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Topic: List of theorems

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List of mathematical theorems

Fundamental theorem of arithmetic

Fundamental theorem of linear algebra

Linear algebra

List of conjectures

Pythagorean theorem

Fundamental theorem of vector analysis

List of fundamental theorems

Theorem

List of mathematical proofs

Speedup theorem

Ham sandwich theorem

Fundamental theorem of algebra

Theory of equations

Euclidean geometry

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	Directory of Theorems (Site not responding. Last check: 2007-11-03)
		Theorem 11: The sum of the opposite angles of a cyclic quadrilateral is 180°
		Theorem 12: In a right-angled triangle, the square of the length of the side opposite to the right angle is equal to the sum of the squares of the lengths of the other two sides.
		Theorem 13: If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle has a right angle and this is opposite the longest side
	www.teachnet.ie /tbrophy/theorems.html (216 words)

	PlanetMath: fundamental theorems in complex analysis (Site not responding. Last check: 2007-11-03)
		The following is a list of fundamental theorems in the subject of complex analysis (single complex variable).
		If a theorem does not yet appear in the encyclopedia, please consider adding it -- Planet Math is a work in progress and even some basic results have not yet been entered.
		This is version 19 of fundamental theorems in complex analysis, born on 2005-01-22, modified 2006-07-19.
	planetmath.org /encyclopedia/FundamentalTheoremsInComplexAnalysis.html (142 words)

	Theorem - Wikipedia, the free encyclopedia
		A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions.
		A description of a formal language and a list of assumptions (axioms) in that language.
		Informally speaking, most such theorems are not of any particular interest; 'theorem' used in this sense is a technical term indicating that a derivation exists and has none of the subjective connotations of importance as when the term is used in general mathematics.
	en.wikipedia.org /wiki/Theorems (934 words)

	Theory
		A theory consists of a list of theorems, a list of constant declarations, and some auxiliary lists of declarations.
		List of identifiers or operators which will eventually be proved as theorems (needed for recursive theorem definitions).
		The first term is a constant name or a constant applied to a list or lists of parameters, which is the left side of the intended theorem; the second term is the right side of the intended theorem.
	math.boisestate.edu /~holmes/mark2/node71.html (1116 words)

	List Of Theorems (list of theorems info) (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-03)
		Theorems may be called fundamental because they are results from which further, more complicated theorems follow, without reaching back to axioms.
		Abel's theorem is frequently useful in dealing with generating functions of real-valued and non-negative sequences, such as probability-generating functions.
		The content of the theorem is that the solution of a higher-degree equation cannot always be expressed by starting with the coefficients and using only finitely many of the operations of addition, subtraction, multiplication, division and extracting roots (radicals).
	wikimiki.info.cob-web.org:8888 /en/list+of+theorems (3505 words)

	List Of Theorems (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-03)
		Going-up and going-down theorems ('' commutative algebra '')
		Multinomial theorem ('' algebra '', '' combinatorics '')
		Stokes' theorem ('' vector calculus, differential topology '')
	www.seattleluxury.com.cob-web.org:8888 /encyclopedia/entry/list_of_theorems (682 words)

	SparkNotes: Review of Geometry II: Theorem Review
		Here is a summary of those theorems in list form, grouped roughly by the figures they involve.
		This list is not comprehensive--there are other things you have to know to construct a good proof.
		Theorems that basically echo a definition (the angles of a rectangle are all 90 degrees, for example) aren't included.
	www.sparknotes.com /math/geometry2/review/theoremlist.html (1187 words)

	Theorem Summary
		A theorem (the term is derived from the Greek theoreo, which means I look at) denotes either a proposition yet to be proven, or a proposition proven correct on the basis of accepted results from some area of mathematics.
		Mathematicians develop new theorems by suggesting a proposition based on experience and observation which seems to be true.
		Since theorems were a direct result of deductive reasoning, which yields unquestionably true conclusions, they believed their theorems were undoubtedly true.
	www.bookrags.com /Theorem (1213 words)

	Formalizing 100 Theorems
		There exists a "top 100" of mathematical theorems on the web, which is a rather arbitrary list (and most of the theorems seem rather elementary), but still is nice to look at.
		Theorems in the list which have not been formalized yet are in italics.
		The difficult proofs in the list (according to John all the others are not a serious challenge "given a week or two") have been underlined.
	www.cs.ru.nl /~freek/100 (358 words)

	[No title]
		If a match ) ( is found, the goal is rewritten according to the matched instance ) ( of the consequent, after which the corresponding hypotheses of ) ( the argument theorems are added to the goal as new conjuncts on ) ( the left.
		For ) ( each list of theorems, the goal is rewritten as much as possible, ) ( until no further changes can be achieved in the goal.
		Each list of theorems is applied ) ( by rewriting with each theorem in it as many times as they apply.
	www.cis.upenn.edu /~hol/quotients/dep_rewrite.sig (1218 words)

	Pythagoras.htm
		A list of theorems attributed to Pythagoras, or rather more generally to the Pythagoreans.
		(ii) The theorem of Pythagoras - for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
		We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side.
	www.cse.ohio-state.edu /~brinkmei/math/Pythagoras.htm (400 words)

	IUA-Seminar:Classifying the complexity of constraint satisfaction problems
		A large list of theorems, conjectures and dichotomies were commented in this talk.
		Theorem 3: Solving systems of equations over a finite group G is tractable if G is abelian.
		Theorem 4: Let B be a boolean structure.
	www.iua.upf.es /activitats/semirec/semi-krokhin.htm (452 words)

	Math 5337 Symmetry Definitions Theorems
		Theorem 0: The only isometries of the plane are combinations of translations, rotations, and reflections.
		This says that Theorem 0 could be restated: any product of a reflection, a rotation and a translation is equivalent to the product of three carefully chosen reflections.
		Theorem 5: Given a pair of isometries A and B, the product AB is not necessarily the same as the product BA.
	www.geom.uiuc.edu /education/math5337/Symmetry/theorems.html (417 words)

	LaTeX Tips: Theorems
		Note that the period after "Proof of the Main Theorem" is supplied by the macro and should not be included in the argument.
		The reason for this behavior is that the theorem environment "eats up" (nearly) any space at the beginning of the theorem, so commands like \hfill or \newline or \par have no effect.
		Theorems quoted from the literature are often stated in a form like "Theorem A (Gauss [3])" or "Theorem A ([3, Theorem 4.6])".
	www.math.uiuc.edu /~hildebr/tex/theorems.html (1490 words)

	DB.theorems (Site not responding. Last check: 2007-11-03)
		An invocation theorems thy, where thy is the name of a currently loaded theory segment, will return a list of the theorems stored in that theory.
		Each theorem is paired with its name in the result.
		If thy is not the name of a currently loaded theory segment, the empty list is returned.
	www.cs.utah.edu /~swalton/hol98/help/Docfiles/HTML/DB.theorems.html (190 words)

	Theorems List (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-03)
		They are proven logically from the assumptions and definitions we make in geometry.
		Theorems are like the leaves or fruit of our geometree.
		The measures of alternate interior angles are equal.
	matcmadison.edu.cob-web.org:8888 /ald/lab/geometry/theorems.htm (65 words)

	Limits Theorems
		Objectives: The following is a list of theorems that can be used to evaluate many limits.
		Theorem A. Suppose that f and g are functions such that f(x) = g(x) for all x in some open interval interval containing a except possibly for a, then
		Theorem B. Suppose that f and g are functions such that the two limits
	archives.math.utk.edu /visual.calculus/1/limits.18/index.html (149 words)

	OpenTheory Article Format Version 1
		Pop a term c; pop a list of terms h; push the theorem (or sequent) h - c with hypothesis h and conclusion c.
		As a rule of thumb, constructing theorems is always better than constructing sequents (since sequents can be recovered from theorems, but not vice-versa), but sometimes this is not possible or even desirable.
		ProofPower searches through the list of theorems on the top of the simulation stack and also the contents of all the objects on the stack looking for an alpha equivalent theorem.
	www.cl.cam.ac.uk /~jeh1004/research/opentheory/article.html (1068 words)

	Online Encyclopedia and Dictionary - Mathematics (Site not responding. Last check: 2007-11-03)
		An alphabetical and subclassified list of mathematical topics is available.
		These are theorems and conjectures that have changed the face of mathematics throughout history.
		Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theorem
	www.fact-archive.com /encyclopedia/Mathematics (2298 words)

	Ring Theory as Applied to the Three Classical Geometric Construction Problems
		Theorem 02: Given x and y in a ring R then x(-y) = (-x)y = -(x*y).
		Theorem 04: F(S) (read as F adjoin S) is the smallest field containing both F and S. Proof
		Theorem 06: ILet E be s subset of F which is in turn a subset of G then the degree of G over E is equal to the degree of G over F time the degree of F over E, i.e.
	www.pha.jhu.edu /~napora/seminar/Theorems.html (213 words)

	"The List" (Site not responding. Last check: 2007-11-03)
		Each evening, in addition to your assigned homework, your implied homework is to maintain a running list of ideas that were taught during the day.
		First review your List and create a Summary List of theorems, definitions, rules and problem strategies that are not yet at your immediate recall.
		The best media for the List is either a looseleaf paper or a spiral bound notebook; a 70-page one should get you through the year unless you have very large handwriting.
	pages.prodigy.net /bderoes/calculus/theLIST.html (352 words)

	Some Basic Theorems (Site not responding. Last check: 2007-11-03)
		Following is a list of basic theorems which one often encounters in the course of proving
		Theorem: If two angles are complements of the same angle, they are equal.
		Theorem: If two straight lines intersect, the vertical angles are equal.
	home.xnet.com /~fidler/triton/math/review/mat075/btheorems/thr1.htm (186 words)

	Linear Algebra, MTH 513
		You will need to recall the theorems that we covered and understand their significance, answer questions in general about implications of these theorems.
		Before each test, I will provide you with a list of theorems from class that I would expect you to be able to prove.
		The homework is to give you practice applying the theorems that we cover in class to new problems.
	hypatia.math.uri.edu /~eaton/mth513.f01.htm (1120 words)

	Syllabus - Introduction to Graph Theory <br> MTH548 - Spring 20000 <br> Mon. Wed. 5:00 - 6:15 (Site not responding. Last check: 2007-11-03)
		When it is time for a test, I will give you a list of the theorems that I expect you to be able to reproduce.
		You should learn the proofs of theorems that are presented in class.
		A list of theorems to be covered will be given before each test.
	www.math.uri.edu /~eaton/course548.html (607 words)

	CSE773 Design Verification, Spring 2003
		Example Use the theorems in the list to rewrite the goal.
		Suppose you have a theorem that is in the form of an implication: A => B, and suppose your current goal is B. Then it is clear that it is sufficent to prove A. MATCH_MP_TAC does this for you, yielding a new goal, A, that must be proved.
		The theorem may be from a library, from the current environment, or from the assumption list.
	www.cis.syr.edu /~stabler/773s03/BTACS.htm (2561 words)

	Propositional Logic (Site not responding. Last check: 2007-11-03)
		In this introduction to propositional logic we will be looking at only two rules of inference for generating new theorems.
		In other words if you have an expression in your list of hypotheses and theorems that match the expression E and F then you can add to your list the expression E.
		modus ponens on theorem 2 & hypotheses 2
	www.cs.mun.ca /~mike/cs1700/logic2.html (164 words)

	ADVANCED MATHEMATICS FOR ENGINEERING AND SCIENCE
		This is a mathematical text suitable for students of engineering and science who are at the third year undergraduate level or beyond.
		Equally, the text has not been written as a book of pure mathematics with a list of theorems followed by their proofs.
		A list of references is provided at the end of the book.
	www.worldscibooks.com /mathematics/5211.html (283 words)

	NonEuclid: Example Exercise (Adjacent Angles)
		In order to determine if this statement is a theorem in Hyperbolic Geometry you should attempt to construct a counter example - an example where the sum DOES NOT equal 180°.
		The Pythagorean Theorem -- In any Right Triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.
		The following is a list of theorems in Euclidean Geometry.
	cs.unm.edu /~joel/NonEuclid/exercise.html (2077 words)

	Goal Oriented Proof: Tactics and Tacticals
		A theorem achieves a goal if the assumptions of the theorem are included in the assumptions of the goal and if the conclusion of the theorems is equal (up to the renaming of bound variables) to the conclusion of the goal.
		Proved theorems are usually stored in the current theory so that they can be used in subsequent sessions.
		If there are no subgoals, the justification function is applied to the theorems solving the subgoals that have been proved and the resulting theorems are printed.
	www.cl.cam.ac.uk /users/mn200/hol-tutorial/tutorial008.html (2683 words)

	Transformation Study Suggestions (Site not responding. Last check: 2007-11-03)
		Don't say "by definition" unless you are really using the definition and not a theorem.
		List all theorems and learn the statements and at least the ideas of the proofs
		Ideas that were emphasized in class or in lab are particularly key ideas for the course.
	www.math.washington.edu /~king/coursedir/m444a04/test/studytrans.html (443 words)

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