivatives on Wall road. The e-book combines an strange mix of real-world derivatives buying and selling event and rigorous educational historical past.

Probability offers the foremost instruments for analysing and valuing derivatives. the cost of a by-product is heavily associated with the predicted price of its pay-out, and definitely scaled spinoff costs are martingales, essentially vital items in chance conception.

The prerequisite for studying the fabric is an introductory undergraduate direction in chance. The e-book is in a different way self-contained and specifically calls for no extra instruction or publicity to finance. it really is compatible for a one-semester path, speedy exposing readers to robust conception and substantive difficulties. The e-book can also entice scholars who've loved chance and feature a wish to see the way it may be utilized. Signposts are given during the textual content to extra complex issues and to diverse methods for these seeking to take the topic additional.

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Concise encyclopedia of mathematics by Eric W. Weisstein

By Eric W. Weisstein

Upon booklet, the 1st variation of the CRC Concise Encyclopedia of arithmetic received overwhelming accolades for its unprecedented scope, clarity, and software. It quickly took its position one of the most sensible promoting books within the heritage of Chapman & Hall/CRC, and its attractiveness keeps unabated.

Yet additionally unabated has been the commitment of writer Eric Weisstein to gathering, cataloging, and referencing mathematical proof, formulation, and definitions. He has now up-to-date lots of the unique entries and extended the Encyclopedia to incorporate one thousand extra pages of illustrated entries.

The accessibility of the Encyclopedia besides its extensive assurance and low cost fee make it beautiful to the widest attainable variety of readers and positively a needs to for libraries, from the secondary to the pro and examine degrees. For mathematical definitions, formulation, figures, tabulations, and references, this can be easily the main awesome compendium available.

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By Eric W. Weisstein

Upon booklet, the 1st variation of the CRC Concise Encyclopedia of arithmetic received overwhelming accolades for its unprecedented scope, clarity, and software. It quickly took its position one of the most sensible promoting books within the heritage of Chapman & Hall/CRC, and its attractiveness keeps unabated.

Yet additionally unabated has been the commitment of writer Eric Weisstein to gathering, cataloging, and referencing mathematical proof, formulation, and definitions. He has now up-to-date lots of the unique entries and extended the Encyclopedia to incorporate one thousand extra pages of illustrated entries.

The accessibility of the Encyclopedia besides its extensive assurance and low cost fee make it beautiful to the widest attainable variety of readers and positively a needs to for libraries, from the secondary to the pro and examine degrees. For mathematical definitions, formulation, figures, tabulations, and references, this can be easily the main awesome compendium available.

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Mathematik by Tilo Arens

By Tilo Arens

Dieses vierfarbige Lehrbuch bietet in einem Band ein lebendiges Bild der „gesamten“ Mathematik für Anwender. Angehende Ingenieure und Naturwissenschaftler finden hier die wichtigen Konzepte und Begriffe ausführlich und mit vielen Beispielen erklärt.

Im Mittelpunkt stehen das Verständnis der Zusammenhänge und die Beherrschung der Rechentechniken.

Herausragende Merkmale sind:

durchgängig vierfarbiges structure mit mehr als 1500 Abbildungen
prägnant formulierte Kerngedanken bilden die Abschnittsüberschriften
Selbsttests in kurzen Abständen ermöglichen Lernkontrolle während des Lesens
farbige Merkkästen heben das Wichtigste hervor
mehr als a hundred Anwendungsboxen erläutern Themen wie „Geometrie hinter dem GPS“, „Pageranking bei Google“ oder „harmonischer Oszillator“
Vertiefungsboxen geben einen Ausblick auf weiterführende Themen
Zusammenfassungen zu jedem Kapitel sowie Übersichtsboxen
mehr als 750 Verständnisfragen, Rechenaufgaben und Anwendungsprobleme

Inhaltlich spannt sich der Bogen von elementaren Grundlagen über die research einer Veränderlichen, der linearen Algebra, der research mehrer Veränderlicher bis hin zu fortgeschrittenen Themen der research, die für die Anwendung besonders wichtig sind, wie partielle Differenzialgleichungen, Fourierreihen und Laplacetransformationen. Numerische Konzepte sind integraler Bestandteil der Kapitel. Der Wahrscheinlichkeitsrechnung un
d Statistik ist einer der sechs Teile des Buchs gewidmet.

Zusätzlich gibt es zum Buch die web site matheweb, die Ihnen u.a. bietet:

Bonusmaterialien zu zahlreichen Kapiteln
Hinweise, Lösungswege und Ergebnisse zu allen Aufgaben
Zusatzmaterialien wie Maple-Worksheets zu verschiedenen Themen des Buchs
die Möglichkeit, zu den Kapiteln Fragen zu stellen

Das Buch wird allen Anwendern der Mathematik
vom Beginn des Studiums über höhere Semester bis in die Berufspraxis hinein ein langjähriger verlässlicher Begleiter sein. Für die three. Auflage ist es vollständig durchgesehen und in info ergänzt und didaktisch weiter verbessert worden.

Stimmen zur 1. Auflage

„Ein Lehrbuch, das Maßstäbe setzt!“ Prof. Dr. Bernd Simeon, TU Kaiserslautern

„Endlich ein deutschsprachiges Mathematikbuch, das so richtig Spaß macht.“ Prof. Dr. Martin Pohl, Hochschule Regensburg

„Ein komplett neues und einmaliges Konzept: optisch und didaktisch geschrieben mit der Anschaulichkeit eines Schulbuches; mathematisch jedoch immer exakt und auch anspruchsvolle Themen erfassend. Meine Kollegen und ich sind begeistert; …“ Dr. Volker Pluschke, Universität Halle-Wittenberg

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By Tilo Arens

Dieses vierfarbige Lehrbuch bietet in einem Band ein lebendiges Bild der „gesamten“ Mathematik für Anwender. Angehende Ingenieure und Naturwissenschaftler finden hier die wichtigen Konzepte und Begriffe ausführlich und mit vielen Beispielen erklärt.

Im Mittelpunkt stehen das Verständnis der Zusammenhänge und die Beherrschung der Rechentechniken.

Herausragende Merkmale sind:

durchgängig vierfarbiges structure mit mehr als 1500 Abbildungen
prägnant formulierte Kerngedanken bilden die Abschnittsüberschriften
Selbsttests in kurzen Abständen ermöglichen Lernkontrolle während des Lesens
farbige Merkkästen heben das Wichtigste hervor
mehr als a hundred Anwendungsboxen erläutern Themen wie „Geometrie hinter dem GPS“, „Pageranking bei Google“ oder „harmonischer Oszillator“
Vertiefungsboxen geben einen Ausblick auf weiterführende Themen
Zusammenfassungen zu jedem Kapitel sowie Übersichtsboxen
mehr als 750 Verständnisfragen, Rechenaufgaben und Anwendungsprobleme

Inhaltlich spannt sich der Bogen von elementaren Grundlagen über die research einer Veränderlichen, der linearen Algebra, der research mehrer Veränderlicher bis hin zu fortgeschrittenen Themen der research, die für die Anwendung besonders wichtig sind, wie partielle Differenzialgleichungen, Fourierreihen und Laplacetransformationen. Numerische Konzepte sind integraler Bestandteil der Kapitel. Der Wahrscheinlichkeitsrechnung un
d Statistik ist einer der sechs Teile des Buchs gewidmet.

Zusätzlich gibt es zum Buch die web site matheweb, die Ihnen u.a. bietet:

Bonusmaterialien zu zahlreichen Kapiteln
Hinweise, Lösungswege und Ergebnisse zu allen Aufgaben
Zusatzmaterialien wie Maple-Worksheets zu verschiedenen Themen des Buchs
die Möglichkeit, zu den Kapiteln Fragen zu stellen

Das Buch wird allen Anwendern der Mathematik
vom Beginn des Studiums über höhere Semester bis in die Berufspraxis hinein ein langjähriger verlässlicher Begleiter sein. Für die three. Auflage ist es vollständig durchgesehen und in info ergänzt und didaktisch weiter verbessert worden.

Stimmen zur 1. Auflage

„Ein Lehrbuch, das Maßstäbe setzt!“ Prof. Dr. Bernd Simeon, TU Kaiserslautern

„Endlich ein deutschsprachiges Mathematikbuch, das so richtig Spaß macht.“ Prof. Dr. Martin Pohl, Hochschule Regensburg

„Ein komplett neues und einmaliges Konzept: optisch und didaktisch geschrieben mit der Anschaulichkeit eines Schulbuches; mathematisch jedoch immer exakt und auch anspruchsvolle Themen erfassend. Meine Kollegen und ich sind begeistert; …“ Dr. Volker Pluschke, Universität Halle-Wittenberg

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