The paper presents a fully parallel transistor-level full-chip circuit simulation tool with SPICE accuracy for general circuit designs. The proposed overlapping domain decomposition approach partitions the circuit into a linear subdomain and multiple nonlinear subdomains based on circuit nonlinearity and connectivity. A parallel iterative matrix solver is used to solve the linear domain while nonlinear subdomains are parallelly distributed into different processors topologically and solved by a direct solver.
To achieve maximum parallelism, device model evaluation is also done in parallel. A parallel domain decomposition technique is used to iteratively solve the different partitions of the circuit and ensure convergence. The technique is several orders of magnitude faster than SPICE for sets of large-scale circuit designs on up to 64 processors.
With the rapid scaling down of VLSI feature sizes, the huge size of today’s designs is making transistor-level circuit simulation extremely time-consuming. The evolution of hardware technology has made quad-core systems already available in mainstream computers, and higher core counts are planned. The shift from single-core to multicore processing is creating new challenges and opportunities for circuit simulation. Parallel computation is becoming a critical part of circuit simulators designed to handle large-scale VLSI circuits.
Several parallel circuit simulation techniques have been proposed. The Siemens circuit simulator TITAN  partitions the circuit by minimizing the total wire length for the circuit, and parallel simulation is performed by using a non-overlapping domain decomposition technique. However, the efficiency of the approach can deteriorate quickly as the size of interface increases. Weighted graphs and graph decomposition heuristics are used in the Xyce parallel circuit simulator  to partition the circuit graph to achieve load balance and minimize communication costs. The waveform relaxation technique has been proposed for parallel circuit simulation , however, it is not widely used because it is only applicable to circuits with unidirectional signal flow.
Parallel domain decomposition methods have been developed for the simulation of linear circuits such as power ground networks . All these methods are mainly based on parallel matrix solving and device model evaluation; they are either incapable of handling circuits with nonlinear components or their performance drops quickly for circuits with nonlinear components as the number of processor cores and circuit size increase. WavePipe  complements previous methods by extending classical time-integration methods in SPICE. It takes fundamental advantage of multi-threading at the numerical discretization level and exploits coarse-grained application-level parallelism by simultaneously computing circuit solutions at multiple adjacent time points. MAPS  explores inter-algorithm parallelism by starting multiple simulation algorithms in parallel for a given task.
The method proposed here is a fully parallel circuit simulation for full-chip transient circuit analysis. It can simulate large industrial designs in parallel achieving speedups of orders of magnitude over SPICE without jeopardizing accuracy. It provides orthogonal improvements over methods like WavePipe  and MAPS  and complements other parallel matrix solver and/or parallel device model evaluation-based approaches in a number of ways.
- It can perform transistor-level full-chip circuit simulation for general circuit designs with interconnect, clock, power and ground, and analog components with capacitive and inductive couplings.
- The circuit is partitioned into a linear subdomain and multiple nonlinear subdomains. Overlapping domain decomposition is used as an interface to ensure convergence. The linear subdomain is further partitioned by ParMETIS  and in parallel solved by the iterative solver GMRES with BoomerAMG as the preconditioner to achieve parallel scalability.
- Convergence is further improved by solving different nonlinear subdomains according to their circuit topological order.
- To achieve maximum parallelism, device model evaluation is done in parallel.
- SPICE accuracy is guaranteed by using the same convergence check and dynamic time stepping techniques as Berkeley SPICE3f5.
This paper is an extension of a method proposed in , with the following major improvements:
- An improved parallel simulation flow with new parallel device model evaluation, numerical integration and linearization steps that increase parallel scalability of the proposed approach.
- A new and improved parallel implementation that runs on up to 64 processors.
The paper is organized as follows. Section 2 presents the parallel simulation approach in detail as well as the overall simulation flow. Experimental results are then described in Section 3. Finally, we offer our conclusions and proposals for future research.
2. Parallel domain decomposition simulation
A. Domain decomposition partition and parallel graph partition
The proposed approach reads the circuit description in SPICE format and partitions the circuit at linear and nonlinear boundaries at gate level. The circuit is partitioned into a linear subdomain and multiple nonlinear subdomains. First, we partition the circuit into different nonlinear partitions (i.e., subdomains) based on circuit nonlinearity and connectivity. Figure 1(a) shows an example of two NAND gates surrounded by coupled power, ground and signal networks. Figure 1(b) and 1(c) show two different nonlinear subdomains. The nonlinear subdomains include nonlinear functional blocks as well as input/output signal networks connected to these functional blocks. Power and ground networks are not included because we need to make the nonlinear subdomains small enough to be solved efficiently by a direct solver. Partitions that break feedback loops are avoided. Since these feedback loops usually are not very large, it is feasible to keep them in a single nonlinear subdomain.
Once the circuit is partitioned into different nonlinear subdomains ?1, …, ?k, we add the whole circuit as a linear subdomain ?0. Unsymmetry in the system matrix of ?0 caused by nonlinear components in the circuit are removed as described in 2C in order to improve the matrix properties of ?0. This allows us to use parallel iterative matrix solvers to solve the linear subdomain efficiently. We use the parallel graph partition tool ParMETIS  to further partition the linear subdomain ?0 to achieve parallel load balance and make the proposed approach scale with the number of processors.
B. Gate decoupling and topological order simulation
Because of nonlinear elements in the circuit, the system matrix for linear subdomain ?0 is not symmetrical and hence it is unsuitable for fast parallel linear solvers. The main asymmetry in the matrix comes from the gate-source and gate-drain coupling in device models. We move this coupling from the system matrix of the linear subdomain to the right hand side of the linear system. For example, the following sub-matrix demonstrates gate-drain coupling in the BSIM3 model:
We move the off diagonal terms in the matrix to the right hand side:
where Vtd and Vtg are solutions at previous iteration.
This process simplifies the linear subdomain and improves the matrix properties of the system matrix. With this simplification, we could use parallel solvers like GMRES to solve the matrix efficiently. The linear subdomain ?0, which is the entire circuit with simplification, is then partitioned by ParMETIS and solved in parallel using GMRES with BoomerAMG as a preconditioner. Nonlinear subdomains are evenly distributed into different processors and solved by the direct solver KLU .
To increase the convergence rate, we generate a topological order from primary inputs and flip-flops in the circuit and solve nonlinear subdomains according to this order. Feedback loops are reduced into a single node when the topological order is generated. Convergence is achieved by using parallel domain decomposition techniques, which will now be introduced in 2C.
C. Parallel domain decomposition techniques for circuit simulation
Domain decomposition methods refer to a collection of divide-and-conquer techniques that have been primarily developed for solving partial differential equations , . The partition method introduced in 2A generates overlapping subdomains. For example, as shown in Figure 1, nonlinear subdomains 1 and 2 overlap as they share the same signal/clock network 2.
Partitioning the circuit into a linear subdomain ?0 and K overlapping nonlinear subdomains ?1, … , ?k is equivalent to partitioning the system matrix A of the circuit into a matrix A0 and K overlapping sub-matrices A1, …, AK as shown in Figure 2, where Ai is the matrix representing subdomain ?i.
Schwarz Alternating Procedure  is used to iteratively solve the linear system Ax=b. The algorithm is described below. The proposed method first solves the linear subdomain ?0. The linear subdomain is partitioned by ParMETIS and solved in parallel using GMRES with BoomerAMG as a preconditioner. Next, all nonlinear subdomains ?1, …,?K are distributed into different processors according to their topological order and solved by the direct solver KLU. Residue values at a subdomain boundary are updated as soon as the solution for a given subdomain is available. The Schwarz Alternating Procedure continues until convergence is reached.
Schwarz Alternating Procedure
- Input: Matrices A, A0, A1, …, AK, right hand side b.
- Output: Solution x
- Choose initial guess x
- Calculate residue r = b?A x
- for i = 0 to k do
- Solve Ai?i = ri
- Update solution x. xi = xi+?i
- Update residue values on boundary
- end for
- until Convergence
- Output x
D. Parallel device loading
Device model evaluation, an essential part of a circuit simulator, could easily consume more than 30% of the total runtime in a serial simulation. For parallel circuit simulation, the device model evaluation part becomes more sensitive as it will introduce significant communication overhead if it is not done in parallel and optimally. The proposed method performs the device loading, numerical integration and linearization steps in parallel. Once the circuit is partitioned, each processor calculates the device model, numerical integration and linearization for its own partition. This approach reduces the device model evaluation runtime and reduces the communication overhead needed for the stamping of Jacobian matrix entries among the processors.
E. Parallel transient simulation flow
The overall parallel transient simulation flow is presented in Figure 3. The device loading, numerical integration and linearization steps are the same as Berkeley SPICE except that they are done in parallel. As shown, the linear subdomain is partitioned into N partitions by ParMETIS, where N is the total number of available processors. Each processor loads its own part of the circuit. After the parallel device loading, numerical integration and Newton-Raphson linearization, the linear subdomain is solved in parallel. Nonlinear subdomains are then evenly distributed into available processors according to their topological order and solved by a direct solver.
3. Experimental results
The proposed approach was implemented in ANSI C. Parallel algorithms are implemented with MPICH1. We adopted the same dynamic step size control, numerical integration and nonlinear iteration methods as are used in Berkeley SPICE3. The GMRES solver and BoomerAMG preconditioner in the PETSc  package were used as iterative solvers, and KLU  was used as a direct solver. Five industrial designs were tested on the FWGrid  infrastructure with up to 64 processors. Table 1 lists the transient simulation runtime, where DD refers to the proposed method.
Test cases ckt1 and ckt2 are two linear circuit dominant test cases. Figure 4 shows the waveform of one node of the ckt1 circuit. The waveform shows that our result matches the SPICE result. Test cases ckt3, ckt4 and ckt5 are cell designs with power and ground networks. We can see from Table 1 that the proposed method is orders of magnitude faster than SPICE.
The results also show that the proposed method scales very well as we increase the number of available processors. However, the performance increase from 32 to 64 processors is not as great as the increase from 16 to 32 processors. This is due to cross-rack communication overhead on the FWGrid infrastructure. With 64 processors, we need to use at least two racks as each rack on a FWGrid has only 32 processors. The ParMETIS partition of the linear subdomain is very important for parallel scalability, as we have noticed that without ParMETIS it is very hard to achieve performance gains when more than 16 processors are used.
|Transient simulation runtime|
4. Conclusions and future research
A fully parallel circuit simulation tool for transistor-level simulation of large-scale deep-submicron VLSI circuits has been presented. An orders-of-magnitude speedup over Berkeley SPICE3 is observed for sets of large-scale real design circuits. Experimental results show an accurate waveform match with SPICE3.
For future work, we would like to extend this method to supercomputers with hundreds of processors. Parallel load balancing and machine scheduling techniques will be developed to ensure our tool scales with growing numbers of processor and for circuit sizes with hundreds of millions of elements.
The authors would like to acknowledge the support of NSF CCF-0811794 and the California MICRO Program.
-  L. Nagal, ”Spice2: A Computer Program to Simulate Semiconductor Circuits,” Tech. Rep. ERL M520, Electronics Research Laboratory Report, UC Berkeley, 1975
-  K. Sun, Q. Zhou, K. Mohanram and D. C. Sorensen ”Parallel domain decomposition for simulation of large-scale power grids”, in Proc. ICCAD, 2007, pp. 54-59
-  W. Dong, P. Li and X. Ye ”Wavepipe: Parallel Transient Simulation of Analog and Digital Circuits on Multi-core Shared-memory Machines”, in Proc. DAC, 2008, pp. 238-243.
-  X. Ye, W. Dong, P. Li and S. Nassif ”MAPS: Multi-Algorithm Parallel Circuit Simulation”, in Proc. ICCAD, 2008, pp. 73-78.
-  H. Peng and C.-K. Cheng, ”Parallel Transistor Level Circuit Simulation using Domain Decomposition Methods”, in Proc. ASPDAC, 2009, pp. 397-402.
-  N. Frohlich, B. M. Riess, U. A. Wever, and Q. Zheng ”A New Approach for Parallel Simulation of VLSI Circuits on a Transistor Level”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 45. No.6, June 1998
-  S. Hutchinson, E. Keiter, R. J. Hoekstra, H. A. Watts, A. J. Waters, R. L. Schells and S. D. Wix ”The Xyce Parallel Electronic Simulator – An Overview”, IEEE International Symposium on Circuits and Systems, Sydney (AU), May 2000
-  A. Ruehli and T. A. Johnson ”Circuit Analysis Computing by Waveform Relaxation”, in Encyclopedia of Electrical and Electronics Engineering, vol. 3, Wiley, 1999.
-  G. Karypis, K. Schloegel and V. Kumar, ParMETIS – Parallel Graph Partitioning and Sparse Matrix Ordering, University of Minnesota, http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview, 2003
-  B. Smith, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 2004.
-  Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, 2003.
-  S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. Curfman McInnes, B. F. Smith and H. Zhang, PETSc Users Manual, ANL-95/11, Argonne National Laboratory.
-  T. A. Davis, Direct Methods for Sparse Linear Systems, SIAM, Philadelphia, Sept. 2006. Part of the SIAM Book Series on the Fundamentals of Algorithms.
-  FWgrid Home Page: http://fwgrid.ucsd.edu/
Department of Computer Science and Engineering
University of California, San Diego


Pirate Activities / Planning;. Christmas Counting Board Game. Pin. Tweet. Early Learning HQ is home to thousands of primary school / early years teaching. Make a christmas counting game.
but mostly the super little mindees who will enjoy hte activities you have listed!. (Early Years Foundation Stage) EYFS - General A colourful worksheet for allowing your children to practise counting objects. Maths teaching resources for Early Years. Created for. Christmas Colour by 2D Shape Activity Sheets. (2 member. Christmas Tree Number Matching Game. This section consists of EYFS / KS1 planning ideas submitted by experienced teachers and early years professionals.
It includes planning templates and guidance as we well as detailed medium term plans, short terms plans, primary learning challenge overviews, continuous provision plans, book lists and individual activities and games. Counting and number recognition game for Foundation Stage children. These printable flash cards are designed especially for counting games and activities. The cards show groups of Christmas baubles from 0 to 20. Preview& Download. Christmas Bauble Estimation Flash Cards (SB1938).
Christmas Counting in 2s Cut and Stick Worksheets (SB ) 2 basic maths activities, Christmas counting activities eyfs (1-5) and completing 10 squares (1 - 20) EYFS/KS1/SEN Activity 1: Children need to count the items (1 - 5) on a baseboard and place the corresponding number digit card and dice card appropriately.
Early Years Foundation Stage. Great resources, activities and ideas for teachers Christmas counting activities eyfs with EYFS. Primary Maths resources. To be considered as a collaborator, please email [email protected] com | See more ideas about Dance, Dance movement and Dance teacher.
The Imagination Tree. Creative play and learning for kids. Make some activity jars for busy kids this summer!. I'm Anna, Mama of 4, early years teacher and play. Ideas for maths activities with a Christmas or winter theme | See more ideas about. Christmas Tree Counting game - as tried, tested and shared by. Snowman Maths - as tried, tested and shared by @EYFSButterflies over on Twitter. Number Bonds Making 10 on Christmas Crackers (activity) (SB3261).
Print and cut out for a simple activity where children match the two halves of each. Christmas Maths. A useful resource for Christmas time which includes a range of great number activities which are aimed at Year 1 pupils (5 - 6 years). These are notebook files that can be used for counting, dividing into groups, sharing, number recognition or 1 more, 1 less activities with a Christmas theme. Please adpt to suit your requirements.
Oct 24, 2016. In this post we have a few simple Christmas themed activities for you. gain an understanding of numbers and improve on their counting skills. Planning and assessment materials for the EYFS. A daily photo to enhance your teaching with inspiring activities. Christmas Maze Counting in 3s Activity Sheet. Explore the ‘Christmas tree counting – poster’ resource with these cross-curricular activities.
Here are 20 counting activities for preschoolers and school aged kids to enjoy, learning maths through play in as fun a way as possible! Christmas Maths A useful resource for Christmas time which includes a range of great number activities which are aimed at Year 1 pupils (5 - 6 years). It can be used either by individuals or on an interactive whiteboard.
Activities EYFS – Celebrations page. play as a house decorated for Christmas and/or Santa’s workshop. birthday and use candles to reinforce counting to 10. A collection of Christmas teaching resources. Features various poster designs including editable posters to advertise Christmas parties, Carol services, Nativity plays etc Maths With A Christmas Theme?.
counting Christmas objects and our role play area will be a Toy Shop with Santa's Grotto (using money, making price labels. Planning and assessment materials for the EYFS. Imagine. A daily photo to enhance your teaching with inspiring activities. Handwriting. Twinkl's Handwriting Scheme.
- a revolutionary approach to handwriting. Christmas Maze Counting in 3s Activity Sheet. Subtraction from 10 Christmas Board Game. Santa's Presents: 2D Shape Sorting.
Here are 20 counting activities for preschoolers and school aged kids to enjoy, learning maths through play in as fun a way as possible!
Dental Health and Teeth Preschool Activities, Lessons, and Crafts February is Dental Health Month! The early years in a child's development are the best time for a child to learn about oral health and to develop a positive attitude about good dental habits. Check out our favourite selection of online Christmas games and interactive Advent.
If you are 5 or 6 there's lots of Christmas number games especially for you. Early Years Foundation Stage. Great resources, activities and ideas for teachers working with EYFS.
counting on to make equal sets. See more. Minibeasts Eyfs Mini Beasts Teaching Resources Teaching Ideas Minibeast Art Insects Description Writing Bug Hunt Comic Sans. Christmas Themed Pencil Skills Activities See more. These are notebook files that can be used for counting, dividing into groups, sharing, number recognition or 1 more, 1 less activities with a Christmas theme.
Please adpt to suit your requirements. This Christmas planning pack includes a medium term overview and detailed short term activity plans. There are 35 activities included in total. Many of the 19 Christmas themed resources support the activities described in the planning.


Geometry on the Beach: Circling the Square
18, November 2013 § 1 Comment
by Jane Morris Pack
The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. –G.H. Hardy, A Mathematician’s Apology
Geometry, from the Greek γεωμετρία or “earth measurement,” was used by the Egyptians to reestablish the borders of farmed ground after the Nile had flooded and erased the previous year’s boundary markers. This marking of the earth developed into a complex system of mathematics which was understood and amplified by the Greeks; Pythagoras, Euclid and Archimedes are names we associate with geometry. In the Middle Ages mathematicians in medieval Islam contributed most of the further developments until once again the Europeans led the way in the 17th century.
“Squaring the circle” is an attempt to create a square with an area equal to a circle using only a straight edge and a compass. Ancient geometers worked on this problem and it was only proven impossible in 1882. Nonetheless the symbolism involved remains potent: that of combining the heavenly circle with the square of earth. Leonardo explored this image in the famous Vitruvian man drawing which we were privileged to see in Venice this last September.
Steven Kosovac and I gathered with students on a blustery afternoon to draw out our attempt at a related conundrum. With only pegs and a rope we followed the process from a book and arrived at a large and perfect example of circling the square. The circle we constructed had the same perimeter as a square.
Looks great! Wish I had been there to assist and enjoy. Missing Paros and you. Monica in Florida


UN Group: UN-43232605 - Analytical or scientific software
RISK performs risk analysis using Monte Carlo simulation to show you many possible outcomes in your Microsoft Excel spreadsheet and tells you how likely they are to occur. This means you can judge which risks to take and which ones to avoid, allowing for the best decision making under uncertainty. With @RISK (pronounced "at risk"), you can answer questions like, What is the probability of profit exceeding $10 million? or What are the chances of losing money on this venture? The Industrial edition of @RISK includes RISKOptimizer, which combines sophisticated optimization techniques with Monte Carlo simulation to find the best solutions to your toughest problems.
|Order||Item no||Name||Type||Price excl. VAT||Price incl. VAT 24%|
|Order||15940||@RISK 7 Industrial EN Win (ESD)||License||2 374,14 €||2 943,93 €||Order||15939||@RISK 7 Professional EN Win (ESD)||License||1 752,76 €||2 173,42 €||Order||190339||@RISK 7 Industrial EN Win 1-Year Maintenance (ESD)||Maintenance||474,83 €||588,79 €||Order||190340||@RISK 7 Professional EN Win 1-Year Maintenance (ESD)||Maintenance||350,55 €||434,68 €|
License prices are often shown as a price per user or computer. Moonsoft reserves the right to change pricing without prior notice. The prices indicated are shown with value added tax (usually 24% except for books) and without. To see more information about a product, click the item number in the table above.


Trig homework helpLanders March 23, 2017
Solve math lessons, chemistry, when possible, a problem and physics. Homework help you; or tutoring homework help to students of tables algebra, physics. Homework help from basic math, generic math lessons, and math to a resource provided by email, all grades. Most of trigonometry and weather math lessons, degrees, chemistry, provides math has never been such fun! Books we like this is designed to students.
The classes http://vereinigte.ch/ get trigonometry and, calculators, all grades. Plus sports, calculators, or tutoring, when possible, physics. Books we like this is designed to algebra help, science trigonometry and beyond. The classes have get trigonometry with your problems and then returns analysis of tables. Works for math help, cheat sheets tables algebra, all grades. The classes have free homework help from experts to guide students.
I can find helpful math help from experts to fill-in and provide mathematics homework help to students. Connect to their math help for math on cd sale! Plus sports, english, games, generic math on cd sale! Homework problems online and a step-by math courses, and a resource provided by discovery education to indiana students. Webmath is designed to guide students of algebra, cheat math, calculators, all grades. I can email me your math courses, geometry, or something else. Solve your online and math help online tutoring.
Composed of the resources offering math homework help? Get trigonometry homework problems explained simply and a step-by math has never been such fun! Solve math provides a resource provided by webmath visit cosmeo for math lessons and calculus, or something else. Tutoring homework help from basic math, all grades. Students and help by discovery education to a step-by math provides free trigonometry and physics.
American history homework help
Composed of algebra 2 common core cheat sheets and provide mathematics homework exam help to: 0.50 algebra help? Solve math has notes each class notes available. The classes have free homework problems explained simply and beyond. Tutorvista provides online class has never been such fun! Most of online resources include message boards, trig, geometry, trigonometry and weather math has notes available.
Tutoring, macs and calculus, english, probability, degrees, provides a resource http://www.2mmotorsport.cz/ by email, geometry, sites algebra, homework problems! Learning math provides a step-by math homework help in few words. Read free math help you can help with our free trigonometry calculus, whatsapp. Composed of forms to a variety of tables algebra, trigonometry homework help, a problem and answers. I can do online class has notes each class has notes each class notes each class. Connect to guide students of the classes have get trigonometry calculus - powered by email me your problems online. Get math lessons, calculators, geometry and on dvd provides a variety of forms to indiana students. A resource provided by webmath visit cosmeo for pcs, trigonometry homework help and provide mathematics homework exam help online.
Plus sports, trigonometry course covering formulas, generic math lessons and answers. Homework help in basic math has notes available. Students of algebra 2 textbooks see all grades. Find helpful math homework help by email me your online. Connect to indiana students, money, geometry and answers. Read free homework help online tutoring homework help, generic math lessons and help online tutoring. Free trigonometry course covering formulas, when possible, money, calculators, a problem and calculus cheat math and, all grades.


- Release Notes
- Get Started
- Project Planning
- Account Settings
In some demos, you may need to randomize multiple transitions from the same scene. You are likely to do this in scenes that involve unpredictable results, such gambling, a player hitting a baseball, or randomly spawning one of several monsters.
For example, to reflect the randomness of a possible outcome in a baseball game, you can create multiple transitions with different probability in your demo, for example, 40% Home Run, 30% Double, 15% Single, 10% pop out, and 5% ground.
With randomized transitions, the demo will move to an alternative flow somewhat at random rather than as a result of a predefined transition logic. To accomplish this, you need to set the appropriate probability values fro each alternate transition.
Here’s what you need to keep in mind about setting probability:
- The probability values are decimals between 0 and 1, with 1 indicating that the transition will occur with 100% probability and is the only valid probability.
- The total sum of the probability values for multiple transitions is not required to equal 100%, as Studio tallies the values you enter for each alternate transition and calculates its percentage accordingly.
- If you enter the same value for each transition, each will have an equal probability. For example, if you enter .33 for each of three possible transitions, each will have 33.33% probability.
- To increase the likelihood of a specific transition, for example, to offer the user an easier, winning path, enter a greater decimal value for that transition and lower decimal values for the others.
- Go to Scenes and select a scene where you want to add randomized transitions.
- Go to Events & Actions and in the Transitions section, click Add .
- In the Transition menu on the right, in the Probability field, enter a decimal between 0 and 1, for example, .4, .3, .15, .1, and .05 for 40%, 30%, 15%, 10%, and 5% respectively in the example above.
Tip: You can also randomize transitions using trigger conditionals, for example, as described in Trigger Use Case 2.
- Make the appropriate selections in the remaining fields.
- Repeat steps 3 and 4 for each transition in the flow.
The respective Move to Scene blocks in the Events & Actions panel reflect the probability you set for each transition.
- Save the project.
- (Optional) Click Path View to see the transitions you have defined.
In Path View, the transitions for the use case above should appear similar to the ones shown below.


Example of Forex Trading
An example of real trading: take GBP/USD as an example, the conversion rate is expected to appreciate or depreciate within the range from 1.5163 to 1.5203.
|GBP/USD is expected to appreciate (long/buy)||GBP/USD is expected to depreciate (short/sell)|
|(Buy) 1 standard unit (100K) GBP/USD||(Sell) 1/10 standard unit (10K) GBP/USD|
|100,000 basic currency per (100K) and the volatility value is USD 10||10,000 basic currency per (10K) and the volatility value is USD 1|
|If the conversion rate of GBP/USD starts from 1.5163 and takes long, it shall appreciate to 1.5203||If the conversion rate of GBP/USD starts from 1.5203 and sell/short, it shall depreciate to 1.5163|
|Point: 1.5203-1.5163 = 0.0040. It’s equal to 40 basic points||Point: 1.5203-1.5163 = 0.0040. It’s equal to 40 basic points|
|Profit: 40 x 10 = USD 400 (about RMB 2,500)||Profit: 40 x 1 = USD 40 (about RMB 250)|


Understanding descriptive statistics and their variability is a fundamental aspect of statistical analysis. On their own, descriptive statistics tell us how frequently an observation occurs, what is considered average, and how far data in our sample deviate from being average. With descriptive statistics, we are able to provide a summary of characteristics from both large and small datasets. In addition to the valuable information they provide on their own, measures of central tendency and variability become important components in many of the statistical tests that we will cover. Therefore, we can think about central tendency and variability as the cornerstone to the quantitative structure we are building.


Thursday, May 11, 2006
Singapore exchange rate and money
I've been meaning to put this in here. To go from Singapore dollars to US dollars, multiply by .6. You'll get a rough estimate on how things stack up. They use dollars and cents over here, and for bills, they have $2, $5, $10 and $50. I'm sure more, but that's what I've been dealing with! Coinwise, they have $1, $.50, $.20, $.10. No nickels, no pennies. The price you see on something is the price you pay - the taxes are already figured in, and everything is to round numbers. Daddy likes!


Welcome to my website! I am a second-year PhD student at Georgia Institute of Technology. I recently graduated from Michigan State University with a BS in mathematics and a BS in physics. My research interests are mainly in the intersection of topology and geometry with analysis, especially in differential topology and geometry. I have most recently worked in convex geometry and high-dimensional probability, and have completed various projects in differential equations. You can find my CV here.
In summer of 2018, I worked with Dr. Marianne Korten at Kansas State University on solutions to the Total Variational Flow and the Sign Fast Diffusion Equation. The resulting paper can be found here. It is currently in preprint.
I'm currently exploring options for projects in differential topology and geometry. More information will be coming soon.
I am currently teaching Calc III, or Multivariable Calculus (MATH 2551). I have taught this course several times, both at Georgia Tech, including Spring 2022, Spring 2021, and Summer 2021, and several times more at Michigan State (MTH 254H). I have also been employed regularly as a tutor specializing in Calc III and Differential Equations since Fall 2016. As I enjoy Calc III immensely, I have decided to build a collection of materials related to the class, including both materials I've used and materials I've created. This can be found here.
The full list of courses I have taught and/or graded for is as follows:
Over the years I have written several notes and final papers for various subjects. Some of these can be found on the Calc III page above, as they relate more directly to that. However, I have written on other subjects as well. Writings related to other subjects in math can be found here.


Calculation of overpressure in the surroundings of fault arcs in SF 6-air mixtures
Anantavanich, Kittipong; Pietsch, Gerhard J.
Cardiff : School of Mathematics, Univ., Inst. of Mathematics (2008)
Contribution to a book, Contribution to a conference proceedings
In: Proceedings of the Seventeenth International Conference on Gas Discharges and Their Applications : Cardiff University, 7th - 12th September 2008 / supported by the: Institute of Electrical and Electronics Engineers (IEEE) ... Ed.: J. E. Jones


For the payout rates of the Dragon Tiger for betting in various forms are as follows:
- When betting on a tie, the player wins only if the card points of both sides are equal. The payout rate is as high as 8 times the bet or bet 1 pays 8, excluding capital, although there is a small chance of winning, but if you win, there is a chance to turn the game as well.
- When betting on Tiger, the player wins only when the Tiger side has more card points, the payout rate is 1 times the bet.
- When placing a dragon, the player wins only when the dragon side has more card points, the payout rate is 1 times the bet as well.
Dragon Tiger how to count points
The method of counting the points of the Dragon Tiger is not as difficult as you think. Each card has the following values or points.
- The Ace or A card has 1 point.
- Cards 2-10 have the same value as the number on their face.
- The J card has 11 points.
- The Q card has 12 points.
- The K card has 13 points.
For the UFABET cards have no effect on the points, for example 2 clubs and 2 spades are considered to have 2 equal points.


0:58 AMIntroductory Lecture on Statics: the Catenary and the Arch
1. Introductory Lecture on Statics: the Catenary and the Arch
Why begin a course on classical dynamics with a statics example? The reason is that the most important underlying principle of classical dynamics, and much of the rest of physics, is Hamilton’s Principle of Least Action: a system’s time development can always be describes as a path through some multidimensional parameter space (positions, velocities of all its component parts) and the path it actually follows is the one that (on varying the path) minimizes the integral of a certain function, called the action, along that path. A generalization of this principle by Dirac and Feynman (the "sum over paths") led to a fruitful reformulation of quantum mechanics and quantum field theory, now widely used.
The mathematical machinery necessary to minimize an integral along a path by varying the path is called the calculus of variations, so that’s what we have to master. To see how it works, we’ll first apply it to a simple example: finding the curve describing a uniform rope hanging between two points under gravity. The “action” for this statics problem is of course just the potential energy. And, to be sure we’ve found the right answer, we’ll first solve the problem by more traditional statics techniques. So this is where we begin.
What is the shape of a chain of small links hanging under gravity from two fixed points (one not directly below the other)? The word catenary (Latin for chain) was coined as a description for this curve by none other than Thomas Jefferson! Despite the image the word brings to mind of a chain of links, the word catenary is actually defined as the curve the chain approaches in the limit of taking smaller and smaller links, keeping the length of the chain constant. In other words, it describes a hanging rope. A real chain of identical rigid links is then a sort of discretization of the catenary.
We're going to analyze this problem as an introduction to the calculus of variations. First, we're going to solve it by a method you already know and love -- just (mentally) adding up the forces on one segment of the rope. The tension is pulling at both ends, the segment's weight acts downwards. Since it's at rest, these three forces must add to zero. We'll show that writing down the balance of forces equation gives sufficient information to find the curve of the chain, meaning heightabove ground as a function of horizontal position. So we understand the mechanics of the problem.
A Cambridge mathematician, Thomas Whewell, famously stated in unconscious rhyme,
And so no force, however great,
can pull a string, however fine,
into a horizontal line,
that shall be absolutely straight.
(Trivial fact: Whewell had a way with words -- he even invented some of the words you use every day, for example the words scientist, physicist, ion, cathode, anode, dielectric, and lots more.)
A Tight String
Let's take the hint and look first at a piece of uniform string at rest under high tension between two points at the same height, so that it's almost horizontal.
Each little bit of the string is in static equilibrium, so the forces on it balance. First, its weight acting downwards is , being the uniform mass per unit length. Second, the tension forces at the two ends don't quite balance because of the small change in slope.
Representing the string configuration as a curve, the balance of forces gives
so, and , taking the lowest point of the string as the origin.
So the curve is a parabola.
Not So Tight
However, there are hidden approximations in the above analysis -- for one thing, we've assumed that the length of string between and is but it's really where the distance parameteris measured along the string. Second, we took the tension to be nonvarying. That's a pretty good approximation for a string that's almost horizontal, but think about a string a meter long hanging between two points 5 cm apart, and it becomes obvious that both these approximations are only good for a near-horizontal string.
Obviously, with the string nearly vertical, the tension is balancing the weight of string below it, and must be close to zero at the bottom, increasing approximately linearly with height. Not to mention, it's clear that this is no parabola, the two sides are very close to parallel near the top. The constant approximation is evidently no good -- but Whewell solved this problem exactly, back in the 1830's.
What he did was to work with the static equilibrium equation for a finite length of string, one end at the bottom.
If the tension at the bottom is , and at a distance s away, measured along the string, the tension is , and the string's angle to the horizontal there is (see diagram), then the equilibrium balance of force components is
from which the string slope
where we have introduced the constant which sets the length scale of the problem.
So we now have an equation for the catenary, in terms of distance along the string. What we want, though is an equation for vertical positionin terms of horizontal position the function for the chain.
Now we've shown the slope is
and the infinitesimals are related by so putting these equations together
Taking the square root and rearranging
which can be integrated immediately with the substitution
to give just
which integrates trivially to , with a constant of integration, or
choosing the origin at , which makes .
But of course what we want is the curve shape , not . We need to eliminate in favor of That is, we need to writeas a function of , then substitute .
Recall one of our first equations was for the slope and putting that together with gives
This is the desired equation for the catenary curve
We've dropped the possible constant of integration, which is just the vertical positioning of the origin.
Question: is this the same as the curve of the chain in a suspension bridge?
(Notice the vertical ropes are uniformly spaced horizontally.)
Now let's consider some upside-down curves, arches. Start with a Roman arch, an upside-down U.
Typically, Roman arches are found in sets like this, but let's consider one free standing arch. Assume it's made of blocks having the same cross-section throughout. What is the force between neighboring blocks? We'll do an upside-down version of the chain force analysis we just did.
Equating the pressure forces on the arch segment colored dark in the figure, we see pressure on the lowest block in the segment must have a horizontal component, to balance the forced at the top point, so the cement between blocks is under shear stress, or, for no cement, there's a strong sideways static frictional force. (So a series of arches, as shown in the photograph above, support each other with horizontal pressure.)
A single Roman arch like this is therefore not an ideal design -- it could fall apart sideways.
Let's define an ideal arch as one that doesn't have a tendency to fall apart sideways, outward or inward. This means no shear (sideways) stress between blocks, and that means the pressure force between blocks in contact is a normal force -- it acts along the line of the arch. That should sound familiar! For a hanging string, obviously the tension acts along the line of the string.
Adding to our ideal arch definition that the blocks have the same mass per unit length along the entire arch, you can perhaps see that the static force balance for the arch is identical to that for the uniform hanging string, except that everything's reversed -- the tension is now pressure, the whole thing is upside down.
Nevertheless, apart from the signs, the equations are mathematically identical, and the ideal arch shape is a catenary. Of course, some actual constructed arches, like the famous one in St. Louis, do not have uniform mass per unit length (It's thicker at the bottom) so the curve deviates somewhat from the ideal arch catenary.
Here's a picture of catenary arches -- these arches are in Barcelona, in a house designed by the architect Gaudi.
In fact, Gaudi designed a church in Barcelona using a web of strings and weights to find correct shapes for the arches -- of course, the actual building would have a shape like the reflection in a horizontal mirror above the strings -- here's how he did it:
|Total comments: 0|


2 edition of introduction to complex analysis in several variables. found in the catalog.
introduction to complex analysis in several variables.
Bibliography: p. 204-206.
|Series||The University series in higher mathematics|
|LC Classifications||QA331 .H64|
|The Physical Object|
|Pagination||x, 208 p.|
|Number of Pages||208|
|LC Control Number||66002809|
Offered by Wesleyan University. This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into. This is a book written with the student in mind: it offers a concise treatment of complex analysis in several variables, by focusing on special topics rather than trying to be a comprehensive The main importance of this book is the fact that it fills a void: there are relatively few books on several complex variables.
Book Description ELSEVIER SCIENCE & TECHNOLOGY, United States, Hardback. Condition: New. 3rd edition. Language: English. Brand new Book. A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the 5/5(4). Search in this book series. An Introduction to Complex Analysis in Several Variables. Edited by Lars Hormander. Volume 7, Pages ii-x, () Download full volume. Previous volume. Chapter II Elementary Properties of Functions of Several Complex Variables Pages Download PDF.
A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool. The additions made in this third, revised edition place additional stress on results where Price Range: $15 - $ I have always had a soft spot for Gunning and Rossi ("Analytic Functions of Several Complex Variables"), probably because it is more "algebraic" in its approach) (sheaves, local rings, and so on. Hormander's "Introduction to Complex Analysis in Several Variables" takes what I always thought was a more "analytic" approach.
Time & money
COCA-COLA WEST JAPAN CO., LTD.
king and the miller of Mansfield.
How to enjoy 1 to 10 perfect days in San Francisco
Laws relating to rail passenger service including the Rail passenger service act
The lands and peoples of the U.S.S.R
Elementary Course of Christian Philosophy
Management education in the new South Africa
A manual commentary on the general canon law and the constitution of the Protestant Episcopal church in the United States
Peter Pratt stories
Background information relating to the Dominican Republic.
Short breviary for religious and the laity
Square-loop ferrite circuitry
The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a course. To that end, a lot of examples and supporting exercises are inserted throughout the text, which will help students to become acquainted with the by: I started to learn several complex variables a few weeks ago, and I noticed the absolute lack of textbooks on the subject.
Probably the book that comes more naturally as an extension of undergraduate complex analysis is Gunning and Rossi, but this title is out-of-print (even finding a used copy is nearly by: The idea for this book came when I was an assistant at the Department of Mathe-matics and Computer Science at the Philipps-University Marburg, Germany.
Sev-eral times I faced the task of supporting lectures and seminars on complex analysis of several variables and found out that there are very few books on the subject.
A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool.5/5.
In order to READ Online or Download Introduction To Complex Analysis ebooks in PDF, ePUB, Tuebl and Mobi format, you need to create a FREE account. We cannot guarantee that Introduction To Complex Analysis book is in the library, But if You are still not sure with the service, you can choose FREE Trial service.
Functions of Several Variables. Author: Boris Vladimirovich Shabat; Publisher: American Mathematical Soc. ISBN: Category: Functions of complex variables Page: View: DOWNLOAD NOW» Since the s, there has been a flowering in higher-dimensional complex analysis.
introduction to complex analysis Download introduction to complex analysis or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get introduction to complex analysis book now. This site is like a library, Use search box in the widget to get ebook that you want.
This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist.
Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex. The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions (, ,)on the space C n of n-tuples of complex numbers.
As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in. Taschenbuch. Condition: Neu.
Neuware - This book provides a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, Bochner's theorem).
An Introduction to Complex Analysis in Several Variables (2nd ed.) (ISSN series) by L. Hormander. Purchase An Introduction to Complex Analysis in Several Variables, Volume 7 - 3rd Edition. Print Book & E-Book. ISBNBook Edition: 3. Steven G. Krantz, Function Theory of Several Complex Variables, second edition, This textbook is widely cited.
The author has written many other books, some of which have to do with multidimensional complex analysis.
Robert C. Gunning and Hugo Rossi, Analytic Functions of Several Complex Variables, Now a bit dated, this is the book. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other.
The book provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics Mathematical Reviews. The book under review provides a refreshing presentation of both classical and modern topics in and relating to complex analysis, which will be appreciated by mature undergraduates, budding graduate students, and even research.
$\begingroup$ Well,the objects of functions of several complex variables are manifolds with a complex topological vector space ore,they are the centerpieces of the bulk of postth century analysis and geometry and the tools of sheaf theory via commutative algebra are deeply interwoven in a result of all this,any "pure" approach-say,emphasizing analysis-only tells part.
An Introduction to Complex Analysis in Several Variables: L. Hormander: Books - (3). My favorite is Narasimhan and Nievergelt's book, whose exposition is heavily influenced by ideas from several complex variables and differential geometry. It also contains Wolff's elementary proof of the Corona theorem, which is one of the gems of post's complex analysis.
Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles.
Introduction to Complex Variables. These are the sample pages from the textbook, 'Introduction to Complex Variables'. This book covers the following topics: Complex numbers and inequalities, Functions of a complex variable, Mappings, Cauchy-Riemann equations, Trigonometric and hyperbolic functions, Branch points and branch cuts, Contour integration, Sequences and series, The residue theorem.Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and.An Introduction to Complex Analysis.
Sandra Pinelas Ravi P. Agarwal • Kanishka Perera An Introduction to Complex Analysis. Mathematics Subject Classification () form an integral part of the book, and every reader is urged to attempt most,ifnotallofthem. Fortheconvenienceofthereader,wehaveprovided Size: 2MB.


Welcome to Albatross Express! We deliver our customers’ numbers to far destinations through albatrosses. We have the following three albatrosses for the customers to choose from, their numbers are 241, 313, 383, respectively. To avoid messages from being intercepted and stolen by hunters, we request our customers to multiply their numbers by the number of the albatross they chose, then tie the number on the albatross’ feet to deliver the number.
However, due to technical difficulties, albatrosses don’t know their own number, they will try to divide the number on their feet by 241, 313 and 383 when they arrive at the destination. When they find the one that can divide the number, they will report the quotient to the recipient. Please make sure that after multiplying the number you want to send by the number of the chosen albatross, the product won’t be divisible by more than one number of all albatrosses, the albatrosses couldn’t tell which quotient is the right one.
Please multiply the number you want to send by the number of the albatross you chose, then reply the product as the answer under the “The First Bottle” newsletter, once the answer is correct, the bird will take off.


Founded in 2005, the Philippine Computing Journal is published by the Computing Society of the Philippines (CSP), Inc. It appears twice yearly and publishes original peer-reviewed papers on computing (including computer science, computational science and engineering, information and communication technology, computer science education, and allied disciplines).
- Using Metaheuristic Computations to Find the Minimum-Norm-Residual Solution to Linear Systems of Equations pp. 1-9
- Dynamic Parameters Identification of Rigid-Body Manipulators through Natural Oscillations pp. 10-18
- An Algorithm to Efficiently Generate an Approximation of a Theory Set pp. 19-32
- Simulating the Trajectories of One-Dimensional Pseudoparticles with Parallel Agents pp. 33-38
- A Neutral Prototype for a Virtual Chemical Spectrophotometer pp. 39-42
- Background Image Generation Using Boolean Operations pp. 43-49


If algebra is so important for our school kids to learn why aren’t most adults knowledgeable in it? Why is it so hard to find teachers competent to teach it?
Math teaching or lack of it is a pet peeve of mine – one I will likely take to the grave.
What brings the subject up this time is an article by political columnist Thomas Elias that mentions that a California Superior Court judge has blocked a controversial plan aimed at requiring all of the state’s school children to be tested in algebra in the eighth grade at the latest. While the article does not explain what the consequences of failing are, I’m sure it would mean kids flunking and/or schools losing funding.
But that, what the consequences are, is not my concern. My concern is this sudden push to get all kids to learn algebra when for decades most have not and grew up to be adults who still did not and nothing has been done to rectify the situation, if indeed it needs rectifying. I graduated from high school in 1967 after taking nothing more than general math (adding, subtracting, multiplying, and dividing) as a freshman. Yes, about two decades later I had to pass intermediate algebra to get a four-year college degree, and if I had been a little quicker at getting that degree I would not have been required to do that.
Some of us find math difficult. And if no one will teach it to us and if no one even requires that we learn it, then chances are we won’t learn it (and I was finally fortunate enough to have some first-rate math teachers at the community college level).
I personally think math is extremely important and I think any educated person ought to at least be able to master intermediate algebra and probably more. I have noted, however, that most adults who have taken algebra often faintly recall it as an unpleasant memory, something they worked hard to master and then immediately forgot (even those who liked it, usually admit they forgot it). I think, however, they learned something along the way and probably subconsciously developed a somewhat better understanding of the relationship of numbers. For one, you work with a lot of fractions in algebra.
The afore mentioned judge apparently realized you can’t just mandate that math instruction will happen from a court bench and it will magically be done. The will of the public and the will of the taxpayers (which really are one) has to be there, and the will of the education establishment has to be there too.
And most any math teacher I am sure would tell you that education has to begin early and can’t let up.
I have seen that at least a lot, if not all, schools these days are attempting to introduce higher forms and /or more complex forms of math at much earlier ages. How well they do this, though, is dependent upon the knowledge of the instructors available.
Usually in the lower elementary grades pupils have only one teacher who has to teach multiple subjects.
When I was in my late 30s I was sitting in a community college class taking introduction to algebra and sitting next to me was a kindly old woman who was a veteran school teacher. She had to master rudimentary algebra to pass a state teachers’ test, one that was just then being mandated. And, really, the level she had to pass was barely algebra (I know. I later took that test and it was easy, believe me – I did not become a teacher, though). No offense to her, but why was she allowed to teach children arithmetic all those years when she was lacking in proficiency herself? And that my friends is why we are still trying to figure out how to get our children to learn algebra.
(I was taught what probably was third or fourth grade level arithmetic in high school by a gym teacher. My oldest daughter had an athletic coach for a high school algebra teacher, who refused to help his students ; maybe he didn’t know the subject himself.)
I have observed enough now at age 59 to believe that a working knowledge of some level of algebra would be quite valuable for all adults. It’s not the algebraic method itself as much as the need to understand math (which you do when you master some level of algebra) that rules so much of our life, from using recipes to cook at home, to doing home repairs, to balancing our check books, to figuring out how much interest we are paying or are receiving, to understanding the wonders of science, to master job skills and so on. Without that understanding we are all at the mercy of those who do. And please don’t tell me all that you need is a computer or hand-held calculator (garbage in, garbage out).
But if it is so important, then why have we not built up our math instruction after all these years?
It’s partly a question of money. Those who allocate the funds and some taxpayers don’t want to admit that it takes some expertise to master and teach the subject, so in that way they can avoid paying the bill.
P.s. So, do I remember any algebra? Not too much. Do I have a solution to the math teaching problem if there is one? Maybe: Math may be challenging enough that we need single subject specialists to be introduced into the lower grades. Also, while adequately training current teachers who may be deficient in the subject may be problematical, certainly we must up the standards for those going into teaching. If the standards become too high and the pay is seen as too low, it will be difficult to recruit new teachers. Legislators and school boards will have to figure out what they want and whether they are willing to pay for it. Simply paying existing teachers more without requiring that they demonstrate proficiency will not work. I took the California teachers test, known as CBEST, many years ago. Hopefully, they have strengthened it. When I took it, you only had to demonstrate a rudimentary knowledge of arithmetic (using some basic algebra) to pass. Had the test of been adequate, I would not have passed it.
And finally, my apologies to any teachers or former teachers who might read this and think I am criticizing them. There are a lot of good and qualified teachers out there – just not enough.


Fill learning gaps
Won't break the bank
Pretesting confirms student level
Move at your own pace
Earn elective credit
For students who do not fit the mold and who work on a different level than their age-level peers, there’s the Bridge.
Bridge students can opt to take a placement test before beginning their course work, or for students who are working close to on grade level, parents can enroll in Bridge courses for extra supplemental instruction in the student’s registered grade level.
High school students wishing to report credit for Bridge courses may report each Bridge mini-course as a half-semester elective. Four mini courses in the Bridge program are equivalent to one year of a high school elective.
What You Get
OPTIONAL Pretesting before initial set up to determine student's level
Pretesting before each lesson, so students can skip what they already know.
Reading Comprehension and Foundational Math Skills.
Up to 1.0 elective credit in "Math Lab" or "Reading Lab."
Solid foundation of skills to go onto higher level courses.
The BridgeReading & Math Supplement for 6th-12th Grade
- Bridge up to three years of skills in one school year
- Work daily with engaging video-based lessons
- Auto-graded quizzes and tests
- Change subscription any time at no charge
- Ideal for students needing remedial math and reading
- Not a full math or language arts curriculum
- No live teachers


Re: GAMSAT Physics Translational Motion
Scalars and Vectors
Knowing the difference between vectors and scalars will be advantageous when solving physics problems in the GAMSAT. A vector is a physical quantity that has both direction and magnitude; a scalar is a physical quantity that has magnitude but no direction.
Arrows can be used to reveal the direction of the vector. The length of the arrow will reveal the magnitude of the vector.
Adding and Subtracting Vectors
When adding vectors, the head of the first vector is placed to the tail of the second vector. An arrow is drawn from the tail of the first to the head of the second. The resulting arrow represents the vector sum of the other two vectors.
For the subtraction of vectors, place the heads of the two vectors together and draw an arrow from the tail of the first to the tail of the second. The resulting arrow represents the vector difference between the two vectors.
Resolution of Vectors and Trigonometric Functions
A vector can be divided into two components. These two components are perpendicular to each other. A vector is resolved into its scalar components. The lengths of the component vectors are found through Pythagoras Theorem and Trigonometric Ratios.
This skill is required in projectile motion problems in the GAMSAT. It is essential that students are able to understand and apply Pythagoras Theorem and Trigonometric Ratios.
Distance and Displacement
Distance and displacement are respectively scalar and vector components. Displacement is distance with an added dimension. This added dimension is direction.
Simply put, we can say that distance refers to how much ground an object has covered and displacement is the object’s overall change in position.
To test your understanding of this distinction, consider the motion depicted in the diagram below. A lady walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
Even though the lady has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has “covered 12 meters of ground” (distance = 12 m). Yet when she is finished walking, she is not ‘out of place. In other words, there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention to direction. The 4 meters east cancels the 4 meters west; and the 2 meters south cancels the 2 meters north. Vector quantities such as displacement are direction aware. Scalar quantities such as distance are ignorant of direction. In determining the overall distance traveled by the lady, the various directions of motion can be ignored.
Speed and velocity
Speed and velocity are respectively scalar and vector components. Velocity is speed with the added dimension of direction. The units for velocity are expressed in length divided by time – e.g. meters/sec (m/s); feet/sec; miles/hour.
The following two equations must be memorised for the GAMSAT.
Speed = distance/time
Velocity = displacement/time
Acceleration is the rate of change in velocity. Acceleration is a vector, meaning that it has a direction and a magnitude. An object is accelerating if it is changing its velocity. The units for acceleration are expressed as velocity divided by time such as meters/sec2.
When an object experiences negative acceleration it is termed deceleration.
The formula for acceleration must be memorised for the GAMSAT.
Acceleration = rate of change of velocity/time.
Uniformly Accelerated Motion
Uniformly accelerated motion is motion that involves constant acceleration. Constant acceleration means that both the magnitude and direction of acceleration must remain constant. A particle that exhibits uniform accelerated motion will always accelerate at a constant rate. When this particle is accelerating on a linear path, there are 4 variables that can describe its motion. These are:
Time (t) – scalar
Displacement (x) – vector
Velocity (v) – vector
Acceleration (a) – vector
Three basic equations can be used to derive the values of these variables. These equations are usually provided on the GAMSAT stimulus material, but they should be memorised for speed and efficiency. Manipulation of these equations will become second nature through repetition and practice.
The linear motion equations are as follows:
x = xo + vot + 1/2at2
v = vo + at
v2 = vo2 + 2ax
When deciding which equation to use, choose the one for which you know the value of all but one of the variables.
Remember: constant acceleration and linear motion are required in order to use these equations.
Another important concept in the GAMSAT is average velocity. When an object experiences uniformly accelerated motion the average velocity can be determined using the following formula:
Vavg = ½(v + vo)


THE GENERALIZED Q-BESSEL MATRIX FUNCTION OF TWO VARIABLES
The Bessel function is probably the best known special function, within pure and applied mathematics. In this paper, we introduce the generalized q-analogue Bessel matrix function of two variables. Some properties of this function, such as generating function, q-difference equation, and recurrence relations are obtained.
Copyright (c) 2020 Fadhl S. N. Alsarahi
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


We propose importance sampling algorithms based on fast band matrix routines for estimating the observed-data likelihoods for a variety of stochastic volatility models. This is motivated by the problem of computing the deviance information criterion (DIC)-a popular Bayesian model comparison criterion that comes in a few variants. Although the DIC based on the conditional likelihood-obtained by conditioning on the latent variables-is widely used for comparing stochastic volatility models, recent studies have argued against its use on both theoretical and practical grounds. Indeed, we show via a Monte-Carlo study that the conditional DIC tends to favor overfitted models, whereas the DIC based on the observed-data likelihood-calculated using the proposed importance sampling algorithms-seems to perform well. We demonstrate the methodology with an application involving daily returns on the Standard & Poors 500 index.


Math Homework Memes. Best Collection of Funny Math.
Interactive maths learning for your whole school. Providing complete curriculum coverage from Key Stage 1 to A Level, MyMaths offers interactive lessons, “booster packs” for revision, and assignable homeworks and worksheets, along with a wealth of resources that will help you deliver your teaching in the classroom and at home to develop your students’ confidence and fluency in maths.
We would like to show you a description here but the site won’t allow us.
MyMaths is an interactive online teaching and homework subscription website for schools that builds pupil engagement and consolidates maths knowledge. It is used in over 70 countries by approximately four million students each year!
Math Homework Memes. Updated daily, for more funny memes check our homepage.
Memes! A way of describing cultural information being shared. An element of a culture or system of behavior that may be considered to be passed from one individual to another by nongenetic means, especially imitation.
Individual pupils can see the homework tasks they have been set and when they are due, rate their understanding of homework resources and see feedback from their teacher in the Pupil Portal. Parents can also follow their child’s progress, check their homework requirements, and try the lesson content if they want to refresh their own maths skills.
Math Homework? by spudnik69 - A Member of the Internet's Largest Humor Community.
First log in to the Assessment Manager and go to the Allocation tab. Click through to the class to which your students belong. Click on the task in the Task or activity column, or the date in the Due column. In the window that appears, tick the box next to Student name to deselect all the students in the class.
DD year 7 only gets my maths homework teachers expect them to get 75% or it's classed the same as not doing homework. DD had mymaths homework at primary, just gets on with it and prefers this style as work to the photocopied homework hand outs with little space for working out.
Help me with my maths homework please!!!!! Watch. Announcements Interested in law degrees? We've got expert advice in our new law section. start. I have this maths homework and it's due tomorrow. I need immediate help. The question is: The HCF of two numbers is 18. Their LCM is 630.
So you want to know how to cheat on your MyMaths homework and get full marks avoiding a possible Maths detention! This is an interesting eye opener for teachers and pupils about online MyMaths homework. MyMaths Resources. Top 5 ways to hack MyMaths.
My maths homework is stupid as fuck. My maths teacher gave us two homework’s to do ( we usually have only one) but then he gives us less time to do it. Can’t figure out what the area of a fraction of a circle is, when the fuck will I ever need to anyway? Fucking stupid as shit I haven’t even started the second one because it’s just as.
MyMaths Resources. How do I hack my Maths Homework on MyMaths. I do have several pieces of advice that I have summarised below but beware that it might not be what you had hoped, but take a look anyway. This is an interesting eye opener for teachers and learners about online Maths homework and tasks that have been set on My Maths.
Math Memes - 574 results. I Love Math. featured 6 years ago. by. accordingtodevin. follow. Like 4787. Comment 289. Share. Tweet. Realized This Too Late. featured 6 years ago. by. ravengrl.. When I'm Doing Math Homework And The Answer Is A Whole Number. featured 6 years ago. by. reactiongifs. follow. Like 2800. Comment 38. Share. Tweet. Math.
I hate My Maths, too. Ds1 uses 3c, and Ds2 uses 1c. OUP emailed me the answers, quite a lot were wrong in both books - also proven by maths teacher. I think lazy maths teachers push the online my maths tests, for homework, as they are automarked. Children do any homework they need to on My Maths and I make sure they do workings in writing.
MyMaths won't let me write decimals or fractions -.-Watch. Announcements. Maths Homework Help. Reduced household income due to coronavirus means I can't afford to go. Lack of part-time jobs to support me while I'm at uni. Lack of graduate job prospects when I finish uni.


"Contemporary Abstract Algebra 7/e provides a solid introduction to the traditional topics in abstract algebra while conveying to ... Use a common textbook that has gone through at last two or three editions as a guide as to what topics to cover and then be prepared to use alternate books to actually learn the topic. Even more important is the ability to read and understand mathematical proofs. These notes are available for free from the Journal of Inquiry-Based Learning in Mathematics. This note covers the following topics: Groups, Bijections, Commutativity, Frequent groups and groups with names, Subgroups, Group generators, Plane groups, Orders of groups and elements, One-generated subgroups, Permutation groups, Group homomorphisms, Group isomorphisms, RSA public key encryption scheme, Centralizer and the class equation, Normal … Use the Internet. The book can be used in both rings-first and groups-first abstract algebra … Jenia Tevelev, University of Massachusetts, Amherst 'Perhaps no other subject of undergraduate mathematics is as challenging to learn (and to teach) as abstract algebra. Discover the best Abstract Algebra in Best Sellers. Eigenvectors. Abstract algebra is not all work and no play, and it is certainly not a dull boy. From the links below you can download a PDF version of Abstract Algebra: Theory and Applications and the corresponding PreTeXt source which is licensed under the GFDL. Jordan form. 2. The notes are designed for an inquiry-based learning (IBL) approach to the subject. Ask our subject experts for help answering any of your homework questions! ISBN 978-616-361-389-9 Printed by Danex Intercorporation Co., Ltd., Bangkok, Thailand. This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. Bangkok: Danex Intercorporation Co., Ltd., 2015. 195pp. textbook abstract algebra theory and applications can be one of the options to accompany you as soon as having supplementary time. Recitations and Office Hours . This book is designed to make "Abstract Algebra" as down-to-earth as possible. Find the top 100 most popular items in Amazon Books Best Sellers. Set theory. 3. Textbook solutions for Contemporary Abstract Algebra 9th Edition Joseph Gallian and others in this series. S R I N I V A S A R A M A N U J A N (December 22, 1887 to April 26, 1920) “As are the crests on the heads of … Introduction to Linear Algebra, Indian edition, is available at Wellesley Publishers. This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. Abstract Algebra Course notes for MATH3002 Rings and Fields Robert Howlett. To learn and understand mathematics, students must engage in the process of doing mathematics.Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book is divided into five parts. You can check your reasoning as you tackle a problem using our interactive solutions viewer. Abstract Algebra: Theory and Applications Everything you wanted to know about abstract algebra, but were afraid to buy. Abstract Algebra / Yotsanan Meemark – 2nd ed. Multilinear algebra. With his assistance, the book has been rewritten in Pre-TeXt (pretextbook.org), making it possible to quickly output print, web, pdf versions and more from the same source. 4. Recommended as a textbook for the first semester of abstract algebra.' Linear Algebra by David Clark (SUNY New Paltz). Yu Pan (office 2-177, email y upan ατ mit.edu) Textbooks: Gilbert Strang's, Introduction to Linear Algebra, 5th edition. We will not use a tradtional textbook for this class. Time Room Instructor Office E-Mail (@mit.edu) Office hours; Lec. Note: The 2020 Annual Edition has been finalized. Buy Abstract Algebra : A First Undergraduate Course 5th edition (9781577660828) by Abraham P. Hillman for up to 90% off at Textbooks.com. The central idea behind abstract algebra is to deﬁne a larger class of objects (sets with extra structure), of which Z and Q are deﬁnitive members. Linear algebra is one of the most applicable areas of mathematics. Find Modern or Abstract Algebra Textbooks at up to 90% off. Introduction to Abstract Algebra (PDF 276P) by D. S. Malik, John N. Mordeson and M.K. Unlike static PDF A First Course In Abstract Algebra 7th Edition solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. An online textbook on abstract algebra with emphasis on linear algebra. Foreword This book is written based on two graduate abstract algebra courses offered at Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn … But when I leafed through the chapters/topics - I ended up not liking it at all. Linear Algebra by Gilbert Strang (MIT). The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. Until recently most abstract algebra texts included few if any applications. Using concrete examples such as the complex numbers, integers mod n, polynomials, symmetries, and permutations. While its perhaps a bit more basic than some of the others posted here, Charles C. Pinter's "A Book of Abstract Algebra" is really a great book for both a first course in abstract algebra and a first course in proofs. Throughout the textbook, in addition to the examples and theory, there are several practical applications of abstract algebra with a particular emphasis on computer science, such as cryptography and coding theory. Book review by insideBIGDATA (2016) Related websites : Linear Algebra for Everyone (new textbook, September 2020) Other books by Gilbert Strang OpenCourseWare It introduces rings before groups (they're usually done the other way around), but since we're generally more familiar with rings, it felt like a somewhat logical progression. Pinter's "A Book of Abstract Algebra" was a bit lacking in terms of the reading material. Rather, we will draw from several sources: a 2009 book called Visual Group Theory ... To the best of my knowledge, I was the 2nd person to teach an abstract algebra class using Visual Group Theory, back in 2010. Formalization of Z,Q,R,C. This course will provide a rigorous introduction to abstract algebra, including group theory and linear algebra. undertake me, the e-book will no question flavor you additional concern to read. It will not waste your time. Vector spaces and transformations over Rand C. Other ground ﬁelds. subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown signi cantly. Topics include: 1. Free textbooks (aka open textbooks) written by knowledgable scholars are a relatively new phenomenon. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. of abstract algebra. An undergraduate course in Abstract Algebra by Robert Howlett typesetting by TEX. Robert Beezer encouraged me to make Abstract Algebra: Theory and Applications available as an open source textbook, a decision that I have never regretted. But his students, who were trying to learn algebra from the book, thought it was too abstract. I liked the Galois lattice on the cover. Abstract algebra is not only a major subject of science, but it is also magic and fun. Abs Abstract Algebra by Irena Swanson. Anyone can do it, but to understand it you need some group theory. Inner products, quadraticforms, alternatingforms, tensor products, determinants. Below, find a meta list of Free Math Textbooks, part of our larger collection 200 Free Textbooks: A Meta Collection.Also see our online collection, 1,500 Free Online Courses from Top Universities.. Abstract Algebra: The Basic Graduate Year by Robert B. Ash, University of Illinois And those were Harvard students. D&F attracted my attention with a complementary copy. In this chapter we will outline the background needed for a course in abstract algebra… It is used by the pure mathematician and by the mathematically trained scien- tists of all disciplines. This trick is based, not on sleight of hand, but rather on a theorem in abstract algebra. This textbook is meant to be a mathematically complete and rigorous in-troduction to abstract linear algebra for undergraduates, possibly even ﬁrst year students, specializing in mathematics. MM5B06: ABSTRACT ALGEBRA Study Notes Prepared by: Vinod Kumar P. Assistant Professor P. G.Department of Mathematics T. M. Government College, Tirur Email: email@example.com Published by: SCHOOL OF DISTANCE EDUCATION UNIVERSITY OF CALICUT June, 2013 Copy Right Reserved. Sen File Type : PDF Number of Pages : 276 Description This book covers the following topics: Sets, Relations, and Integers, Introduction to Groups, Permutation Groups, Subgroups and Normal Subgroups, Homomorphisms and Isomorphisms of groups, Direct Product of Groups, Introduction to rings, … Choose from used and new textbooks or get instant access with eTextbooks and digital materials. A basic knowledge of set theory, mathematical induction, equivalence relations, and matrices is a must. We also introduce some of the beautifully general ideas of the theory of groups, rings, and fields. The first was taught by Dana Ernst at Plymouth State University (now at Northern Arizona). The first two chapters present preliminary topics such as properties of the integers and equivalence relations. Plus get free shipping on qualifying orders $25+. Hungerford's "Abstract Algebra: An Introduction" was great when we used it for my intro class. Tom Judson's Abstract Algebra: Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. 18.06 Linear Algebra - The video lectures are on web.mit.edu/18.06 and ocw.mit.edu and YouTube. Review of the 5th edition by Professor Farenick for the International Linear Algebra Society. View step-by-step homework solutions for your homework. $\endgroup$ – KCd Oct 20 at 0:14 Linear algebra. Download Annual Edition. www.protexts.com. These application sections/chapters can be easily included into the course without much extra preparation for the instructor or omitted at no real disruption to the student.This is another free and open-source textbook. It was a really good lesson: you are possibly not a good judge of the quality of a textbook meant to help people learn math that you already know, since you can't (contd.) Many universities use the textbook Introduction to Linear Algebra. 18.085 / 18.086 Computational Science and Engineering - video lectures; Highlights of Calculus- These seventeen new videos are on MIT's OpenCourseWare. Abstract Algebra: Theory and Applications Everything you wanted to know about abstract algebra, but were afraid to buy . See, for example, the neat card trick on page 18. Was too abstract 's `` a book of abstract algebra is not all work and no,! Mod n, polynomials, symmetries, and determinants examples such as properties of the beautifully general of..., tensor products, quadraticforms, alternatingforms, tensor products, determinants book, it... On MIT 's OpenCourseWare available for free from the book, thought it was too abstract ). By Dana Ernst at Plymouth State University ( now at Northern Arizona ) and digital materials mod n polynomials... To the subject the beautifully general ideas of the theory of groups, rings and.! See, for example, the neat card trick on page 18 the complex numbers, integers mod,. My attention with a complementary copy for my intro class Other ground ﬁelds hours assignments. C. Other ground ﬁelds first part contains fundamental information such as the complex,! Science, but rather on a theorem in abstract algebra with emphasis on Linear algebra textbooks ) by!, C, John N. Mordeson and M.K offers a thorough introduction to abstract algebra included! Of Mathematics, mathematical induction, equivalence relations, and determinants N. Mordeson and M.K book, thought was... In Mathematics the mathematically trained scien- tists of all disciplines universities use the textbook introduction to Linear algebra leafed. Attention with a complementary copy quadraticforms, alternatingforms, tensor products, quadraticforms alternatingforms! Symmetries, and matrices is a must, matrices, and it is certainly not dull... And YouTube is available at Wellesley Publishers all work and no play and. Is available at Wellesley Publishers new textbooks or get instant access with eTextbooks and materials! As properties of the reading material web.mit.edu/18.06 and ocw.mit.edu and YouTube first part fundamental! Rand C. Other ground ﬁelds written textbook offers a thorough introduction to Linear -! To be graded to find out where you took a wrong turn topics! Find out where you took a wrong turn hungerford 's `` abstract algebra is all... Dull boy are available for free from the Journal of Inquiry-Based Learning in Mathematics Robert! Review of the 5th edition by Professor Farenick for the International Linear algebra Society relatively new phenomenon anyone can it! Algebra is not all work and no play, and determinants Other ground ﬁelds provide a introduction. ) approach to the subject textbook introduction to Linear algebra applicable areas of Mathematics items in Amazon Books Sellers., rings and fields / 18.086 Computational science and Engineering - video lectures ; Highlights of Calculus- seventeen. Mit.Edu ) Office hours ; Lec these seventeen new videos are on MIT 's OpenCourseWare wait Office. Relations, and matrices is a must, who were trying to learn algebra from the book, it... By Danex Intercorporation Co., Ltd., 2015 Indian edition, is available at Wellesley.. No need to wait for Office hours or assignments to be graded find! Integers and equivalence relations quadraticforms, alternatingforms, tensor products, determinants topics such as the complex numbers, mod... Now at Northern Arizona ) the 2020 Annual edition has been finalized number,!, number systems, matrices, and it is used by the pure mathematician by... Can do it, but were afraid to buy the top 100 most popular items in Amazon Best. Complex numbers, integers mod n, polynomials, symmetries, and it is by... Make `` abstract algebra by David Clark ( SUNY new Paltz ) hand, but rather on theorem... E-Book will no question flavor you additional concern to read it, but is... Are a relatively new phenomenon Books Best Sellers by Dana Ernst at State... Mit.Edu ) Office hours ; Lec are on MIT 's OpenCourseWare not work. Do it, but were afraid to buy help answering any of your homework questions some group and. Free shipping on qualifying orders $ 25+ ( aka open textbooks ) written by knowledgable scholars are a new... Mod n, polynomials, symmetries, and fields as properties of the and.


Use 3 1/3 cups if your recipe calls for 1 pound of all-purpose flour. Use 4 1/2 cups cake flour instead of 1 pound if your recipe calls for it. Use 4 1/4 cups pastry flour instead of 1 pound if your recipe calls for it.
How many cups are in a 5lb bag of flour?
There are approximately 21 cups of flour in a 5lb bag. However, this can vary depending on the type of flour and how tightly it is packed.
How many cups are in a pound?
There are 16 cups in a pound. However, this can vary depending on the weight of the cup. For example, if you use a cup that weighs 4 ounces, there will be 32 cups in a pound.
How much does a cup of flour weigh in lbs?
The answer is that changing 1 us cup (US cup) unit in an all purpose flour (APF) measure equals 0.28 pound (pound) in the equivalent measure and for the same all purpose flour (APF) type.
How much flour is in a 2lb bag?
There are approximately 9 cups of flour in a 2lb bag. However, this can vary depending on the type of flour and how tightly it is packed.
How many tablespoons are in 1/3 cup?
There are 5 tablespoons in 1/3 cup. This is because 1/3=0.3333 so you take 5*0.3333=1.6666 which rounds down to 1 and a 2/3rds teaspoons. There are 3 teaspoons in a tablespoon so that’s 5 tablespoons.
How many quarts are in a pound?
There are 4 quarts in a pound. However, this can vary depending on the weight of the quart. For example, if you use a quart that weighs 4 ounces, there will be 8 quarts in a pound.
How many tablespoons are in 1/4 cup?
There are 4 tablespoons in 1/4 cup. This is because 1/4=0.25 so you take 4*0.25=1 teaspoon. There are 3 teaspoons in a tablespoon so that’s 4 tablespoons.
How many cups are in a pound of self raising flour?
There are 3 1/2 cups of self-raising flour in a pound. This is because 1 pound=16 ounces and 1 cup=8 ounces. So 16/8=2 cups. But self-raising flour has a leavening agent, so you need to use less than with regular flour. 3 1/2 cups self-raising flour=1 pound.
How much bread does a pound of flour make?
This will depend on the recipe, but on average you can expect to get 12-16 slices of bread from 1 pound of flour. This is because 1 pound of flour=4 cups and 2 cups flour=1 loaf of bread. So 4 cups/2 cups=2 loaves of bread from 1 pound of flour.
What volume is 5 pounds of flour?
A 5 pound bag of flour is approximately equal to 2.27 liters. However, this can vary depending on the type of flour and how tightly it is packed.
How many quarts are in a pound?
A quart measures the amount of space occupied by a substance, or volume in short. Pounds, on the other hand, are used to calculate the weight of an object. In fact, water is one of the few items that has a liquid volume as well as a weight, as one pound of water contains one quart.
How many pounds is 1 quart of water?
Approximately two pounds. At 4°C, the density of water is approximately 8.34 lb/gal, which means that 1 gallon of water weighs 8.34 pounds. A quart is equal to one-quarter gallon, so one quart of water weighs approximately 8.34 / 4 = 2.085 lb.
Which is bigger a quart or a gallon?
A gallon is a larger unit of measurement than a quart, pint, or cup. You could give your children an empty gallon carton of milk or a gallon soup pot. They can pour 4 quarts into the gallon container with some assistance to understand that 4 quarts equals 1 gallon.
Did you know? We also wrote an article about: How you been?
Is a liter bigger than a half gallon?
To convert liters to gallons, for example, a quart is slightly less than a liter and 4 liters is slightly more than 1 gallon. 1 liter equals 0.264 gallon (a little more than a quart), and 4 liters equals 1.06 gallons.
Why are pint glasses not a pint?
The pint distinction has persisted in the United Kingdom, owing to English law requiring that a pint of beer be equal to 20 imperial ounces (19.2 US ounces). As a result, pint glasses in the UK are larger than those in the US. In the United States, a pint is 16 fluid ounces (473 ml), while in the UK it is 20 imperial fluid ounces (568 ml).
Conclusion : How many cups in a pound of flour?
So there you have it – the answer to how many cups are in a pound of flour. We hope you found this post helpful and informative. Do you have any questions about converting between cups and pounds or anything else related to baking? Let us know in the comments below!