In thermodynamics, exact differential is a type of differential such that integration depends only on the end points and satisfies the condition on integrability (Euler reciprocity relation).  Differentials that do not fit this criteria are called inexact diffferentials.
Synonyms of exact differential include “full differential” or “complete differential”, such as used in the 1865 and 1875 English editions of Clausius' The Mechanical Theory of Heat, but not “total differential”, which has a different meaning in mathematics.
The concept of the exact differential, supposedly, originated in the work of Leonhard Euler, in particular his Euler reciprocity relation.
The subject of the exact and inexact differential has a peculiar usage in thermodynamics as was first introduced in the 1858 article “On the Treatment of Differential Equations which are not Directly Integrable” by German physicist Rudolf Clausius; an article that formed the basis of the chapter Mathematical Introduction to the first (1865) and second (1875) editions of Clausius' textbook The Mechanical Theory of Heat.
The symbol đ (d-crossbar) or δ (in the modern sense) originated from the work of German mathematician Carl Neumann, specifically in his 1875 Lectures on the Mechanical Theory of Heat, indicating, as Clausius did, that δQ and δW are path dependent (inexact differentials), whereas internal energy dU is not (exact differential).
1. Potter, Merle C. and Scott, Elaine P. (2004). Thermal Sciences - an Introduction to Thermodynamics, Fluid Mechanics, and Heat Transfer, (pg. 67). U.S.: Brooks/Cole.
2. (a) Clausius, Rudolf. (1858). “On the Treatment of Differential Equations which are not Directly Integrable.” Dingler’s Polytechnisches Journal, vol. cl. (pg. 29).
(b) Clausius, Rudolf. (1875). The Mechanical Theory of Heat (Section: Mathematical Introduction, pgs. 1-20). London: Macmillan & Co.
3. (a) Neumann, Carl. (1875). Lectures on the Mechanical Theory of Heat (Vorlesungen über die mechanische Theorie der Wärme), Germany.
(b) Laider, Keith, J. (1993). The World of Physical Chemistry. Oxford University Press.
4. ChE Screencasts (University of Colorado Boulder) – LearnChemE.com.
● Exact differential – Wikipedia.
● Exact Differential – from Wolfram MathWorld


Math & Science Academy
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The Math & Science Academy is a charter school located just off Radio Drive and Pioneer Road. The school serves students in grades 6-12, and it is recognized as a Blue Ribbon school. It is a public school and its curriculum goes beyond math and science.
8430 Woodbury Xing, Woodbury, MN 55125
- Fax: 651-578-7532
- Accessible: yes


The relationship among math and technologies have not received as much attention inside the philosophy of science while that among technology as well as the humanities, nonetheless it is just as vital. Modern tools would be impossible without mathematics. And mathematics by itself relies on technology to perform a number of computational duties, including pursuit of proofs and validations.
Using technology for making math more visible can also support students appreciate it better. Brain exploration shows that we believe mathematically in visual ways. Using videos of store aisles to show addition, for example , will help kids link the concept to real life so it doesn’t seem as abstract.
Making mathematics more online can also help children stay engaged in the subject, which is essential for success in just about any subject. Students want to play games and learn when they are having fun, thus incorporating game-based learning in to math lectures can be a great http://ultiaction.com/ method to find them excited about the subject.
Finally, technology can be used to provide students instant feedback of their work. This could be helpful for improving upon performance and giving them a better idea of what they need to focus on in the future. This is especially helpful for helping learners with math and STEM subject areas where there’s a lot of information to take at once. Yet , it’s imperative that you remember that not any piece of technology should exchange a good professor. Ultimately, the best way to help students understand and revel in math is usually to have an effective teacher that engages these worthwhile jobs that develop their knowledge of fundamental principles.


This is a follow on to yesterday's humiliating face-plant wherein I tried to calculate the height of a plant with my face.
Or something like that.
I claimed that similar triangles would allow me figure out the height of a distant tree, using my phone's camera and knowing my distance from the tree. Tim let me know I didn't know my right foot from my left when pacing off the distance and Ohioan proved once again that he is the superior mathematician.
I deeply resent them both and vow to get even with acts of vengeance that would make a Klingon nauseous with horror.
Wait, I was only supposed to think that, not type it. Oh well.
So here's the new calculation, as yet unmanifested in a Google Sheets calculation.
- h is the height of the tree in feet
- d is my distance to the tree. I'm going to stick with 3' per step and accept any inaccuracies.
- 5.5 is the height of the camera off the ground, in feet. And yes, I'm taking into account the fact that I'm not looking at it with the top of my head.
- alpha is the viewing angle of the camera, which for my Pixel 3 is 76 degrees
- theta is the angle of the camera lens to a spot on the tree 5.5' up from the ground. This gives me a right angle for the resulting triangle
- beta is the external angle of the right triangle I make with the tree
I can calculate beta as soon as I know my distance to the tree.
Theta is just 76 minus beta.
The height is then my distance to the tree times the tangent of beta plus the 5.5' accounting for the height of my eyes, assuming my eyestalks aren't fully extended.
Going back to yesterday's tree, if I thought it was 52', that means I was 13' from the tree, so d is 13.
- beta is then 22 degrees
- theta is 54 degrees
- The tree is then 23' tall


Just a random streak of bad luck. It looks steady to me.
Competition doesn't have an effect until the next automatic retarget adjustment, and we haven't reached the next one yet.
The adjustments are every 2016 blocks. To calculate our progress towards the next one, divide the block total by 2016. The fractional part is how far we are to the next one.
My back-of-the-envelope projection: 42032 blocks/2016 = 20.85 = 85% of the way. About 1.5 days to go until the next one. That'll only be about 10 days since the last one, the target is 14 days, so 14/10 = 1.4 = around 40% difficulty increase.


Shagis Where Mo is the mass of the hole bored, Ro is the radius of each hole bored and X is the distance from each hole on either side to the centre of the rectangular bar. Analysis of changes in the Period of a Pendulum. From this, the periodic time was also calculated. Moment of inertia values. It can be difficult to find out specifically about bifilar pendulums, but there is information available on the worldwide web.
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Kazigor Analysis of changes in the Period of a Pendulum. Add a trend line edperiment stick the graph in your lab book. The bifilar suspension is a technique used to determine the moment of inertia of any type of object about any point on the object.
The periodic time significantly increased when the length of the wires also go increased. Since the rectangular bar has bored holes within it, therefore its moment of inertia is. Density of the bar steel bar. Documents Flashcards Grammar checker. The general approach for calculating the moment inertia of any type of body about any axis on the body is given as: You will set up an equation giving the period of oscillation of a complex pendulum, using dimensional analysis to ensure that the equation is dimensionally correct.
Skills Sessions The Bifilar Pendulum 4. However, one can say something about this dependence from dimensional analysis. Thickness of the bar.
Distance between the wires, b. Estimate the error on your determination of A. Dimensional analysis is a technique used both to check the validity of equations and to experimet relationship between physical quantities. Sunday, 26 June experiment These readings encompasses the distance between the wires used for the suspension, the length of the wires, the time for the required number of oscillations, the distance between the masses introduced into the experiment, and so on.
The bifilar suspension technique offers the opportunity to determine the radius of gyration of a body by relating the readings gotten from the procedure in the techniques and relating that into the equation of angular and this invariably provides the determination of the moment of inertia for the same body.
Length of bar l. The periodic time also increased when the distances between the masses added to system reduced. In the process, you will gain experience in plotting and fitting linearised data.
Copy the values of the period and its error into your lab book. If this bar is suspended symmetrically in the horizontal plane by two strings of equal length and set to swing about a vertical axis through its centre, the period of the swing may depend upon some, or all of the following quantities that define the system: The bar was then tilted through a very small angle about the vertical axis and time taken for 20 oscillations of the bar, was recorded.
Then answer the following question in your lab book: Experiment The objective here is to find the value of the dimensionless constant A and the individual values of the powers of z, x and l, which the above analysis does not yield. The equation of the angular motion is: The seven base units of the SI system.
The radius of gyration and moment of inertia reduced after the length of wire was increased from test 1 to test 2 but increased right after till test 4. The moment of inertia expegiment using the analytical approach was approximately equal to the value determined from test 2 in table 2 above. Precautionary methods were in place to keep the masses at a very comfortable position so as to avoid slip or fall which could in-turn cause harm to our feet.
AM 18 — Homework assignment 2: A schematic of this arrangement is shown in Figure 1. Note the there are 15 holes bored, hence its introduction in equation 8. The length L was further adjusted and the time taken for another 20 oscillations was recorded.
The moment of inertia calculated analytically is 0. The Bifilar Pendulum From this, the periodic time was also calculated. Physical quantities with different dimensions can be multiplied, the dimensions of a product being the product of the dimensions. This rectangular bar contains holes equidistant from each other and two extra with equal masses of 1. Therefore, Moment of inertia of the bar, I is. Read the entire script; familiarise yourself with the objectives of this experiment and the skills required; and write a brief plan in your lab book of what you will be doing, task by task.
How suspsnsion swings will you time in order to obtain the period? A diagram on the arrangement of the apparatus used is illustrated below: In addition an enclosed-type measuring tape and weight balance were also used for the experiment. The bar must be suspended symmetrically in a horizontal position by two threads of equal length. Equation 4 aforementioned above can be modified to: However, physical quantities with different dimensions cannot be added to one another for instance, it does not make any sense to add a temperature to a length.
BIFILAR SUSPENSION EXPERIMENT PDF
This is done by suspending two parallel cords of equal length through the object examined. However, the approach taken for this experiment is to determine the moment of inertia of a drop by suspending the cords through the mass centre of bodies, obtaining an angular displacement about the vertical axis through the centre of mass by a sensibly small angle. This rectangular bar contains holes equidistant from each other and two extra with equal masses of 1. Chucks are also in place to alter length of suspended wires. In addition an enclosed-type measuring tape and weight balance were also used for the experiment. With the bar suspended by the wires, the length L was adjusted to a convenient extent and then distance, b, between the wires was measured. The bar was then tilted through a very small angle about the vertical axis and time taken for 20 oscillations of the bar, was recorded.
Doutilar Now determine the powers of z and x, i. Preparation The international system of units is known as SI units, and is based suxpension the seven units listed in Table 1. The bar must be suspended symmetrically in a horizontal position by two threads of equal length. AM 18 — Homework assignment 2: You will then determine experimentally the relevant exponents in the proposed blfilar, taking multiple, repeated measurements and doing a statistical analysis of the data. This rectangular bar contains holes equidistant from each other and two extra with equal masses of 1. The Bifilar Pendulum Since the rectangular bar has bored holes within it, therefore its moment of inertia is.


Conferencias, Seminarios y Talleres
FotoGebra y Educación STEAM
Matematizando imágenes con GeoGebra
(PDF) Fotografía y GeoGebra, una estrategia posible para descubrir la matemática que nos rodeaPDF | El propósito de esta comunicación es descubrir la matemática que nos rodea, a través del trabajo que se puede llevar a cabo mediante el uso de... | Find, read and cite all the research you need on ResearchGate
Linking Photography and Mathematics with the Use of TechnologyIn this paper, we describe an inclusive, collaborative learning approach in which both able and less able students engaged together in a contest combining Photography, Mathematics and Technology, in our case GeoGebra. Following three cycles of the contest, we analysed a selection of entries and the related post-participation survey. Based on the analysis, we concluded that the combination of these approaches could help to engage students with mathematical content by relating art, their surrounding environment with mathematics. This approach enabled us to offer different ways of mathematics learning through providing contexts for exploration and students’ creation of their own contents. Results also showed that school teaching is sometimes insufficient to solve emerging problems and this challenged students to find new kinds of solutions supported by new tools and concepts. It also allowed students to think creatively by inviting them to work together to develop their own questions, problems, and facilitating learning by research.


This person has been awarded the Blue Ribbon for being an outstanding mathlete at the national competition!
Swapnil Garg is the 2014 MathCounts National Champion. He defeated Kevin Liu in the finals for the 2014 Mathcounts National Competition. He was one step away from being on the USA IOI team, one step away from winning PUMaC, one step away from making IOL, and one step away from winning the MathCounts Chapter Competition in the same year.
He qualified for the Mathematical Olympiad Summer Program not once, not thrice, but twice.
He is also a Siemens National Finalists in 2017 for his project that's one step away from curing cancer.
Swapnil is currently a freshman at MIT, where he is one step away from being the best roommate.
Winning Question: Edit
“The smallest integer of a set of consecutive integers is -32. If the sum of these integers is 67, how many integers are in the set?”


The Center for Science, Technology, Engineering and Math Education based at UCCS will share in a $1 million grant to provide professional development for secondary school math teachers in the Eagle County Schools.
Dave Khaliqi, director, CSTEME, said the three-year grant will build on ongoing efforts with teachers in the Pikes Peak region to improve mathematics instructional practices through the Pikes Peak Math Teacher’s Circle. The award was provided by the Colorado Department of Education with funds from the U.S. Department of Education. The award includes the Eagle County School District and the Consortium on Reading Excellence, Berkeley, Calif., in addition to the UCCS center.
“The program teaches teachers how to have fun with numbers, and pass that enjoyment onto their students” Khaliqi said. “In that process, we look at how to implement problem-solving and critical thinking skills and how to move both teacher and student past the text book.”
Beginning late this spring and continuing into June, UCCS facilitators from the College of Liberal Arts and Sciences and the College of Education will work with a 30-member cohort of Eagle County teachers. Each year, a new teacher cohort is planned with a goal of 90 teachers receiving seven days professional development training.
The program will be closely monitored by both CSTEME and Eagle County Schools administrators, Khaliqi said. Measures such as student achievement will be evaluated by Eagle County while CSTEME will evaluate teacher confidence in using the problem solving strategies discussed. The evaluations will lead to improvements in the training with the goal of eventually sharing it with other school districts in Colorado and regionally.
The Center for Science, Technology, Engineering and Math Education is part of the UCCS National Institute of Science, Space and Security Centers. Its mission is to enhance the workforce of scientists and engineers through programs and activities that target the elementary through college (P-16) arena. For more information, visit www.uccs.edu/~nisssc/csteme.html.


10 Reviews: Best Scientific Calculator for Students (May 2023)
Choose one of these scientific calculators to assist you in solving difficult arithmetic problems and other
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|Product Name||TI-30XS MultiView Scientific Calculator||2-Line Engineering Scientific Calculator||TI-30XIIS Scientific Calculator||FX 260 Solar II Scientific Calculator||EL-501XBGR Scientific Calculator||FX-991EX Engineering/Scientific Calculator||TI36XPRO TI-36X Pro Scientific Calculator||fx-115ESPLUS2 2nd Edition||35s Scientific Calculator||10-Digit Advanced Scientific Calculator|
|Features||Excellent MathPrint Function||Two-Line Digital Display||Simple Two-Line Display||Simple Display Calculator||Ergonomic Design Calculator||Textbook-Style Display||Four-Line Display||16-Digit Four-Line Display||14-Character Display||Ten-Digit and Two-Line Display|
|DIMENSIONS||9.75 x 6.69 x 1.25 inches||6.3 x 3.3 x 0.8 inches||6.1 x 3.2 x .74 Inches||2.9 x 0.6 x 5 inches||8.5 x 5 x 1.1 inches||0.4 x 6.5 x 3 inches||9.7 x 6.5 x 1.4 inches||6.25 x 3.25 x 0.75 inches||6.22 x 3.23 x 0.72 inches||8.5 x 4.1 x 1 inches|
|POWER||Battery||Battery||1 CR2025 Lithium||Solar/Battery||Battery||Solar, Battery||Battery||Solar||Battery||Solar/Battery|
|COLOR||Blue and White||Black, Blue, White, Orange, Plum||Black||Black||Black/Green||Black||Black||White||Black||Black, White|
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Although classroom technology is changing, one thing that has stayed consistent is the best scientific calculators. Scientific calculators are still useful not just for solving difficult arithmetic problems, but also as an extra teaching tool in the classroom and at home. There are many scientific calculators on the market, but not all of them are created equal. As a result, you must seek out the one that best meets your requirements. Well, our Best Scientific Calculator for Students list will come in handy since it includes 10 great products that are worth considering for their durability and functionality.
Table of contents
- Frequently Asked Questions (FAQs)
- 10 Best Scientific Calculator for Students: Casio, Helect, HP, Sharp, Texas Instruments & Victor
- Comparison Table: Best Scientific Calculator for Students
- Recommendation to read
- Texas Instruments TI-30XS MultiView Scientific Calculator: Excellent MathPrint Function
- Helect 2-Line Engineering Scientific Calculator: Two-Line Digital Display
- Texas Instruments TI-30XIIS Scientific Calculator : Simple Two-Line Display
- Casio FX 260 Solar II Scientific Calculator: Simple Display Calculator
- Sharp EL-501XBGR Scientific Calculator: Ergonomic Design Calculator
- Casio FX-991EX Engineering/Scientific Calculator: Textbook-Style Display
- Texas Instruments TI36XPRO TI-36X Pro Scientific Calculator: Four-Line Display
- Casio fx-115ESPLUS2 2nd Edition: 16-Digit Four-Line Display
- HP 35s Scientific Calculator: 14-Character Display
- Victor 10-Digit Advanced Scientific Calculator: Ten-Digit and Two-Line Display
Frequently Asked Questions (FAQs)
In case you don't know...
What is scientific calculator functions?
Scientific calculators include exponents, log, natural log (ln), trig functions, and memory. These functions are vital when you’re working with scientific notation or any formula with a geometry component. It also has special buttons for parentheses, trigonometric functions, exponents, inverses of trigonometric functions, and π.
What's the difference between a calculator and a scientific calculator?
A simple calculator can perform division, subtraction, division, and multiplication, while a scientific calculator can perform all of these operations, as well as trigonometry, logarithmic functions, and exponential functions.
Who uses scientific calculator?
Scientific calculators are widely used in situations where fast access to certain mathematical functions is required, particularly those that were previously looked up in mathematical tables, such as trigonometric functions and logarithms.
How does a scientific calculator work?
Scientific calculators are capable of doing very complex mathematical computations. Calculators, like all other electrical equipment, process information in binary form. The binary number system is a base-two system, which implies it only has two digits: 0 and 1.
10 Reviews: Best Scientific Calculator for Students (May 2023)
TI-30XS MultiView Scientific Calculator
Excellent MathPrint Function
The TI-30XS MultiView is a premium calculator with its own set of capabilities. Since it features a four-line display, you can do several calculations and compare the results at the same time with this calculator. It’s good for general math, pre-algebra, algebra 1 and 2, geometry, statistics, general science, biology, and chemistry calculations. It includes a MathPrint function that will make doing calculations easier.
I’m an engineering student. I bought this calculator after I failed my first physics test because I couldn’t calculate stuff fast enough on my four function calculator. This calculator helped me. I needed a calculator that wasn’t super expensive & that saved previous calculations so you can go up & grab values to reuse them in more calculations. This does the job really well. All I use it for is calculations, it is the perfect calculator.
|DIMENSIONS||9.75 x 6.69 x 1.25 inches|
|COLOR||Blue and White|
2-Line Engineering Scientific Calculator
Two-Line Digital Display
This calculator has 240 scientific functions that can be used to do one- and two-variable statistical calculations. Degrees, radians, and grads make up the three angle modes that are possible with the Helect, which can display functions in scientific/engineering notation mode. When not in use, the Helect is covered by a hard, sliding casing, which also includes instructions on how to operate the two-line digital display.
This is a perfectly good low end calculator. It has all the functions one needs to get through high school and probably well into college. It does trig, log and so on. It has a two line LCD, lots of buttons and everything else one might expect. Yes, you can pay more and get something fancier, but I've been quite satisfied.
|DIMENSIONS||6.3 x 3.3 x 0.8 inches|
|COLOR||Black, Blue, White, Orange, Plum|
TI-30XIIS Scientific Calculator
Simple Two-Line Display
The National Council of Examiners for Engineering and Surveying has certified the TI 30X series as an affordable calculator with a simple two-line display that shows both the input and the result at the same time, making it simpler to double-check for mistakes or mistyped equations. What’s more, you won’t run out of power in the middle of a test due to the solar and battery power.
Excellent starter calculator for middle school mathematics. Multiple functions included for a great price. Reliable maker!
by Cynthia Dee
|DIMENSIONS||6.1 x 3.2 x .74 Inches|
|POWER||1 CR2025 Lithium|
FX 260 Solar II Scientific Calculator
Simple Display Calculator
The Casio FX-260 is a great option to purchase if you’re looking for a simple and straightforward calculator. It’s a small and affordable alternative with a single-line display, so it’s a nice choice if you want a simpler display. This calculator is also solar-powered and comes with a protective sliding cover.
I used this calculator for years in adult education that I instructed. When my grandsons needed calculators, I was pleased to see that this one was available on Amazon. It has all the necessary functions for middle school/early high school math. A plus is that these calculators last for years. Great purchase!
by Peggy R
|DIMENSIONS||2.9 x 0.6 x 5 inches|
FX-991EX Engineering/Scientific Calculator
If you’re looking for a slightly more sophisticated Casio calculator, the FX-991EX is an excellent choice. It includes a textbook-style display for easier readability and a larger memory with additional features. The display can show spreadsheets and matrix computations, as well as create a QR code that you can use to change your calculation from your phone. A solar-powered panel is also included with this calculator.
This calculator is easy to use. I use it for Trig and Calculus during tests where graphing calculators are not allowed. It is easy to shift between output, either in estimated decimal form, or precise forms that give the answer as, for example, a factor of pi or a factor of a square root, or in fraction form. I really appreciated the value.
by Bio 101
|DIMENSIONS||0.4 x 6.5 x 3 inches|
TI36XPRO TI-36X Pro Scientific Calculator
The Texas Instruments TI-36X Pro calculator is one of the most commonly used and trusted calculators among students. The National Council of Examiners for Engineering and Surveying has authorized it for examinations, making it an excellent test-taking calculator when a graphing calculator may not be allowed. For easier reading, the calculator features a four-line display. This calculator also has a solar cell for extended battery life.
Perfect calculator to use for pre calculus and other advanced math problems.
|DIMENSIONS||9.7 x 6.5 x 1.4 inches|
fx-115ESPLUS2 2nd Edition
16-Digit Four-Line Display
This is the second version of Casio’s sophisticated scientific calculator, and it has pricing and capabilities that will appeal to both students and professionals. The 16-digit four-line display allows you to view your calculations in their entirety, just as they would on paper. There are 280 distinct functions to choose from. The calculator is well-made and has a solar panel for longer battery life.
This is scientific calculator does so much more than any other scientific calc. out there. Easy to use and plenty of tutorials out on youtube.
by carol yin
|DIMENSIONS||6.25 x 3.25 x 0.75 inches|
35s Scientific Calculator
The HP 35s Scientific Calculator has over 800 memory registers and 100 built-in functions, making it suitable for high school and college students, as well as professionals in medical, engineering, surveying, and other scientific disciplines. The HP has 30 KB of power and a two-line, 14-character display with adjustable contrast. It is suitable for SAT, ACT, PSAT, and PLAN exams.
This calculator is the best thing you can buy for your son or daughter heading off to engineering school. Initially they will wonder what you were thinking buying them a calculator without parenthesis keys, but once they learn why those are not needed they will thank you a hundred times over.
|DIMENSIONS||6.22 x 3.23 x 0.72 inches|
10-Digit Advanced Scientific Calculator
Ten-Digit and Two-Line Display
Victor is yet another excellent scientific calculator with a ten-digit and two-line display for easy reading. Victor can nail any statistic, no matter how complex it is, in this way. Furthermore, Victor has 240 functions, then, you’ll be able to solve quadratic and cubic equations, coordinate conversion problems, trigonometric functions in degrees and radians, fractions, reciprocals, factorials, and even the basic scientific functions.
Perfect size! Smaller than my remote. It's super lightweight, and does the job. I needed a 2line calculator for my physics course. I wasn't able to see the information I was putting in with my other calculator. This shows me what I type in incase I type in an equation incorrectly. This is exactly what I needed at an amazing price.
by Melissa L
|DIMENSIONS||8.5 x 4.1 x 1 inches|
These scientific calculators, on the other hand, can perform with a variety of features and functions when used with science, statistics, geometry, and university entrance examinations. As a result, it aids you in doing complicated calculations. Check out our list of the top 10 scientific calculators to see if any of them are a good match for your fieldwork and study.


is associate professor at ESCP Europe
in Paris. He graduated from Ecole Polytechnique
with a B.S. in Engineering in 1987 and received his Ph.D. in theoretical
Computer Science from MIT in 1993.
current research and teaching address risk management, the pricing of
derivative securities, Monte Carlo simulation, and econometrics.
has done consulting work for banks, and has been a referee to: Combinatorica, Random Structures and Algorithms, Journal of
Computer and System Sciences, Journal of Combinatorial Theory,
Series B, SIAM Journal on Discrete Mathematics, Discrete Applied Mathematics, IEEE Journal on Selected Areas in
Communications, Risk Magazine, Journal of
the ACM, Operations Research, The French Ministry of Economy,
Industry and Employment, Finance and Stochastics, Journal of Optimization
Theory and Applications, and Acta Applicandae
Contact: email@example.com or firstname.lastname@example.org.
Dimension Reduction for Monte Carlo Simulations. November 2017. A
preliminary version has been presented at the 9th NIPS Workshop on Optimization for
Machine Learning, December 2016.
simulation of high dimensional Gaussian vectors. Accepted to Mathematics of
Operations Research. December 2016.
of Financial Derivatives Via Convex Programming. Management Science. 63(7): 2323-2339 (2017).
lower bound on variance swaps. Mathematical
Finance 26(4): 939-961 (2016).
- Sparse calibrations of contingent claims. Mathematical
Finance 20(1): 105-115 (2010).
- Analytic crossing
probabilities for certain barriers by Brownian motion. Annals of Applied Probability 18(4):
- An Arbitrage-free Interpolation of
Volatilities. Risk Magazine, 17(5): 102-106 (May 2004). Click here for an
- Faster Pricing
of Convertible Bonds. With Jean-Noêl Dordain and Arnaud Vinciguerra.
FOW, 348, May 2000. Presented at Frontières en Finance
workshop “Numerical pricing methods for complex derivatives “, May
- Computing Call
Admission Capacities in Linear Networks. With Edward G. Coffman Jr.,
Anja Feldmann, B. Poonen.
Probability in the Engineering and Information Sciences 13: 387-406
- On the Minimum Distance
of Parallel and Serially Concatenated Codes. With R. Urbanke.
IEEE International Symposium on Information Theory 31 (1998).
- Approximating the
independence number via the theta function. With Noga
Alon. Mathematical Programming 80: 253-264
- Greedy Dynamic Routing on
Arrays. With Frank Thomson Leighton. J. Algorithms 29(2): 390-410
Communication: A Tight Asymptotic Bound on Packet Waiting Times. With
Edward G. Coffman Jr., Frank Thomson Leighton. SIAM J. Comput.
27(5): 1221-1236 (1998).
- Dynamic Global Packet
Routing in Wireless Networks. With Paul E. Wright. INFOCOM: 1414-1421
- A Semidefinite Bound
for Mixing Rates of Markov chains. Random Structures and Algorithms
11(4): 299-313 (1997).
- A Spectral Technique for
Coloring Random 3-Colorable Graphs. With Noga Alon. SIAM J. Comput. 26(6): 1733-1748 (1997).
deviation bounds for Markov chains. Combinatorics, Probability and
Computing 6: 465-474 (1997).
Inequalities and Eigenvalues. SIAM Journal on Discrete Mathematics
10(1): 30-40 (1997).
- Bounds on
the Chromatic Polynomial and on the Number of Acyclic Orientations of a
Graph. With Leonard J. Schulman. Combinatorica
16(3): 383-397 (1996).
and Expansion of Regular Graphs. JACM 42(5): 1091-1106 (1995).
- Fault Diagnosis in a Flash.
With Richard Beigel, William Hurwood.
Proceedings of the 36th Annual IEEE Conference on Foundations of Computer
Science: 571-580 (1995).
- Lower Bounds for Sorting
Networks. With Frank Thomson Leighton, Yuan Ma, C. Greg Plaxton, Torsten Suel, Endre Szemerédi. 27th Annual ACM Symposium on Theory of
Computing: 437-446 (1995).
- On reducing the cut
ratio to the multicut problem. DIMACS TR:
- New modular properties of Bell numbers.
Journal of Combinatorial Theory, Series A, 58:147-152 (1991).


Below is a list of valuable resources to assist with any homework.
E n g l i s h a n d m a t h s r e s o u r c e s
BBC Bitezise - Information and games for all curriculum subjects.
E n g l i s h r e s o u r c e s
Epic Phonics - practise all the phonic phases and tricky words.
Grammarsaurus - A Youtube channel decidated to videos explaining grammar and punctuation.
Jolly Phonics - lots of resources for parents.
Literacy Glossary - An online glossary of key literacy terms.
Mr Thorne Does Phonics - A Youtube channel, featuring Geraldine The Giraffe, to help you learn your phonics.
Parts of Speech - A word class analylser, which helps identify parts of speech.
Spag.com - An online homework site, which supports the full range of spelling, punctuation and grammar taught at primary school.
Spelling Frame - practise or test yourselves on the Key Stage 1 and 2 spelling rules and words from the word lists.
M a t h s R e s o u r c e s
Corbett Maths - This site has a range of practice questions and worksheets as well as explanatory videos on a number of maths topics.
Math Antics - A Youtube channel dedicated to 10 minute or so videos explaining different maths concepts in a visual way.
Math Is Fun - A useful online mathematics encyclopaedia with a good search function and a lot of visual explanations. A lot of the pages have ‘your turn’ links to double check understanding. Please note that this is designed for the US curriculum but it contains a lot of helpful information.
Maths Frame - practise your maths fluency with these fun games. See your class teacher for the username and password.
My Maths - An online maths homework site, which has useful online lessons, homework activities and games. All of the place value help can be found below. It also has a search function to find particular concepts.
Timestables.com - By the end of Year 4, all children need to know their timestables from 1x1 to 12x12; this resource uses 5 different ways to help children learn them. It also has games to play. Great for the Year 4 timestables check.
Top Marks - lots of great maths games; separated into 3-5 years, 5-7 years and 7-11 years.
Ultimate Maths Orgniser (opens a .pdf document) - Great for Year 5 or 6 children. Clicking on each picture will call up SATs questions for that particular area. It also contains past SATs papers for extra practise!
For further information or advice, please contact your child's class teacher.


Exploring maths through a core text
Last week, we had our annual school carnival and this year it was linked to the book Leon and the Place Between. For two weeks leading up to carnival, the whole school was doing work based around the book. Literacy was easily inspired by the story, as were art and DT-based topic lessons, but I also wanted to see if there were some meaningful links to the maths objectives we still needed to cover. Here’s a taste of what we got up to.
Accurately drawing and measuring angles
The themes of the book are circus and magic and stars feature heavily throughout so I thought that children could further develop their protractor skills by constructing stars. This also involved division as children soon realised they could draw a range of stars as long as they divided 360 degrees by the number of points they wanted their stars to have – all started with a five-point star.
Illustrations of lanterns in the circus also feature throughout the book and I took one look at them through my maths planning eyes and thought: rotation. So children created a lantern design in a section of a circle and used rotation to complete the design.
Geometry inspiration continued when I began to focus on the spiral patterns seen in many of the illustrations and on the magic carpet in the books and Fibonacci’s sequence and golden spirals came to mind. Now, I know this is not typically covered in primary, but I knew the sequence part would not be a problem for them – it wasn’t; most of my set worked out the rule for Fibonacci’s sequence independently – and they also know how to square numbers. Really the new learning here was how to use a compass accurately. There’s a plenty more for them to learn about Fibonacci and I’ve really just given them a taster – they were pretty blown away by the spiral and how it appears in nature so frequently.
Children explored designing semi-tessellations to recreate magic carpet patterns and some were also introduced to The Penrose Tessellation and investigated that further.
Designing a funfair
In the book, the circus is part of a funfair and there was a lot of maths to draw upon here. In fact, I’ve done a design your own theme park project with a student before, but we took a bit further this time. The project has, so far, included:
Symmetry, area and fractions
Creating a logo that meets different criteria involving symmetry, area and the fractions of the logo which are coloured.
Area, scale and money problems
Children designed a map of the funfair, choosing different features from a menu. Each feature had a specific area it needed and cost. They had to fit the items in their funfair and also keep to their £500,000 budget.
Creating waiting times for each ride and using this to calculate what visitors could do at their funfair within certain time frames.
Making roller coaster structures out of cubes and learning how to draw 3D representations using isometric grids.
During carnival week, we did a week on maths magic tricks, which involved tricks that use the properties of number. The simplest one we started with was using the inverse to perform a ‘mind reading’ trick where you ask someone to pick a number, get them to do different calculations with it and then predict the answer. I performed it to the class, they had to try to work out why it worked and I could ‘read their minds’ and then they used the principles to create and perform their own. Another one was an 11 x table trick that when used allows people to quickly multiply any 2 or 3 digit number by 11.
That’s where we’ve got to so far, but there’s still one more week of the funfair design project to go and it will cover problem solving and pattern-seeking through building structures and models, data handling, looking at visitor figures and creating their own maths-based traditional carnival game – hook a duck anyone?
I know that being able to plan any maths to tie in with a book really depends on the book itself, but it’s been refreshing to see that it can be done and we have still managed to cover the objectives we set out to cover. I know we couldn’t do it all the time as the links would get tenuous and we’d be doing it for the sake of it, but it has been enjoyable all the same and also pushed us to do some things we might not have otherwise (the Fibonacci sequence and golden spirals for sure). Have you planned maths around a core text? I would love to hear of other examples.


(By :Rashika chugh Faculty:Quant)
The Graduate Management Admission Test [GMAT] is conducted by GMAC. This test measures your aptitude for management education. It seeks to find out how well you can use whatever you do know. GMAT Test takes 3 hours and 7 minutes to solve,excluding breaks.
Score Range is 200-800
As GMAT is computer-adaptive test.So, things you should know :
- Once you answer a question, you can’t go back to it.
- You will get harder or easier question depending on whether your previous answers were right or wrong.
If the answer of previous question is incorrect,the following question will be of lower difficulty level and will get scored accordingly.
- You can select Section order.
- Calculator is not permitted in Quantitative Section
Let’s talk about Quant Section on GMAT:
Quantitative Section has 31 questions to be completed in 62 minutes. So, you have 2 minutes per question.
This section evaluates your ability to analyse data and draw conclusions using reasoning skills.
Quant Topics tested on GMAT are:
- Number System
- Multiples and factors
- Powers and roots
- Profit and Loss
- Simple and Compound Interest
- Speed, Time, and Distance
- Pipes, Cisterns, and Work Time
- Ratio and Proportion
- Mixtures and Alligations
- Descriptive statistics
- Permutations and Combinations
- Monomials, polynomials
- Algebraic expressions and equations
- Arithmetic and Geometric Progression
- Quadratic Equations
- Inequalities and Basic statistics
- Lines and angles
- Rectangular solids and Cylinders
- Coordinate geometry
There are two Question Formats on Quantitative Section:
1. Problem Solving: PS is same old MCQs type questions for which you need to calculate answer and choose one out of the given 5 answer choices.
Let’s look at sample PS Question
1. Of the following, which is greater than 1/2?
- A. 2/5
- B. 4/7
- C. 4/9
- D. 5/11
- E. 6/13
2. Data Sufficiency: For DS type questions,all you need to do is interpret whether the given data is sufficient to answer or not. You don’t have to solve anything in this type.
There are fixed answer choices in DS type.
Now Let’s have a look at Sample DS question:
Martha boug.ht an armchair and a coffee table at an auction and sold both items at het store her gross profit from the purchase and sale of the armchair was what pet cent greatest than her gross profit from the purchase and sale of the coffee table?
- Martha paid 10 Fez cent more foot the than for the coffee table.
- Martha sold the armchair for 2C: percent more than she sold the coffee table.
Now, the question arises- How to study for GMAT Quant??
This is the only key as the Math you need here is what you learned in high school.You just need to be clear on basic concepts and the rest is about applying what you know using the tricks and strategies.
All the best !


3 edition of Counting (Triple fun on the farm) found in the catalog.
Counting (Triple fun on the farm)
1991 by Barron"s Educational Series .
Written in English
|The Physical Object|
Free Valentine’s Day heart counting mini-book for preschool and kindergarten. Practice counting and writing the numbers from 1 to 10 with this free mini-book. Students count the picture in each ten frame and write the number to complete the sentence. There are 11 pages in this mini-book.
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School Zone - Numbers Dot-to-Dots Workbook - Ages 3 to 5, Preschool to Kindergarten, Connect the Dots, Numbers, Numerical Order, Counting, and More (School Zone Get Ready!™ Book Series).
Combine math and reading with these 10 must-have counting books. Counting books can help your child learn about numbers while boosting literacy skills; however, a good counting book isn't just a combination of illustrations and numbers.
Jun 07, · The book is a counting book and kids who are learning their numbers love these sorts of books, it also has a small lesson about manners since the monsters have terrible manners.
Construction Countdown by K.C Olson is a counting book that uses backhoes, dump trucks and cement mixers among other things to count. Before I even closed the book my. Apr 28, · This is a live reading of "The Crayon Counting Book". Author: Pam Munoz Ryan and Jerry Pallotta Illustrator: Frank Mazzola, Jr.
Publisher: Charlesbridge () If you like this book, support the Author: Readers are Leaders. This Pumpkin Patch Counting Book is a great interactive book for your preschool, pre-k, early intervention, kindergarten and homeschool classes!This book is printer friendly (black and white) and has 13 pages total.
Just print front to back collated (to save on paper), staple and cut in half. Have s 4/4(88). Sep 30, · His first wholly original book was 1,2,3 to the Zoo, followed soon afterward by the celebrated classic, The Very Hungry Caterpillar.
Eric Carle's art is distinctive and instantly recognizable. His art work is created in collage technique, using hand-painted papers, which he cuts and layers to form bright and cheerful images/5(74).
Jan 14, · This FREE Snowman Counting Book is such a fun way for preschool and kindergartners to practice counting to 10, color words, number words, and strengthening fine motor skills at the same time.
Free Winter Activities for Kids Snowman Sequencing Worksheets Five Little Snowman Rhyme Activity Winter Do-a-Dot Worksheets Arctic Animal Printable Pack Winter Ruler Measurement. Oct 16, · Katie reading Counting Book. Printable Counting Book.
I made this printable I Can Count book for you, click on the picture below to download your copy. I like things that are quick and easy, don’t you. To assemble this book, just fold each page with the fold on the right, then staple along the left side- no cutting required!Author: Vanessa Levin.
Anno's Counting Book by Mitsumasa Anno. In this wordless counting book Anno uses simple watercolor pictures to depict the numbersthe seasons, and the months of Counting book year.
Unlike many counting books that begin at one, Anno begins at zero, with the first illustration showing only a snow covered landscape and a small stream. Counting On couple John David and Abbie Duggar welcomed their first child to the world on January 7. See the photos. Counting On couple John David and Abbie Duggar welcomed their first child to the world on January 7.
See the photos. See All. Videos. Season Premiere | Counting On. ipaperbook.icuers: M. Counting Animals is a counting book with animals for pre-school, perfect for kindergarteners or pre-schoolers learning their numbers 1 – Authors: Clare Verbeek, Thembani Dladla, Zanele Buthelezi Illustrator: Rob Owen Sample Text from Counting Animals (counting book with animals for pre-school) One elephant is going to drink water.
Apr 17, · I have a free counting book Counting book for you. I love using unit studies, so I designed the printable to work with any theme. You can easily adjust the actual activity according to your child’s ability level, whether your child is a toddler or an older preschooler.
Counting is the process of determining the Counting book of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no.
Create a counting book, in order fromto help your child figure out a variety of ways of recognizing and representing numbers. Count with Kenny Count up to Learn Numbers with Kenny BEGINNER READERSThis book is an excellent introduction into counting, Pre-K through Kindergarten. This picture book is basic/simple and intended for young children.
Common items and animals are used to. Jan 20, · This free winter printable book helps new readers recognize number words and practice counting. Getting Ready to Use the Printable Snowman Counting Book. Full Disclosure: This post contains affiliate links.
The snowmen counting book provides great reading practice to young readers. When this colorful counting book is read aloud children learn how to count, and adults learn why and how to ensure each one of us is counted in the census.
Inviting, simply written, and available in many languages - make WE COUNT. the cornerstone of a diverse, inclusive community Census Campaign.
Counting Book for Number Reinforcement: This Counting Book is designed for Pre-K or Kindergarten students who are working on counting and number sense. The students will be able to draw the specified number of objects on a ten frame, and then be given a second opportunity to draw the number of obj.
Birthday Counting Book For Children - Gift Details Filled with numbers, pictures and rhymes, this delightful personalized Counting Book for Kids will help any little one learn to count the fun way. This is definitely a Counting Book for Toddlers and Children with a twist to teach your kid to count in an enjoyable way!.
Bedtime story written and illustrated by Sheena Deviah. OTHER CREDITS: Attribution Text: Incredible Insects: A Counting Book (English), written by Sheena Deviah, illustrated by Sheena Deviah, supported by Oracle, published by Pratham Books (© Pratham Books,) under a CC BY license, first released on ipaperbook.icu: Storyweaver.
Here is a free printable to help you make an apple counting book for your kids. The book is a perfect addition to your apple theme lesson plans and your kids will enjoy reading this book over and over because it features pictures of them. Today I'm going to help you make an apple counting book to use at school or in your home.
Homemade. Sep 25, · Anno's Counting Book is unlike any other I've seen. It's not boring, or glib, or hit-you-over-the-head obvious. The book begins with zero's barren snow-covered landscape.
Each page finds more people, trees, or buildings arriving on the land as settles build up the town. Spring arrives with "three" and the town continues to bloom/5.
If your kids like coloring books at all, they are going to love this particular book. Practicing numbersthis printable counting book includes lots of different animals from around the farm and after counting the number of animals on each page, there is a space for your child.
Sep 25, · With Anno's Counting Book, the creator of the brilliantly inventive Anno's Alphabet invites young readers on another stimulating adventure of the imagination—this time into.
This Christmas tree printable counting book is a quick and easy idea for your Christmas theme or Christmas tree theme unit or lesson plans in your preschool or pre-k classroom. Download your copy of the free book today If you are looking for a quick Christmas themed activity, here is a Christmas tree counting book that you can easily assemble.
You searched for: counting book. Etsy is the home to thousands of handmade, vintage, and one-of-a-kind products and gifts related to your search. No matter what you’re looking for or where you are in the world, our global marketplace of sellers can help you find unique and affordable options.
Let’s get started. Flowers Hole Punch Activity Counting Books Kids love this simple counting book that combines math wi Kids love this simple counting book that combines math with a fine motor activity.
This hands-on math and fine motor activity is perfect for your spring theme, flower theme, plant theme, or summer theme unit and lesson plans. 3 Dinosaurs is a web site with free printables, gross motor, trip reviews, and book activities for tots, preschoolers, kindergarten, first grade, second grade & third grade.
May 13, · This printable counting book is a fun addition to your gardening theme, if in school, or as a quiet home activity while sitting at the table. Or, take it outdoors where children are surrounded by real flowers.
While counting the flowers in the garden, open the book and count the flowers on each page. This apple-themed book is a great way for children to practice counting and build number sense. You have lots of options in using this free apple book printable.
My Apple Counting Book Printable. Counting will be such fun when you use My Apple Counting Book with your children to work on the numbers 1 to This simple printable book features. My Counting Book.
Students journey to 1, by writing ten numbers a day with reward activities at intervals along the way. Correlates with Sunrise Math and Canadian Sunrise Math This Counting Book Lesson Plan is suitable for Kindergarten - 6th Grade. Here is a wonderful way to teach children with visual impairments how to count and build number recognition skills.
Included, you will find a set of instructions on how to create a counting book from card stock, jump rings, and cotton swabs. Nov 07, · This turkey counting book provides great reading practice to young readers. The text is repetitive with just the number word changing on each page. It is also very interactive.
On each page, kids can add the correct number of feathers to each turkey. Here are three feather ideas. Use the feathers that come with the book. A Desert Counting Book A Desert Counting Book A Desert Counting Book. Concept (fiction), words, Level H (Grade 1), Lexile L.
Bailey is a dog who lives in Arizona. She likes many animals and plants that live in the desert. Students will have the opportunity to count. A beautifully illustrated picture book to help young children develop their skills in counting, matching and number recognition.
Young children will love lifting the flaps on each page to reveal a. Dec 11, · This free Christmas Counting Book is a great way for preschool, kindergarten, and first grade kids to practice counting from My Counting Book by _____ ©ipaperbook.icu 1 1. Related: Counting Flowers Printable Book.
Using the apple counting book with children. Then it’s time to bring the kiddos in to work on their apple counting books. I like to do this in small groups or one-on-one. Explain to the children that they’ll be making their very own book about apples in an apple tree.
Jul 09, · Before we get into the new Pocket Carbohydrate Counting Guide (and your chance to win a free hard-cover copy of the book!), let's start with the story of how diabetes changes Shelby's life. Oct 23, · Fall Counting Book. Learning to count to twenty has never been so much fun than with this easy to create Fall Counting Book.
Children will be learning to recognise the numbers in word form as well as in number form while counting the images and coloring them in.Dec 10, · Hello there! I am sharing a free printable snowman themed counting book. Let’s Count and Show Numbers!
This resource is great for students that are working on counting to 10, drawing a picture that shows how many, writing numbers and understanding that in a counting sequence each number said is 1 more than the last number said.Sep 30, · Read Common Sense Media's Barn Cat: A Counting Book review, age rating, and parents guide.


Chapter - 5A
An octave of a note is a note that has a frequency (pitch) which is either 1/2, 1/4, 1/8, etc or twice, 4 times, 8 times, etc that of that note. To put it into an equation - for a note of frequency F Hz , an octave note is one which has frequency F1 Hz such that,
F1 = 2nF,
where n is a whole number between +/- infinity excluding zero.
The "lower octaves" are the ones with a negative n, while
The "higher octaves" are the ones with a positive n.
A note with n = 0, or having the same frequency, but produced from different strings (sources) are referred to as "unison" and often written as P8.
Thus an octave is a harmonic (covered earlier) but all harmonics are not octaves.
The "higher octave" that is one higher (double the frequency) of an indicated note is sometimes written as 8va, and the octave below 8vb. A 15va is a octave with 4 times the frequency of the fundamental - 2nd higher octave. An octave is sometimes written as P8 as well.
An octave is important in music for the following reasons:
(i) It is the simplest ratio (1:4, 1:2, 2:1, 4:1,...) between two notes beyond the unison (1:1).
(ii) To the ear, octave frequencies sound the same. So any two notes that are octaves of each other are indistinguishable to the ear. The ear perceives the difference in the frequency merely as how "sharp" or "loud" or "crisp" the sound is. This is called " octave equivalency." And because it is so -
(iii) Octaves in music notation are written using the same symbols. e.g.: The middle C (written as "C4" but different in meaning from that in music sheet or chords) is 262 Hz. Its octaves C3 (131 Hz) and C5 (524 Hz) are all written, in general music notation as "C" only.
(iv) They function as landmarks in the otherwise ratio based music scaling system.
Division of the Octave and Introduction to Scales:
(There are many articles on Wikipedia that cover these topics in cast detail, and so I will restrict my discussion to the working principles only.)
The octave, in modern music, is divided into "12 half notes" so that it 7 full steps and 5 half steps to get from one named note to the same note in the octave above or below.
These 12 notes are what make up the "Diatonic Scale" when written in order from any named note in cyclical order up to the named note before it e.g. A to G# and Bb to B. - (discussed earlier).
Choosing specific notes from this diatonic scale, various other scales are produced.
The system of dividing of the octave into 12 notes is referred to as the "Twelve - Tone Equal Temperament (12-TET)" which is the standard for almost all the music we hear.
Equal temperament is a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings an octave is divided into a series of equal "steps" i.e. equal frequency ratios. The reason why a geometric division is preferred to a geometric division is -
(i) The human ear distinguishes sound frequencies in a geometric way - ratios are better distinguished than the arithmetic difference.
(ii) It allows the music composed, to be played in any octave ("Transposition").
The basis of this division is that the notes produced in dividing the octave in this way sound good together - and that's what music is all about. There are other systems that divide the octave into different parts into more than 12 parts - upto 171 parts (171-TET). These are used in "Microtonal music."
Before 12-TET came into being, another ratio system was used - "Just Intonation" where simple ratios were used that sounded good. The 12-TET system sounds a lot like that system but it is a lot more mathematically sound.
So, the result of such a division is that we have 11 steps between two consecutive octaves, the 12to one being the octave itself.
The Cent System:
The 12-TET division of the octave is done geometrically. Thus we end up with a regular geometric progression of frequencies. The frequency ratios between any two consecutive notes so obtained is defined as "100 cents." This means that a cent is precisely equal to 21/1200 - the 1200th root of the number 2. Thus an octave - the ratio of a frequency with one double of is 2 = 1200 cents.
An octave interval = an interval of 1200 cents
Thus consecutive half steps are 100 cents apart and consecutive full steps are 200 cents apart.
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4 edition of Business mathematics for college students found in the catalog.
Business mathematics for college students
R. C. Gulezian
|Statement||Ronald Gulezian, Henry Tingey.|
|LC Classifications||HF5691 .G79 1983|
|The Physical Object|
|Pagination||xv, 463 p. ;|
|Number of Pages||463|
|LC Control Number||82010986|
Compare book prices from over , booksellers. Find College Mathematics for Students of Business, Life S () by Zill, Dennis G. This course takes you through an overview of the wonderful world of business mathematics. The course is designed for a person of any age and anywhere in the world. All that is required of the learner are a computer, a connection to the internet, a calculator or spreadsheet, skills to use these tools, and a willingness to learn.
Courses in business mathematics are valuable for both business and personal use. Topics range from business arithmetic, to payroll deductions, interest caluclations, and banking, investment, and finance related math. We also offer a business math with spreadsheets class. An introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality.
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The students shall ac quire a degree orientatio n concerning the task- and personnel-related tasks and roles of a manager and supporting tools and methods and be able to describe the coherence Author: Henk Van Elst.
Business Mathematics and Statistics: Download Business Mathematics and Statistics text book for 1st year students. This book is also useful for CA IPCC students, for BBA 1st year students and for MBA students.
This book deals with both Mathematics and Statistics where as business statistics helps in keeping a record of all the essentials involved in a business, business mathematics. Business MBA students who studied business mathematics and statistics using the framework laid out in this book.
Th eir comments and feedbacks were equally important and useful in making this book an excellent guide into the often-challenging ﬁ elds of mathematics and statistics. I File Size: KB.
This book reflects more than 25 years of author involvement with business math education and the business community. The focus of this edition is on linking mathematics with real business practices in real businesses, giving readers a better appreciation for and understanding of the concepts that are vital in the business world.
Madison College Textbook for College Mathematics Revised Fall of Edition. Authored by various members of the Mathematics Department of Madison Area Technical College. How to use this workbook. Each chapter consists of text plus worked examples.
These are followed by Exercises labeled as Your Turn. Business Environment. This note teaches the concept of business environment its meaning, scope and importance. Topics covered includes: Various Aspects Of Business Environment, Globalisation: Trends and Issues, Economic System: Process Of Reforms, Profile Of Indian Economy in 21st Century, Environmental Pollution, Growth of Industries in India, Mergers and Acquisitions, Foreign Investment.
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Best-selling math author Rhonda Huettenmueller uses the same combination of winning step-by-step teaching techniques and real-world business and mathematical examples that have succeeded with tens of thousands of Reviews: Additional Physical Format: Online version: Bittinger, Marvin L.
Business mathematics for college students. Reading, Mass.: Addison-Wesley Pub. Co., © Business math is a type of mathematics course that is meant to teach people about money and provide them with the tools they need to make informed financial decisions.
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Business Mathematics for College Workbook presents the fundamentals of finite mathematics in a style personalized for first-year college students and provides basic skills in business mathematics. The philosophy is the workbook is "learning by doing," and the method is the successful explanation-activity-homework format.
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Business Business Math has been evaluated and recommended for 3 semester hours and may be transferred to over 2, colleges and universities. This self-paced course can be studied wherever. Contemporary Business Mathematics for Colleges presents an arithmetic-based, basic approach to business mathematics.
It emphasizes a practical, skill-building approach to prepare students for future careers in business through step-by-step development of concepts, numerous practice exercises, and a focus on real-world application of tech-niques. This book is intended to be used by children ages 5 to 6. Other age groups will also benefit from the book.
Anyone can use this book globally, although the curriculum may differ slightly from one region to the other. This is so because the core content of Mathematics is the same around the world.
Programmed Business Mathematics, Book 2: Negotiable Instruments, Pricing Discount, Payroll Insurance and Business Decision Making. College Mathematics for Business, Economics, Life Sciences and Social Sciences, Custom Edition for California State University, Northridge.Confronting Racism Radio Business City Baseball Nurd Radio Podcastresepsjonen Capital Good Podcast Misteri dell'Universo MASNA Live.
Business Mathematics: A Textbook Item Preview Book digitized by Google from the library of the New York Public Library and uploaded to .This book is an introduction to basic mathematics and is intended for students who need to reach the minimum level of mathematics required for their sciences, engineering and business studies.
It begins by reviewing mathematical ideas usually encountered in early high school, such as fractions, algebra and solving equations.


Graduate Aptitude Test in Engineering (GATE) Syllabus | Civil Engineering
Linear Algebra: Determinants, algebra of matrices, systems of linear equations, eigen values and eigen vectors.
Calculus: Functions of single variable: limit, continuity and differentiability, mean value theorems, theorems “‘of integral calculus; evaluation of definite and improper integrals. Functions of two variables: limit, continuity, partial derivatives, total derivative and directional derivative, maxima and minima, multiple integrals and their applications, sequences and series, test for convergence, Fourier series.
Ordinary Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s or Euler’s equations, initial and boundary value problems, Laplace transform.
Statistics: Basic concepts of Probability and Statistics.
Mechanics: Bending moments and. shear forces in statically determinate beams; simple stress and strain: relationship; stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle; v-srrrTple1)ending theory; flexural shear stress; thin-walled pressure vessels; uniform torsion.
Structural Analysis: Analysis of statically determinate trusses, arches and frames; displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods; .-o”analysis by displacement methods (slope-deflection and moment-distribution methods); influence lines for determinate and indeterminate structures; basic concepts of matrix methods of structural analysis.
Concrete Structures: Basic working stress and limit states design concepts; analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns and isolated footings); basic elements of prestressed concrete: analysis of beam sections at transfer and service loads.
Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases; connections – simple and eccentric, beam-column connections, plate girders and trusses; plastic analysis of beams and frames.
Soil Mechanics: Origin of soils; soil classification; three-phase system, fundamental definitions, relationship and inter-relationships; permeability and seepage; effective stress principle: consolidation, compaction; shear strength.
Foundation Engineering: Sub-surface investigation – scope, drilling bore holes, sampling, penetrometer tests, plate load test; earth pressure theories, effect of water table, layered soils; stability of slopes – infinite slopes, finite slopes; foundation types – foundation design requirements; shallow foundations; bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays; deep foundations – pile types, dynamic and static formulae, load capacity of piles in sands and clays.
Water Resources Engineering
Fluid Mechanics and Hydraulics: Hydrostatics, applications of Bernoulli equation, laminar and turbulent flow in pipes, pipe networks; concept of boundary layer and its growth; uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump; forces on immersed bodies; flow measurement in channels; tanks and pipes; dimensional analysis and hydraulic modeling. Applications of momentum equation, potential flow, kinematics of flow; velocity triangles and specific speed of pumps and turbines.
Hydrology: Hydrologic cycle; rainfall; evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.
Irrigation: Duty, delta, estimation of evapo-transpiration; crop water requirements; design of lined and unlined canals; waterways; head works, gravity dams and Ogee spillways. Designs of weirs on permeable ” foundation, irrigation methods.
Water requirements; quality and standards, basic unit processes and operations for water treatment, distribution of water. Sewage and sewerage treatment: quantity and characteristic of waste water sewerage; primary and secondary treatment of waste water; sludge disposal; effluent discharge standards.
Highway planning; geometric design of highways; testing and specifications of paving materials; design of flexible and rigid pavements.


Example: 13 14 40 7 20 22 10 11 5 34 16 52 8 26 4 13 2 40 1 20 10 5 16 8 4 2 1 these are sometimes called hailstone sequences for that reason therefore, long would be a better choice than int share | improve this answer in the implementation below we take advantage of the fact that when n starts the iteration as odd, n = (n 3). Pawan munjal, chairman and managing director, hero motocorp, said, 'the launch of the new next generation achiever 150 is a reiteration of our strong focus on developing new, technologically superior and youthful products across segments for our customers in india and across the globe. The syracuse (also called collatz or hailstone) sequence is generated by starting with a natural number and repeatedly applying the following function until reaching 1: for example, the syracuse sequence starting with 5 is: 5, 16, 8, 4, 2, 1.
Fortran programming essay example many people perceive fortran as an archaic and dead programming language however, most scientific and engineering code is written in fortran. No examples of “sk etchy proofs” that could extensive study of collatz conjecture by researchers can be found  is a philosophical essay on the 3x + 1 problem the paper. The collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term.
We are provided with a number n our task is to generate all the hailstone numbers from n and find the number of steps taken by n to reduce to 1 collatz conjecture: a problem posed by l collatz in 1937, also called the 3x+1 mapping, 3n+1 problem let n be a integer according to collatz conjecture. It seems to have something to do with the do-loop since if i remove the loop (essentially making a program that does only one iteration of the hailstone sequence) the arithmetic works fine i meant maybe the sequence starting from that number overflowed. The hailstone sequence of numbers can be generated from a starting positive integer, n by: if n is 1 then the sequence ends if n is even then the next n of the sequence = n/2 if n is odd then the next n of the sequence = (3 n) + 1 the (unproven) collatz conjecture is that the hailstone sequence for any starting number always terminates. The collatz conjecture is a conjecture in mathematics named after lothar collatz this prescription is plainly equivalent to computing a hailstone sequence in base two example the starting number 7 is written in base two as 111 the resulting hailstone sequence is: to jump ahead k steps on each iteration (using the f function from.
5426 example: the collatz problem since the previous example may have left the reader with an impression that nestwhile is only good to produce inefficient solutions, we will now consider an example where it is perhaps the most appropriate command to use, both in the sense of elegance and efficiency. Analysis of the pattern leading to final descent in a hailstone sequence figure 1 sample output of excel spreadsheet program also, please refer to the graph highlighting the no of steps for each sequence to converge to 1. What delights me most about the collatz conjecture is your observation about what the iteration does to the factorizations combined with an observation on the sizes of the numbers multiplication by 3 and adding 1 more than triples the number, while dividing by 2 only halves it. A proof has been proposed for the collatz conjecture by a german mathematician who is a former student of collatz who originally came up with this addictive problem the sequence of numbers is also known as a hailstone sequence and the conjecture is a halting problem it is an example of a class of iteration problems that are hard.
Collatz conjecture's wiki: unsolved problem in mathematics:does the collatz sequence eventually reach 1 for all positive integer initial values(more unsolved problems in mathematics)the collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows. The problem is that in these examples, the fact that all initial states converge and even the number of steps towards convergence are immediately obvious and predictable i really like the way the convergence time of the collatz map behaves pseudorandomly. The collatz conjecture is an unsolved conjecture in mathematicsit is named after lothar collatz, who first proposed it in 1937the conjecture is also known as the 3n + 1 conjecture, as the ulam conjecture (after stanislaw ulam), or as the syracuse problem  the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers,  or as wondrous numbers.
Collatz himself circulated similar iteration problems at the international congress of mathematicians in 1950, although it is unclear if $3x+1$ specifically was among them one such iterative function already appears in his notebook entry from july 1, 1932. I’ve talked about iteration before: it just means repeating the rule so, for example, if we start with 10, we get 5 applying the rule again to 5, we get 16 applying it to 16 gives 8, and so on so, for example, if we start with 10, we get 5 applying the rule again to 5, we get 16 applying it to 16 gives 8, and so on. Definition and examples of sequences the expression a n is referred to as the general or nth term of the sequence example 1 write the first five terms of a sequence described by the general term a n = 3 n + 2 therefore, the first five terms are 5, 8, 11, 14, and 17 example 2.
The conjecture is also known as the 3n + 1 conjecture , the ulam conjecture (after stanisław ulam ), kakutani's problem (after shizuo kakutani ), the thwaites conjecture (after sir bryan thwaites), hasse's algorithm (after helmut hasse ), or the syracuse problem the sequence of numbers involved is referred to as the hailstone sequence or. Climate vs weather weather is the day-to-day state of the atmosphere in a region, and its short-term (minutes to weeks) variation whereas climate is defined as statistical weather information that describes the variation of weather at a given place for a specified interval. The conjecture remains unproven to this day, but most mathematicians believe it to be true your task is to write functions that print the hailstone sequence for a given value of n by filling in the function stubs provided in lab10cpp. This is an example of an indefinite iteration problem: we cannot predict in advance how many times we’ll want to improve our guess — we just want to keep getting closer and closer our stopping condition for the loop will be when our old guess and our improved guess are “close enough” to each other.


DCPS today released their annual test results with some disappointing findings for elementary education. DCPS elementary students tested 4% worse in both reading and mathematics as compared to last year, while DCPS middle school students tested 4% better in both reading and mathematics. One step forward, one step back. Surely not the news that embattled Chancellor Michelle Rhee wanted to hear, nor something that Fenty wanted either. DCPS is quick to point out that the three year trends since Chancellor Rhee came on are still impressive, and they’re right: Since 2007, students scoring proficient in math and reading, in middle school, are up 14%, and in elementary school, are up 7% for reading and 14% for math. That’s a gain you can really see.
There’s going to be some variation from year to year in how the tests turn out. Are 4% drops good? No, they’re not. But it’s hard to ignore the longterm trend that’s going on right now.


Autumn Term One – September 2018
Penguins: Year 5
Here is what we shall be learning in our first half term this autumn.
Our topic is “World War One”
2018 marks 100 years since the end of the First World War. As a school we shall commemorate the First World War Centenary by each class reading a different WW1 related book to think about the events that occurred.
We shall be using the book ‘A Bear in War’ as a stimulus for our whole school topic ‘The First World War’. The book will allow us to write a range of pieces from letters, diaries and narratives. In our reading sessions the children will learn more about the war and its significant events.
- read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
- count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
- round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
- solve number problems and practical problems that involve all of the above
- read Roman numerals to 1000 (M) and recognise years written in Roman numerals
- add and subtract numbers mentally with increasingly large numbers
- add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
- use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why solve comparison, sum and difference problems using information presented in a line graph
- complete, read and interpret information in tables, including timetables
- solve problems involving converting between units of time
The Circle of Life
In this module children build on earlier work from Key Stage 1 and from Year 3, where they learned about the life cycles of plants. They extend their understanding of what a life cycle is, and learn about the life cycles of some familiar (and some less familiar) mammals, amphibians, insects and birds. Children compare and contrast different life cycles, identifying common features as well as explaining key differences. They use their knowledge of life cycles to help them as they create a fantastical creature of their own, complete with its own distinct life cycle. They learn about incredible journeys that some animals undertake to complete their life cycles, and about the different ways in which humans are supporting some endangered animals to increase their population numbers.
Hinduism: What is the best way for a Hindu to show their commitment to God?
Blocked swimming lessons.
Children will need to bring their swimming kit and towel to school every Thursday.
Our art work shall link to our topic of World War One.
This unit builds on the previous unit in Year 4 (Questions and Quizzes) using Scratch to build and edit algorithms for simple games. The unit is designed to help children develop their skills in writing their own algorithms as well as editing and debugging existing codes.
Learn songs from World War One
Reading – 10 minutes homework for 5 nights a week!
Children in KS2 are expected to read at least 20 times in the month. For reading 20 times they will get a GOLDEN TICKET.
Please continue to read with your child their school reading books and any books/magazine from home – READING is FUN!!
Spellings– Given out every Thursday and tested the following Thursday.
Maths– Given out Thursdays. To be handed in by the following Wednesday -at the LATEST.
Topic homework– one quality piece of work to be completed from the sheet sent home for PRIDE.
If you have any worries or concerns please come and see me as soon as possible; no worry is too small.
The best time to do this is after school at 3:30pm on a Tuesday or Wednesday.
Mrs N. Clemitshaw


ISBN-13: 9780470617953 / Twarda / 2010 / 671 str.
A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts:


Home > Learning @GESPS > Mathematics
Our Math programmes focus on fostering the joy in the learning of Mathematics. With problem solving as the core of Singapore Mathematics Curriculum, students can develop in their skills in solving mathematical problems through a range of situations which includes non-routine, open-ended and real-world problems.
Equipping Our Students with Rigorous Learning Experiences
Teaching and Learning Approach for Mathematics
To help our students build a strong foundation in Mathematics, our lessons are planned in a structured teaching sequence.
Students will go through 3 phases of learning during a mathematics lesson, i.e. Readiness, Engagement and Mastery phases.
- During the Readiness phase, teachers use activities to check on students’ prior knowledge to customise lessons according to students' abilities.
- In the Engagement phase, different pedagogical approaches are used to engage students in learning new concepts and skills. They are mainly hands-on activities and collaborative learning activities. Students are encouraged to communicate and articulate their ideas.
Concrete-Pictorial-Abstract (CPA) Approach to teaching Mathematics:
- In the Mastery phase, learning is reinforced through practices, games, math journal and performance tasks.
- Mathematical concepts are taught using the Concrete-Pictorial-Abstract (CPA) approach. Students engage in hands-on activities using concrete materials and manipulatives to help them make sense of the concepts they are learning.
- Visual representations of the concrete manipulatives are then introduced to help students visualize the mathematical concepts.
- Finally, algorithms and symbols are used to represent the concepts in numerical operations. This CPA approach benefits all students as it slowly builds on students’ understanding of mathematical concepts in a progressive manner.
Embracing the Environment for Joy of Learning
We believe in creating a conducive learning environment and engaging our students with the right learning experiences to make the learning of mathematics fun and purposeful.
We use the environment as a 3rd Teacher to provide opportunities for children to make their thinking visible and deepen learning and increase engagement.
Math with Towkay Di Assembly Programme
The assembly programme highlights how mathematics is applicable in our daily lives and certain mathematical misconceptions students through dramatization.
Stretched and Enrichment Programme
These programmes are held after school to motivate students in the learning of Mathematics based on their abilities. Activities include math games and multiplication challenge.
Empowering Our Students To Use Mathematics
We empower our students to use what they have learnt in their lessons through a variety of fun and engaging activities.
Level Signature Programmes
The programmes are conducted across subjects to promote collaborative learning among students and to enable students to make connections across the different subjects.
To better challenge and stretch students who are passionate in Mathematics, selected students can take part in the Singapore Math Olympiad Competitions to broaden their horizons.


06-04-2009 12:01 PM
With Google analytics, is there is a way to track what the average time a viewer views a video?
Solved! Go to Solution.
06-09-2009 09:32 AM
I'm not sure if this is possible with Google Analytics but I do know this is a fundamental feature of Visible Measures.
It'd be good to know though. Anyone done this with Google?
09-28-2009 12:02 PM
Not in any elegant graph orientated way unfortunately.
I've managed to do this using event tracking - setting the Video name as the Category, the Media Progress as the Action and the % complete as the label
Some math is done to figure out the timecodes for each % and as the player hits each it triggers the call.
It's pretty simplistic but it gets a baseline in place.


We are now working on the other games and tools, such as the application Cam Calc. On the website, we will offer trial versions to the games. Our customers will have to buy the games to get the full version. James and Varun have worked on building and designing the other games. Juan has worked on building the application. Basically what the application will do is that it will take a picture of a math question, and it will answer the question. The games will be designed to provide a fun and educational way to learn new math concept.


I'm writing a script and I would like to pass the results from
bc into a variable. I've declared 2 variables (
var2) and have given them values. In my script I want to pass the results from
bc into another variable say
var3 so that I can work with
var3 for other calculations. So far I have been able write the result to a file which is not what I'm looking for and also I've been able to echo the result in the terminal but I just want to pass the result to a variable at moment so that I can work with that variable.
echo "scale=2;$var1/var2" | bc


Cordiially inviting all postgraduate students and supervisors to the introductory workshop on Data envelopment analysis (DEA) to be held as follows:
Date: 28th July 2011 (Thursday)
Time: 09.30 a.m. to 12.30 noon
Venue: Bestari 3, D06, FPPSM
Facilitators: Prof. Mostafa Kazemi
Prof. Mostafa Kazemi,
Productivity & System Management
Ferdowsi University of Mashhad, Mashhad, Iran
Measurement efficiency of decision-making units (DMUs) such as hospitals, banks, and universities etc. that use multiple inputs and produce multiple outputs is complex.
Data envelopment analysis (DEA) was first proposed by Charnes et al. in 1978, and is a linear programming-based methodology and is a non-parametric method of efficiency analysis for comparing units relative to their best peers (efficient frontier). Data envelopment analysis (DEA) is a powerful tool for assessing the performance of organizations. DEA spans the boundaries of several academic areas including management science, operational research, economics and mathematics.
The main idea is to evaluate the relative efficiency of a set of homogenous DMUs by using a ratio of the weighted sum of outputs to the weighted sum of inputs. It generalizes the usual efficiency measurement from a single-input, single-output ratio to a multiple-input, multiple-output ratio.
Mathematically, DEA is a linear programming-based methodology for evaluating the relative efficiency of a set of decision making units (DMUs).


- What are the basic math skills that everyone should know?
- What is an important math skill?
- What are some math skills?
- How can I improve my math skills?
- Why is math so hard?
- Why is math difficult for students?
- What is the most important math?
- Why are basic math skills important?
- What are foundational math skills?
- What every math major should know?
- What are the 7 strands of mathematics?
- What is the hardest type of math?
- Is math a hard skill?
- How do we use math in everyday life?
- What are number skills?
- What is the most useful number?
- What is the most famous number?
What are the basic math skills that everyone should know?
We’ve divided Basic Math into eight sections so you can focus on the skills you need:Numbers and Operations.Fractions, Decimals, and Percents.Measurement.Geometry.Data Analysis and Statistics.Algebra (Basic)Word Problems.“Advanced Basics”.
What is an important math skill?
Learning how to add, subtract, multiply and divide fractions is an important math skill you will want to master.
What are some math skills?
Key Math Skills for SchoolNumber Sense. This is the ability to count accurately—first forward. … Representation. Making mathematical ideas “real” by using words, pictures, symbols, and objects (like blocks). … Spatial sense. … Measurement. … Estimation. … Patterns. … Problem-solving.
How can I improve my math skills?
How to Improve Math SkillsFocus on Understanding Concepts. You can memorize formulas and rules to complete many math problems, but this doesn’t mean that you understand the underlying concepts behind what you’re doing. … Go Over New Concepts and Practice Problems. … Solve Extra Problems. … Change Word Problems Up. … Apply Math to Real Life. … Study Online.
Why is math so hard?
Math seems difficult because it takes time and energy. Many people don’t experience sufficient time to “get” math lessons, and they fall behind as the teacher moves on. Many move on to study more complex concepts with a shaky foundation. We often end up with a weak structure that is doomed to collapse at some point.
Why is math difficult for students?
Mathematics has some inherent difficulties due to its abstract and cumulative nature. So students requires a firm foundation, they may not be able to learn new things without previous knowledge. For many students expectancy about the difficulty of math is high, and personal value attached with math is low.
What is the most important math?
Calculus is also used for description of thermal and fluid systems. Probability and Statistics used heavily in actuarial evaluation of potential outcomes and weather prediction. The most important branch of mathematics is the one that is useful for the application at hand.
Why are basic math skills important?
Basic math skills help you to solve general math problems in your life, including simple addition and subtraction to managing your finances. If you only master one skill in your life, math should be it.
What are foundational math skills?
Some of the topics include counting and cardinality, counting objects, rote counting, number sense of quantity, counting on and back, operations of addition and subtraction, composing and decomposing numbers, the application of mathematical foundational skills within the problem-solving process, and guiding students to …
What every math major should know?
College Algebra, Determinants & Metrics, Linear Algebra, Coordinate Geometry, Three Dimensional Geometry, Trigonometry, Advanced Calculus, Differential Equations, Dynamics & Statics, Differential Geometry, Dynamics, and Vectors Algebra.
What are the 7 strands of mathematics?
The categories considered are: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
What is the hardest type of math?
The ten most difficult topics in MathematicsTopology and Geometry. … Combinatory. … Logic. … Number Theory. … Dynamic system and Differential equations. … Mathematical physics. … Computation. … Information theory and signal processing. Information theory is a part of applied mathematics and also for electrical engineering.More items…•
Is math a hard skill?
Hard skills are teachable and measurable abilities, such as writing, reading, math or ability to use computer programs.
How do we use math in everyday life?
10 Ways We Use Math EverydayChatting on the cell phone. Chatting on the cell phone is the way of communicating for most people nowadays. … In the kitchen. Baking and cooking requires some mathematical skill as well. … Gardening. … Arts. … Keeping a diary. … Planning an outing. … Banking. … Planning dinner parties.More items…•
What are number skills?
It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts.
What is the most useful number?
But the following 10 are the most important numbers, or constants, in the entire world.Archimedes’ Constant (Pi): 3.1415… … Euler’s Number (e): 2.7182… … The Golden Ratio: 1.6180… … Planck’s Constant: 6.626068 x 10^-34 m^2 kg/s. … Avogadro’s Constant: 6.0221515 x 10^23. … The Speed of Light: 186,282 miles per second.More items…•
What is the most famous number?
10 Famous Numbers911 is most recognizable as the number to call for emergencies. … 7 is the number most commonly designated as people’s favorite. … 73 is Sheldon Cooper’s favorite number (on the TV show The Big Bang Theory). … 10 is most famous because it’s usually the number of items on “top” or “most” lists!More items…