One way of winning in online lotto games is to select a fixed pattern of numbers and then go for that particular sequence repeatedly. While selecting the number sequences, keep in mind that picking a random number combination does not mean that it will definitely come true. There are also certain lottery tickets that are based on certain 15 number combinations also.
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This is a game of probability keo nha cai hom nay. Although there are numbers that are very improbable to win, there are still ways by which you can increase your chances of winning. You can easily win online lottery if you play the games for longer durations. You should try to play these lottery games for at least two weeks if you are serious in winning the jackpot prize.
There are some strategies or systems that can increase your chances of winning. You can use these number patterns in different kinds of lottery games. For instance, if you want to win quick jackpot prizes in online lotteries, you should bet numbers that are more commonly picked by lottery to win quick prizes. If you play for longer durations, you will increase your chances of winning huge jackpots. Most players go after a fixed number pattern and never stray from it. Such players win frequently.
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There are also numbers combinations that have been used for centuries. Playing with numbers from history can really help you in winning. Try using numbers from ancient cultures to see if they can provide you with numbers that are perfect for playing lotto games.


Douglas Holtz-Eakin, a former Director of the Congressional Budget Office and current chief McCain economic advisor, is an honest man--which means he's something of a liability on the Straight Talk Express. A few months ago, he admitted to my colleague, Michael Scherer, that Barack Obama's economic plan would reduce taxes for most people. And now, in a forthcoming book by Fortune columnist Matt Miller, he makes it clear that the next President is going to have to raise taxes.And the futures market is also betting on rising taxes according to Mankiw.
"If you do nothing on the spending side, you're going to have to raise taxes whether you're a Republican, a Democrat or a Martian," he tells Miller...and then he immediately makes it clear that the "spending side" part of the argument is nothing more than a political fig-leaf.
The top income tax rate is now 35 percent. According to the betting at Intrade, the probability that the top income tax rate in 2011 will exceed 38 percent is 0.87. Call this P(tax hike).
Barack Obama has made such a tax hike part of his campaign promises, and there is no reason to think the Congress won't deliver for him. So let's assume Obama is certain to get the tax hike if he wins. That is, P(tax hike / Obama) = 1.0. (If this assumption is wrong, and this conditional probability is less than one, then my conclusion below would be even stronger.)
According to Intrade, the probability of Obama being the next president is 0.53. Call this P(Obama). And P(McCain) = 0.47.
Now we can calculate the probability of a tax hike conditional on McCain winning. It comes from the formula
= P(tax hike/Obama) P(Obama) + P(tax hike/McCain) P(McCain),
and plugging in the above numbers. It tells us that
P(tax hike / McCain) = 0.74.


C. 1065 - 1136 C.1065-1136 ABRAHAM BAR HIYYA aka Savasorda (Spain)
Philosopher, astronomer, astrologer, and mathematician. He wrote numerous original works in Hebrew. These include Yesod ha-Tevunah u-Migdal ha-Emunah (The Foundation of Understanding and the Tower of Faith) an encyclopedia of math astronomy, optics, and music. His definite work on astronomy Khochmat ha-Chiza'yon consisted of two parts Tzurat ha-Aretz ve-Tavnit Kaddurei ha-Raki'a ("Form of the Earth and Figure of the Celestial Spheres ") and Kheshbon Mahalekhot ha-Kokhavim ("Calculation of the Courses of the Stars parts of which were translated into Latin. His Chibbur ha-Meshichah ve-ha-Tishboret (Treatise on Measurement and Calculation) (1116) was translated into Latin in 1145 by Plato of Tivoli as Liber Embadorum. It gave the area of a circle and helped introduce trigonometry to the west. He also translated many Arabic mathematical and scientific texts into Hebrew.


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How Three Kings Bloggers Breakdown The LA Kings Playoff Points Threshold And How They Could All Be Wrong.
By Paul Armbruster • KingsNewsDaily.com •
The consensus among 3 Kings bloggers is that the Kings will need 55 points to make the playoffs, give or take a point. But is that really true? Or could the playoff point threshold be considerably lower?
Quisp, doing his best Brad Pitt in 12 Monkeys impersonation said:
“In the several million simulations run every day by Sportsclubstats, 55 points is enough to make it into the playoffs in over 90% of simulations.”
Well ok then. Based on a site that gave the Kings almost no shot to make the playoffs last year, let alone win the whole shebang, he filters the rest of his game-block projections through a faulty probability matrix. He finishes with this, “It’s not an exaggeration to say that every game is a playoff game now. And it’s a fact that a losing streak at any point is almost certain to be the kiss of death.”
But it is an exaggeration. It’s not the playoffs. Yet.
Neisy, who appears to get the magic number 55 from Quisp, says:
“an unusually high number of 3-point games in the West, though, it could take even more.”
Well yes, but so could an unusually low number of 3-point games make it even less. Again, a faulty probability matrix spits out a number that may or may not be a true benchmark.
Player-X, on the other hand, broke it down this way:
“The West has averaged a requirement of 93.8 points over the last 5 years, being 95, 97, 95, 91 and 91. 93.8 out of a possible 164 equals getting 54.91 points from a possible 96. So, we round to 55, and our range is likely to be 54-56 points for the lowest team to get in with.”
I imagine Sportsclubstats takes all these numbers into account as well, but maybe not. Regardless, it certainly makes sense given the averages cited that the playoff threshold could end up being in that range.
However, it appears that no one has considered the only other 48 game season (in the modern era) as a means of calculating the possbile outcome of this season. At the end of the shortened 1994-95 season only 3 teams in the West had point totals 55 or above to make the playoffs and only 4 in the East. The Sharks and Stars made it in with only 42 points!
Yes, yes, I know. 3 point games weren’t invented by Bettman yet. But does that mean these numbers are irrelevant? Maybe. Maybe not.
A cursory examination of the final standings that year reveal that even with 3-point games added in, many teams would have made the playoffs with less than 54 points.
Take San Jose, for example, who finished in 7th place with 42 points. They had 4 ties. Let’s be generous and give them 4 more wins and points. That’s only 46 points, good for 7th place and a playoff berth. Or take Vancouver who had 12 ties and finished in 6th place with 48 points. Giving them a reasonable 6 more points lands them at 54… and that’s good enough for 6th place.
Perhaps a math whiz can explain why the only other lockout-shortened season means absolutely nothing from a statistical standpoint. Or maybe there’s something to it and Kings fans can breathe a sigh of relief knowing their team is far from out of it, even with a losing streak built in.
Editor’s note: The clip above of Quisp, er, I mean Brad Pitt got me thinking about another aspect of the 1994-95 season. What if the entire approach to a 48 game season, with all the truncated game decision permutations and incalculable human emotions has an effect on the outcome that is vastly different than an 82 game season? Strategy, preparation, mindset, focus, travel, etc. All these things are not equal to a simple slicing of game numbers from a full season through a suspect Artificial Intelligence algorithm that does not calculate critically important factors.
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2 edition of high-order direct solver for Helmholtz equations with Neumann boundary conditions found in the catalog.
high-order direct solver for Helmholtz equations with Neumann boundary conditions
by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, VA, [Springfield, Va
Written in English
|Other titles||High order direct solver for Helmholtz equations with Neumann boundary conditions, ICASE 25th anniversary|
|Statement||Xian-He Sun, Yu Zhuang.|
|Series||ICASE report -- no. 97-11, NASA contractor report -- 201658, NASA contractor report -- NASA CR-201658.|
|Contributions||Zhuang, Yu., Institute for Computer Applications in Science and Engineering., Langley Research Center.|
|The Physical Object|
|Pagination||i, 25 p.|
|Number of Pages||25|
A High-Order Fast Direct Solver for Singular Poisson Equations Yu Zhuang and Xian-He Sun Department of Computer Science, Illinois Institute of Technology, Chicago, Illinois Received October 7, ; revised Aug We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations. The solution of elliptic partial differential equations on regions with corners is a famously refractory problem. The solutions are known to be singular at corners, and one of the major difficulties has been finding a precise description of their behavior. In this paper, we observe that when the Helmholtz equation is solved using integral equations, the solutions are .
The Dirichlet Problem for the Helmholtz Equation Since the integrand in (4.t7) is infinitely differentiable for P0, pCB and B is. not infinite, it follows that Ur and in fact is infinitely differentiable. as long as p and Po are not on the boundary. deﬁnes the boundary condition on /. When we use a PML, the positive parameter 7 gives the thickness of the layer and @ gives the trace of on the boundary /. Thus, the problem is a variable-coefﬁcient Helmholtz equation with Dirichlet boundary conditions on all the boundaries. In the case 7, we use a second-order absorbing boundary condition File Size: KB.
This paper deals with the solution of the Helmholtz equation on polygonal domains with either Dirichlet or Neumann boundary conditions. There are two additional boundary conditions that have not yet been analyzed in detail: the Robin condition, which specifies a linear combination of the values of the solution and the values of its derivative. Solving the Helmholtz equation on a square with Neumann boundary conditions. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Provide details and share your research! Poisson partial differential equation under Neumann boundary conditions. 1.
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A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions Xian-He Sun* Yu Zhuang Department of Computer Science Louisiana State University Baton Rouge, LA Abstract In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular Size: 1MB.
In this study, a compact nite-di erence discretization is rst developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability.
Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains.
Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and sep-arability. A high-order direct solver for Helmholtz equations with Neumann boundary conditions. By Xian-he Sun and Yu ZhuangXian-he Sun and Yu Zhuang. Abstract.
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann.
We demonstrate the resulting numerical capabilities by solving a range of nonstandard boundary value problems for the Helmholtz equation. These include problems with variable coefficient Robin boundary conditions (including discontinuous coefficients) and problems with mixed (Dirichlet/Neumann) boundary by: A high-order direct solver for Helmholtz equations with Neumann boundary conditions.
By Xian-he Sun and Yu Zhuang. Abstract. In this study, a compact nite-di erence discretization is rst developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to Author: Xian-he Sun and Yu Zhuang.
We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations.
Such problems arise in the solution process of incompressible Navier–Stokes equations and in the time-harmonic wave propagation in the frequence space with the zero by: Using certain boundary conditions, in our case the Neumann condition for this integral equation, we hope.
to –nd an approximate solution to exterior boundary value problem. As we will use Green™s Theorem, we. solve the Helmholtz equation only on the boundary Author: Jane Pleskunas.
Helmholtz Equation and High Frequency Approximations. 1 The Helmholtz equation. TheHelmholtzequation, u(x) + n(x)2!2u(x) = f(x); x2Rd; (1) is a time-independent linear partial diﬀerential equation. The interpretation of the unknown u(x) and the parameters n(x),!and f(x) depends on what the equation Size: KB.
partial diﬀerential equation (the Helmholtz equation) which is to be solved subject to the requirement that certain boundary conditions hold (e.g. the impedance boundary condition and, when the domain is unbounded, also the Sommerfeld radiation condition, which can be viewed as a boundary condition at inﬁnity).
A high-order direct solver for helmholtz equations with neumann boundary conditions Author: Xian-He Sun ; Yu Zhuang ; Institute for Computer Applications in Science and Engineering. HELMHOLTZ EQUATION WITH ARTIFICIAL BOUNDARY CONDITIONS IN A TWO-DIMENSIONAL WAVEQUIDE D.A.
MITSOUDIS yx, CH. MAKRIDAKIS zx, AND M. PLEXOUSAKIS Abstract. We consider a time-harmonic acoustic wave propagation problem in a two dimensional water waveguide con ned between a horizontal surface and a locally varying File Size: KB.
One of the high-order schemes is based on generalizations of the Padé approximation. The second scheme is based on high-order approximation to the derivative calculated from the Helmholtz equation itself. A symmetric high-order representation is developed for a Neumann boundary by: We solve a Dirichlet boundary problem for the Helmholtz equation.
We also extend the method to the solution of mixed problems, where Dirichlet boundary conditions are specified on some faces and Neumann boundary conditions are specified on other faces.
High-order accuracy is achieved by a comparatively small number of by: A High-Order Fast Direct Solver for Singular Poisson Equations. of the eigenvalues analysis to Neumann boundary conditions and non-uniform meshes. A High-Order Direct Solver for Helmholtz.
or the Helmholtz equation () Δu+k2u = u xx +u yy +u zz +k2u = f(x,y,z) in a 3-D domain Ω with Dirichlet () u =Φ(x,y)on∂Ω boundary conditions by domain decomposition (DD) methods. The present 3-D algorithm is based on the fast spectral Helmholtz solver which was developed in .
It incorporates the application of the FFT with a prelimi. 2 = 2, the \homogenizing" function is u. 1(x;t) = 3 2 x2 5x + 3 4 t: Subtracting this from u yields a problem with homogeneous boundary conditions and initial condition u(x;0) = 0 u.
1(x;0) = 3 2 x2 + 5x: Daileda Neumann and Robin conditions. • Helmholtz’ equation • Classiﬁcation of second order, linear PDEs • Hyperbolic equations and the wave equation 2.
Lecture Two: Solutions to PDEs with boundary conditions and initial conditions • Boundary and initial conditions • Cauchy, Dirichlet, and Neumann conditions • Well-posed problems • Existence and uniqueness theoremsCited by: 2.
Key words. Half–plane, Boundary integral equations, Helmholtz equation, uniqueness. Introduction. In this paper a boundary integral equation formulation for the two–dimensional Helmholtz equation in a locally perturbed half–plane is developed to calculate sound propagation out of a cutting of arbitrary cross–section and surface.
Heat equation Our goal is to solve the following problem ut = Duxx + f(x,t), x 2(0, a), (1) u(x,0) = f(x), (2) and u satisﬁes one of the above boundary conditions. In order to achieve this goal we ﬁrst consider a problem when f(x,t) = 0, h(t) = 0, g(t) = 0 and use the method of separation of variables to obtain solution.
To illustrate File Size: KB. Pressure poisson equation. Abstract. Studying an inverse problem always requires a solid knowledge of the theory for the corresponding direct problem. Therefore, the following two chapters of our book are devoted to presenting the foundations of obstacle scattering problems for time-harmonic acoustic waves, i.e., to exterior boundary value problems for the scalar Helmholtz : David Colton, Rainer Kress.A High-Order Accurate Compact Finite Difference Algorithm for the Incompressible Navier-Stokes Equations.
() A high-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions, ICASE Report No. Google by: 1.


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Today, a thirteen year old boy suffered from acute cognitive dysfunction after learning that he was not going to have his usual twice a week chocolate milk shake. This horrible mental attack was marked by irritability, distraction and sudden loss of all mathematical facility. As a consequence he was unable to complete his summer math homework.
The surprise arrival of cookies seemed to alleviate some of his symptoms and he was able to successfully work on his current math assignment and smile again. He reflected thoughtfully on the unfinished summer math, "If I get all 102 out of 150 problems I did finish correct that will be about 70% and I'll still pass the assignment."
This was today's tempest in a teapot.


In Reading last week, preschoolers listened to the read-alouds “My Q Book” by Jane Belk Moncure; “The Snowy Day” by Ezra Jack Keats; “Snowman’s Story” by Will Hillenbrand; and “The Little Snowflake’s Big Adventure” by Steve Metzger.
In Nursery Rhymes, we sang “Four Seasons,” “What’s the Weather,” and the “Queen of Hearts.”
In Language, students learned about the Letter Q through several literacy and sensory centers: playing with queen crowns, using quarter stamps on paper, and playing withpretend jars of quince. They made a Quilling Art Activity and a Letter Q Collage by pasting question marks on the Letter Q.
In Math, preschoolers worked on several concepts: more or less, 5 Senses, andcounting up to 14. At the Math Center, students played a Marshmallow Math Counting Game. First, they saw a big marshmallow stuffed with many pretzels (symbolic of quills) and a white board with a dry erase marker. Then each student had to answer the question: How many quills can you count? After they counted each pretzel (quill) stuck in the marshmallow, they had to write the correct number of quills on the small white board.
In Autonomy and Social Skills, we played the “Quickly Hide, Guess Who is Missing” game! This was a great way to teach students the how to take turns.


KMR Research seminar on geometric group theory 2014
Agol's Theorem on special cube complexes.
Organizers: Matthias Blank, Clara Löh.
Special cube complexes are a particular class of non-positively curved cube complexes, that can be defined by some simple geometric properties. They were introduced by Frédéric Haglund and Daniel Wise, who showed that the fundamental
group of such a cube complex embeds into a right-angled Artin group and is in particular linear. Last year, Ian Agol proved the
outstanding result that hyperbolic
groups that act geometrically on a CAT(0) cube complex have finite index subgroups that are the fundamental
group of a special cube complex. These results have many direct applications to the topology of 3-manifolds. For instance, they imply the virtual Haken conjecture.
Our aim is to get acquainted with the theory of special cube complexes and their applications and will introduce and study all the
above mentioned concepts. We will then, in detail, discuss the proofs of Haglund-Wise and Agol. Finally, we will also see how this relates to 3-manifolds.
An overview of the talks can be found here
The schedule can be found here
- Matthias Blank
- Sabine Braun
- Lukas Buggisch
- Alexander Engel
- Stefan Friedl
- Julia Heller
- Robin Loose
- Gabriele Link
- Clara Löh
- Rupert McCallum
- Matthias Nagel
- Christoforos Neofytidis
- Cristina Pagliantini
- Henrik Rüping
- Petra Schwer
- Daniel Skodlerack
- Werner Thumann
- Olga Varghese
- Gabriela Weitze-Schmithüsen
- Stefan Witzel
The seminar will take place at the University of Regensburg, Room M101 in the building of the Faculty of Mathematics.
The KMR Seminar 2012
took place in Münster.
Here you can find the conference poster.
I. Agol, The virtual Haken conjecture
I. Agol, Criteria for virtual fibering
I. Agol, D. Grobes, J. Manning Residual finiteness, QCERF, and fillings of hyperbolic groups
M. Aschenbrenner, S. Friedl, H. Wilton, 3-manifold groups
N. Bergeron, D. Wise, A boundary criterion for cubulation
M. Bestvina, Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston's vision
M. Bridson, A. Haefliger, Metric spaces of non-positive curvature
D. Calegari, Notes on Agol's Virtual Haken Theorem,
R. Charney, An introduction to right-angled Artin groups,
M. Davis, The Geometry and Topology of Coxeter Groups
J. Kahn, V. Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold
S. Friedl, T. Kitayama, The virtual fibering theorem for 3-manifolds
F. Haglund, D. Wise, Special Cube Complexes
M. Sageev, Ends of group pairs and non-positively curved cube complexes
M. Sageev, Codimension-1 subgroups and splittings of groups,
M. Sageev, CAT(0) Cube Complexes and Groups
P. Schwer, Lecture notes on CAT(0) cube complexes
D. Wise, From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups and Cubical Geometry
If you have any question regarding the seminar, please contact Matthias
Last edit: February 3rd, 2014.


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Bhaskara is also known as Bhaskara II or as Bhaskaracharya, this latter name meaning “Bhaskara the Teacher”. Since he is known in India as Bhaskaracharya . Bhaskara II is a famous Indian mathematician. He also goes by the name of Bhaskara or Bhaskaracharya, which means Bhaskara the Teacher. Bhaskaracharya (Bhāskara the teacher) was an Indian mathematician and astronomer of 12th century AD. He is refered as Bhāskara II to avoid confusion with.
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He reached an understanding of calculus, astronomythe number systems, and solving equations, which were not to be achieved anywhere else in the world for several centuries.
Similar to our current decimal system, these words were bhaskarz such that each number assigns the factor of the power of ten corresponding to its position, only in reverse order: He was born near Vijjadavida Bijapur in modern Karnataka. Your contribution may be further edited by our staff, and its publication bhaskraa subject to our final approval. Bhaskara’s arithmetic text Lilavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.
Bhaskara I’s sine approximation formula. He became head of the astronomical observatory at Ujjaincontinuing bhhaskara mathematical tradition of Varahamihira and Brahmagupta. His Bijaganita ” Algebra ” was a work in twelve chapters. He also had a profound and direct influence on Islamic and Byzantine astronomy.
Composed in Sanskrit Language, the treatise consists of verses.
Bhaskaracharya – The great Astronomer and Mathmatician | Mystery of India
Bhaskara covered a number amthematician other topics in Lilavati as well, such as trigonometry and mensuration, and even included a number of problems that readers of the book could work on. An SI day or mean solar day equals SI seconds. At the bottom of the article, feel free to list any sources that support your changes, so that we can fully understand their context.
More specifically the contents include:. This would mean that all numbers are the same, which is obviously not true. Sir Isaac Newton, English physicist and mathematician, who was the culminating figure of the scientific….
Bhaskaracharya – The great Astronomer and Mathmatician
The history of earlier contributions by wikipedians is accessible to researchers here:. It was the first text to recognize that a positive number has two square roots a positive and negative square root. Identify Singers By Eyes. He and Brahmagupta are two of the most renowned Indian mathematicians who made considerable contributions to the study of fractions. This book consists of twelve chapters and covers a variety of astronomical topics. Bhaskaracharya learnt mathematics from his father. Please help improve it or discuss these issues on matheematician talk page.
November Learn how and when to remove this mathematicuan message. He is the first to introduce Chakrawal, a cyclic method of solving algebraic equations. This advance allows astronomers to accurately measure planetary bhzskara. And otherwise, when one has set down those parts of the figure there [merely] seeing [it is sufficient].
Please help improve this article by checking for citation inaccuracies. Then find the correct latitudes of those two places and mathfmatician between the latitudes.
Walter Eugene Clark David Pingree. Mystery of India is a culture and society website that presents facts about India, that have been erased from history. This page was last edited on 28 Decemberat In this book, Bhaskara wrote about his discovery that each positive number can have both a positive square root and a negative square root.
Bhaskara II wrote the first work with full and systematic use of the decimal number system and also wrote extensively on other mathematical techniques and on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, and geography. The only way to prevent the death was to make sure that the marriage happened exactly at a specific time.
He placed the cup in the water so that it would sink at the exact time Lilavati was supposed to get married. Attempt Of Conversion To Mosque. To prevent that, he placed a cup with a small hole at the bottom of a vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour.
In chapter 7, he gives a remarkable approximation formula for sin xthat is. The rules that Bhaskara wrote about were the same rules that European mathematicians would come up bhaskraa almost five hundred years later. Casteism in India has gotten a lot of criticism, and rightly so.
The Editors of Encyclopaedia Britannica. He was born near Vijjadavida believed to be Bijjaragi of Vijayapur in modern Karnataka. In fact, half of bhaaskara most famous work dealt with mathematical astronomy.
The Ganitadhyaya deals with mathematical astronomy.
Bhāskara II | Indian mathematician |
In astronomy, Bhaskaracharya is renowned for his concept of Tatkalikagati, bhaaskara motion in physical terms. Bhaskaracharya, as he was known in India, was born to Mahesvara, another famous astrologer.
The book deals with definitions and terms as well as looking at the properties of zero. It has verses and is divided into four parts; although, sometimes the books are viewed as separate books. Bhaskara’s arithmetic text Leelavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometrysolid geometrythe shadow of the gnomonmethods to solve indeterminate equations, and combinations.


While it is traditionally considered a science, many Arts students specialize in Mathematics.
The Department of Mathematics offers a large selection of courses in various areas of pure and applied Mathematics. Programs available include Honours, Major, and Minor as well as Combined Majors in Mathematics and Economics.
Students are advised to consult a Mathematics advisor to design a coherent program of study suitable to their interests and abilities.
The major or minor can be declared on the Student Service Centre (SSC) when you have second-year standing.
Asha Padmanabhan enrolled in the Bachelor of Education program at UBC after graduating with a Bachelor of Arts in math. Today, she teaches math and calculus at a Richmond high school. “I got my dream job pretty fast,” she says.


Charlotte Perrelli - Wikipedia
Although 0.1 is usually used as the simplest example of an exact decimal number which can't be represented exactly in binary floating point, arguably 0.2 is a simpler example as it's 1/5 - and 5 is the prime that causes problems between decimal and binary. 2017-09-25 · Have translated: 3.25 of Decimal numeration system to Binary number system. Date and time of calculation 2017-09-25 14:03 UTC Each hex digit represents four binary digits; therefore, hex is a language to write binary in an abbreviated form. Four binary digits (also called nibbles) make up half a byte.
Example: Represent (-15) 10 in its 1's complement form. Solution: (15) 10 in binary form can be represented as (1111) 2. Now, to represent its negative sign, we will add a sign bit 1. Thus, (-15) 10 = (1,1111) 2. 1-bit 2-bit 3-bit 4-bit 5-bit 6-bit 7-bit 8-bit 9-bit 10-bit 11-bit 12-bit 13-bit 14-bit 15-bit 16-bit 17-bit 18-bit 19-bit 20-bit 21-bit 22-bit 23-bit 24-bit 25-bit. What is “hello” in Binary Code? The word “hello” in binary code is: 0110100001100101011011000110110001101111 By dividing this into eight-digit segments it is easier to see the binary byte corresponding to each letter: 01101000 01100101 01101100 01101100 01101111 – you can verify that with the binary translator.
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master's programs that were recorded during the Master's Fair on March 25, 2021: https://play.kth.se/…/Masterm%25C3%25A4ssan%2B2021%2…/416813. If yes is represented by the binary digit ”1”, and no by ”0”, the value in the above 2006 Computer Networks 25 LAN, MAN och WAN Lokalt nätverk Spring 2006 Example: 5726 would cause the binary values in registers 2 and 6 to be ADD the bit patterns in registers S and T as though they represented CBOR Web Token (CWT) is a compact means of representing claims to be transferred between two parties. The claims in a CWT are encoded in the Concise Binary Object Representation (CBOR), and CBOR Object IETF 25 september 2015.
In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one). The binary numbers here are expressed in the base-2 numeral system. For example, (101) 2 is a binary number. Each digit in this system is said to be a bit.
CLK. D. Q. 0 ms. 5 ms. 10 ms What is the smallest and largest number that can be represented? av J Havermark · 2018 — Example 4. The tuple (4, 1) and the digit string 10001 represent the binary number 1.0001.
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Translating normal text in binary numbers allow the computer’s processor to execute the given instructions 2. The two most common Standards used for Information Interchange and to represent text in binary are ASCII and Unicode. 2019-02-21 · When an integer binary number is positive, the sign is represented by 0 and the magnitude by a positive binary number. When the number is negative, the sign is represented by 1 but the rest of the number may be represented in one of three possible ways: Sign-Magnitude method, 1’s Complement method, and 2’s complement method.
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Bit-Vector Approximations of Floating-Point - Diva Portal
1. 2019-01-24 · Given a real number between 0 and 1 (e.g., 0.72) that is passed in as a double, print the binary representation. If the number cannot be represented accurately in binary with at most 32 characters, print” ERROR:’ Examples: Input : (0.625) 10 Output : (0.101) 2 Input : (0.72) 10 Output : ERROR Figure 2: binary number 13 . Once we translate each bit by noting it’s place value and its numerical value, we simply add the numbers together (just like you mentally already do in base 10): 8 + 4 + 0 + 1 = 13. Figure 3 shows all the binary number from zero to fifteen with bit A being the MSB and bit D being the LSB. Figure 3: binary numbers Binary Logic MODULE 1 Basic Computing Notes Computer Science 25 In the previous lesson, you have learnt about computer fundamentals.
Computers store all characters as numbers stored as binary data. Binary code uses the digits of 0 and 1 (binary numbers) to represent computer instructions or text. Each instruction or symbol gets a bit string assignment. The strings can correspond to instructions, letters, or symbols. This is a decimal/binary to two’s complement converter and a two’s complement to decimal converter.
Computer Networks A. 25. 25 January 2021 25 January 2021 25 November 2020 of a multiplex network where each layer is represented by a derivatives asset class market. Comparing the prediction performance with a standard binary early warning model The R25 is the resistance of the thermistor at 25ºC. The graphic above (8-bit binary 4.4 fixed point representation) shows this same calculation, but provides a av D Calvo · 2013 · Citerat av 21 — 10.15 ihörsalen Sappören, Sprängkullsgatan 25, Göteborg.


By Morton Swimmer, Mark Chimley, and Adam Tuaima
Quantum mechanics enables us to build computers that are, in some ways, much more powerful than classical computers. Small, gated quantum computers and experimental quantum computers already exist, but the world might soon see the arrival of quantum computers capable of demonstrating quantum advantage over their classical counterparts. When that happens, it will leave little time for the lengthy process of migrating to new cryptographic algorithms, so it’s best to plan ahead and consider post-quantum cryptography now.
In this entry, the second in our series on post-quantum cryptography, we delve into the history of quantum computing, its foundation in quantum mechanics, and the kind of complex problems quantum computers will be able to solve.
To better comprehend quantum mechanics, it helps to understand how mathematics evolved over time, and with it, our understanding of nature.
Early in history, people’s mathematical understanding of the world was simpler than now: at first, only natural numbers (1, 2, 3, 4, 5, etc.) were used to count. Later, negative numbers (…, -3, -2, -1, 0, 1, 2, 3, ….) were incorporated as well. Eventually, multiplication and division were needed, and these required the concept of fractions created from positive integers. These were classified as rational numbers.
Rational numbers serve well in many practical applications of physics or classical mechanics, where the goal is to measure or approximate something to a sufficient degree of accuracy. However, when the ancient Egyptians wanted to calculate the area of a circle, they tried using fractions in their formula, but the results were not quite accurate. Further examination revealed that a certain number, which will eventually be called pi (symbolized by π and has the value of 3.14159…), can instead be used for this operation. This sparked the idea that there are numbers that cannot be represented by fractions. We call such as real numbers because there’s a tacit assumption that they describe how nature works. So, for a long time, people believed that the world exists on a continuum of scales.
However, the advent of nuclear physics in the late 19th and early 20th centuries started to challenge this view. The smallest unit of matter was initially thought to be the atom, thus it was so named — the ancient Greek “atomos” translates to “indivisible,” or more literally “uncuttable.” In the late 19th century, however, Sir Joseph John Thompson discovered a sub-atomic particle, the electron, and proposed the ‘plum pudding’ model of an atom. In the early 20th century, Ernest Rutherford first theorized the existence of protons and neutrons in an atom’s nucleus, a fact then proven by James Chadwick. Rutherford proposed a model of the atom where the electrons orbited the nucleus like planets around the sun.
Figure 1. Rutherford Atomic Model
But trouble was on the horizon for the planetary model of an atom. Viewed through the lens of classical electromagnetic physics, the electrons would have to continuously lose energy and their orbits would decay rapidly, resulting in the collapse of the atom; but this was not happening.
Meanwhile, Albert Einstein proved Max Planck’s hypothesis that matter has both particle and wave characteristics, for which he later won the Nobel Prize. This is called the wave/particle duality. With this, Niels Bohr, one of the founding fathers of quantum theory, presented a superseding model of the atom in which electrons occupy a set of discrete (or quantized) positions (orbits) based on their energy levels. Describing each orbital by the wave function of the electron explains why the orbitals do not collapse: the smallest orbital is the one composed of a single standing wave. Electrons can move from one discrete state (quantum) to another, but they do so discontinuously; that is, they jump between quanta in a quantum leap. Each jump goes from one wave harmonic to another. The earlier assumption that the world is based on real numbers was proven incorrect. Wolfgang Ernst Pauli later determined that no two electrons can inhabit the same state at the same time, making the model useful in predicting an atom’s chemical properties.
Figure 2. Bohr Model
Most of these might be hard to relate to everyday experiences, but they sit coherently within the quantum mechanical model in terms of mathematics. While many scientists in the early 20th century — for instance, Einstein — were skeptical of quantum mechanics, over time, the field has proven to be sound and useful.
Other observations that fit the quantum model include Heisenberg's uncertainty principle, which states that it is not possible to precisely determine both the momentum and position of an electron. The more accurately we discern one aspect (either momentum or position), the less accurately the other aspect is determined. This is not a limitation of the apparatus. This is a fundamental property of quantum mechanics and plays an important role in quantum computing.
Figure 3. Heisenberg’s Uncertainty Principle
As shown in the left portion of the illustration above, if we use a high frequency to determine the location of an electron, we will not know its momentum with good accuracy. If we use a low frequency, we can find its momentum with good accuracy but will then not know its location well. In the quantum mechanical world, any measurement comes with a trade-off.
Heisenberg’s uncertainty principle changes how we think about computation. While in a classical computer, reading from a memory location doesn’t change it, the same is not true in a quantum computer. Reading the state of a quantum system will invalidate its state, so algorithms need to be designed appropriately.
Two other important topics in quantum mechanics are superposition and entanglement. These are central to quantum computing. Together, they make quantum computing possible.
Until they are measured, particles can exist in infinitely many states. Take an electron, for instance. It is said that it can spin on the x, y, and z axes, as shown in Figure 4. When an electron’s spin is clockwise along some axis, we can call this the “1” state and when it is spinning counterclockwise, we call this the “0” state. However, before measuring the spin, the electron is in a superposition of all possible states. Think of a spinning coin: we cannot say it is in a heads or tails state while it is spinning. Rather, it is in some other in-between state. It’s in a superposition. (Note that the electron doesn’t actually spin. This is just a measurable property of it that we chose to call “spin”.)
The particle is in superposition while it is not observed. When the spin is measured, the state will “collapse” on one choice dictated by its probability distribution, just like when the coin flops down on one side or the other with a 50% chance of being either.
Figure 4. An electron can “spin” on the x, y, and z axes
This is the basis of the famous Schrödinger’s Cat thought experiment (Figure 5). An imaginary cat is placed in a box with a vial of poison and a radioactive source. If radioactive decay is detected, the vial of poison breaks and ends the imaginary cat’s life. But radioactive decay is a random process which may or may not happen.
While this was originally meant to demonstrate the absurdity of quantum mechanics, it turned out to be a reasonable explainer of superposition. When the box is shut, there is no way of observing what happens inside. Whether the cat is alive or dead cannot be concluded. From an observer’s point of view, the cat is in a superposition of dead and alive. In quantum mechanics, opening the box causes the superposition to collapse into a single state of the cat being either dead or alive.
Figure 5. The Schrödinger’s Cat thought experiment
In a classical computer, the smallest unit of storage is called a bit, which can either take a 0 or a 1. In a quantum computer, particles can be used to perform calculations, and these are called qubits (quantum bits). Qubits are different from ordinary bits in that through superposition, they can assume an infinite number of states at the same time, which gives them exponentially more computational power. Qubits are used in quantum circuits, which are comparable to algorithms on a classical computer. The goal of these circuits is to run to the end and amplify the correct result so that the answers can be read by measuring the resulting states. In practice, the circuit is re-run thousands of times to obtain a probability distribution from which the answer is derived. However, a circuit needs gates, and the use of multiple gates requires entanglement. The following section delves into this concept.
In a classical computer, a logic gate can take bits as input and produce a value as output. For example, a “1” bit and another “1” bit combined at an AND gate will result in “1”. On their own, these bits do nothing. However, in a quantum computer, two particles can become “entangled,” which means an operation on one will influence the state of the other, even if they are far apart. This is like picturing two spinning coins that always land down the same way: either showing both heads or both tails. The two particles are not communicating with each other to do this. Instead, imagine them as twins that behave the same even when they are separated. In this way, they are not violating special relativity that disallows travel at the speed of light or faster. In the macro world, however, this would be strange, and we would not expect coins to behave this way.
Einstein was not a fan of the idea and described it as “spooky action at a distance.” It might take some convincing to believe that that two particles could influence each other remotely, but it is mathematically proven by and shown in experiments. Between 1980 and 1982, Alain Aspect performed various experiments proving entanglement is real, for which he won the Nobel Prize in 2022.
Entanglement makes useful algorithms possible. By linking two qubits, conditional quantum gates can be created in quantum circuits. With that, algorithms can be implemented.
When the first serious efforts to build a quantum computer were made in the mid-1990s, one of the main questions raised was, what would it be good for? Actually, this very question serves as the answer itself to one of the main motivations why these computers are developed: they were built so their full potential can be discovered and unleashed.
The original idea of quantum computing was proposed by Paul Benioff and Richard P. Feynman around 1980. Simulations of physical systems, for instance tracking all interactions between atoms in a molecule, are often impossible to run on classical computers because the difficulty of the problem grows exponentially with the number of atoms. In contrast, quantum computers can tackle exponentially larger problems for every qubit in the quantum computer and can deal with this complexity.
Now, while experimental quantum computers are emerging, there are still challenges on how their usefulness can be most effectively maximized. Machines with sufficiently large numbers of usable qubits remain elusive. Furthermore, scalability and noise management remain a concern. Noise could limit scalability. In this context, noise pertains to electromagnetic radiation, magnetic fields, cosmic rays, and the like. For this reason, most quantum computers are operated at temperatures close to absolute zero (which is 0 Kelvin, -273.15℃, or -459.67 ℉) and are heavily shielded from radiation.
With the current crop of quantum computers, attempts to mitigate noise are done by using redundant noisy physical qubits to create noise-free logical qubits. The current generation of quantum computers is called Noisy Intermediate-Scale Quantum (NISQ) computers. The number of logical qubits is much lower than the number of physical qubits in these systems. This means that a useful quantum computer will have to have several dozen times as many physical qubits as required logical qubits in order to execute a given quantum circuit.
Despite the challenges, many algorithms for quantum computers have been proposed, showing how versatile the platform may one day be. As of now that question of their purpose still stands, although perhaps not much longer.
Quantum advantage pertains to the milestone where a quantum computer can solve problems faster than a classical computer can. While several claims of quantum advantage have been made recently, none of them solves useful problems. They are therefore not convincing — yet. Because the simulation of physical systems often requires far fewer qubits, we will probably see the first practical uses here. On the other hand, a quantum computer for solving large computer science problems is probably over a decade away. These simulations would be valuable as they would enable major chemical, physical, and medicinal discoveries. This is why the development of quantum computers has garnered so much attention lately.
In an attempt to horizontally scale the current generation of experimental quantum computers, there have been experiments using circuit knitting or surface-code architectures. These experiments take small quantum computers and combine them using classical or quantum connections to form a larger machine. However, it is not clear if quantum advantage can be achieved this way, as these separate circuits need to be connected, which incurs overhead and a change to the algorithms. The last limiting factor is the number of quantum gates that can be used, but little has been published on this for existing quantum computers.
Small, gated quantum computers containing a few hundred physical qubits, are now available as a cloud service from various vendors. Adiabatic quantum computers (AQC) that are restricted to a special optimization process already have thousands of qubits but have yet to show meaningful speedup over classical computers.
A recent finding from a university in Switzerland showed that merely quadratic speedup over classical algorithms will not be enough to compensate for the overhead that quantum computers have in loading the data and circuit. Given this finding, there are some doubts that they will ever be useful for big-data applications at all, unless some engineering solution is found.
As mentioned, quantum computers can solve some problems in minutes that would take years on a classical computer. In this section, let’s look at the classes of problems that quantum computers can solve.
A complexity class refers to a set of problems that are solvable with relatable time requirements on a Turing machine, which is a theoretical computational model. Without going into details, a nondeterministic Turing machine is exponentially faster than the deterministic variant. We strive to use polynomial-time algorithms (or better) because the time they take only goes up moderately with the problem size. We call these “P” problems. Many real-world problems are “NP” problems that require much greater resources and typically grow in time and space requirements exponentially with the size of the input problem. We say that a problem is NP-Complete if it can be proven that no algorithm solves the problem better than a non-deterministic Turing machine would need in polynomial time. The entire space of decidable problems that a Turing machine can solve is called PSPACE.
The complexity class for quantum algorithms solvable in polynomial time is called Bounded-Error Quantum Polynomial Time complexity (BQP). This class is not thoroughly explored, but we believe it includes the whole P class and some of the NP and PSPACE classes, but no NP-Complete problems (as shown in Figure 6 below). Solving some of the NP problems in BQP time complexity is a game changer, even if it might disappoint some that NP-complete problems still stay exponentially difficult.
Figure 6. Quantum computer complexity classes
What quantum computers cannot do is solve completely intractable and (classically) undecidable problems. And while there are problems that are difficult for classical computers but relatively easy for quantum computers, the reverse is also true.
The rise in interest in quantum computing algorithms has also revived creativity in classical algorithm design. Some heuristic algorithms can now be seen emerging from this research. These are often optimization algorithms that are called Quantum Inspired Optimization (QIO) or sometimes Quantum-Inspired Algorithms (QIA). Therefore, research into quantum computing is leading to speedups in classical real-world algorithms, which might turn out to be more of a game changer than quantum computers themselves.
Quantum computers are vastly different from classical computers in fundamental ways. This is shown through a variety of factors, from the probabilistic nature of their operation to the resulting complexity classes of the algorithms that can be implemented on quantum computers. This article looked into the history of quantum computing, pertinent concepts in quantum mechanics, and the type of problems quantum computers can help solve. It also touched on the types of gates that can be used in quantum circuits. In the next parts of this research, we will look at how quantum computer cryptanalysis works and why there are worries about these nascent computers.
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a Matlab Tool for image restoration with Newton-like Projection methods
NPTool is a software package for image denoising and deblurrig from Gaussian or Poisson corrupted data.
The image formation process is modeled as
The image restoration problem is formulated as the nonnegatively constrained minimization problem
- A is the blurring operator (A is the identity operator in denoising applications)
- bg is the (possible) constant value of the background
- gn is the acquired image corrupted by blur and noise
NPTool is a Matlab implementation of some Newton-like Projection algorithms
for the solution of the previously described constrained optimization problem.
- The data fitting term J0(x) depends on the noise affecting the data:
in the case of Poisson data, J0(x) is the Kullback-Leibler divergence;
in the case of Gaussian data, J0(x) is the Least-Squares term.
- The regularization term JR(x) can be chosen to be the Tikhonov regularization functional (
JR(x)=0.5*||x||^2) or the Total Variation functional.
- Version 1.1, July 2011. The software has been tested on Windows operating system.
The code can be obtained from Netlib (http://www.netlib.org/numeralgo/)
as the na35 package or by clicking here. The code has been developed using Matlab version 7.5.
The Matlab functions are included into a zipped .rar file. Once you have downloaded and unpacked it in your Matlab working directory, type
There is a "Readme" file to guide you in the use of the codes.
The software has been developed by G. Landi and E. Loli Piccolomini.
For any information or comments, please contact landig(at)dm.unibo.it
-  G. Landi, E. Loli Piccolomini. A fast projected quasi-newton method for nonnegative Tikhonov regularization. International Journal of Mathematics and Computer Science 3, 199-213, 2008.
-  G. Landi, E. Loli Piccolomini. A projected Newton-CG method for nonnegative astronomical image deblurring. Numerical Algorithms 48, 279-300, 2008.
-  G. Landi, E. Loli Piccolomini. An improved Newton projection method for
nonnegative deblurring of Poisson-corrupted images with Tikhonov regularization,
Numerical Algorithms, DOI 10.1007/s11075-011-9517-y, 2011.
-  G. Landi, E. Loli Piccolomini. Quasi-Newton projection method for nonnegatively constrained image deblurring, Optimization Online, Applied Mathematics and Computation, 218:2091-2107, 2011.
-  S. Bonettini, G. Landi, E. Loli Piccolomini, L. Zanni. On the scaled gradient projection methods for image deblurring, 2011, submitted.
-  G. Landi, E. Loli Piccolomini. An efficient method for nonnegatively constrained Total-Variation based denoising of medical images corrupted by Poisson noise, Computerized Medical Imaging and Graphics, Vol. 36(1), pp. 38-46, 2012.
This work has been partially supported by the Ministero dell' UniversitÓ e della Ricerca under the Grant number 2006018748.


Thanks to a generous donation of the Foundation Advancement of Mathematics we can offer a number of student grants for participation in MTNS 2022 without conference fee. This free registration includes all features of the standard student registration.
Applications for these grants should be sent by email to
until 30 June 2022.
The application should include
- a CV
- a motivation letter
- a proof of student status (e.g., a student ID or a letter from the supervisor).
In case the number of applications exceeds the available grants, priority will be given to students who would have difficulties to participate without a grant.
The decision about the grants will be sent out until 6 July 2022. Students who applied for the grant should not register before this date.


The 5 Platonic Solids - Shungite Set
Our most unique man-made item to date! Mined, carved and polished by hand in Russia, this set of the 5 platonic solids is made from solid black shungite. The set has 5 pieces: the tetrahedron (4 sides), hexahedron (6 sides), octahedron (8 sides), icosahedron (12 sides), and dodecahedron (20 sides). Each is highly polished, with very crisp, straight edges. Small mineral inclusions are sometimes visible.
The set of these 5 shapes is named after Plato, who described them as being regular, convex polyhedrons. They comprise the only 5 perfectly symmetrical, three-dimensional solid shapes possible; no others exist. Plato used them to explain his theory of the 4 classic elements plus outer space: earth (the hexahedron/cube), air (the octahedron), water (the icosahedron), fire (the tetrahedron/pyramid), and space (the dodecahedron).
They make interesting, unique decor, and inspire new ways of thinking. They also make great gifts for the math student/engineer/astronaut!
The entire set weighs about 15 ounces - a lot of shungite! Each piece is between about 1 1/2 and 2 inches long across the widest part.
Unit for sale: 1 set of 5 shapes
Mined and made in Russia


The LTV ratio varies according to the trading activity and liquidity of your chosen collateral. Most collateral types have an LTV ratio of 66% for 1 year loans or shorter. That means we require 150% of the loan value in collateral. For each month after the first year, we require an extra 5% of the loan value in collateral.
For example, if you were to request a loan for 15 months, the collateral due would be 150% + (3*5)% = 165% of the loan value in collateral, which brings your LTV ratio to 60.6%.
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Sakura Quick Math
Sakura Quick Math by Shiny Things Software is an app which provides a fun, self-competitive environment for practicing math facts. It harnesses handwriting recognition to recognize the students’ answers as they race the clock to answer math problems in addition, subtraction, multiplication, division or a combination of all of these.
Quick Math is a fairly basic math app, but the interface makes this app very interesting to me. Math problems are presented and the answers are input by simply writing the missing number anywhere on the screen. The handwriting analysis seems very quick and very accurate. It rarely had trouble interpreting my handwritten numerals.Very cool interface…. but interface to what exactly?
The user can choose the operation they want to practice and the difficulty level of the problems. For example in the addition problem sets there are not just the standard find-the-sum problems, but a mix of those and problems with missing addends. A sample screenshot of the mixed operation menu selection is below.
Multiple students can save their avatars on within the app and their speed scores will be kept. When a game is completed the student sees the time for their latest round of that skill and level as it compares to other times they have tried to complete the level.
Students I watched use this app were between 7 and 11 years old. They were much more motivated to beat their own times than I would have expected. They continued to repeat levels working to improve their times, over and over again. When I asked them why, they replied they “want to beat my old score.”
Clearly this is an app that is for repetitious math problem solving with a goal of increasing accuracy and speed. The ease of answer entry (handwritten numerals rather than keying in entries) makes the focus on the problem solving. The thing which sets this app apart is that ease of entry and the motivating nature of competing against your own best time. Is this high-level mathematical thinking or problem solving? No. The seamless, engaging, easy-to-use interface provides a platform for practicing mathematical fluency in a way which may be superior to the more standard “one minute” math drills often seen in classrooms.
Sakura Quick Math
$1.99 (when posted on 7/19/2013)
Compatible with iPhone 3GS, iPhone 4, iPhone 4S, iPhone 5, iPod touch (3rd generation), iPod touch (4th generation), iPod touch (5th generation) and iPad. Requires iOS 5.0 or later. This app is optimized for iPhone 5.


Wow! What a whirlwind!
I've been absent from "Greasy" for way too long.
I enrolled in FOUR classes for the Fall semester after taking THREE over two months in the summer. I thought, "How bad could it be? I got through those two months and now it's spread out over four months."
Then, when I had a chance to drop them before incurring any charges, I couldn't get them dropped due to some technicality in the bursar's office. Sooooo...I'm still taking FOUR classes during one of the busiest times of the year.
THEN THERE'S MATH!!! Ok, I used to be really good at math. Used to be. This Math Analysis for Business is eating my lunch! It's calculus and I've forgotten so much of what comes before calculus that I'm playing a frantic game of catch-up and I'm still not sure it isn't going to tank my GPA (which matters to me only because it always has, no logical reason).
I spend literally hours on the homework and when I return to it in a day or two I cannot remember what is supposed to happen. Fortunately, there are not very many high-level math classes required for this degree.
On a brighter note, I'm finally scratching the learning itch that went neglected for far too long. Some, including close family, think I'm crazy for wasting money on a degree, but they don't understand it's not about the paper. It's about learning and it's something I enjoy immensely. Hopefully, I can turn it into something profitable sooner or later.
The girls are back to school and the steady hum of home life is soothing, although quite lively most of the time. The church is hanging in there, although I wish I were better at that part of my work. Seems like what worked in Mexico isn't working here.
Wish me luck. I'm gonna need it for the next 13 weeks! LOL


When I DERIVED the equation for the Hypergeometrical Force – the Grand Unification Force - used a setup with two infinitesimal elements of current (or mass flow).
These infinitesimal elements of current or flow defined a direction within the four dimensional spatial manifold. This direction is shown as velocities in the formulas. Despite of having velocities, these formulas were derived for constant velocities, where the velocities were referred from a relaxed Fabric of Space reference system. To eliminate this constraint one has to derived the potential through adiabatic integration followed by the derivation of a generalized force according to Lagrangian formalism!!!
These means that the force equations below are constant velocity forces. Despite of this constraint, they are quite usefull for making simplied reasonings about dynamics.
Here are the equations for Electromagnetism and Gravitation:
Where C1 and C2 are the charges traveling at V1 and V2 and c is the speed of light. R12 is a vector from charge 1 to charge 2.
Similarly for Gravitation:
Notice that the only difference is the proportionality coefficient. This means that the interaction is the same – dilaton field-dilator interaction controlled by the Quantum Lagrangian Principle. The proportionality coefficient ratio is given by the ratio of these two angles a0
R0 is the age of the Universe times the speed of light (15.82 billion light years) and λ1 is the Compton wavelength of a Hydrogen atom. To be precise, this ratio has to be multiplied by an elastic coefficient of the Fabric of Space. This coefficient is the reason why dilaton and Gravitational waves exist.
The humongous (1036
) factor is easy to understand by this simple figure. A more detailed analysis can be found in the pdf containing the theory.
This equation can be simplified for the case where there is no rotation and one of the bodies is much larger than the other (Sun and Mercury for instance) into:
This is the first time a force is actually derived from a purely geometrical theory of the Universe, so it took me some time to understand that this equation has to be integrated upon R (distance) to yield the amount of energy that can be shared into Kinetic and Potential at any position.
Adiabatic integration upon R yields the potential
This potential is the one used in the Precession of Mercury's Perihelion problem. Applying it to Lagrangian Formalism yields the more appropriate force formula for physical bodies or charges:
Similarly for F one obtains:
Thus F becomes:
Expanding it in powers of
Neglecting terms above the second order
This means that my Gravitational Force does not contains first order dependence upon v/c and also that it perfectly describes all celestial dynamics. It produces the same formula for the Precession of Mercury or Earth or anything else Perihelion…J
In summary, my formula produces not one but TWO formulas for force. One for constructs that cannot change speed (e.g. Light) and another for bodies. They are reproduced without approximations below:
The second formula is used to derive the Gravitational Lensinng (Gerber failed to do so since he only ansatz (guessed) right the first formula).
The more complex formulation for the Force per unit mass (for double jets Black Holes or White Orifices) is given by:
To understand the rest of the Universe, one only need to add the Fundamental Dilator paradigm.
The Fundamental Dilator is a coherence between two deformation states within the 4D spatial manifold. The orientation of the letters in the figure below maps the orientation of the dilator deformation with respect to our 3D Hypersurface. A vertical lettering means that the dilator overlaps minimally with our 3DUniverse (the Fundamental Dilator is quite flat (along the fourth dimension).
The Fundamental Dilator can be represented by this diagram:


This is the oldest and well established department at Nyanchwa Boys. It has four competent teachers
- Mr. Nyandondi (H.O.D
- Mr. Mogire (D.O.S)
- Mr. Kubencha Ezekiel
- Mr. Makori Daniel
The major objectives of the department are, learners should be able
i) to develop a positive attitude towards leaning mathematics
ii) Perform mathematical operations and manipulations with confidence, speed and accuracy.
iii) Think and reason precisely, logically and critically in any given situation.
iv) Develop investigative skills in mathematics.
v) Identify, concretize, symbols and use mathematical relationships in everyday life.
vi) Collect, organize, represent analyze, interpret data and make conclusions and predictions from its results.
vii) Apply mathematical knowledge and skills to familiar and unfamiliar situations.
viii) Appreciate the role value and use of mathematics in society.
ix) develop a willingness to work collaboratively
x) Acquire knowledge and skills for further educations and training.
She following are some of the strategies put in place to enable the department achieve its objectives
1) Early syllabus coverage
2) teach teaching
3) exposure of learners to many exams
4) exposure of learners to contests
5) use of KNEC papers from revision
6) embracing discussion groups and beer teaching
7) learner motivation and reinforcement
The department enjoys good relationship support and harmony form the administration


Timothy Blek was the winner of the free Graphics Server software. Congratulations! We are giving away another copy this month, so if you haven't yet entered, do it at http://www.codeoftheweek.com/contest.html now! If you entered last month, please be sure to enter again because your entry from last month does not count towards the prize this month.
This issue we are introducing a routine to convert a number from one base to another. For example base 16 (hexadecimal) to base 2 (binary).
This source code is designed for VB 3.0 and up. Pedro Dias submitted most of this source code. Questions? Email us at email@example.com.
The AnyBase function has three parameters: the value to convert, the base the number is in and the base you want to convert to. Some common base values that you might use are 2 for binary, 10 for decimal and 16 for hexadecimal. This routine supports conversions from Base 2 through Base 36. The source number must be in the range of a Long data type which is from -2,147,483,648 to 2,147,483,647.
Just in case some of you do not understand what base means in this context, we will give a short description. Our numerical system is called base 10 because there are 10 digits that are possible (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Base 2 consists of only 0 and 1. Base 16 would be the numbers from 0 to 9 and the letters from A to F with A=10, B=11, etc. These are the most common bases that are used in the programming world. Some older systems use octal which is base 8 or the numbers 0 through 7.
Function AnyBase(sValueToConvert As String, iBaseIn As Integer, iBaseOut As Integer) As String
Error 51 if the value in sValueToConvert does not match the base supplied in iBaseIn. If successful it will return a string that represents the sValueToConvert in base iBaseOut.
MsgBox AnyBase("FFCA", 16, 10) ' Will print 65482 in a message box MsgBox AnyBase("FFCA", 16, 2) ' Will print 1111111111001010 in a message box MsgBox AnyBase("74292", 10, 16) ' Will print 12234 in a message box
To see the source code for this issue you must be a subscriber to Code of the Week. If you are a subscriber the source code is available at the following address: http://www.codeoftheweek.com/membersonly/bi/0069.html


Via Reason on Teach for America (TFA)
The best evidence we had before today was a randomized evaluation conducted by Mathematica Policy Research between 2001 and 2003, which found that TFA teachers bested other teachers at teaching math — with gains for students equal to about a month of additional instruction — and were not significantly different from them on teaching reading.
A follow-up using the same data showed that that result held for students across the math score distribution, not just the average student. “These results suggest that allowing highly qualified teachers, who in the absence of TFA would not have taught in these disadvantaged neighborhoods, should have a positive influence not just on students at the top of the achievement distribution but across the entire math test score distribution,” the authors concluded.
We sponsor a TFA teacher each year, and have fun doing a few little things for their classroom through the year (we collect school supplies at the beginning of the year, bring presents during the holidays). Short of the school choice we really need, this is the best way we have found to help K-12 education.


How to Play 3 Card Baccarat Games?
3 Card (3 Picture/Face) Baccarat is one of baccarat playing way. Player and Banker bet on points and picture cards and also bet on ordered sets. It’s straightforward and speedy. This Article is going to tell you how to play 3 Card Baccarat!
More About 3 Card Baccarat on How to Calculate
>>Online Baccarat Rules of Baccarat Point Calculation
3 Face/3 Picture Baccarat is a gambling game playing with Banker. If the total of three cards on Player’s hand is bigger than Banker’s, Player wins. The biggest one is called 3 Face. Other people sum up the points of three cards. If it’s over 10, please minus 10. If it’s over 20, please minus 20.
1. The Biggest Set：3P，Sets of 3 picture cards （J、Q、K）
2. The Secondary Bigger Set：2 picture cards and card number 9.
3. The Third Bigger Set：1 picture card + the sum of 2 cards equals 9.
Share You 3 Card Baccarat Casino Playing Ways and Odds
– 3 Card Baccarat Playing Ways
1. Bet with Banker：It’s a common playing way. Player bets with Banker, one who gets bigger digit wins. If it’s even, Player can’t retrieve the stake. The stake stays until the final result.
2. Bet Even：Player can also bet even. If it’s even, and Player predicts the points of Banker correctly, Player wins. You can’t bet even until other people have already bet all the other items.
3. 3 Face Bet：Bet on Banker and receive 3 Face.
4. Total Point Bet：Bet on the total points of Banker.
– 3 Card Baccarat Odds
|Player/Banker||Bet on Banker or Player, and one of them wins.||1: 1|
|Tie||Bet on Banker or Player, and the result is even.||1: 8|
|3 Card||Bet on Banker, and getting 3 Card (Face).||1: 16|
|1||3P||3 picture cards (J, Q, K)|
|2||2P9||2 picture cards +9|
|3||P9||1 picture card + sum of 2 cards = 9|
|4||9||Sum of 3 cards = 9, without picture cards|
|5||2P8||2 picture cards + 8|
|6||P8||1 picture card + sum of 2 cards = 8|
|7||8||Sum of 3 cards = 8, without picture cards|
|8||2P7||2 picture cards + 7|
|9||P7||1 picture card + sum of 2 cards = 7|
|10||7||Sum of 3 cards = 7, without picture cards|
|11||2P6||2 picture cards + 6|
|12||P6||1 picture card + sum of 2 cards = 6|
|13||6||Sum of 3 cards = 6, without picture cards|
|14||2P5||2 picture cards + 5|
|15||P5||1 picture card + sum of 2 cards = 5|
|16||5||Sum of 3 cards = 5, without picture cards|
|17||2P4||2 picture cards + 4|
|18||P4||1 picture card + sum of 2 cards = 4|
|19||4||Sum of 3 cards = 4, without picture cards|
|20||2P3||2 picture cards + 3|
|21||P3||1 picture card + sum of 2 cards = 3|
|22||3||Sum of 3 cards = 3, without picture cards|
|23||2P2||2 picture cards + 2|
|24||P2||1 picture card + sum of 2 cards = 2|
|25||2||Sum of 3 cards = 2, without picture cards|
|26||2P1||2 picture cards + 1|
|27||P1||1 picture card + sum of 2 cards = 1|
|28||1||Sum of 3 cards = 1, without picture cards|
|29||2P0||2 picture cards + 10|
|30||P0||1 picture cards + sum of 2 cards = 0 (10 or 20)|
|31||0||Sum of 3 cards = 0 (10 or 20), without picture cards|
Simply saying is that 3 Face is comparing points first, and then comparing the Face cards.
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Awesome Educational Websites!
Newsela is an innovative way to build reading comprehension with nonfiction that's always relevant: daily news.
This website will have the weekly
spelling list on it so students can practice at home.
This website will help students prepare for the ISAT
This website will help students memorize their math facts.
This website has educational games for kids in all subject areas
This website will help students learn vocabulary/spelling words. I will put
vocabulary words and spelling words on this website so students can practice at
home. They need to type in 4th grade stambaugh in the search bar in order to find their list
This website will help enhance vocabulary and math skills while earning "rice" which will
help third world nations.
This website is a web-based curriculum that is individualized for individual needs.
Fourth Grade MathSymmetry (Level Hard)- CCSS.Math.Content.4.G.A.3
Rounding 2- CCSS.Math.Content.4.NBT.A.3
Fraction Addition- CCSS.Math.Content.4.NF.B.3a


Curriculum & Materials
Homeschooling gives you the freedom to choose the materials that you see fit for your family. Some families know what approach or materials they want to use, whereas other families prefer guidance and recommendations from professionals in the field of education, such as the suggestions linked below.
We recommend using these choices because we believe in the multi-sensory practices or the educational frameworks embedded in the programs. You are welcome to use or purchase your own materials, however we encourage you to explore the possibility of purchasing any of the below listed resources.
Our recommended curriculum resources for K-5 are below. Some links might bring you to an affiliate website where you can purchase the resources. The following materials are not faith-based. If you'd like to add faith into your studies, we support your choice to do so.
Phonics / Intensive Intervention
UFLI Foundations and
Recipe for Reading and
Shiller Math - Montessori math and language arts manipulatives
Hand 2 Mind offers manipulatives and lessons for language arts, math, science, etc.
Multisensory Math by Marilyn Zecher is an Orton-Gillingham-style math approach.
Shiller Montessori Math - curriculum and materials for multi-sensory Montessori math
Hand 2 Mind - Math manipulatives and materials
Woodin Math - a multi-sensory math approach
Michael Minas - math games
We encourage you to visit museums and local historical places of interest as part of your studies in this content area. We also recommend reading historical non-fiction books with your child.
Hands-on-History is a possible option recommended for an active, hands-on learner.


By Ovidiu Calin
The aim of this e-book is to provide Stochastic Calculus at an introductory point and never at its greatest mathematical element. the writer goals to seize up to attainable the spirit of user-friendly deterministic Calculus, at which scholars were already uncovered. This assumes a presentation that mimics comparable homes of deterministic Calculus, which enables figuring out of extra advanced issues of Stochastic Calculus.
Read Online or Download An Informal Introduction to Stochastic Calculus with Applications PDF
Similar calculus books
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Der vorliegende Band stellt den dritten Teil eines Analysis-Kurses für Studierende der Mathematik und Physik dar und behandelt die Integralrechnung im IRn mit Anwendungen, insbesondere solche, die für die theoretische Physik correct sind. Der textual content wurde für die 7. Auflage weiter überarbeitet und es kamen einige neue Aufgaben und Abbildungen sowie ein Symbolverzeichnis hinzu.
This booklet covers the speculation of derivatives pricing and hedging in addition to strategies utilized in mathematical finance. The authors use a top-down strategy, beginning with basics earlier than relocating to purposes, and current theoretical advancements along numerous routines, delivering many examples of functional curiosity.
My formulation books are designed to movement with a latest university direction from begin to end. the scholar may perhaps use this fabric as a short reference through the path or as a assessment for destiny classes. the cloth additionally serves as a brief refresher for college kids returning to college or getting ready for graduate university checks.
- Handbook of Differential Equations
- Handbook of Differential Equations: Stationary Partial Differential Equations: 4
- An Introduction to Difference Equations (Undergraduate Texts in Mathematics)
- Calculus Know-It-ALL: Beginner to Advanced, and Everything in Between (Electronics)
Extra resources for An Informal Introduction to Stochastic Calculus with Applications


Jan 23, 2018
Now you can use Variable feature to store values after performing arithmetic operations on values or attributes. The accepted mathematical operations are Plus, Minus, Division and Multiplication (+,-, /,*).
Give Variable name the value to be assigned in the variable. It can be any mathematical operations from: Plus, Minus, Division and Multiplication (+,-,/,*).
For Example: If you want to display the profit amount in the flow, then you can perform operation between sale price and purchase price. This will save the profit value in the variable to display it further.
Below screenshot shows the use of variable in ticket booking chatbot. After the input of all the information. To display total number of adults, the difference between the total number of passengers and children are stored in “adults” variable.


Mathematics is often considered a subject that is to be understood rather than to be memorized. Compared to subjects like history where one needs to know the facts and cannot just deduce historical facts, mathematics has often had the reputation of something that can be concluded. Although the multiplication table is an exception and is a part of mathematics that needs to be learned.
While multiplication tables can go all the way to infinity, it is the multiplication tables from 1 to 20 that need to be learned by children. Memorizing the tables from 1 to 20 will help children to have more comfort with numbers and a better understanding of how they are interrelated. Mathematics is a subject that deals with pattern solving. It helps greatly if one has in memory the fundamental relations of numbers as this will allow the children to consciously and even unconsciously connect the dots between the numbers. For example, to notice the standard numbers that appear in the multiplication tables of different numbers and how every even number appears in the multiplication table for number 2. The memory of multiplication tables will let children think and play with the numbers on the go, and they don’t need to sit down and have a pen and paper to do mathematics. Such skill with arithmetic is indeed required as a part of the daily life itself. For example, when buying 7 bottles of drink each worth 15 bucks, one needs to multiply 15 and 7 to know the price as adding 15 seven times while standing in the shop may not be practical.
As seen above, to have a memory of multiplication tables from 1 to 20 is not only useful to pave the way for better understanding of mathematics and develop a strong foundation to learn higher mathematics but also the memory of multiplication tables at least from 1 to 20 is important in our day to day life. Indeed, having the multiplication table in memory improves the speed of calculation, so for time-bound situations like a mathematics exam, it’s beneficial to do basic multiplications very quickly.
When children learn the multiplication table of 2 and 4, they will notice that all the numbers appearing in the multiplication table of four appear in the multiplication table of two, but the vice versa is not true. By memorizing the tables from 1 to 20, children will understand multiplication itself and how it is equivalent to multiple times. To multiply the smaller number, tables will help children play with the patterns of numbers themselves as all multiplication tables are essentially patterns in themselves. For example, a multiplication table of seven reveals how it is different from other numbers and how multiplication tables of certain numbers are very similar. What is the reason for number seven to have a different pattern from the rest or how in the multiplication table often we always have zero in the end are among many other questions that will naturally come to children’s mind when they know the multiplication table of 1 to 20.
Children should be encouraged to start with skip counting like 2, 4, 6, 8 and then graduating to skip counting with three gaps like 3, 6, 9 etc. Such skip counting essentially will lay the groundwork for times tables. Once the kid can say out loud the skip level counting of 2 and 3, they could then be shown how it is the same as the multiplication table of 2 and 3 and then lead them to learn the multiplication tables of number 4 and ahead. Many math games help memorize multiplication tables, which are a very good way to introduce the child to a fun and interesting subject.


Back in kindergarten, your child probably spent lots of time counting things one by one, whether leaves, toes, or fingers. Now that first grade is here, though, your child will need to be able to count in groups, and especially by fives.
It’s an important step in math, as kids move from concrete connections to more abstract ones. But that doesn’t have to mean it stops being fun. Here’s an activity you can do just about any day at home, using simple stuff to boost newly complex math thinking for your six-year-old.
What You Need:
- 5 plastic cups
- Ink pen
- 1 plastic bowl and spoon
- Masking Tape
- 5 Ziploc bags
- 25 marbles (various colors- 5 of each color)
- 1 cup sand
What You Do:
- Set the scene: Invite your child on a math expedition- digging for marbles! Have your child prepare the bowl by placing all marbles in the bottom of the bowl and covering them with sand.
- Label cups. Have your child write each marble group color on a piece of masking tape, and stick it on a different cup.
- Tell your child to use the spoon to dig for marbles and sort them into the five labeled cups. Red marbles will go in the cup marked red, and so on.
- Count! Does each cup have five marbles now? Great! Now count together aloud by fives, pointing to each cup as you say the number. Then have your child do it alone…and perhaps label each cup with a number as well: 5, 10, 15, 20.
- Save it for later. With skills like this, it’s hard to get enough practice. When your child has had enough, put the stuff in a Ziploc bag, label it and save it for another day. Pull it out anytime you’ve got a lull and your kid seems ready for more learning fun.
Why it works:
Counting by fives marks an important jump from counting on fingers to counting in your head. From there, another exciting world beckons, as kids learn addition and subtraction facts. In a fun, down-home way, activities like “Digging for Marbles” reinforce this basic knowledge and provide an important foundation for success later on. Even if your kid doesn’t thank you now, your first grade teacher will, once the tougher stuff kicks in!
Guest post by Holly Jachowski at Education.com


How roulette software works varies from company to company, but can the right mathematical equations in the various programs really give you the needed edge to winning your fair share? With the age of technology and the explosion of online casinos, more and more people have access to all the games a casino has to offer.
Everybody wants to have fun playing their favourite games and a lot of people are drawn to roulette as their game of choice. How cool is it to be able to sit behind the computer and get the same rush as you would in Vegas, Jersey or anywhere they have action?
So the question comes up, with all this technology, is there a way you can beat the odds and make some moola with roulette software? Well, knowing how roulette software works can maybe help you answer this question.
How roulette software works is really all about statistics and math. But a word of warning up front, a lot of people claim that if you purchase their software you’ll be raking in the bucks. Don’t buy into that hype. Roulette as well as all the other casino games are set up to always favour the house. It will always be a game of chance with you on the losing end more often than the winning side. If there was some software out there that was foolproof, then you and everyone else would be a millionaire and casinos would be out of business.
O.K.’s back to,” How roulette software works?” Basically, most all roulette software is established on mathematical calculations and each different piece of software has its own propriety method of predicting what the wheel is going to do next based on your input in the form of spins.
For example, how roulette software works for one particular company I reviewed tracks how many times a particular set of numbers didn’t get hit. Based on that data, the software will compute the top counts and specific ratios for a particular set of numbers and then will let you know when to bet as well as where and how much to bet.
How roulette software works simply is about working on the best odds you have of predicting where the ball is going to land based on all previous spins. How roulette software works really depends on who put the program together. It’s really a good idea to do some in-depth research and look around before buying any of the software out there on the market. A lot of them simply don’t work while others give you a far greater chance of succeeding. How roulette software works is really like any other piece of software that you use. The person using it has to have an idea what they are doing and you can’t rely on any piece of software to do everything for you.
How roulette software works and how you keep learning the game of roulette will go hand in hand. Even if one of these companies make all these claims about what the software can do for you, take it with a grain of salt. If it’s going to be making you all this money with just a push of the button, then they better be making consistent money with it using it on their own.
In conclusion find out how roulette software works by researching the various software programs on the market and what the results others have had with it. You just might find one that can give help you win some extra cash.