Dr. Robert A. Herrmann

FREE BOOKS

As a former employee of the Federal Government, I must make the following books available free of charge since they were written using federal funds. These books are written in Plain Tex, the well-known technical word processor. The files have been reprocessed so that they can be "read" and printed by use of the Adobe Reader. If you do not have this software, then free software can be obtained from Adobe. With the exception of book 2, in order to save as much disk space as possible, the files have also been additionally compressed by means of zip software. If you do not have "unzipping" software, then evaluation shareware is available. Simply go to PKware. The Adobe reader should only be considered as a "pre-viewer." Suggestions as to the best magnification for such viewing will be given on the "content" pages. However, the "reader" will yield excellent and perfectly printed copies at 300 DPI. [Note: There may be one or two instances were a standard Roman type "comma" has been translated into a capital Gamma.]

If you find any of the files faulty, please E-mail me with an appropriate identification and I will attempt to correct the problem. I am aware that disk space may not now be available for you to download and "unzip" an entire book. The number that appears after each file's name is the unzipped pdf file size and the books have been constructed so that they may be easily reproduced in duplex form. I cannot sell these books to the general public since they were mostly financed by government funds.



BOOK 1 (2.048MB)

"Logic for Everyone," (A $60 value) (1994) Math. Dept., U. S. Naval Academy, Annapolis MD 21402-5002 (USA)

As far as I can tell, this is the most elementary book in Mathematical Logic available that also covers all of the basic material in the propositional and predicate calculus. This is the book written especially for the Midshipmen at the United States Naval Academy with the general view that it is a terminal course. Enough material is covered so that certain topics in elementary model theory can be included and all mathematical proofs are of the most elementary nature requiring no specialized mathematical procedures. Applications include a very elementary introduction to nonstandard models as they are obtained by means of the "compactness" theorem, and the generation of weak "ultrawords" and an "ultralogic" operator. A complete set of answers for all exercise problems and 6 figures in the form of gif images are included.

CONTENTS - BOOK 1


BOOK 2 (1.50MB)
The following free book was under a research grant from the U. S. Naval Academy Research Council. (Unfortunately, it is probably not totally free from minor typographical errors.) It has been used by numerously many individuals throughout the world to teach themselves the new rigorous Robinson methods of infinitesimal analysis and the new rules for rigorous modeling. In particular, it has been used by scientists at NASA for this purpose.

"Some Applications of Nonstandard Analysis to Advanced Undergraduate Mathematics -- Infinitesimal Modeling, Elementary Physics, Generalized Functions'' (A $180 value) 1989-1991 Instructional Development Project, Math. Dept., U. S. Naval Academy, Annapolis MD 21402-5002 (USA)

This 217 book is constructed in a somewhat unusual manner. It is composed of three "manuals". In the first manual, the rigorous rules and procedures are presented and examples are given as to their use. With the exception of chapter 9, the actual proofs of the mathematical theorems that are so applied appear in a series of appendices.

The second much smaller manual applies these rigorous methods to some areas in physics not covered in the first manual. Such things as an actual formal derivation of Newton's Second Law of motion from more fundamental observations is given. Certain methods used in physics that deal with the concept of point masses are shown to be incorrectly expressed in the language that appears in elementary texts and the proper concept is presented.

As an added feature, the third manual deals with a very significant concept within nonstandard analysis, not specifically identified previously, the enlargement and the saturation properties for a model. In order to give appropriate instruction in the use of such concepts, they are applied to the important scientific and mathematical subject known as generalized functions or distributions.

CONTENTS - BOOK 2


BOOK 3 (1.96MB)

"The Theory of Ultralogics," (A $160 value) (1993) Institute for Mathematics and Philosophy (Typographical corrections and improvements are being made to this book and this version often supersedes, by a year, the version that appears at www.arxiv.org.)

The research presented in this book may be the most significant scientific work of my entire professional career. It was in Oct. 1978 when the concepts were first discovered that have produced the significant mathematical structure developed within the pages of this book. It began with the idea that it might be possible to model mathematically the concept known as subliminal perception and other similar notions that do not lend themselves to numerical modeling. The G-model, the D-world model, the GGU-model and the MA-model are four of the mathematical models obtained by application of these mathematical results. Information relative to these models can be found throughout these web pages. After many, many years of refinement, the methods that appear are, I believe, the simplest possible and are based upon a few human linguistic experiences that are practiced trillions of time a day within our earthly environment. The mathematical structure and processes were purposely chosen to be the simplest and least controversial. Indeed, to individuals who do research within nonstandard analysis these mathematical methods would be considered as very elementary in character. However, the intuitive interpretation and application of these methods my be difficult to grasp without considerable effort and reflection. As far as can be determined, there are no logical nor conceptual errors within this book. Typographical errors will not alter any specific result.

CONTENTS - BOOK 3



BOOK 4 (1.29MB)

"Einstein Corrected," (A $60 value) (1995) (Nonstandard Analysis Applied to Special and General Relativity -The Theory of Infinitesimal Light-clocks.) Math. Dept U. S. Naval Academy, Annapolis, MD 21402-5002. (Many typographical corrections are being made and this version supersedes the one that appears at www.arxiv.org.)

It is actually dangerous for me to present the material that appears within this book due to the usual misunderstandings. Any scientist who claims that there are fundamental errors within the foundational methods used to obtain Einstein's General and Special Theories of relativity may be greatly ridiculed by his colleagues who do not read carefully. The reason for this has nothing to do with science but has everything to do with scientific careers, research grants and the like. Thousands upon thousands of individuals have built their entire professional careers upon these two theories and their ramifications. The theoretical science produced is claimed to be ``rational'' since it follows the patterns of a mathematical structure. As a mathematician who produces such structures, it is particular abhorrent to the scientific community if I make such a claim. Mathematicians seem to have an unsettling effect upon some members of the physical science community, especially when a mathematician delves into a natural science. After all, it was the mathematician Hilbert who, without any great effort, was actually the first to present, in a public form, the so-called Einstein gravitational field equations.

Now please read the following very carefully. The results presented here and in my published papers on this subject are not intended to denigrate those scientists who have, in the past, contributed to these Einstein theories or who continue to do so. The corrections I have made are in the foundations for these theories. The corrections are totally related to how the results are interpreted physically. These corrections do not contradict the results obtained when the Einstein approach and the language used are considered as models for behavior. These corrections are based upon newly discovered rules for rigorous infinitesimal modeling. These results may also be significant to those that hold to the belief that many events within the natural world are produced classically by a zero-point radiation field.

Many unqualified individuals continue to present their own alternatives to these Einstein theories, some claiming that the results are but an exercise in high- school algebra. Further, many of these alternate theories ignore or contradict quantum physical descriptions for natural-system behavior. Certain scientific groups tend to categorize any and all criticisms of the Einstein theories as coming from the unqualified and lump such criticisms into the same unworthy category. However, many highly qualified scientists of the past such as Builder, Fock, Ives and Dingle have made such claims relative to the foundations of these two theories. For Ives and Dingle, the fundamental approach was to assume that length contraction, and not time dilation, is a real natural effect and it is this that leads to the Einstein conclusions. In order to eliminate these criticisms, Lawden states the "modern" interpretation that length contraction has no physical meaning, and only "time dilation" is of significance. This modern assumption is certainly rather ad hoc in character. Further, many, many theory paradoxes still appear within the literature and are simply ignored by the scientific community. There is, however, a reason for this.

In 1992, the Einstein approach was shown explicitly to contain logical error. It was not possible to show this until many years after the theory was fully developed. Further, the original approach to Einstein's General Theory utilizes a "geometric language," a language that has been criticized by many including John Wheeler as the incorrect approach to analyze the fundamental behavior of universe in which we dwell. Einstein's theory is but a "model" for physical behavior, a model for physical behavior that does not, at present, foundationally correspond to objective reality. As Patton and Wheeler stated it,

". . . geometry is as far from giving an understanding of space as elasticity is from giving an understanding of a solid. . . . the basic structure is something deeper than geometry, that underlies both geometry and particles . . . what is the substance out of which the universe is made?"
Although Einstein used an explicit operational approach in his Special Theory, he was unable to use a mathematical approach that encapsulates his operational definitions since the actual mathematics was not discovered until 1961. Einstein and Hilbert used what was available to them at the time. Further, I respectfully submit that one of the greatest absurdities within modern science is that the concept of "time" is altered by physical behavior or physical entities as if "time" itself is a particle or field entity or the like. It is the measurement of this concept that is used to describe alterations in physical behavior. In this book, this absurdity has been eliminated by showing that one specific measurement of time is altered and, using this specific altered entity, all other appropriate behavioral alterations are predicted. Further, using the modern corrected theory of the infinitesimal and infinite numbers as discovered by Robinson, all logical errors and paradoxes are removed. Moreover, the recently discovered correct rules for infinitesimal modeling are used, and this eliminates the need for tensor analysis and Riemannian geometry. One important aspect of this new approach is that it does not in any manner contradict or eliminate any quantum physical theory. This new approach indirectly shows the existence of an additional electromagnetic interaction with a substratum composed of entities from the nonstandard physical world; a "world" that is distinct from what one defines as our natural world. This is a portion of a substratum, a subquantum region, "below" the vacuum of particle physics that is required for most modern quantum physical theories.

Some interesting results produced by this new investigation are (1) these theories are relative to electromagnetic properties only. (2) All alterations in natural system behavior rigorously predicted by these theories would indirectly indicate an electromagnetic interaction is taking place. (3) These theories need not apply under all physical conditions. (4) The non-rigorous methods used to establish the universal constancy of a "speed for electromagnetic informational transmissions" need not hold unless a specific rigorous derivation, not using the "observer" notion, is applied.

CONTENTS - BOOK 4

Click back button, or if you retrieved this file directly from the Internet, then return to top of home page. In you retrieved this file while on my website, then return to top of home page.