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Topic: List of mathematical theorems

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 Metamath Proof Explorer Home Page
When an axiom or theorem with a distinct variable condition is referenced in a proof, the distinct variable conditions attached the theorem being proved must satisfy those of the referenced axiom or theorem after substitutions are made into the referenced axiom or theorem.
For example, in traditional mathematics it would be implicit that the two variables in theorem dtru must be distinct (since one is bound and the other is free), but in Metamath this requirement must be made explicit.
Theorems of propositional calculus - Whitehead and Russell.
us.metamath.org /mpegif/mmset.html   (9321 words)

 Godel's Theorems
In general, diagonalization shows that a set of objects (sequences, programs, provable theorems, true facts) either can't be listed, computed or defined in a nice way or else a simple-to-construct diagonal or self-referential object is not one of the set's objects.
Roughly either the objects can't be listed or they aren't closed under the substitution and complementation operations used to construct a diagonal.
The reason they escape the conclusion of the first incompleteness theorem is their inadequacy, they can't encode and computably deal with finite sequences.
www.math.hawaii.edu /~dale/godel/godel.html   (2115 words)

Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation.
Were he right that the universe is effectively a computer, then Godel's theorems would require that nature, as a whole be understood only outside nature because no finite system is sufficient for itself.
The mathematics of the infinite cannot be understood apart from Judeo-Christianity.
www.evanwiggs.com /articles/GODEL.html   (3094 words)

 List_of_reference_tables   (Site not responding. Last check: 2007-10-21)
List of Judicial Committees of the Privy Council and House of Lords cases
List of items for which possession is restricted
List of the core beliefs of the Conservative Party of 2004
www.usedmotorcoaches.com /search.php?title=List_of_reference_tables   (1042 words)

 Collected Papers of R.A. Fisher Relating to Statistical & Mathematical Theory and Applications
A Mathematical Examination of the Methods of Determining the Accuracy of an Observation by the Mean Error, and by the Mean Square Error.
The Influence of Rainfall on the Yield of Wheat at Rothamsted.
Mathematical Tables, 1: xxvi-xxxv, British Association for the Advancement of Science (1931) Reproduced with permission of the Association.
www.library.adelaide.edu.au /digitised/fisher/stat_math.html   (2361 words)

 List of mathematical proofs - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-21)
2 Articles devoted to theorems of which a (sketch of a) proof is given
Theorems of which articles are exclusively devoted to proving them
Articles devoted to theorems of which a (sketch of a) proof is given
www.peacelink.de /keyword/List_of_mathematical_proofs.php   (202 words)

 List of reference tables - Unipedia   (Site not responding. Last check: 2007-10-21)
List of monasteries dissolved by Henry VIII of England
This includes lists by surname, nationality, occupation, office held, and belief.
List of lesbian, gay, bisexual and transgender community centers
www.unipedia.info /List_of_reference_tables.html   (1053 words)

 Mathematics Archives - K12 Internet Sites
The Hub is an Internetworked resource for mathematics and science education funded by the Eisenhower Regional Consortia and operated by TERC on behalf of the Regional Alliance for Mathematics and Science Education Reform.
Mathematical Mayhem is a non-profit mathematical journal written by and for high school and undergraduate university students.
Mathematics in Context (MiC) is an NSF-funded, comprehensive middle-school mathematics curriculum for grades 5-8 that reflects the philosophy and pedagogy of the NCTM standards.
archives.math.utk.edu /k12.html   (9883 words)

 Learn more about List of mathematical topics in the online encyclopedia.   (Site not responding. Last check: 2007-10-21)
Everything remotely connected to mathematics, including articles about mathematicians, should be listed here.
(For a much nicer list of mathematicians, see list of mathematicians.) The list is not necessarily complete or up to date - if you see an article that should be here but isn't (or one that shouldn't be here but is), please do update the page accordingly.
The main purpose of these pages is to make it easy for those interested in the subject to monitor changes to these pages.
www.onlineencyclopedia.org /l/li/list_of_mathematical_topics.html   (249 words)

 List of theorems -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-21)
In some fields, theorem can be considered as a (Click link for more info and facts about courtesy title) courtesy title, given to major results, although with a content that would not satisfy a mathematician.
Most of the results do come from mathematics, but there are others from (Click link for more info and facts about theoretical physics) theoretical physics, (The branch of social science that deals with the production and distribution and consumption of goods and services and their management) economics and so on.
(Click link for more info and facts about Banach fixed point theorem) Banach fixed point theorem ((A set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality) metric spaces, (An equation containing differentials of a function) differential equations)
www.absoluteastronomy.com /encyclopedia/l/li/list_of_theorems.htm   (5777 words)

 Riesz representation theorems   (Site not responding. Last check: 2007-10-21)
A Riesz representation theorem for cone-valued functions, Walter Roth...
Integral Representation Theorems in Partially Ordered Vector Spaces...
List of mathematical theorems article - List of mathematical theorems mathematic...
www.scienceoxygen.com /math/541.html   (94 words)

 Mathematics Archives - Other Software Sites
MAS views mathematics in the sense of universal algebra and model theory and is in some parts influenced by category theory.
The Guide to Available Mathematical Software (GAMS) project of the National Institute of Standards and Technology (NIST) studies techniques to provide scientists and engineers with improved access to reusable computer software which is available to them for use in mathematical modeling and statistical analysis.
Transmath is a computer-based mathematics tutor designed to strengthen and consolidate the basic mathematical knowledge of students commencing numerate degree courses.
archives.math.utk.edu /cgi-bin/all_software.html   (15185 words)

 Science Forums and Debate - Set List of Theorems
It is very confusing talking to someone with a different textbook, and referring to theorem #1, when yours is something like "all right angles are congruent", and his is, "If a radius is perpendicular to a chord, then it bisects a chord".
You also have to remember that your average mathematician probably has a small library of mathematical textbooks in their office, and usually there'll be some kind of campus library.
On top of that, theorems are almost always stated in proofs - I just don't see the point in trying to categorise what must be millions of theorems for no apparent reason.
www.scienceforums.net /forums/printthread.php?t=6495   (1260 words)

 Gödel's Incompleteness Theorem
Gödel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths...
I am reminded of Gödel's second theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent.
All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally.
www.miskatonic.org /godel.html   (1160 words)

 Mathematical Programming Glossary - D   (Site not responding. Last check: 2007-10-21)
For example, if a bisection method is used (as in searching a sorted list), the divide and conquer recurrence is T(n) = T(n/2) + 2 for n=2,4,6,8,...
Another mathematical program with the property that its objective is always a bound on the original mathematical program, called the primal.
An example is that the class of cutting plane methods, associated with the Lagrangian dual, is dual to the column generation method of Dantzig-Wolfe decomposition.
carbon.cudenver.edu /~hgreenbe/glossary/D.html   (2386 words)

 Completeness Theorems. Model Theory. Mathematical Logic. Part 4.
Gödel's results were a landmark in 20th-century mathematics, showing that mathematics is not a finished object, as had been believed.
Model Existence Theorem says that (syntactic!) consistency of a theory is sufficient: if a theory does not contain contradictions, then it is a "theory of something" - it describes at least some kind of "mathematical reality".
This theorem says that if some formal theory T does not have models, then the logical axioms and rules of inference are strong enough to derive a contradiction from the axioms of T. But the proof of the Model Existence Theorem we will consider below, is positive, not negative!
www.ltn.lv /~podnieks/mlog/ml4.htm   (7959 words)

Mathematical ideas and notions of quantum field theory by Pavel Etingof
Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.
Mathematics of Rubik's cube by David Joyner is a good source for discrete group theory with applications to permutation puzzles.
us.geocities.com /alex_stef/mylist.html   (2371 words)

 [No title]
Mathematicians were not immune, and at a mathematics conference in July, 1999, Paul and Jack Abad presented their list of "The Hundred Greatest Theorems." Their ranking is based on the following criteria: "the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result."
The list is of course as arbitrary as the movie and book list, but the theorems here are all certainly worthy results.
I hope to over time include links to the proofs of them all; for now, you'll have to content yourself with the list itself and the biographies of the principals.
personal.stevens.edu /~nkahl/Top100Theorems.html   (217 words)

 Publications, Mathematical Foundations of Computer Science   (Site not responding. Last check: 2007-10-21)
SO(AE) sentences and their asymptotic probabilities, Mathematical Logic Quarterly, vol.
Preservation theorems for two-variable logic, Mathematical Logic Quarterly, vol.
Otto, EM Functors for a Class of Generalized Quantifiers, Archive for Mathematical Logic, vol.
www-mgi.informatik.rwth-aachen.de /Publications/publications.html   (2755 words)

 Books Online
- If you know of links to research-level mathematics (or mathematically related) books online, please send email to online-books@ams.org.
We hope to provide a comprehensive list of books available online which will grow over time.
Fundamentals of Model Theory, by William Weiss and Cherie D'Mello
www.ams.org /online_bks/online-books-web.html   (122 words)

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