1. F. Conjectures (Math 413, Number Theory) A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references. http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Thm: The only zeros of Z( s ) are at s s Conj: The only zeros of Z( s ) are at s =-2, -4, -6, ... and on the line Re( s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M

2. Peter Flach's PhD Thesis PhD thesis of Peter Flach, investigating the `logic of induction' from philosophical and machinelearning perspectives. http://www.cs.bris.ac.uk/~flach/Conjectures/

Bristol CS Index ML group Peter Flach ... Presentations Conjectures An inquiry concerning the logic of induction Peter Flach This thesis gives an account of my investigations into the logical foundations of inductive reasoning. I combine perspectives from philosophy, logic, and artificial intelligence. Summary Introduction and overview Conclusions Table of Contents and PDF/PostScript ... Download all PostScript (compressed tar archive, 780K) PhD defence picture P A Flach Peter.Flach@bristol.ac.uk . Last modified on Friday 20 November 1998 at 15:35. University of Bristol

3. Conference On Stark's Conjectures Johns Hopkins University, Baltimore, MD, USA; 59 August 2002. Online registration. http://www.mathematics.jhu.edu/stark/

For Lecture Notes Click Here Conference on Stark's Conjectures and Related Topics Johns Hopkins University, Department of Mathematics August 5-9, 2002 A conference funded by the National Science Foundation, the Number Theory Foundation and Johns Hopkins University. Organizing Committee David Burns , King's College London, UK, david.burns@kcl.ac.uk Cristian Popescu , Johns Hopkins University, USA, cpopescu@math.jhu.edu Jonathan Sands , University of Vermont, USA, sands@math.uvm.edu David Solomon , King's College London, UK, solomon@mth.kcl.ac.uk Description of the conference In the last few years there has been a surge in research activity dedicated towards obtaining further explicit evidence for Stark's Conjecture, and in formulating and investigating natural variants, refinements or generalizations thereof. By bringing together the leading exponents of these different strands of research this conference aims to improve understanding of the links between them. In addition, the conference program will include a series of survey talks aimed at making accessible to as wide an audience as possible the main aspects of recent research into Stark's Conjecture. At this time, confirmed main speakers include.

4. Institutt For Matematiske Fag Summer School. Nordfjordeid, Norway; 1219 August 2001. http://www.math.ntnu.no/~oyvinso/Nordfjordeid/

Summer School 2001: Homological conjectures for finite dimensional algebras August 12th - 19th, Nordfjordeid, Norway Announcements Invitation Program for the first part Distribution of lectures in the first part References for the first part ... Unoffical summer school picture Addresses, sources of information Organisers The Sophus Lie conference center Travel information Registration/Participants Participants of the summer school Support Financial Support of Young Researchers Application form The summer school is supported by the European Union, The Research Council of Norway, Nansenfondet og de dermed forbundne fond, The department of mathematical sciences, NTNU. NTNU Fakultet Institutt Teknisk ansvarlig: Webmaster Oppdatert:

5. On Conjectures Of Graffiti Graffiti is a computer program that makes conjectures in mathematics and chemistry.Links to the conjectures and bibliography. http://cms.dt.uh.edu/faculty/delavinae/research/wowref.htm

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6. The Lichtenbaum Conjectures: Progress & Prospects In honor of the 65th birthday of Stephen Lichtenbaum. Brown University, RI, USA;1820 March 2005. http://www.math.brown.edu/slicht_conf/

The Lichtenbaum Conjectures: Progress and Prospects in Honor of the 65th birthday of Stephen Lichtenbaum Brown University March 18-20 2005 Conference Poster Speakers Schedule Registration ... Local Dining The theme of the conference will be a survey of the state of the art concerning Lichtenbaum's conjectures. Andrei Suslin will deliver a Colloquium talk on the Quillen-Lichtenbaum conjectures on Friday, March 18 from 3:00-4:00 PM. The conference will feature several talks which will survey the historical background, the current state of development and prospects for future progress. Speakers: Spencer Bloch, University of Chicago John Coates, Cambridge University Ted Chinburg, University of Pennsylvania Eric Friedlander, Northwestern University Alexander Goncharov, Brown University Nicholas Katz, Princeton University Niranjan Ramachandran, University of Maryland Andrei Suslin, Northwestern University John Tate, University of Texas at Austin Registered Participants: To register for the conference, please see the Registration link below.

7. Some Open Problems Open problems and conjectures concerning the determination of properties offamilies of graphs. However, there are several conjectures, open questions, http://www.eecs.umich.edu/~qstout/constantques.html

Some Open Problems and Conjectures These problems and conjectures concern the determination of properties of families of graphs. For example, one property of a graph is its domination number. For a graph G , a set S of vertices is a dominating set if every vertex of G is in S or adjacent to a member of S . The domination number of G is the minimum size of a dominating set of G . Determining the domination number of a graph is an NP-complete problem, but can often be done for many graphs encountered in practice. One topic of some interest has been to determine the dominating numbers of grid graphs (meshes), which are just graphs of the form P(n) x P(m) , where P(n) is the path of n vertices. Marilynn Livingston and I showed that for any graph G , the domination number of the family G x P(n) has a closed formula (as a function of n ), which can be found computationally. This appears in M.L. Livingston and Q.F. Stout, ``Constant time computation of minimum dominating sets'', Congresses Numerantium (1994), pp. 116-128. Abstract Paper.ps

8. Conjectures In Geometry Basic concepts, conjectures, and theorems found in typical geometry texts are Tangents to Circles conjectures A tangent to a circle is perpendicular to http://www.geom.uiuc.edu/~dwiggins/mainpage.html

Conjectures in Geometry An educational web site created for high school geometry students by Jodi Crane, Linda Stevens, and Dave Wiggins Introduction: This site constitutes our final project for Math 5337-Computational Methods in Elementary Geometry , taken at the University of Minnesota's Geometry Center during Winter of 1996. This course could be entitled "Technology in the Geometry Classroom" as one of its more important objectives is to provide students (presumably math educators) with a wide variety of activities (demonstrations and assignments) utilizing computer software that could be incorporated into a high school geometry classroom. This page has been designed to provide an interactive technological resource for students studying elementary high school geometry. Basic concepts, conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated. Follow-up activities are provided to further demonstrate meanings and applications of concepts. The objective is to ensure that students develop a firm understanding of both the content and applications of each main idea given below in the list of conjectures. Working towards this objective, we have included:

9. Definition Of Conjecture Translation Links Translation of Conjecture An, Arrive, At, By, Concerning, Conjecture, conjectures, Defective, Evidence, Form, Formed, Guess http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Conjectures In Geometry: Parallelogram Conjectures The parallel line conjectures will help us to understand that the opposite anglesin a parallelogram are The precise statement of the conjectures are http://www.geom.uiuc.edu/~dwiggins/conj22.html

Parallelogram Conjectures Explanation: A parallelogram is a quadrilateral with two pairs of parallel sides. If we extend the sides of the parallelogram in both directions, we now have two parallel lines cut by two parallel transversals. The parallel line conjectures will help us to understand that the opposite angles in a parallelogram are equal in measure. When two parallel lines are cut by a transversal corresponding angles are equal in measure. Also, the vertical angles are equal in measure. Now we need to extend our knowledge to two parallel lines cut by two parallel transversals. We have new pairs of corresponding angles What can be said about the adjacent angles of a parallelogram. Again the parallel line conjectures and linear pairs conjecture can help us. The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary. The precise statement of the conjectures are: Conjecture ( Parallelogram Conjecture I Opposite angles in a parallelogram are congruent. Conjecture ( Parallelogram Conjecture II Adjacent angles in a parallelogram are supplementary.

11. Conjectures In Geometry conjectures in Geometry http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Sir Karl Popper Science conjectures and Refutations. Mr. Turnbull had predicted evil (2)The actual procedure of science is to operate with conjectures to jump to http://cla.calpoly.edu/~fotoole/321.1/popper.html

Sir Karl Popper Science: Conjectures and Refutations Mr. Turnbull had predicted evil consequences, . . . and was now doing the best in his power to bring about the verification of his own prophecies. ANTHONY TROLLOPE When I received the list of participants in this course and realized that I had been asked to speak to philosophical colleagues I thought, after some hesitation and consultation, that you would probably prefer me to speak about those problems which interest me most, and about those developments with which I am most intimately acquainted. I therefore decided to do what I have never done before: to give you a report on my own work in the philosophy of science, since the autumn of1919 when I first began to grapple with the problem, "When should a theory be ranked as scientific?" or "Is there a criterion for the scientific character or status of a theory?" The problem which troubled me at the time was neither, "When is a theory true?"nor, "When is a theory acceptable?" My problem was different. I wished to distinguish between science and pseudo-science;

13. On Conjectures Of Graffiti Graffiti is a computer program that makes conjectures in mathematics and chemistry. Links to the conjectures and bibliography. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Spring Lecture Series 2003 28th Annual University of Arkansas Spring Lecture Series in the Mathematical Sciences. Fayetteville, Arkansas, USA; 1012 April 2003. http://www.uark.edu/depts/mathinfo/activities/SpringLecture/SL2003.html

28th Annual University of Arkansas Spring Lecture Series in the Mathematical Sciences Department of Mathematics University of Arkansas Accomodations Travel ... Spring Lecture Series The Andrews-Curtis and the Poincare Conjectures April 10-12, 2003 Fayetteville, Arkansas First Announcement Principal Lecturer Andrew Casson (Yale University) Invited Speakers, Titles and Abstracts Stephen Bigelow (UC Santa Barbara) Martin Bridson (Imperial College, U.K.) Danny Calegari (Caltech) ... Peter Shalen (UIC) Special Public Lecture Jeff Weeks The Shape of Space Contributed Speakers and other Participants, Titles of the talks Ian Agol Mark Brittenham Sergio Fenley ... Jennifer Schultens Organizers Chaim Goodman-Strauss Yo'av Rieck

15. Ermelinda DeLaVina Research Interests and resolving many conjectures, I have resumed extending the list of conjectures Written on the Wall II generated by Graffiti (conjectures 1 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Prime Conjectures And Open Question Another page about Prime Numbers and related topics. http://primes.utm.edu/notes/conjectures/

Prime Conjectures and Open Questions (Another of the Prime Pages ' resources) Home Search Site Largest The 5000 ... Submit primes Below are just a few of the many conjectures concerning primes. Goldbach's Conjecture: Every even n Goldbach wrote a letter to Euler in 1742 suggesting that . Euler replied that this is equivalent to this is now know as Goldbach's conjecture. Schnizel showed that Goldbach's conjecture is equivalent to distinct primes It has been proven that every even integer is the sum of at most six primes [ ] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P ). In 1993 Sinisalo verified Goldbach's conjecture for all integers less than 4 ]. More recently Jean-Marc Deshouillers, Yannick Saouter and Herman te Riele have verified this up to 10 with the help, of a Cray C90 and various workstations. In July 1998, Joerg Richstein completed a verification to 4

17. Conjectures In Geometry Quadrilateral Sum Next Polygon Sum Conjecture Previous Triangle Sum Conjecture Back conjectures in Geometry Conjecture List or to the Introduction. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. The Prime Page's Links++: Theory/conjectures Prime number theory if full of onjectures and open problemsin fact much of theresearch has been driven by just a few of these questions. http://primes.utm.edu/links/theory/conjectures/

Links related to Prime Numbers Add Update New Popular Prime number theory if full of onjectures and open problemsin fact much of the research has been driven by just a few of these questions. Top theory : conjectures Categories in theory : conjectures Goldbach Goldbach's conjecture suggests that every even number greater than 2 is the sum of two primes. Riemann The Riemann Hypothesis is perhaps the most central and important of all prime number conjectures. Resources in theory : conjectures Prime Conjectures and Open Questions - A short list of conjectures and open questions related to prime numbers. (Added: 3-Aug-2000 Hits: 1956 Rating: 4.50 Votes: 2) Rate It The abc conjecture - many conjectures could be proven by just proving this one difficult result. This page includes the abc conjecture, generalizations, consequences, tables, bibliography... (Added: 4-Aug-2000 Hits: 1449 Rating: 8.00 Votes: 3) Rate It The New Mersenne Conjecture - Table of the Mersenne primes and how the satisfy the New Mersenne Conjecture (Added: 23-Aug-2000 Hits: 733 Rating: 10.00 Votes: 1)

19. Thèse G. Chenevier th¨se, Ga«tan Chenevier, Paris 7, 2003. http://www.dma.ens.fr/~chenevie/articles/abstract.html

Familles p-adiques de formes automorphes et applications aux conjectures de Bloch-Kato J. Bellaïche Abstract: This work is a contribution to the study of p-adic deformations of automorphic forms. In the first part, we construct p-adic families of finite slope eigenforms for unitary groups G/Q such that G(R) is the compact unitary group and G(Qp)=GLn(Qp). As a consequence, we obtain p-adic refined deformations of the Galois representations studied by Clozel, Kottwitz and Harris-Taylor. In a second part, we show that the Jaquet-Langlands correspondence between usual and quaternionic modular forms extends to a rigid-analytic isomorphism between some eigencurves. In the last part, in collaboration with J.Bellaïche , we apply the results of the first chapter to some non tempered endoscopic forms for U(3) studied by Rogawski, in order to construct extensions between some Galois characters which are predicted by Bloch-Kato conjectures. ps pdf text in french

20. Conjectures In Geometry Linear Pair Next Triangle Sum Conjecture Previous Vertical Angles Conjecture Back conjectures in Geometry Conjecture List or to the Introduction. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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