41. CHOICE Magazine | About Choice Magazine a theorem usually assume, as an article of faith, that the statement in questionhas a definite truth value, either true or false, the famous theorems of Godel http://www.ala.org/acrl/choice/35-3912.html

Site Map Contact Us About Choice Magazine About ALA ... Sample Reviews Mathematics CIP Adamowicz, Zofia. Logic of mathematics: a modern course of classical logic, by Zofia Adamowicz and Pawel Zbierski. Wiley, 1997. 260p bibl index afp ISBN 0-471-06026-7, $49.95 MARC Smullyan, Raymond. Knopf, 1997. 224p ISBN 0-679-44634-6, $22.00 CHOICE is a publication of the a division of American Library Association. For questions or comments, contact the Website editor. American Library Association. Site designed and developed by Fyrsta.com ChoiceReviews.online Reviews since 1988

42. Geometry Calculators Elements. An Interactive Proof of Pythagoras' theorem An animatedproof of one of the most famous theorems of geometry ; Dudeny's http://www.ifigure.com/math/geometry/geometry.htm

your source for online planning, calculating and decision-making Home Plan Calculate Convert ... Decide Mathematics Basic Math Algebra Geometry Trigonometry ... Tutorials Guides Math Guide Physics Guide Chemistry Guide Computer Science ... Geology Guide Geometry Calculators Interactive Geometry Concepts Euclid's Elements An interactive text on Euclid's Elements, covering all 13 books. The figures in the text are illustrated using the Geometry Applet. By moving points in the figures, you can translate, rotate or resize the figures. Mathlab.com "Using virtual straightedge and compass our Euclid applet can draw lines and circles." Examples are provided showing how to use the applet to illustrate propositions from Euclid's Elements. An Interactive Proof of Pythagoras' theorem "An animated proof of one of the most famous theorems of geometry" Dudeny's Dissection Another animated proof of the Pythagorean theorem. Gallery of Interactive Geometry A large number of interactive geometry programs Compute implicitly defined curves in the plane, a mathematical model of light passing through a water droplet, generate Penrose tilings, an interactive editor for symmetric patterns of the plane, an interactive 3D viewer, projective conics, explore the effects of negatively curved space, explore Teichmuller space, experiment with numerical integration of data sets, visualize families of Riemann surfaces, work with any discrete symmetry group of the hyperbolic plane. Java Gallery of Interactive Geometry A number of geometry Java applets hyperbolic triangles, simulation of the Lorenz equations, interation of a quadratic map, a version of the Tetris game, Leap fractal chaos game, creating and animating fractals, generate wallpaper patterns.

43. Dirac Notation: Proof of the Two famous theorems Regarding Hermitian Operators Let q be a HermitianOperator and let 1 and 2 be two eigenfunctions of q with respective http://people.deas.harvard.edu/~jones/ap216/lectures/ls_2/ls2_u1/dirac_notation/

Dirac Notation: State Function: Each state function is denoted by a ket y Observable Quantites: If we denote an observable quantity by Q , we will denote the corresponding quantum mechanical operator by Q (i.e. the same symbol, but bold-faced). A quantum mechanical operator operates on kets and transforms them into other kets , as Q Q is defined if its effect on all allowable kets is known. In general, quantum mechanical operators need not commute ; i.e. Q Q Q Q The commutator of two operators (itself an operator) Q Q Q Q Q is a measure of whether or not two operators commute, and plays a very important role in quantum mechanics Eigenvalues and Eigenkets (Eigenvectors) If Q eigenket of the operator Q and a is called the associated eigenvalue A ket is often labelled by its eigenvalues, as Q > = a The completeness postulate y > may be expanded in terms of the eigenkets of Q , as y > = c > + c > + c where the c i y = c *c (with proper normalization) gives the probability that if a measurement of Q is made, the result will be a Dual (Bra) Space and Scalar Products To each ket there corresponds a dual or adjoint quantity called by Dirac a bra ; it is not a ket rather it exists in a totally different space. The generalized scalar product is defined in analogy with the ordinary scalar product that you are familiar with as a combination of a

44. Secondary Literature About Julius Petersen for help. Sylow had then just shown his famous theorems in group theoryand they were useful in helping Petersen. The article reproduces http://www.math.ku.dk/ths/petersen_j/seclit.htm

Secondary literature about Julius Petersen Major secondary publications Minor secondary publications Obituaries Encyclopedia articles ... Articles on the World Wide Web Major secondary publications of Petersen The mathematical journal Discrete Mathematics celebrated the centennial of Petersen's article on graph theory in 1991. Volume 100 and 101 of the journal consisted solely of articles with connection to Petersen and his works. Together with the article by Lützen (item 4) this is the most important secondary sources of Petersen's life and works. Julius Petersen 1839-1910: A biography. Discrete Mathematics (1992), pp. 9-82. Article in English. This is the most detailed biography in English of Petersen. It discusses Petersen's mathematical works, but it also includes his economical, social and pedagogical activities. Sabidussi, Gert: Correspondence between Sylvester, Petersen, Hilbert and Klein on invariants and the factorisation of graphs 1889-1891. Discrete Mathematics (1992), pp. 99-155. Article in English containing 47 letters (translated into English) shedding some light on the background and origin of Petersen's famous paper on graph factorisation, and on his abortive collaboration with Sylvester.

45. CSC 310 - Information Theory as a measure of information content is central to both of these problems, andis the basis for an elegant theory centred on two famous theorems proved by http://www.cs.toronto.edu/~radford/csc310.S02/

CSC 310 - Information Theory (Jan-Apr 2002) Here are the term and final exam marks . You can collect assignments and tests from my office. Phone ahead to see if I'm in before coming by. Information theory arises from two important problems: How to represent information compactly, and how to transmit information reliably in the presence of noise. The concept of `entropy' as a measure of information content is central to both of these problems, and is the basis for an elegant theory centred on two famous theorems proved by Claude Shannon over 50 years ago. Only in recent years has the promise of these theorems been fully realized, however. In this course, the elements of information theory will be presented, along with some of the practical techniques needed to construct the data compression and error-correction methods that play a large role in modern communications and storage systems. Instructor: Radford Neal Phone: Email: radford@cs.utoronto.ca Office Hours: Mondays 1:10-2:00 and Thursdays 2:30-3:30, in SS 6016A Lectures: Mondays and Wednesdays, from 3:10pm to 4:00pm, in SS 1073

46. Baltimore AMS Special Session (16 January 2003) Special session at the AMS/MAA Joint Meetings. Baltimore, MD, USA; 1617 January 2003.Category Science Math Algebraic Geometry Events Past Events...... The famous theorems of Bertini imply that most members of a pencil of algebraicplane curves have no singularities outside the base points, and if the pencil http://www.algebraiccurves.net/Baltimore.html

AMS Special Session: Computational Algebraic and Analytic Geometry for Low-dimensional Varieties Baltimore, January 2003 Organized by (Florida State University) and Emil Volcheck (National Security Agency). This special session will be held Thursday and Friday, 16-17 January 2003, at the Baltimore Joint Mathematics Meetings . This is the third special session on this topic to be held at the AMS/MAA Joint Mathematics Meetings. The first special session was held in 1999 at the San Antonio Joint Meetings, and the second special session was held in 2001 at the New Orleans Joint Meetings. Scope This session is devoted to algorithms and computational techniques for algebraic curves, Riemann surfaces, algebraic surfaces, and low-dimensional varieties. We are interested in reports on algorithms to solve problems or on a significant use of computational algebraic or analytic techniques to obtain results. Algorithmic, algebraic, arithmetic, and analytic aspects of curves and surfaces are appropriate topics. Read the list of speakers and their abstracts for the special sessions in and on computational algebraic geometry for curves and surfaces to see what previous speakers in this series of special sessions have presented.

47. Harold Jacobs Math Books Reasoning 2.1 Conditional Statements 2.2 Definitions 2.3 Direct Proof 2.4 IndirectProof 2.5 A Deductive System 2.6 Some famous theorems of Geometry Chapter 3 http://www.fun-books.com/books/Jacobs-TOC.htm

For a lifetime of learning fun! If you are unable to see the blue navigation buttons below, go to Contents for text links or use our Search function. Table of Contents for various texts by Harold Jacobs Mathematics - A Human Endeavor Elementary Algebra Geometry - Seeing, Doing, Understanding Mathematics - A Human Endeavor 1. Mathematical Ways of Thinking The Path of the Billiard Ball More Billiard-Ball Mathematics Inductive Reasoning: Finding and Extending Patterns The Limitations of Inductive Reasoning Deductive Reasoning: Mathematical Proof Number Tricks and Deductive Reasoning 2. Number Sequences Arithmetic Sequences Geometric Sequences The Binary Sequence The Sequence of Squares The Sequence of Cubes Fibonacci Sequence 3. Functions and Their Graphs The Idea of a Function Descartes and the Coordinate Graph Functions with Line Graphs Functions with Parabolic Graphs More Functions with Curved Graphs Interpolation and Extrapolation: Guessing Between and Beyond 4. Large Numbers and Logarithms

48. Oxford University Press Part II ranges widely through related topics, including mapcolouring on surfaceswith holes, the famous theorems of Kuratowski, Vizing, and Brooks, the http://www.oup.com/ca/isbn/0-19-851062-4

/local_assets/ca Click here for quick links About OUP Contact Us Search the Catalogue Services and Resources Site Map How to Order OUP Worldwide Home OUP Canada Home Education K-12 Higher Education English as a Second Language General and Reference Book Information Online Order Form Search the catalogue Features Table of Contents Graphs, Colourings and the four-colour theorem Robert A. Wilson , Professor of Group Theory, The University of Birmingham Price: $ 58.50 CDN ISBN: 0-19-851062-4 Publication date: February 2002 OUP UK 150 pages, numerous figures, 156 mm x 234 mm There is an alternative edition (Cloth) Ordering Customers in Canada can place an order using our online order form Over 100 diagrams illustrating and clarifying definitions and proofs, etc Contains exercises in every chapter. Introductory and well paced explanations of the proof of the four-colour theorem. Suitable for any level from late undergraduate upwards. Description The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory.

49. Colloquium Announcement For December 13, 2001 Abstract. The FourColor Theorem (proved in 1976) is one of the mostfamous theorems of mathematics. I will show how modern computation http://www.math.binghamton.edu/dept/colloquia/011213.html

MATHEMATICAL SCIENCES COLLOQUIUM DATE: Thursday, December 13, 2001 TIME: 4:30-5:30 PM PLACE: LN 2205 SPEAKER: Stan Wagon (Macalester College) TITLE: A Computational View of the Four-Color Theorem: A Resuscitation of a Famous False Proof Abstract The Four-Color Theorem (proved in 1976) is one of the most famous theorems of mathematics. I will show how modern computation helps us understand the coloring of maps and graphs, using ideas stemming from the famous false proof of 1879 and also from a well-known hoax of April Fools Day, 1975. These ideas led to the resolution of a long-standing conjecture about coloring Penrose tilings. I will also discuss a recent result of D. Finn, showing how one can create a curved unicycle track that a bicycle can follow. R E F R E S H M E N T S 4:00 To 4:25 PM Kenneth W. Anderson Memorial Reading Room

50. Courses At UW Math: Undergraduate Course Descriptions: Math 461 first part of the semester to the study of triangles and circles in Euclidean Geometry,their constructions, properties and some of the most famous theorems. http://www.math.wisc.edu/~maribeff/courses/461.html

Math 461 - College Geometry I Prerequisites: Math 234. Frequency: Fall (I), Spring (II) Student Body: The primary audience for this course is math majors specializing in secondary education, and for them, Math 461 is required. The course is not restricted to prospective high school teachers, however, and some students take the course simply because they are interested in geometry. Credits: 3. (N-A) Recent Texts: Geometry for College Students, by I.M. Isaacs (Brooks-Cole). Geometry Revisited, MAA 19, 1967. (H.S.M. Coexeter and S.L. Greitzer) Course Coordinator: I.M. Isaacs Background and Goals: An introduction to Euclidean or non-Euclidean geometry at the college level. This course will cover some topics mainly in Euclidean geometry and a final explanation of non-Euclidean Geometries with an emphasis in Hyperbolic Geometry. We will devote the first part of the semester to the study of triangles and circles in Euclidean Geometry, their constructions, properties and some of the most famous Theorems. The second part will develop the study of isometries and wallpaper patterns. As an application of those we will prove the famous theorem on decomposability of polygons. The last part corresponds to a quick review of Hyperbolic Geometry, hyperbolic tesselations and the prints of M.C. Escher. Alternatives: N/A Subsequent Courses: N/A Content coverage: The extended law of sines. Ceva's theorem.

51. Course.asp Using this background, three famous theorems are proved the PaleyWienertheorem, the Foures-Segal theorem and the sampling theorem. http://washer.ee.ic.ac.uk/www/course.asp?c=ISE3.7&s=J3

52. ClonedHawking There are some famous theorems that give conditions under which there must be asingularity, but they don't imply the existence of an event horizon eg, the http://www.brandonsanders.com/Cloned Hawking/clonedhawking1.htm

Advice Column *BrandonSanders.com CLONED STEPHEN HAWKING ADVICE COLUMN by Cloned Stephen SEND ME A QUESTION D. Concepcion writes: The dogs inside my brain keep barking; and I will drown them with the blood of all sinners in the pain of time. My question is; Is there an easy way to tell if a given space-time (i.e. set of solutions) does or does not have (or the capacity to have) an event horizon? "There are some famous theorems that give conditions under which there must be a singularity, but they don't imply the existence of an event horizon: e.g., the big bang is a singularity without an event horizon. There may also be theorems that imply the existence of an event horizon under certain conditions, but I don't know about them - for that, you should probably ask a real expert on classical GR. So, all I can do is guess and check. Obviously, physical intuition helps one guess these things. On a side note you frighten me, and never write to me again. " B. Sullivan writes: How

53. Chris Wood: Project Titles Careful marshalling of this topological information allows us to prove many ofthe famous theorems of classical topology, such as the Jordan Curve Theorem. http://www-users.york.ac.uk/~cmw4/proj.html

Project Titles The Geometry of Curves BA/BSc Project Although we spend a certain amount of time in the first two years of the York maths degree dealing with curves, most of the time they are treated merely as "things to integrate over" and not (with the exception of the conics, which we meet in the first year) studied for their own sake. In the third year, there is a handful of lectures on the geometry of curves in the Differential Geometry module, but these merely scratch the surface. This is a shame, because the geometry of curves has consistently delighted and intrigued mathematicians through the ages: for example, from the ancient Greek Cissoid of Diocles (discovered in connection with the problem of "duplicating the cube"), through the curiously named Witch of Agnesi, to the Bezier curves theory of contact ), and a range of geometric techniques for producing new curves from old ones (such as roulettes, evolutes, involutes, envelopes, orthotomics, caustics). These constructional techniques, which are interesting in their own right, are also useful because they throw up relationships between curves which at first sight look quite different (for example, the tractrix is the involute of the catenary), and help to identify certain geometric features (for example, the inflexion points of a curve, which are usually hard to spot by direct inspection, turn out to correspond to cusps on the evolute, which are blindingly obvious!). Prerequisites: calculus, upto the level of Vector Calculus I (

54. Opinio05 Pythagoras is well known among the students specially to the mathematics studentsat their lower levels because of the famous theorems in Geometry. http://www.island.lk/2002/05/12/opinio05.html

Opinion The Buddha and Pythagoras Pythagoras is well known among the students specially to the mathematics students at their lower levels because of the famous theorems in Geometry. But many of us rarely come across the fact that he is a contemporary of the Buddha. He was born in about 580 B.C. Very interesting and valuable facts about Pythagoras are included in one of his publications written by late Sirisena Maitipe to commemorate his 50th birth anniversary. In my childhood I knew Sirisena Maitipe as a popular poet. But it is only very recently that I had the opportunity of reading a collection of books written by him. I have heard that he is the author of several valuable books including a book on kamasutra. He was also an astrologer and was well versed in the English language than Sinhala. The latent and mysterious event of the meeting of Buddha and Pythagoras is revealed in his book namely "Ma Dutu Gandaraya" which is some sort of a research work about the life and times of the Buddha in ancient India. He has written this book after travelling all-over the sacred and ancient cities and examining the ruins of the places and his work is a collection of ideas gathered by reading literature from Nepal, Tibet, China and India and some of the western countries as well. In the ancient days there were no books and libraries as in the modern world for students even at the Taxila which was the only university available in India during that era. The philosophers or students or scholars who ever they were the only means by which study and exchange ideas and broaden knowledge by travelling long distances and meeting other similar scholars or students and discussing whatever problems they had. Many travelled from western as well as eastern countries to Taxila (and India) which was the centre of learning at that time. In fact Taxila existed eight or nine centuries prior to the birth of the Buddha.

55. Pensions And Investments, June 12, 2000 Mr. Miller collaborated with Franco Modigliani to produce two famous theorems,for which they both at different times won the Nobel prize in economics. http://www.kellogg.northwestern.edu/news/hits/000612pi.htm

Top Headlines Kellogg in the Media Alums in the Media Media Relations ... Northwestern University Search Kellogg School Search Help Nobel Laureate: Merton Miller remembered as 'champion of free markets' By: Barry B. Burr June 12, 2000 Pensions and Investments CHICAGO Merton H. Miller, a "romantic warrior of ideas," "champion of free markets," and Nobel laureate in economics, changed dramatically the practice of corporate finance and thinking on derivatives. Mr. Miller, a professor emeritus at the Graduate School of Business, University of Chicago, died of lymphoma June 3 at his home in Chicago. He was 77. "When I was at business school, we used to refer to him as the professor of everything," said Rex A. Sinquefield, chairman and chief investment officer at Dimensional Fund Advisors Inc., Santa Monica, Calif. Mr. Sinquefield was a student of Mr. Miller's. Since DFA's founding in 1981, Mr. Miller had been a director on the board of its mutual fund company, renowned for its pioneering small-cap indexing. "He was a scholar's scholar," Mr. Sinquefield added.

56. Archimedes Upon testing the crown Archimedes found that it wasn't. One of Archimedesmore famous theorems, known as the Archimedes' Principal. http://www.andrews.edu/~calkins/math/biograph/199899/bioarch.htm

Back to the Table of Contents Biographies of Mathematicians - Archimedes Table of Contents Introduction Biography Accomplishments Introduction Archimedes was one of the greatest mathematicians of all time, and everyone knows it. However he might be unknown for some of his other accomplishments. in this report, we will tell you about the man that was basically the father of Geometry, as well as his other accomplishments. We did our report on Archimedes the mathematician. He made contributions to the fields of science and geometry. Archimedes is well known for his studies of geometry and for his important inventions. He is well known for his discoveries of buoyancuy and for his many inventions. But Archimedes himself considered his works in geometry more important and thought his inventions were just a hobby. Some of the things Archimedes is well known for are the Golden Crown mystery and his invention of the Archimedes Screw Biography of Archimedes Archimedes was born in Syracuse, Sicily in

57. Re: Quick Question About Space-times And Event Horizons John Baez baez@galaxy.ucr.edu wrote There are some famous theorems that giveconditions under which there must be a singularity, but they don't imply http://www.lns.cornell.edu/spr/2002-02/msg0039125.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re: Quick question about space-times and Event Horizons Subject : Re: Quick question about space-times and Event Horizons From Date : Mon, 4 Feb 2002 19:52:27 +0000 (UTC) Approved : baez@math.ucr.edu Message-ID a3mopr$24d$1@woodrow.ucdavis.edu Newsgroups : sci.physics.research Organization : University of California, Davis References a3evdp$l1g$1@glue.ucr.edu User-Agent : tin/1.4.5-20010409 ("One More Nightmare") (UNIX) (Linux/2.4.9-21 (i686)) Follow-Ups Re: Quick question about space-times and Event Horizons From: egibbs@my-deja.com (Ed Gibbs) References Re: Quick question about space-times and Event Horizons From: baez@galaxy.ucr.edu (John Baez) Prev by Date: Re: Gravitational counterpart to Maxwell's Equations (and more about Next by Date: Re: Couloumb's Law and the Permittivity Constant... Prev by thread: Re: Quick question about space-times and Event Horizons Next by thread: Re: Quick question about space-times and Event Horizons Index(es): Date Thread

58. Re: Quick Question About Space-times And Event Horizons John Baez baez@galaxy.ucr.edu wrote There are some famous theorems thatgive conditions under which there must be a singularity, but they don't http://www.lns.cornell.edu/spr/2002-02/msg0039162.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re: Quick question about space-times and Event Horizons Subject : Re: Quick question about space-times and Event Horizons From : egibbs@my-deja.com (Ed Gibbs) Date : 6 Feb 2002 04:32:21 -0800 Approved : baez@math.ucr.edu Message-ID 8e1dab98.0202060432.5116c911@posting.google.com Newsgroups : sci.physics.research Organization : http://groups.google.com/ References a3evdp$l1g$1@glue.ucr.edu a3mopr$24d$1@woodrow.ucdavis.edu a3mopr$24d$1@woodrow.ucdavis.edu Follow-Ups Re: Quick question about space-times and Event Horizons From: baez@galaxy.ucr.edu (John Baez) References Re: Quick question about space-times and Event Horizons From: baez@galaxy.ucr.edu (John Baez) Re: Quick question about space-times and Event Horizons From: Prev by Date: Re: The cosmological distance scale Next by Date: Re: Energy density of gravitational fields [Re: Quantum Gravity?] Prev by thread: Re: Quick question about space-times and Event Horizons Next by thread: Re: Quick question about space-times and Event Horizons Index(es): Date Thread

59. Badolato, Medieval City, Calabria, Southern Italy, Culture, Gastronomy, Italian He addressed various sciences in the study of arithmetic and geometry, revealingsuch famous theorems as the rightangled triangle based on abstact http://www.intercomm.it/badolatomeddream/bad_famosi/bad_calab_famosi_pitigora.ht

Navigate the Badolato Website HOME PAGE A Visit to Badolato New Year's Eve in Italy Virtual Tour of Calabria Cooking with Love Home Gourmet Food Store Badolato Renaissance Badolato "U" Badolato Bookstore Newsletters Links Italian Culinary Institute Welcome from Mayor of Badolato Buying historical ... Q and A Badolato Monthly Gazette Click here for the latest news Click here for a spectacular view of the walled city Click here to see the beautiful nearby beaches Lady Barrow's Annual New Year's Celebration December 28, 2001- January 5, 2002 Lady Barrow welcomes you to Badolato for the greatest New Year's Eve celebration in Italy. COOKING WITH LOVE at the ROMANTIC TIMES BOOKLOVERS CONVENTION Orlando, Florida, USA November 14-18, 2001 5 days to satisfy all of your Epicurean indulgences! Italy's hottest chefs join us in Orlando to reveal the secrets of Italian Cuisine and the most sensuous desserts in Europe. Click

60. UIUC Mathematics Weekly Calendar This intuitive reasoning, which is supported by some famous theorems ofring theory, suggests that there can be no noncommutative curves. http://www.math.uiuc.edu/Bulletin/March/mar26-01wkly.html

Weekly Calendar March 26-30, 2001 Monday Tuesday Wednesday Thursday ... Calendar Archive Items for inclusion in the Weekly Calendar should be submitted via e-mail to Hilda Britt Deadline for inclusion in the Weekly Calendar is 5 p.m. Thursdays. Speakers are encouraged to provide abstracts. MONDAY, MARCH 26 245 Altgeld Hall, 4:00 p.m. MATH 400 - INTRODUCTION TO GRADUATE MATHEMATICS cancelled because of Coble Lecture at 4 p.m. in 314 Altgeld 314 Altgeld Hall, 4:00 p.m. ARTHUR B. COBLE MEMORIAL LECTURE Michael Artin, MIT Geometry of Noncommutative Algebraic Surfaces: 1. Noncommutative Algebra in Dimension 2 Abstract: Functions on a curve are functions of one variable, and hence they must commute with each other. This intuitive reasoning, which is supported by some famous theorems of ring theory, suggests that there can be no noncommutative curves. So the critical dimension for noncommutative algebra is 2. As yet little is known about general domains of dimension two, but some interesting special algebras have been studied extensively. The study of these algebras has turned up empirical phenomena which, if they can be proved to hold more generally, will clarify the geometry and birational structure of noncommutative surfaces. This talk will review the current state of the theory. A reception will be held in the Colonial Room, Illini Union, from 5:15 to 6:30 p.m., Tuesday, March 27

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