200 Milliliters In Cups
Conversion units The units involved in this conversion are milliliters and cups. This is how they are defined: Milliliter A milliliter (also written “millilitre”, SI symbol ml) is a non-SI metric system unit of volume which is commonly used as liquid unit. It is equal to 1/1000
What is 700 Milliliters in Cups? Convert 700 ml to cup
The conversion factor from Milliliters to Cups is 0.0042267528198649. To find out how many Milliliters in Cups, multiply by the conversion factor or use the Volume converter above. Seven hundred Milliliters is equivalent to two point nine five nine Cups.
Conversion Charts • Original Authentic German Recipes
Cups Conversion (Liquids) Metric to US Standard Cups Note: These are approximate measures that only apply to liquid measure. The tables below do not apply to UK or Australian cups: 1 US cup = 237 ml (milliliters) 1 UK cup = 284 ml, 1 Aus. cup = 250 ml
Conversion tables – Chef in disguise
I only just came across your conversion chart which is totally awesome! I live in Nova Scotia Canada and am used to our general measurements-cups, teaspoons and ounces. I’m an ‘Ole school’ kinda girl who is presently somewhat confused.
Your Ultimate Guide to Cooking and Baking Conversions
This handy conversion chart will help you cook with ease, no matter which measurement unit your recipe uses. It is a good time to cook. Thanks to the Internet and more cookbooks than ever, there are countless recipes available to the home cook to choose from., there are countless recipes available to the home cook to choose from.
Metric Measurement and Temperature Conversion Charts
Precise Conversion Calculator Use this chart, along with your calculator, to precisely convert from the U.S. and imperial to metric measurements. This will give you precise figures. To convert from metric to U.S. and imperial, work from right to left and replace the
1/3 Cups to Milliliters Conversion
Cups to milliliters Conversion Chart 1 cup 237 milliliters 1.1 cups 260 milliliters 1.2 cups 284 milliliters 1.3 cups 308 milliliters 1.4 cups 331 milliliters 1 1 2 cups 355 milliliters 1.6 cups 379 milliliters 1.7 cups 402 milliliters 1.8 cups 426 milliliters 1.9 cups 2 cups
· Concerning mini mallow equivalents, your chart of is a bit confusing. You tell us that 1 cup = 2 oz., and that a 10 oz. bag contains 6 cups. I’ve not actually measured out a 10 oz. bag, but a mathematical equivalent shows that there are five 2 oz. portions in 10 oz
FREE Printable Kitchen Conversion Chart
Free printable conversion chart With how much I know you all love to bake, I thought it would be nice to have a printable cheat sheet of all the baking conversions. Below you’ll find a free printable conversion chart for when you need to quickly cut a recipe in half.
Convert Milligram (mg) to Cup (cups)
Cup cups Easily convert Milligram (mg) to Cup (cups) using this free online unit conversion calculator. Simple online unit conversion tool to convert milligram (mg) into cup (cups).
Recipe Measures Conversion Chart (US Imperial to AUS Metric)
· PDF 檔案and Ball®, TMs Ball Corporation used under license. 7/13 Recipe Measures Conversion Chart 2WEIGHT 1 oz 30 g 1.75 oz 49 to 57 g 2 oz 60 g 3 oz 90 g 4 oz / ¼ lb 125 g 5 oz 155 g 6 oz 185 g 7 oz 220 g 8 oz / ½ lb 250 g 9 oz 280 g 10 oz 315 g 11 oz
Printable Fluid Ounces to Milliliters Conversion Chart
Free Printable Chart to Convert Fluid Ounces to Milliliters. Print a list of Fluid Ounces to Milliliters Conversions. How to Convert Fluid Ounces to Milliliters. Printables Home Printable Word Scrambles Printable Letters Printable Numbers Printable Animals Printable
Measurement Conversion Chart
A measurement conversion chart is a must have kitchen tool. Enjoy this pretty printable chart for your kitchen that includes a variety of dry and liquid conversions. Easily convert teaspoons into tablespoons, tablespoons into cups, ounces, pints, quarts, gallons, and
On sourdough courses baking conversion charts are …
Spoons Conversion Chart ml tsp / tbsp 1.25 ml ¼ tsp 2.5 ml ½ tsp 5 ml 1 tsp 10 ml 2 tsp 15 ml 1 tbsp 30 ml 2 tbsp 45 ml 3 tbsp 60 ml 4 tbsp 75 ml 5 tbsp 90 ml 6 tbsp g / kg oz / lb 5 g ⅛ oz
Cups to Grams Conversions for Common Ingredients
Finally after four years I can check something off my to do list: make a cups to gram conversion chart for common cooking ingredients! 15 grams/ml.5 ounces 1/8 US cup 30 grams/ml 1 ounces 1/4 US cup 60 grams/ml 2.1 ounces 1/3 US cup 80 grams/ml


Mathematics at Hexton
We aim to provide a high quality mathematics education, promoting an appreciation of the mysterious power of mathematics, and a sense of pleasure and curiosity in mathematical learning. We aim to develop mathematical understanding alongside mathematical processes, developing pupils’ fluency and mastery of key concepts, skills and processes. Our pupils learn to reason and to solve problems by applying their maths in a range of contexts.
At Hexton JMI, we follow White Rose maths planning. We adapt the materials to ensure we are using dyslexia-friendly approaches to teaching and learning, and include one day a week of investigations to encourage children to reason and problem solve. Wherever possible, we adopt a CPA (Concrete, Pictorial, Abstract) approach to mathematics. This involves using concrete resources and visual or pictorial representations to explain mathematical concepts, alongside the traditional abstract or “written method.”
In pupil workbooks, children respond to feedback from staff using a green pen and record their thinking using ‘red for reasoning’ pens.
We are part of two Maths Hubs projects this academic year – Mastering Number and Teaching for Mastery. This involves great CPD for teachers, allowing them to observe and embed strong new practice by regularly visiting other schools.
Pupils in all year groups from Year One have weekly maths fluency sessions separate to their maths lessons. These sessions are short, fun lessons. Fluency sessions never include new learning, but are instead about going over material children have already learnt but need to rehearse in order to embed. Usually, these sessions are either practical or have children learning on whiteboards. Sessions usually have up to three topics to focus on at a time, and the focus will remain the same for several weeks.
Mathematics in the EYFS:
Mathematics in the Early Years Foundation Stage Curriculum comes under two strands, each of which has an Early Learning Goal attached:-
Early Learning Goal: Have a deep understanding of number to 10, including the composition of each number;
– Subitise (recognise quantities without counting) up to 5;
– Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
Early Learning Goal: Verbally count beyond 20, recognising the pattern of the counting system;
– Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
– Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.
The Early Learning Goals define the level of development children are expected to attain by the end of the Reception year.
The National Curriculum for Mathematics:
Programmes of study
Reading, writing, comparing and recognising numbers, place value, addition, subtraction, estimate and use the inverse, multiplication, division, fractions, decimals and percentages, rounding, roman numerals, negative numbers, square and cubed numbers.
Length, height, mass, weight, capacity, volume, time (analogue and digital), money, chronology, volume, area and perimeter, metric and imperial unit conversion.
2d shapes, 3d shapes, position and direction, patterns and sequences, lines – horizontal, vertical, parallel and perpendicular, angles, symmetry, co-ordinates, translating, reflecting and plotting shapes.
Interpreting data, pictograms, bar charts, tables, graphs, line graphs, timetables.
Ratio and proportion
Relative size problems, percentages of amounts, scale factors, applying knowledge of fractions and multiples.
Formulae, linear number sequences, missing number problems, solving equations.


In a linear combination it is easy to create arbitrarily long sequences of pairs of weights (thetas) and input values (x). But first, just a quick recap of how a simple linear combination might look like.
score = theta_1 * x_1 + theta_2 * x_2 + theta_3 * x_3
Since each x value is multiplied with the theta, we can very easily disable the variable by setting the theta to 0. When working with real world data this procedure of setting the theta to 0 to disable it is commonly used in the practical implementation since it allows for a more optimized implementation.
In coming videos we are going to put these x values and thetas in vectors. Instead of having dynamically sized vectors we can then have vectors static in size, where some items in this vectors are set to 0. Knowing the size of the vector beforehand gives some really good benefits since you can use some tools from python, such as sparse vectors and matrices. These implementations of sparse vectors and matrices are much more effective and uses much less RAM (about 10 times as little) than the python lists which are composed of python objects. But in order to use these implementations from the python library numpy we need to set the size of the array before executing the program.


Boundary Element Methods
To calculate the resonant frequencies of superconducting cavity resonators for particle accelerators, one needs numerical methods capable of achieving accuracies that push established techniques to their limit. This is mostly due to the lacking precision of the geometry description. We investigate a new approach to the solution of Maxwell’s eigenvalue problem that combines building blocks of state-of the-art numerical methods.
The geometry of the resonators is described with Non-Uniform Rational B-Splines (NURBS), which can, contrary to the usual triangulations, exactly describe the geometry. NURBS became popular within the framework of Isogeometric Analysis (IGA) and have proven themselves already in the context of finite element methods. Because the creation of a volumetric representation of this kind requires a lot of manual effort, and the boundary data of the required format are already given by CAD systems, we combined the isogeometric approach with a Boundary Element Method (BEM).
Thanks to modern compression techniques and preconditioning, BEM is an important alternative to a finite element method. The algebraic eigenvalue problems generated by the boundary element method are nonlinear. A novel contour integral method is used for their solution.
The resulting IGA-BEM code has been published in the library BEMBEL.
Classical electrodynamics has been taught since the time of Oliver Heaviside by using vector analysis. Heaviside formulated Maxwell's theory in this form in the 1880s. Later, Henri Poincaré, Élie Cartan, and other mathematicians began to establish differential geometry and algebraic topology. They pioneered a new and more powerful framework for describing electrodynamics.
In recent decades, the electromagnetic research community has made great scientific advances in the adoption of geometric methods. Particularly important results are:
- the understanding of the de Rham complex (after Georges de Rham)
- the application of homology and co-homology
- the separation of topological and metric structures
- the recognition of the Hodge operator’s significance (after William Hodge)
We may depict electrodynamics in a concise diagram (Tonti 2013, d: exterior derivative, ∗: Hodge operator), see Figure 1.
Whitney forms (after Hassler Whitney) and, more generally, discrete differential forms, provide a tool to preserve the essential properties of electrodynamics in spaces of finite dimension. Many advances have been made in understanding the convergence of discrete solutions towards those of the continuous theory.
Among other things, ongoing research seeks to further develop these findings for discretization on dual grid systems and in the context of isogeometric analysis.
Relativity in Engineering
Field problems involving moving bodies are often challenging to solve. An additional difficulty arises from misguided intuition. There are relatively simple examples in which the electric and magnetic fields combined with non-uniform motion can lead to paradoxical interpretations (Schiff 1939).
Such difficulties can be overcome by associating generalized observers with accelerating and deforming bodies. Generalized observers are described by fiber bundles over space-time. The underlying mathematics is that of a gauge theory on a fiber bundle, which is equipped with a so-called Ehresmann connection. This knowledge has not yet found its way into relativity in engineering, let alone into the design of codes for the simulation of electromagnetic fields.
In numerical methods, space and time are usually discretized separately, after a fixed observer has been introduced to determine the decomposition of space-time. A larger class of problems can be tackled if the discretization acts directly on space-time and is chosen locally. For example, an asynchronous time-stepping scheme may be introduced in which each spatial element is assigned its own time step, thereby increasing the simulation’s robustness and efficiency.
Typical applications include scattering from rotating bodies (e.g. helicopter blades) and optical rotation sensors based on the Sagnac effect. The Sagnac effect, on a larger scale, plays an important role in the design of the global positioning system GPS.


Randy Wanye is currently a Data Manager & Senior Analyst in the Health System Analytics team of the Health Quality Council of Alberta (HQCA). Prior to joining the HQCA, he worked in supply chain management alongside doing statistical consulting. He obtained his M.Sc. in Applied Mathematics from the University of Alberta, Canada after completing his B.Sc. (Hons) in Mathematics from the University of Cape Coast, Ghana. Randy has extensive experience in analyzing and interpreting various kinds of data, and building mathematical models for real world problems. He is passionate about mathematics and storytelling with data. Randy is looking forward to working with individuals with similar interests or individuals who are curious about data and mathematics.


- The network "Developing Quality in Mathematics Education II" will be a continuation of the associated project "Developing Quality in Mathematics Education". It will be an extension of the very productive and transferable results attained so far, and an expansion from four to eleven participating countries.
- Because we have in each country groups consisting of universities, teacher education institutions and schools, a special feature of this project will be the strong connection between theory and practice and between the research and development of mathematics education. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils will be continued by developing quality in mathematics education, especially in the area of mathematical modelling.
- The quality and application of the developed learning materials will also be guaranteed by using, comparing and modifying them in eleven different countries. This comparison will lead to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus it is hoped to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century.
- Using the available technology of today (for example the communication platform) we hope to provide far reaching and exciting possibilities for sharing ideas and methods and exchanging materials, including video-sequences, to get a better understanding of the development of epistemological aspects of mathematics education.
- An exciting, extraordinary and substantial consequence of this project will be that the community of mathematics educators in Europe will be able to expand and share their professional relations and collaboration opportunities.


This unique site solves mathematical problems online. The problems could be basic maths, pre-algebra, algebra, geometry, trigonometry, calculus, statistics, linear algebra and more!
Just enter your problem in the box and click on Evaluate, and up pops the answer! Very cool for school and college kids and engineering students who need to evaluate complex problems in a jiffy.
Apart from solving maths problems, you have a section on graphs where you can do step-by-step graphing, linear equations and functions, etc. You can also create maths worksheets for use in a class (if you are a teacher). And, finally, there is a Glossary section where you could get definitions of various mathematical terms.
They have also launched an app on Android which does not require Internet access to run. The basic modules are free, but if you wish to see the actual logic and calculation, you have to pay a small fee. Ideal for teachers and students alike. But NOT recommended for cheating at school because actually knowing maths is very important for times when you don’t have Internet access to get to this site, especially in your examination hall! https://goo.gl/Tn9bZt


In Danville, CA, the best preschool options include a high-quality Montessori program that offers wonderful enrichment programs in a developmentally appropriate and caring environment.
What Makes Montessori Different?
Unlike a traditional classroom, Montessori schools are centered around the concept of a holistic approach to education. In addition to the core subjects of math and reading, the Montessori method places a great deal of emphasis on learning real life skills and social-emotional lessons. Children are also given a great deal of freedom to choose the lessons they would like to work on each day and work through them at their own pace. Because of the independence and self-pacing of the lessons, many children thrive in this type of environment.
What do Children Learn in a Montessori Preschool?
A Montessori classroom consists of four core subjects and several other lessons to create a whole-child approach to education.
Practical Life lessons teach the child how to care for themselves and their environment. These lessons teach important life skills such as grooming, cleaning up after oneself, using tools and utensils and refining their fine and gross motor skills. These lessons are often among some fo the first lessons children learn when entering a Montessori classroom.
Sensorial lessons use hands-on materials to engage all of the child’s senses. Through these lessons, children learn visual discrimination, order and foundational math skills to prepare them for future skills.
The language lessons range from basic pre-reading skills such as matching, rhyming and finding things that go together to advanced reading and writing lessons. By walking through important reading skills one at a time, children are able to learn all the fundamental tools needed to become great readers.
The Montessori math lessons build on many of the Sensorial lessons to refine the child’s ability to discriminate quantities and numerals. In a primary Montessori classroom, children learn with hands-on materials to count and complete advanced math functions. Each child is given the opportunity to build a solid mathematical foundation by providing all the building blocks they need to truly understand the math concepts.
In addition to these core subjects, a Montessori classroom contains rich materials that teach children about geography, science, peace education, art, music and movement. All of these lessons are designed to give the child an understanding of their place in the world and help them reach their fullest potential. They help unlock the creative and compassionate natures of the children.
Our Danville location also includes the opportunity for children to participate in a Mandarin immersion program. With robust exposure to a new language, young children can typically learn much easier than adults. Children can experience many benefits to participating in a language immersion program in an early childcare setting.
To learn more about the best preschool in Danville, CA, contact us at Fountainhead Montessori today. Our staff can tell you more about the wonderful offerings a Montessori experience can bring to your young child and family as a whole.


List of accepted papers
(In order of appearance)
Track B: Logic, Semantics and Theory of Programming
- Modular Algorithms for Heterogeneous Modal Logics
- Lutz Schröder and Dirk Pattinson
State-based systems and modal logics for reasoning about them often
heterogeneously combine a number of features such as non-determinism and
probabilities. Here, we show that the combination of features can
be reflected algorithmically and develop modular decision procedures for
heterogeneous modal logics. The modularity is achieved by formalising
the underlying state-based systems as multi-sorted coalgebras and
associating both a logical and an algorithmic description to a number of
basic building blocks. Our main result is that logics arising as
combinations of these building blocks can be decided in polynomial space
provided that this is the case for the components. By instantiating the
general framework to concrete cases, we obtain PSPACE decision
procedures for a wide variety of structurally different logics,
describing e.g. Segala systems and games with uncertain information.
- Co-Logic Programming: Extending Logic Programming with Coinduction
- Luke Simon, Ajay Bansal, Ajay Mallya and Gopal Gupta
In this paper we present the theory and practice of co-logic
programming (co-LP for brevity), a paradigm that combines both
inductive and coinductive logic programming. Co-LP is a natural
generalization of logic programming and coinductive logic programming,
which in turn generalizes other extensions of logic programming, such as
infinite trees, lazy predicates, and concurrent communicating
predicates. Co-LP has applications to rational trees, verifying
infinitary properties, lazy evaluation, concurrent LP, model checking,
bisimilarity proofs, etc.
- Maximal Infinite-Valued Constraint Languages
- Manuel Bodirsky, Hubie Chen, Jan Kára and Timo von Oertzen
We systematically investigate the computational complexity of constraint
satisfaction problems for constraint languages over an infinite domain.
In particular, we study a generalization of the well-established notion
of maximal constraint languages
from finite to infinite domains.
If the constraint language can be defined with an ω-categorical
structure, then maximal constraint languages are in one-to-one
correspondence to minimal oligomorphic clones.
Based on this correspondence, we derive
general tractability and hardness criteria for the
corresponding constraint satisfaction problems.
- Affine Systems of Equations and Counting Infinitary Logic
- Albert Atserias, Andrei Bulatov and Anuj Dawar
We study the definability of constraint satisfaction problems (CSP)
in various fixed-point and infinitary logics. We show that testing the
solvability of systems of equations over a finite Abelian group, a
tractable CSP that was previously known not to be definable in Datalog,
is not definable in an infinitary logic with counting and hence that it
is not definable in least fixed point logic or its extension with
counting. We relate definability of CSPs to their classification
obtained from tame congruence theory of the varieties generated by the
algebra of polymorphisms of the template structure. In particular, we
show that if this variety admits either the unary or affine type, the
corresponding CSP is not definable in the infinitary logic with
counting. We also study the complexity of determining whether a CSP
omits unary and affine types.
- Boundedness of Monadic FO over Acyclic Structures
- Stephan Kreutzer, Martin Otto and Nicole Schweikardt
We study the boundedness problem for monadic least fixed points
as a decision problem. While this problem is known to be undecidable
in general and
even for syntactically very restricted classes of underlying
first-order formulae, we here obtain a decidability result for the
boundedness issue for monadic fixed points over arbitrary first-order
formulae in restriction to acyclic structures.
- Equational Systems and Free Constructions
- Marcelo Fiore and Chung-Kil Hur
The purpose of this paper is threefold: to present
a general abstract, yet practical, notion of equational system; to
investigate and develop a theory of free constructions for such
equational systems; and to illustrate the use of equational systems
as needed in modern applications, specifically to the
theory of substitution in the presence of variable binding and to
models of name-passing process calculi.
- Categorical Views on Computations on Trees
- Ichiro Hasuo, Bart Jacobs and Tarmo Uustalu
Computations on trees form a classical topic in computing. These
computations can be described in terms of machines (typically called
tree transducers), or in terms of functions. This paper focuses on
three flavors of bottom-up computations, of increasing generality. It
brings categorical clarity by identifying a category of tree transducers
together with two different behavior functors. The first sends a tree
transducer to a coKleisli or biKleisli map (describing the contribution
of each local node in an input tree to the global transformation) and
the second to a tree function (the global tree transformation). The
first behavior functor has an adjoint realization functor, like in
Goguen's early work on automata. Further categorical structure, in the
form of Hughes's Arrows, appears in properly parameterized versions of
- A Fully Abstract Trace Semantics for General References
- James Laird
We describe a fully abstract trace semantics for a functional language
with locally declared general references (a fragment of Standard ML).
It is based on a bipartite LTS in which states alternate between program
and environment configurations and labels carry only (sets of) basic
values, location and pointer names. Interaction between programs and
environments is either direct (initiating or terminating subprocedures)
or indirect (by the overwriting of shared locations): actions reflect
this by carrying updates to the shared part of the store.
The trace-sets of programs and contexts may be viewed as deterministic
strategies and counter-strategies in the sense of game semantics: we
prove soundness of the semantics by showing that the evaluation of a
program in an environment tracks the interaction between the
corresponding strategies. We establish full abstraction by proving a
definability result: every bounded deterministic strategy of a given
type is the trace-set of a configuration of that type.
- Aliased Register Allocation for Straight-line Programs is NP-Complete
- Jonathan K. Lee, Jens Palsberg and Fernando Magno Quintão Pereira
Register allocation is NP-complete in general but can be solved in
linear time for straight-line programs where each variable has at most
one definition point if the bank of registers is homogeneous. In this
paper we study registers which may alias: an aliased register can be
used both independently or in combination with an adjacent register.
Such registers are found in commonly-used architectures such as x86, the
HP PA-RISC, the Sun SPARC processor, and MIPS floating point. In 2004,
Smith, Ramsey, and Holloway presented the best algorithm for aliased
register allocation so far; their algorithm is based on a heuristic for
coloring of general graphs. Most architectures with register aliasing
allow only aligned registers to be combined: for example, the
low-address register must have an even number. Open until now is the
question of whether working with restricted classes of programs can
improve the complexity of aliased register allocation with alignment
restrictions. In this paper we show that aliased register allocation
with alignment restrictions for straight-line programs is
- Conservative Ambiguity Detection in Context-Free Grammars
- Sylvain Schmitz
The ability to detect ambiguities in context-free grammars is vital
for their use in several fields, but the problem is undecidable in the
general case. We present a safe, conservative approach, where the
approximations cannot result in overlooked ambiguous cases. We analyze
the complexity of the verification, and provide formal comparisons with
several other ambiguity detection methods.
- Undecidability of 2-Label BPP Equivalences and Behavioral Type Systems for the π-Calculus
- Naoki Kobayashi and Takashi Suto
The trace equivalence of BPP was shown to be undecidable
by Hirshfeld. We show that the trace equivalence remains
undecidable even if the number of labels is restricted
to two. The undecidability result holds also for the
simulation of two-label BPP processes. These results imply
undecidability of some behavioral type systems for the
- Ready Simulation for Concurrency: It's Logical!
- Gerald Lüttgen and Walter Vogler
This paper provides new insight into the connection between the
trace-based lower part of van Glabbeek's linear-time, branching-time
spectrum and its simulation-based upper part. We establish that ready
simulation is fully abstract with respect to failures inclusion, when
adding the conjunction operator that was proposed by the authors in
[TCS 373(1–2):19–40] to the standard setting of
labelled transition systems with (CSP-style) parallel composition. More
precisely, we actually prove a stronger result by considering a coarser
relation than failures inclusion, namely a preorder that relates
processes with respect to inconsistencies that may arise under
conjunctive composition. Ready simulation is also shown to satisfy
standard logic properties and thus commends itself for studying mixed
operational and logic languages.
- Continuous Capacities on Continuous State Spaces
- Jean Goubault-Larrecq
We propose axiomatizing some stochastic games, in a continuous state
space setting, using continuous belief functions, resp. plausibilities,
instead of measures. Then, stochastic games are just variations on
continuous Markov chains. We argue that drawing at random along a
belief function is the same as letting the probabilistic player P play
first, then letting the non-deterministic player C play demonically.
The same holds for an angelic C, using plausibilities instead. We then
define a simple modal logic, and characterize simulation in terms of
formulae of this logic. Finally, we show that (discounted) payoffs are
defined and unique, where in the demonic case, P maximizes payoff, while
C minimizes it.
- A Generalization of Cobham's Theorem to Automata over Real Numbers
- Bernard Boigelot and Julien Brusten
This paper studies the expressive power of finite-state automata
recognizing sets of real numbers encoded positionally. It is known
that the sets that are definable in the first-order additive theory of
real and integer variables 〈R,Z,+,<〉 can
all be recognized by weak deterministic Büchi automata, regardless of
the encoding base r>1. In this paper, we prove the reciprocal
property, i.e., that a subset of R that is recognizable by
weak deterministic automata in every base r>1 is necessarily
definable in 〈R,Z,+,<〉. This result
generalizes to real numbers the well-known Cobham's theorem on the
finite-state recognizability of sets of integers. Our proof gives
interesting insight into the internal structure of automata
recognizing sets of real numbers, which may lead to efficient data
structures for handling these sets.
- Minimum-Time Reachability in Timed Games
- Thomas Brihaye, Thomas A. Henzinger, Vinayak S. Prabhu and Jean-François Raskin
We consider the minimum-time reachability problem
in concurrent two-player timed automaton game structures.
We show how to compute the minimum time needed by a player to reach a
target location against all possible choices of the opponent.
We do not put any syntactic restriction on the game structure,
nor do we require any player to guarantee time divergence.
We only require players to use receptive strategies which do not block time.
The minimal time is computed in part using a fixpoint expression,
which we show can be evaluated on equivalence classes of a
non-trivial extension of the clock-region equivalence
relation for timed automata.
- Reachability-Time Games on Timed Automata
- Marcin Jurdziński and Ashutosh Trivedi
In a reachability-time game, players Min and Max choose moves so that
the time to reach a final state in a timed automaton is minimised or
maximised, respectively. Asarin and Maler showed decidability of
reachability-time games on strongly non-Zeno timed automata using a
value iteration algorithm. This paper complements their work by
providing a strategy improvement algorithm for the problem. It also
generalizes their decidability result because the proposed strategy
improvement algorithm solves reachability-time games on all timed
automata. The exact computational complexity of solving
reachability-time games is also established: the problem is
EXPTIME-complete for timed automata with at least two clocks.
- Perfect Information Stochastic Priority Games
- Hugo Gimbert and Wiesław Zielonka
We introduce stochastic priority games —
a new class of perfect information stochastic games.
These games can take two different, but equivalent,
stopping priority games a play can be stopped by the environment after a
finite number of stages, however, infinite plays are
In discounted priority games only infinite plays are possible and the
payoff is a linear combination of the classical discount payoff and of
a limit payoff evaluating the performance at infinity.
games and parity games are special
extreme cases of priority games.
- Bounded Depth Data Trees
- Henrik Björklund and Mikołaj Bojańczyk
A data tree is a tree where each node has a label from a finite set,
and a data value from a possibly infinite set. We consider data
trees whose depth is bounded beforehand. By developing an
appropriate automaton model, we show that under this assumption
various formalisms, including a two variable first-order logic and a
subset of XPath, have decidable emptiness problems.
- Unranked Tree Automata with Sibling Equalities and Disequalities
- Wong Karianto and Christof Löding
We propose an extension of the tree automata with constraints between
direct subtrees (Bogaert and Tison, 1992) to unranked trees.
Our approach uses MSO-formulas to capture the possibility of comparing
unboundedly many direct subtrees.
Our main result is that the nonemptiness problem for the deterministic
automata, as in the ranked setting, is decidable.
Furthermore, we show that the nondeterministic automata are more expressive
than the deterministic ones.
- Regular Languages of Nested Words: Fixed Points, Automata, and Synchronization
- Marcelo Arenas, Pablo Barceló and Leonid Libkin
Nested words are a restriction of the class of visibly pushdown
languages that provide a natural model of runs of programs with
recursive procedure calls. The usual connection between monadic
second-order logic (MSO) and automata extends from words to nested
words and gives us a natural notion of regular languages of nested
In this paper we look at some well-known aspects of regular languages
— their characterization via fixed points, deterministic and
alternating automata for them, and synchronization for defining
regular relations — and extend them to nested words. We show that
mu-calculus is as expressive as MSO over finite and infinite nested
words, and the equivalence holds, more generally, for mu-calculus with
past modalities evaluated in arbitrary positions in a word, not only
in the first position. We introduce the notion of alternating automata
for nested words, show that they are as expressive as the usual
automata, and also prove that Muller automata can be determinized
(unlike in the case of visibly pushdown languages). Finally we look
at synchronization over nested words. We show that the usual
letter-to-letter synchronization is completely incompatible with
nested words (in the sense that even the weakest form of it leads to
an undecidable formalism) and present an alternative form of
synchronization that gives us decidable notions of regular relations.
- A Combinatorial Theorem for Trees
- Thomas Colcombet
Following the idea developed by I. Simon in his
theorem of Ramseyan factorisation forests,
we develop a result of "deterministic factorisations".
This extra determinism property makes it usable on trees
(finite or infinite).
We apply our result for proving that, over trees,
every monadic interpretation is equivalent to the composition of
a first-order interpretation (with access to the ancestor relation)
and a monadic marking. Using this remark,
we give new characterisations for prefix-recognisable structures
and for the Caucal hierarchy.
Furthermore, we believe that this approach has other potential
- Model Theory Makes Formulas Large
- Anuj Dawar, Martin Grohe, Stephan Kreutzer and Nicole Schweikardt
Gaifman's locality theorem states that every first-order sentence is
equivalent to a local sentence. We show that there is no elementary
bound on the length of the local sentence in terms of the original.
The classical Łoś-Tarski theorem states that every first-order
sentence preserved under extensions is equivalent to an existential
sentence. We show that there is no elementary bound on the length of the
existential sentence in terms of the original. Recently, variants of the
Łoś-Tarski theorem have been proved for certain classes of finite
structures, among them the class of finite acyclic structures and more
generally classes of structures of bounded tree width. Our lower bound
also applies to these variants.
We further prove that a version of the Feferman-Vaught theorem based
on a restriction by formula length necessarily entails a non-elementary
blow-up in formula size.
All these results are based on a similar technique of encoding large
numbers by trees of small height in such a way that small formulas can
speak about these numbers. Notably, our lower bounds do not apply to
restrictions of the results to structures of bounded degree. For such
structures, we obtain elementary upper bounds in all cases. However,
even there we can prove at least doubly exponential lower bounds.
- Decision Problems for Lower/Upper Bound Parametric Timed Automata
- Laura Bozzelli and Salvatore La Torre
We investigate a class of parametric timed automata, called lower
bound/upper bound (L/U) automata, where each parameter occurs in
the timing constraints either as a lower bound or as un upper
bound. For such automata, we show that checking if for a parameter
valuation (resp., all parameter valuations) there is an infinite
accepting run is PSPACE-complete. We extend these results by
allowing the specification of constraints on parameters as a
linear system. We show that the considered decision problems are
still PSPACE-complete, if the lower bound parameters are not
compared to the upper bound parameters in the linear system, and
are undecidable in general. Finally, we consider a parametric
extension of MITL0,∞,
and prove that the related satisfiability and
model checking (w.r.t. L/U automata) problems are
- On the Complexity of LTL Model-Checking of Recursive State Machines
- Gennaro Parlato and Salvatore La Torre
Recursive state machines (RSMs) are models for
programs with recursive procedural calls. While LTL
model-checking is EXPTIME-complete on such models, on
finite-state machines, it is PSPACE-complete in general
and becomes NP-complete for interesting fragments. In
this paper, we systematically study the computational complexity of
model-checking RSMs against several syntactic fragments
of LTL. Our main result shows that if in the
specification we disallow next and until, and retain
only the box and diamond operators, model-checking is
in NP. Thus, differently from the full logic, for this
fragment the abstract complexity of model-checking does not change
moving from finite-state machines to RSMs. Our results on
the other studied fragments confirm this trend, in the sense that,
moving from finite-state machines to RSMs, the complexity
of model-checking either rises from PSPACE-complete to
EXPTIME-complete, or stays within NP.


Max and his two brothers hop into a car and go looking for problems they can solve. They cruise down highway number 4 on their way to Shapeville, but they see an abandoned number along the way. Is it a 6? Is it a 9? And what’s it doing on the side of the road? Once the trio reach Shapeville, there’s another problem: a flood washed away all of the squares. Max and his brothers show the town that putting together two triangles will bring their shapes back together, and then they follow the residents on a trip to Count Town, where they put the missing number back in its place in the countdown to a rocket’s blastoff.
Words and illustrations work in tandem to bring numbers, shapes, and other mathematical wonders to life in a fun story that is easily accessible to young readers.
Even as an adult, I’ve never been a big numbers person — but Max’s Math puts math into the context of a story, making it much more easily to grasp. But the prose alone isn’t what really brings the math to life in a fun, easy to understand manner — it’s Banks’ story in combination with Kulikov’s illustrations that make the story — and the math — sing and come alive.
Max’s Math is in stores March 10th.


I often program in the Django web framework. Recently, I became interested in how it tracks the information of users that have already logged in.
By default, Django uses a cookie named
sessionid and contains a 32 character string built from lowercase letters and digits, or 36 possible characters. Therefore, there are a total of 3632 or 63,340,286,662,973,277,706,162,286,946,811,886,609,896,461,828,096 possibilities for your session key. This number is between 2165 and 2166 and is slightly larger than the possibilities produced by a good cryptographic hash.
But what are the chances that two randomly generated session keys in a large collection of session keys will be equal? The solution to this problem is actually counter-intuitive and is summarized in a similar problem:
The Birthday Problem is to find the probability that, in a group of N people, there is at least one pair of people who have the same birthday. Birthday Problem
While some people estimate this number to be over 100,000, it is much less than that, since to determine a “collision” of birthdays we have to compare not just your birthday to everyone, but everybody’s birthday to each other.
Turns out, there only needs to be 23 people before the chance of two of them sharing a birthday is greater than 50%.
So how many sessions have to exist before a key collision becomes likely? We can estimate this value using the equation:
Q(H) = √(π / 2 * H)
H is the number of possibilities. In our case,
H is 3632, the number of unique sessions, giving a result of 9.97 * 1024 or about 283.
That’s still 10 septillion sessions before our first collision is likely.


Parachute Surface Area
Most recent answer: 10/22/2007
- Jenna (age 13)
Collegeville, Pa, US
The answer to your question is a bit more complex than you were probably expecting, but here goes...
The force of air resistance on a parachute (figuring the parachute is basically spread out flat against the air) is directly proportional to the parachutes surface area, so long as the parachute is moving fairly quickly through the air. That means that if you double the surface area you double the force of air resistance:
Fair resistance = SurfaceArea x OtherStuff
Nows where weve gotta do a little math... The net downward force on the parachuter is the force of gravity minus the force of air resistance. So:
Fnet = (9.81 m/s^2 x Mass) - (SurfaceArea x OtherStuff)
The net force on the parachuter determines their acceleration (the rate at which they speed up or slow down): F=ma, so...
(Mass x Acceleration) = (9.81m/s^2 x Mass) - (SurfaceArea x OtherStuff)
Do a little rearranging and you get this:
Acceleration = 9.81 m/s^2 - (SurfaceArea)(OtherStuff)/(Mass)
Getting from knowing the Acceleration to knowing the actual Speed is tricky, because that "OtherStuff" actually includes the parachuters velocity. Im not going to go into the details of solving that for you here, but i think the basic gist should be clear:
The Moral of This Story
More Surface Area = Falling More Slowly
(published on 10/22/2007)
Follow-Up #1: effect of parachute area on time of the fall
The short answer to your question is that, after a certain point, doubling the size of a parachute does not affect the time of fall (or your velocity).
A really amazing experimental explanation of this is here:
The parachute very rapidly acquires almost its terminal velocity, reached when the air friction is enough to just cancel the force of gravity. The friction is proportional to the area. If the parachutes are made out of the same cloth, their masses (and hence the gravitational forces) are also just proportional to the area. If there's an extra weight on the parachute, the fall will slow as you make the parachute bigger until the parachute's own mass is large compared to the other mass.
The time is approximately proportional to the inverse of the terminal velocity, so it's approximately proportional to Area/Mtotal = A/(Mp +Mw), where A is the area, Mp is the parachute mass and Mw is the other mass. Once Mp is much bigger than Mw. this reaches a constant. That means that the velocity for a parachute with twice the area (and twice the mass) is going to be the same as for the original parachute. If, on the other hand, the parachute were very light compared to the load, then doubling its area would approximately double the time to fall.
Hope that helps!
(published on 11/13/2010)


Elementary Summer Learning is a 10 week curriculum where students are able to work at their own pace. Instructional videos for each grade level are available for every two weeks materials. Watch these fun videos to preview the skills being reviewed in the Scholastic Weekly Reader: Summer Express. Each video provides a quick tip for completing different weekly activities. Be sure to watch to the end for a cute guest.
Electronic Resources for rising Kindergarten-5th Grade Students*
Reading/ Language Arts
|Smarty Ants||Grades K-2. Smarty Ants builds reading skills & accelerates learning in an engaging interactive online learning environment.||Students enrolled in Polk County Public Schools during the 2019-20 School year as K-2 students: visit https://polkschoolsfl.com and log-in through ClassLink. New kindergarten students for the 2020-21 school year, please follow directions at https://tinyurl.com/2020smartyants.||15 minutes 3 days per week.|
|KidBiz3000||Reading & writing activities available only to select primary students who have successfully completed all Smarty Ants lessons.||Download directions: KidBizDownload. Then visit https://polkschoolsfl.com and log-in through ClassLink.||20 minutes 3 days per week.|
|Istation||Grades 3-5. Istation uses a gamebased approach to teach & reinforce reading skills.||Visit https://polkschoolsfl.com and log-in through ClassLink.||30 minutes 3 days per week.|
|Tumble Book Library||Tumblebooks has thousands of ebooks, non-fiction books, videos, & games for elementary-aged students.||Visit https://polkschoolsfl.com and log-in through ClassLink. Please follow the directions at https://tinyurl.com/tumblebooks2020||30 minutes 3 days a week OR anytime you wish to explore new ideas, places, or ideas!|
Mathematics and Science
|Freckle||Adaptive math practice across different skills & topics.||Visit https://polkschoolsfl.com and log-in through ClassLink.||15 minutes 3 days a week|
|Tivitz||A baseball themed game combining strategy & mathematical fluency.||Visit https://polkschoolsfl.com and log-in through ClassLink.||15 minutes 2 days a week|
|Legends of Learning||Game-based games about life, physical, Earth, & space science.||Visit https://polkschoolsfl.com and log-in through ClassLink.||15 minutes 3 days a week|
Online games and tutorials paired with paper-based educational activities provide students a fun way to continue learning over the summer while helping to ensure students are ready for school this fall.


STEM (Science, Technology, Engineering and Math)
STEM is an integrated, interdisciplinary, and student-centered approach to learning that encourages curiosity, creativity, artistic expression, collaboration, communication, problem solving, critical thinking and design thinking. All students will learn to apply STEM concepts and habits of mind through inquiry and authentic project based learning that connects school (early childhood through postsecondary) with needs and opportunities in the community, and those problems presented by business and industry, resulting in a STEM fluent and STEM skilled citizenry for the future of Pennsylvania.
- STEM Lending Center
- STEM Connection
- Professional Learning
- Math Network
- Carnegie STEM Excellence Pathway


Free Delivery on all orders over €25/£25 (Ireland and the UK)
Maths Box Bundle
Get all of this for only €200!
The Maths Box
The Maths Box series is a set of six boxes of cards, one for each class from First to Sixth.
Each box covers the strands of Number, Algebra, Shape and Space, Measures, and Data. Some of the larger strands (for example, Number and Measures) are divided into strand units.
Each box contains:
75 high-interest, brightly-coloured laminated cards (2 of each card, 150 cards in total).
75 colourful answer cards.
1 comprehensive, photocopiable Teachers Guide.
FREE digital version of the Teachers Guide.
Follow Me Loop Card Games Maths eBook
Follow Me – Loop Card Games – Maths is a series of three eBooks designed to reinforce basic mathematical skills using auditory discrimination as the major focus. Using interactive game cards, pupils work in small groups or as a whole class to complete a chain of questions and answers. Each pupil maintains involvement in the game by using the supporting active listening enrichment copymaster, designed to track the progress of the game.
Maths Posters Set
colourful A2 posters
set of 6 - laminated A2 (595mm x 420mm)
designed to introduce and consolidate a variety of number concepts
easy-to-read text at pupils' level of understanding - help pupils to develop efficient numeracy strategies in mental and written maths
Reverse of each poster contains:
detailed teacher notes
including suggestions for whole-class discussions and group/individual activities
activities to help introduce and reinforce the mathematical concept
Maths Box Bundle 1 = Maths Box 1st Class + Follow Me Loop Cards Maths eBook Lower + The Maths Poster Set 2
Maths Box Bundle 2 = Maths Box 2nd Class + Follow Me Loop Cards Maths eBook Lower + The Maths Poster Set 2
Maths Box Bundle 3 = Maths Box 3rd Class + Follow Me Loop Cards Maths eBook Middle + The Maths Poster Set 3
Maths Box Bundle 4 = Maths Box 4th Class + Follow Me Loop Cards Maths eBook Middle + The Maths Poster Set 3
Maths Box Bundle 5 = Maths Box 5th Class + Follow Me Loop Cards Maths eBook Upper + The Maths Poster Set 4
Maths Box Bundle 6 = Maths Box 6th Class + Follow Me Loop Cards Maths eBook Upper + The Maths Poster Set 4


James Ryan Requeimablog | photos | github | obeymath
My Curriculum Vitae.
I'm currently a PhD student studying machine learning at the University of Cambridge in the Computational and Biological Learning Lab. My advisor is Dr. Richard Turner. I'm interested in Bayesian optimization, reinforcement learning, approximate inference methods, and deep generative models.
Previously, I completed a Master's in machine learning, speech and language technology at the University of Cambridge where my advisor was Dr. Zoubin Ghahramani. During my Master's, I worked on an information theoretic acquisition function called IPES for Bayesian optimization. You can find my thesis and code here.
I’m also a researcher at Invenia Technical Computing based in Winnipeg, Manitoba. We use machine learning techniques to forecast demand for power in the electricity grid, energy production from wind farms, and electricity prices in wholesale power markets. I helped set up our research offices in Montréal, Canada and Cambridge, England.
My colleagues at Invenia and I did some analysis on electricity price time series for a couple of North American wholesale electricity markets. You can find our paper here.
When studying mathematics, my specialization was geometric group theory, combinatorial group theory, and algebraic topology. I studied under Dani Wise at McGill University, who was recently awarded a Guggenheim Fellowship and the Oswald Veblen Prize in Geometry. Here is my Master’s thesis.
I enjoy travelling and taking photographs. So far, I have been to Iceland, England, Portugal, Greece, France, Belgium, Germany, Denmark, Sweden, Italy, Cuba, China, Japan, Korea, Cambodia, Thailand and India. You can read about some of my adventures here or check out some photos here.
I'm currently playing ice hockey for the Cambridge University Blues. If you want to follow our results you can do so here.


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In this note I’d like to give proof to a well known probabilistic interpretation of the AUC model fit statistic. I’ve had trouble locating an intuitive proof of this result online and in the literature.
This argument is entirely due to my co-worker Jack Bennetto, I’ve just made some figures and typed it up.
The AUC is a popular measurement used for comparing goodness of fit of classification models in machine learning. The AUC makes sense for any model that produces a scoring of the data points in a set, with the model assigning a higher score to those data points it feels are more likely to belong to the positive class. The most popular ranking models actually estimate conditional probabilities of class membership:
To calculate the AUC of a model (on a dataset), we must first draw an ROC curve. This curve is produced by thresholding the model’s predicted probabilities at various places between zero and one, and taking the points scored above the threshold as predicted members of the positive class, and those below the threshold as predicted negative classes. The proportion of positive classes correctly predicted is called the true positive rate of a thresholding, and the proportion of negative classes incorrectly predicted is called the false positive rate. Each threshold then produces a pair
Plotting all of these pairs as the threshold is varied across its range traces out the ROC curve.
The ROC curve always passes through (0, 0) and (1, 1), and decreasing the threshold moves up along the curve towards (1, 1).
The AUC is the area under the ROC curve. It is a number between zero and one, because the ROC curve fits inside a unit square. Any model worth much of anything has an AUC larger than 0.5, as the line segment running between (0, 0) and (1, 1) represents a model that randomly guesses class membership.
The AUC seems arbitrary when first encountered. It certainly has some nice properties, but it has an ad-hoc and slapdash flavor, and it’s unclear if it is attempting to communicate anything essential about the world. Luckily, the AUC has a very nice probabilistic interpretation:
The AUC is the probability the model will score a randomly chosen positive class higher than a randomly chosen negative class.
Our intention here is to give a proof to this fact.
We will give a geometric proof by setting up a lattice in which the lattice points under the ROC curve correspond to those pairs of positive and negative classes in which the model ranks the positive class higher than the negative class.
Consider the following diagram:
We have layed the positive classes in our dataset equally spaced along the y-axis. The positive data point ranked highest by the model is placed closest to (0, 0), and the model score of the data points decrease as we move in the positive y-direction. We’ve neglected to lay a point at (0, 0), which is a technical detail that helps the counting work out.
The same was down with the negative classes, this time along the x-axis. If the coordinates of these two layouts are taken together, the result is a rectangular lattice in the square, which is also pictured.
Now consider picking a random positive class, coloring it orange, and drawing the horizontal line through the square that leaves from that point. Say that this is the $k$’th positive class.
This horizontal line first meets the ROC curve at one of the lattice points, the green point below:
Since the y-coordinate of a point on the ROC curve is the true positive rate at the threshold producing the point on the curve, the true positive rate at the green point is its y-coordinate
But the positive classes were layed down along the y-axis in order of decreasing score, so the actual points that are correctly classified to produce this true positive rate are the first $k$ points along the y-axis. Consequently, the threshold corresponding to the green point on the ROC curve is the minimal possible threshold that classifies the orange point correctly (i.e. as a positive class).
The same is true for a randomly chosen point along the x-axis. The threshold associated with the point along the ROC curve where a vertical line drawn from the point meets is the minimal possible threshold incorrectly classifying it as positive.
Now consider choosing two points
- A random positive class along the y-axis.
- A random negative class along the x-axis.
and drawing the corresponding horizontal and vertical lines.
Recall that the associated thresholds decrease as we move along the ROC curve towards the top-right corner. So, if the horizontal line meets the ROC curve to the left of the meeting with the vertical line, than the chosen positive class is scored higher than the chosen negative class. Under this setup the horizontal and vertical lines meet at a lattice point under the ROC curve. If the roles had been reversed, then the positive class would be scored lower than the negative class, and our intersection point would lie above the ROC curve.
Every lattice point under the curve is produced in this way: from those pairs of positive and negative classes in which the positive class is scored higher than the negative classes. So the proportion of pairs in which the positive class is ranked above the negative class is the same as the proportion of lattice points that lie under the ROC curve. It’s easy to see that this proportion of lattice points is the area under the ROC curve, which completes our proof.


What range imply in math? What’s a function in math? What’s a function in math?
For this a single, do not forget that the function named the square root is an object that has a name, and when it’s becoming expressed, you are able to place the name inside the square brackets. It can be referred to as a function due to its formula. If you want to express the square root with regards to a product, the formula is then X=R3.
What do you consider will be the equation for the square root? R3. In this case, the square root is named the derivative. So the square root could be described by two formulas.
The 1st formula can be represented by the quantity (R3). custom term paper writing Then the derivative is represented by the word the. If you replace the word the using the word differentiation, you can get the equation for the square root. This would contain a product, a value in addition to a time. This could be a time that is certainly diverse from the original.
Here is what is the equation for the square root? Now it’s an ordinary item between the solution along with the value.
How would you describe what’s the square root with regards to a time? Well, it is actually the derivative of the time with respect towards the value, and it can be the solution in the two values.
So the time would be the derivative of the worth, that is constantly equal for the product from the time plus the worth. Consequently, if you add these issues up, you get the value. For those who take the derivative of your worth, you get the time. Consequently, you’ve got to take the time into account once you are acquiring the derivative. So the square root is an expression for time. But what is a time?
Time can be a price at which we are able to repeat an action or a procedure. When the action or course of action is continuous, then the time will often be exactly the same.
You can compare the time to a point around the procedure. A value might be thought of as a point within a course of action.
In this case, the factor that has an impact on the time would be the value. Any time you measure time, you happen to be measuring how the procedure is going. So to get the value, you’ve got to add the time to the worth.


We all need a calculator sooner or later and having it integrated into our smartphone is a nice plus. Whenever you have to split the bill at a restaurant, when you want to calculate the percentage of VAT on a price, when you do math at school, when you have to make quick calculations that you don't want to go wrong, you can use the application of the calculator.
Both on Android smartphones and tablets and on iPhones and iPads the calculator is an app already installed (on iPhone it is also a scientific calculator), but if you want a better app than the standard one, let's see here, among the many that there are, the best 10 calculators to install for free, with different graphics, more comfortable and beautiful to look at, and also with tools to solve complex mathematical problems.
1) Calculator Plus
Calculator Plus (for Android and iPhone) is one of the simplest calculator apps that you can use on smartphones, which graphically reproduces the calculators of yesteryear. You can then make quick calculations that remain in memory to have a history. a scientific calculator is missing here.
2) Calculator (Google)
Google's Calculator app, available only for Android, is the one that comes pre-installed in Pixel smartphones and has a nice interface to easily solve math problems and simple and complex calculations. The scientific calculator, in addition to simple calculations such as addition, subtraction, multiplication and division, also specializes in scientific operations such as logarithmic, trigonometric and exponential functions.
3) Uno Calculator
Uno Calculator (Android and iPhone) is a special app because it is a "port" of the Windows 10 calculator that Microsoft has made open source. In practice, it is the same Windows 10 calculator that is now available, free and without advertising, as an app for Android smartphones, for iPhones, iPads. As a calculator it is really complete and powerful, not only usable to solve even complex calculations, but also to enter HEX, BIN, OCT and DEC codes, to write functions and equations and then also to convert units of measurement such as weight, energy , coins, temperatures and much more. This is probably the best app to use a calculator on your phone, especially for those used to using the same app on Windows 10.
Uno Calculator can also be used and tested from the calculator.platform.uno website
4) CALCU elegant calculator
As the name of the app says, Elegant Calculator (for Android) is one of the calculator apps with the best graphics, with the ability to choose colors and gesture-based control. If we talk about the functionalities of Stylish Calculator, the app specializes in scientific calculation and basic calculations.
ClevCalc for Android and iPhone is a scientific calculator that shows all calculations in a single line, with also a loan and percentage operations calculator, currency converter and unit of measurement (length, weight, width, time, temperature, pressure, speed).
6) The Calculator +
Calculator + is the best and most popular iPhone app to replace Apple's calculator already installed in IOS. Among its functions we have basic calculations, scientific calculations, fractions and currency converter, writing equations, calculating degrees and radians. it also supports calculation history, dark theme, drag and drop and can also be used from Apple Watch.
7) Calculator ++
This Android application with calculator function for Android is an excellent app to replace the default app already installed in the phone, with an interface very similar to the Google calculator seen in point 2 and many features. In Standard mode, there are operators to do simple calculations, while in Engineer mode you enter the scientific calculator with advanced features for solving complex problems of trigonometry, logarithmic functions and much more.
8) Financial Calculators
Financial Calculators for Android and iPhone brings a series of tools for financial calculation (TVM) that are very useful both for managing everyday expenses, taxes, interest on loans, and also for carrying out even complex financial mathematics operations such as the calculation of the ROI, the internal rate of return, the amortization plan and much more. Financial Calculators is definitely the best calculator app for anyone working in the financial sector.
PhotoMath, for Android and iPhone is a very popular calculator among students because it allows you to solve complex mathematical equations by taking a photo from a book or even from a handwritten notebook.
Best of all, Photomath breaks down every math problem into simple, easy-to-understand steps and is one of them best apps for school.
10 ) Other great calculator apps for Android
On the Google Play store you can also find other very good free calculator apps that are worth trying if you are still not happy with those already presented above. Among these we mention those with the best reviews:
- Mobi Calculator, with a beautiful customizable graphical interface.
- Mathlab Graphing Calculator, ideal for school.
- Quickey calculator, very colorful.
Best calculator app for Android and iPhone


|Course Starting||1st Or 2nd Week Of April 2016|
|Course Ends||2nd Week of June 2017|
|Course Duration||1 Year CLP|
|Class Schedule||4 days a Week|
This Course is for the students who are studying in 12 Class and want to score good marks in CBSE Board Exams along with Selection in IIT-JEE / BITSAT
This Course Covers all the concept of Physics,Chemistry & Mathematics for CBSE + IIT-JEE.Focus on both CBSE +IIT-JEE is given by highly Exp. Faculty.Focus on both CBSE +IIT-JEE is given by highly Exp. Faculty.


Fractions – Sequences and Patterns Exploring interesting patterns and sequences generated with fractions. This collection of resources is designed to help students improve their understanding of topics in Number. Full Screen Version If you can see this message Flash may not be working in your browser Please see http: Can you explain how I know? Ratio Sudoku 1 Age 11 to 16 Challenge Level: Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. An investigation involving adding and subtracting sets of consecutive numbers.
What were the interesting questions that needed to be asked, and where did they lead? Weekly Problem 24 – Can you put these very close fractions into order? Matching Fractions Age 7 to 11 Challenge Level: Can you explain how I know? Fractions Age 5 to 7 The activities in this feature give you chance to explore fractions.
What is the sum of the denominator and numerator?
Tiny Nines Age 14 to 16 Challenge Level: Can you picture it? Filter by resource type problems games articles general resources interactive environments EYFS Resources projects Lists Filter by age 5 to 7 7 to 11 11 to 14 nruch to 16 16 to Have a go at this challenging task! Match the cards of the same value.
Pick two rods of different colours. I need a figure for the fish population in a lake.
Exploring Fractions Age 5 to 11 This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help. Can you see how to build a harmonic triangle?
The discs for this game are kept in a flat square box with a square hole for each.
Fractions, Decimals and Percentages – Short Problems :
Where on the track will they meet? Now where’s the mark? Can you find combinations of strips of paper which equal the length of the black strip? Ben’s Game Age 11 to 14 Challenge Level: Try this matching game and see.
1213 Matches for fractions problems
Can you find a number that is halfway between two fractions? Tiny Nines Age 14 to 16 Challenge Level: Weekly Problem 43 – Rachel and Ross share a bottle of water.
Take a look at the video and try to find a sequence of moves that will untangle the ropes. What fraction is left behind?
Fractional Wall Age 7 to 11 Challenge Level: What is the ratio of boys to girls among these members? Age 11 to 14 Short Challenge Level: This collection of resources is designed to help you to improve your understanding of topics in Number. Forgot the Numbers Age 7 to 11 Challenge Level: Bargain Age 14 to 16 Short Challenge Solvinb Tumbling Down Age 7 to 11 Challenge Level: A group of interactive resources to support work on percentages Key Stage 4.
Folding Fractions Age 14 to 16 Challenge Level: How do they compare if you use 24 beads?
Fractions, Decimals, Percentages, Ratio and Proportion :: Fractions :
Can all unit fractions be written as the sum of two unit fractions? Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and sovling eats one.
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben.
Stetch it out to match the original length.


In practice, many different squashing functions are used. Kosko and Taber for example suggest the use of a simple binary function, but more complex functions are possible as well. However, it is surprising that literature does not place much emphasis on this topic, although the chosen function strongly affects the results. Identifying concept-specific squashing functions is very important, unfortunately, so far no publication has yet dealt with that problem.
To get an idea what squashing functions do please have a look at this article.


Below you will find links to toddler, preschool, and math activity Pinterest boards. Within each board, there are four pins that pertain to each math content area. As a reminder, the five math content areas are Number Sense, Spatial Sense and Geometry, Exploring Data, Measurement, and Patterns and Relationships. Using activities found within pins can make lesson planning very simple and a great resource for parents as well. It can be really fun to find inspiration through Pinterest and to apply specific vocabulary and language targets to appropriate math activities.
Take a look at my Pinterest boards and let me know what you think!
Featured image- http://www.scholastic.com/parents/resources/article/what-to-expect-grade/preparing-preschool-math


XinXing is a STEM School
STEM is not just about learning science, technology, engineering, and math in silos. The most effective and true STEM learning is a hands-on integration of all these disciplines, through experiments and development of real-world problem-solving skills.
Thanks to a U.S. Department of Education grant, in collaboration with the University of Minnesota, we developed interdisciplinary STEM units for Chinese immersion students. Our advanced STEM curriculum prepares students for a highly technical future. Currently, STEM instruction is available for grades 2,3,4, 5 and 6. Next year we will be extending STEM into first grade.
Our nationally recognized and researched elementary core STEM curriculum, Engineering in Elementary (EiE), was developed by the Museum of Science, Boston. XinXing students experience the full benefit of the STEM core in Chinese. STEM units are enhanced by interactive white board technology in each classroom.
Hopkins Public Schools STEM initiative
We will embed STEM concepts and skills within real-world curriculum at every level, to better prepare our students for the 21st century.
Our commitment to preparing students for a highly technical future has led Hopkins Public Schools to integrate STEM curriculum into all of our schools. Our curriculum, our teachers, and our extensive technology are all geared toward giving our students the extra edge in these disciplines.
Students need STEM project-based learning to build 21st century skills. Science and engineering jobs are growing 70 percent faster than other occupations. This means our students will be at an advantage when competing for the high-tech, high-wage jobs of the future.
Learning by doing is inviting and exciting so students remember more. Successful, hands-on experiences exploring engineering can have a major influence on motivation and confidence in learning. Ultimately, we hope to inspire students to challenge themselves and consider careers in STEM fields.


Table of Contents :
Top Suggestions Worksheet First Grade Addition And Subtraction Large Print :
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1st Grade Subtraction Worksheets Free Printable K5
Worksheets Math Grade 1 Subtraction Grade 1 Subtraction Worksheets Our Grade 1 Subtraction Worksheets Provide Practice In Solving Basic Subtraction Problems Exercises Begin With Simple Subtraction Facts Using Pictures Or Number Lines Followed By 1 Digit Subtraction Facts And And Progress To Subtraction Of 2 Digit Numbers In Columns And Subtraction Word Problems
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Mixed Addition And Subtraction Worksheets
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Worksheet First Grade Addition And Subtraction Large Print. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
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Supported Rhino/Grasshopper geometry
Packhunt supports the Rhino/Grasshopper solver.
In your Rhino/Grasshopper definition:
- You can output geometry using the Packhunt
- Each geometry type should be using a different
outputcomponent. (i.e. Don’t mix geometry types in a single
Packhunt supports all Rhino/Grasshopper geometry types except SubD geometry.
- For surface geometry (including both NURBS surfaces and BReps), materials can be assigned in Grasshopper using the Packhunt
- For line geometry (including lines, polylines, curves, arcs, circles and ellipses), a default black material is assigned. This default material can currently not be changed.
Packhunt also has additional object types for specific use cases.
Below is additional information about certain geometry and object types.


Academic Research Associate at Institute of Statistics of the Pontificia Universidad Católica de Valparaíso, Chile. In August 2006, I completed my doctorate degree in Statistics at University of São Paulo, Brazil under the direction of Dr. Gilberto A. Paula.
My research interests lie in the fields of sensitivity and influence diagnostics as a mean to criticize and to improve the statistical modeling. In particular, I focus on the development of estimation and influence procedures in mixed-effects models and longitudinal data under non-normal distributions as well as the computational implementation of such techniques.
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Spatial Relationships Between Two Georeferenced Variables: with Applications in R.
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Likelihood-based tests for the covariance matrix of multivariate t distribution: return assessment of the Chilean pension system..
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Testing equality of Sharpe ratios using the multivariate t distribution.
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Estimation of spatial models with partially linear covariance structure.
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Statistical estimation of structural similarity coefficients for images.
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Smoothing parameter selection and outliers accommodation for smoothing splines.
In Proceedings of the 58th World Statistics Congress of the International Statistical Institute, Dublin, Ireland. Session CPS008, 6037-6042.
De la Cruz, R., Eyheramendy, S., Meza, C., Osorio, F. (2010).
Exact estimation procedures in a spatial mixed-effects probit model with binary outcomes.
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