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mandatory for teachers
If you are aiming to learn Calculus softly and thoroughly, then choose another book: Karl Menger's is far probably a manifest on teaching calculus rather than a textbook. If you are trying to find out why can't you understand more clearly the underlying concepts the "soft book" intends to clarify, then go to "Calculus: a Modern Approach". If you teach Calculus and you're aware that your students face difficulties, read Menger's works. They are not conventional. As a matter of fact, Menger remakes the whole world in a few more days than the previous Creator, but this time in a little bit more consistent fashion, or at least guided by some criticism. Menger is either loved or hated. His detractors once managed to insert at the front matter in one of his works, disguised as a print error: Karl Menger, University of Dame Notre. Since to him everything should be done in a different and particular way, Notre Dame naturally should be written Dame Notre. Foes are foes, but "Calculus: a Modern Approach" should be a mandatory text for calculus teachers and be always kept in unending reeditions.

Experimental Approach
Disclaim: I've studied calculus several yeas ago.

First, this book is not really "advanced" in contents, covering the standard topics of any undergraduate course in calculus. What differentiates it from other texts are several non common ideas in the use of the symbols that arguably result in a more consistent treatment if the subjects.

Specifically interesting is the use of the normally implicit identity function (here named "j") that upon judicious introduction brings a lot of clarity and consistency to the expressions. The author indicates this innovation is the equivalent (in calculus) to the ancient introduction of the symbol for zero in the arithmetic.

Another topic where the author devotes several paragraphs is the meaning of the concept of "variable", making explicit its different contexts of application. This is the most common pattern of the book: making explicit (and extending) several ideas that are usually taken for granted without enough reflection.

The final result could be confusing for anybody used to traditional calculus books, but deserves attention from educators, math writers and mathematicians in general.

Concerns about "Calculus: A Modern Approach"
I own this book. It dives straight into derivatives and continues on from there - a very steep dive indeed for anyone new to the subject. In my opinion it proceeds with excessively complex explanations of what should be easily comprehended concepts of calculus. It may, in my opinion, be suitable for the calculus-adept student or teacher but falls significantly short in any attempt to teach the subject to a novice. I do NOT recommend this book to anyone attempting to understand calculus on his or her own (i.e. beginners). If this method is considered a modern approach, then perhaps we should fall back to methods that have turned fewer newcomers off to the subject. Consider "Calculus Made Easy" by Silvanus P. Thompson and "Teach Yourself Calculus" by Hugh Neil instead. ... Read more

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Principles of Economics ushered in modern economics.Principles not only revolutionized value, price, andmarginal utility theories, but it was also used as theprimary textbook by several generations of Austrian studentsand scholars, including Ludwig von Mises and F. A. von Hayek. No economist's library is complete without a copy of thisclassic work. New printing in 1994! ... Read more

Customer Reviews (16)

A True Classic
Carl Menger played a pivotal role in the history of economic ideas.With this treatise, he simultaneously established himself as the founder of the Austrian School as well as a leader in the Marginal Revolution - one of the most important events in economics.Although Menger completed this book in the early 1870s, his contributions to subjective value theory, price formation, methodology, and time economization remain relevant even today.Anyone interested in economics should definitely pick up a copy.

Principles of Economics
The significance of this book hardly needs to be stressed. W. Stanley Jevons had stated the utility principle before, but his book was published in the same year as was Menger's. Léon Walras followed somewhat later. Although he was therefore not alone in developing the theory of diminishing utility, Menger nevertheless exerted a special influence through his students, several of whom became outstanding economists. Together with Menger they constitute the Austrian School of economists of which Menger is therefore of course the founder. The term marginal utility was later introduced by one of them, Friedrich von Wieser.

Here is the famous paragraph in which Menger states his marginal utility proposition:
"Accordingly, in every concrete case, of all the satisfactions secured by means of the whole quantity of a good at the disposal of an economizing individual, only those that have the least importance to him are dependent on the availability of a given portion of the whole quantity. Hence the value to this person of any portion of the whole available quantity of the good is equal to the importance to him of the satisfactions of least importance among those assured by the whole quantity and achieved with an equal portion." (p. 132)

Here, is Menger (comparatively very briefly) on complementarity:
"The additional complexity arising with goods of higher than second order lies rather in the fact that even command of all the goods required for the production of a good of the next lower order does not necessarily establish their goods-character unless men also have command of all their complementary goods of this next and of all still lower orders." (p. 61)

The development of subjective value theory represented a challenge of the first importance to the classical cost theories and particularly to the socialist theories of labor-power as the source of value. The task of reconciling what sometimes appeared to be an excessive stress on demand on the part of the Austrians and the more or less exclusive analysis of value in terms of cost or supply on the part of the classical writers remained for neoclassical writers to pursue. The foregoing comments cover familiar ground. However, there seems to be an importance to the Austrian School which often appears to be overlooked by American economists. The various writers, from Menger through von Wieser, Bohm-Bawerk, Mises, and Hayek, developed their views by careful reasoning and with due regard for what, taken together, may be called Austrian theory. In the development of their views regarding capital, interest, business fluctuations, and the nature of the economic system there is a logical cohesiveness which might well be understood more widely. Frequently only fragments of their views are presented for critical evaluation and attack. This is well illustrated in a general way by the criticism which the opposition on the part of Mises and Hayek to interventionism and socialism generally evokes in some quarters. Although their opposition is entirely consistent with their own system of thought, their opponents have not attacked the logical structure as such.

The Essential Guide to Economics From Goods to the Origin of Money
Carl Menger's `Principles of Economics' is the most thorough and accessible survey of basic economics I have come across. Anyone interested in the roots of our modern institutions will find this book to be an excellent resource. Though it was written more than a hundred years ago and does not cover banking or other more complex financial aspects of economics, this book will help anyone attempting to understand the problems we face today and offer a reasonable approach to help solve them.

Writing in an age of science, Menger sets a very scientific tone from the beginning. His suggestion in the preface that `Principles' is an empirical study seems to be the mistake of an overzealous fan of the scientific method, since the book is anything but empirical. `Principles' is outright a theoretical work. This fact does not prevent it from being scientific, however, and Menger sets forth on his task in a very meticulous, one might say Aristotelian fashion.

It is a good thing that the book is theoretical too because, as such, `Principles' is perhaps the most useful and timeless work in all of the discipline. Once Menger explores the character of goods and economic goods (and, by extension, property and wealth), the author arrives at the meat of the work--his Marginal Utility Theory of Value. Though he never uses the term `marginal,' Menger's explanation is the most lucid and practical out there (Jevins and Walras developed similar theories independently around the same time period).

The idea behind marginal utility is rather intuitive. A good's value is based on two relevant factors: the good's usefulness to a person and its availability. In short, if a good is very useful and not widely available, it has a high value to that person; if a good is not very useful and widely available, it has low value. Despite this very logical conclusion, the theory was seen as revolutionary at the time because it dispelled the popular concept of value established by Smith and extended by Ricardo and Marx. Those classical economists held that the value of a given good was based on the labor put into it. The Marginal Theory sufficiently corrected the Labor Theory's faults and offered a definitive framework for the science of economics.

In the second half of the book, Menger's analysis of exchange, price, commodities, and money follows naturally from his theory of value, thus establishing a complete economic theory from goods to money. Menger's work was the basis for the Austrian School of Economics, which was added to subsequently by noted economists Ludwig von Mises and F.A. Hayek.

Altogether, `Principles' is an absolute masterpiece of economic theory that must be studied by anyone who hopes to make a sound judgment on today's economic and political climate or economics in general.

Good intro to economics
Menger, The Father of Austrian economics, lays out the framework of how the human economy functions.
He starts off by explaining how a good comes into play and the requirements needed for an item to be considered a good. He also takes time to explain the idea of goods of a first order, which is the consumption good, and goods of a higher order, which are intermediate goods, and how prices for goods of a higher order are set by the goods of a first order, and not the other way around, as many mistakenly think. Menger quickly touches up on how property and economy have a joint economic origin, and thus a mutually exclusive relationship. Next Menger talks about the differences between economic goods, and non-economic good, and how in some places economic goods can be considered non-economic, and also in the same place at different times, the same relationship can be present. He also talks about the relationship between economic and non economic goods. Menger then talks about the nature and the origin of value and shows how value is purely a subjective notion.He distinguishes the difference between use-value and exchange-value, and also talks about the concept of thelabor theory of value, and also speaks of the value of capital, land, as well as the relationships they have with interest. Next is the theory of exchange, as well as the theory of prices, The theory of commodity, and finishes it off with a theory into the origins of money.

This is a very easy to read, introductory text to the Austrian school of economics.

The Mark Of A Genius, But A Dense Book
Carl Menger was the founder of the Austrian School of economics. In this book we can see the mark of his genius as he covers:
1. The General Theory Of The Good
2. Economy and Economic Goods
3. The Theory Of Value
4. The Theory Of Exchange
5. The Theory Of Price
6. Use Value and Exchange Value
7. The Theory Of The Commodity
8. The Theory Of Money
The book is not that easy to read as it follows a dense writing style, where the author demonstrates each basic concept and builds new concepts based on previous demonstrations. For the general reader, on the subject of the Austrian School of economics I would greatly recommend Economics for Real People or Economics in One Lesson: 50th Anniversary Edition ... Read more

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Volume 2 deals with topics as diverse as topology, geometry, analysis and algebra, as well as writing on economics, sociology, logic, philosophy and mathematical results. A monument to the diversity and originality of Menger's ideas. ... Read more

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This Book Is In German. ... Read more

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Deals with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas. ... Read more

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Karl Menger (1902--1985), a pure mathematician of distinction, also took an active interest in both philosophy and economics. In this memoir, which he was composing at the time of his death, he relates how all these subjects developed and flourished against the Viennese background (itself described in depth and with affection), and did so despite the political developments of the '20s and '30s, which depressed but did not silence him. He continued his work in the United States. The memoir describes his membership of the Vienna Circle (the scientifically minded philosophers that gathered around Moritz Schlick) for whom he was an invaluable intermediary, bringing them into contact with Brouwer's intuitionism, with the work of the Polish logicians, especially that of Tarski, but more generally with rigorous mathematical thinking.Indeed, the other Viennese group described here is the Mathematical Colloquium, which he founded, whose Proceedings (still read) show it to have been a powerhouse of ideas. There are also valuable chapters on philosophy and mathematics in the Poland of the '20s and '30s and the U.S. of the '30s and '40s. The memoir devotes particular attention to Wittgenstein (with whose family Menger was acquainted) and to Godel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work abounds in mathematical examples lucidly applied to that subject. This volume (which can now be placed beside the two by Menger already published in the Vienna Circle Collection) gives an unequalled impression of the fruitful interdisciplinarity of the tradition to which he partly belonged and partly created. It testifies both to Menger's power to inspire and to the critical eye he always turned on even the philosophers he most approved of. A brief account of his life is given in an Introduction by the Editors (all of whom knew him personally), and his important contribution to the social sciences -- only touched on in the text -- is elucidated by Professor Lionello Punzo. ... Read more

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Karl Menger (1902-1985) was the mathematician son of the famous economist Carl Menger. He was professor of geometry at the University of Vienna from 1927 to 1938. During that period, which was crucial from an historical and philosophical point of view, he joined the Vienna Circle and founded his Mathematical Colloquium. The present volume of Advances in Austrian Economics offers the transcription of those unpublished parts of Menger's notes written between 1923-1938. It is hoped that these notes, together with the Editor's contextual explanations, provide a subtext to Menger's biography during this influential period. ... Read more

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Chapters: Herbert Simon, Ludwig Mies Van Der Rohe, Leon M. Lederman, Karl Menger, László Moholy-Nagy, Leonid Hurwicz, Albert Henry Krehbiel, Sergey Degayev, Lee de Forest, Frank W. Gunsaulus, Tamara Sher, Nambury S. Raju, William Alden Edson, William J. Mitsch, S. I. Hayakawa, Ralph Brill, Randy Barnett, Edward Wagenknecht, Edward T. Hall, Jane Heap, Angelo Mangiarotti, Lori Andrews, Hubert Stanley Wall, John Henry Waddell, Walter Mccrone, Aaron Siskind, Victor Conrad, Arthur E. Martell, Robert Piotrowski, Myron L. Bender, Leon Stover, Max Dehn, Jeanne Gang, Dennis Schmitz, Cosmo Campoli, Ludwig Hilberseimer, Alfred Caldwell, James Armsey, Serge Chermayeff, Lewis Collens, John L. Anderson, John Rettaliata, Sarah Whiting, Harry Callahan, Stuart L. Deutsch, Jane Calvin, John F. O. Bilson, Henry Holmes Smith, Mohammad Shahidehpour, Michael Davis, James G. Carr, Joe Baugher, Hans Reissner, David P. Boder, Patrick Corrigan, Muhammad S. Eissa, Harry Gunning, Thomas Lyle Martin, Jr., Walter Peterhans, George Anselevicius, Henry Townley Heald, Edward Reingold. Source: Wikipedia. Pages: 287. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Ludwig Mies van der Rohe, born Maria Ludwig Michael Mies (March 27, 1886 August 17, 1969) was a German-American architect. He was commonly referred to and addressed by his surname, Mies, by his colleagues, students, writers, and others. Ludwig Mies van der Rohe, along with Walter Gropius and Le Corbusier, is widely regarded as one of the pioneering masters of Modern architecture. Mies, like many of his post World War I contemporaries, sought to establish a new architectural style that could represent modern times just as Classical and Gothic did for their own eras. He created an influential 20th century architectural style, stated with extreme clarity and simplicit...More: http://booksllc.net/?id=17897 ... Read more

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Chapters: Kurt Gödel, Christian Doppler, Georg Joachim Rheticus, Leopold Vietoris, Karl Menger, Georg Von Peuerbach, Emil Artin, Richard Von Mises, Hilda Geiringer, Otto E. Neugebauer, Simon Von Stampfer, Johann Radon, Eberhard Hopf, Leo Perutz, Hellmuth Stachel, Nikolaus Hofreiter, Theodor Von Oppolzer, Georg Kreisel, Salomon Bochner, Karl Sigmund, Andreas Von Ettingshausen, Sy Friedman, Frank Spitzer, Georg Alexander Pick, Franz Alt, Bruno Buchberger, Henry O. Pollak, Edmund Hlawka, Hermann Rothe, Felix Pollaczek, Leopold Gegenbauer, Andreas Stoberl, Otto Stolz, Wilhelm Wirtinger, Adam Tanner, Karl Zsigmondy, Karl Weissenberg, Hans Weinberger, Josef Finger, Wolfgang Gröbner, Walther Mayer, Philipp Furtwängler, Ernst Sigismund Fischer, Wilhelm Blaschke, Otto Schreier, Heinrich Franz Friedrich Tietze, Emil Weyr, Anton Felkel, August Adler, Eduard Helly, Herta Freitag. Source: Wikipedia. Pages: 175. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Emil Artin (March 3, 1898, in Vienna December 20, 1962, in Hamburg) was an Austrian-Armenian mathematician. The mathematician Emil Artin was born on March 3, 1898 in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent. Several documents, including Emils birth certificate, list the fathers occupation as opera singer though others list it as art dealer. It seems at least plausible that he and Emma had met as colleagues in the theater. They had been married in St. Stephen's Parish on July 24, 1895. Emil entered school in September 1904, presumably in Vienna. By then, his father was already suffering symptoms of advanced syphilis, among them increasing mental instability, and was eventually institutionalized at the rece...More: http://booksllc.net/?id=245351 ... Read more

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Chapters: Kurt Gödel, Alfred Jules Ayer, Rudolf Carnap, Otto Neurath, Karl Menger, Richard Von Mises, Louis Rougier, Moritz Schlick, Rose Rand, Eino Kaila, Edgar Zilsel, Gustav Bergmann, Herbert Feigl, Victor Kraft, Friedrich Waismann, Philipp Frank, Hans Hahn, Olga Taussky-Todd, Verification Theory, Olga Hahn-Neurath, Josef Frank. Source: Wikipedia. Pages: 109. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Kurt Gödel (German pronunciation: ; April 28, 1906, Brno, Moravia, AustriaHungary January 14, 1978, Princeton, New Jersey, USA) was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape WWII. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics. Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers. He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic...More: http://booksllc.net/?id=16736 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Alvin Plantinga, Knute Rockne, Hugo Steinhaus, Karl Menger, Paul Erdős, Tariq Ramadan, Vittorio Hösle, Kevin Hart, Douglas Kmiec, Donald Gutierrez, Henri Nouwen, Alasdair Macintyre, John Howard Yoder, Charles P. Neill, Jaegwon Kim, Richard Mcbrien, Dan Lipinski, Moonis Ahmar, John Finnis, Peter Van Inwagen, John P. Meier, James Tabor, John Joseph Haldane, Steven Schwarzschild, G. Robert Blakey, Ralph Mcinerny, Maurice Francis Egan, Nick Trakakis, Albert-László Barabási, Theodore Hesburgh, Charles Malik, John I. Jenkins, Amitabh Mattoo, Edward Malloy, Thomas V. Morris, Yozo Matsushima, Drago Kolar, Charles E. Rice, Alejandro Foxley, Mar Sarhad Yawsip Jammo, Henry H. Carter, Ruth Abbey, Christopher Hollis, Mark Noll, Julius Nieuwland, Daniel J. Myers, Stanley Hauerwas, Bei Dao, Pablo Eisenberg, Rose Rand, Bernard Lander, Elliot R. Wolfson, John T. Noonan, Jr., Anne Norton, Theodor Paleologu, Ernan Mcmullin, Cristina Bicchieri, Jack Miller, Yves Simon, Nathan O. Hatch, David N. Livingstone, Geoffrey Wainwright, John Augustine Zahm, Christian Smith, George Marsden, Virgilio Elizondo, Juan E. Méndez, Robert Audi, Allan Stitt, John L. Kelley, Yum-Tong Siu, Bruce L. Gordon, Laurence Thomas, James Gahagan, Michael Slinger, M. Brian Blake, Malaquías Montoya, Catherine Lacugna, Arnold Ross, Alan Gallay, Carol Ann Mooney, William K. Kelley, George A. Lopez, Gustavo Gutiérrez, Bill Slavick, Eugene Guth, John Paul Lederach, Frank P. Incropera, Asma Afsaruddin, Eugene Ulrich, Guillermo O'donnell, John Logan, Philip Mirowski, Pinchas Hacohen Peli, Dudley G. Wooten, Wladimir Seidel, Matthew V. Storin, Donald T. Critchlow, Paul F. Bradshaw, Rufus Isaacs, John Ferguson, Kenneth Francis Ripple, Thomas F. Konop, Karl-Ludwig Kratz, Janet E. Smith, Michael Joncas, John Henry Morgan, Donald George Vogl...More: http://booksllc.net/?id=584063 ... Read more