Triplet sum divisor hackerearth solution
Please Login in order to post a comment. Can you please explain the logic here of how did you deduce the total number of pairs modding to k?
The idea is that you separate elements into buckets depending on their mod k. Because you don't need to print the actual pairs, you need to store only the number of elements in each list.
It is an optimal solution, but keep in mind: Reading the input sizes is really important in a competition. Small input size: You don't have to think that hard and you can implementend a simpler solution, which needs less time to write the code for and debug.
Yes, but this second solution is a better learning tool for modular arithmetics. The other solution is trivial. There is always a tradeoff between space and time complexity. Otherwise we might be in a better world!! The space complexity can be reduced to O min n,k if a hashtable is used instead of an array.
So space complexity and time complexity both scale linearly. But in the problem it is given as we have to print the number of i,j pairs and the given condition is i. Thanks usinha02 for the algo, and petreeftime for the explanation.
Here's an implementation in Python. Some bits are a little clunky. Feedback Please. So it will always be 1 value bigger than i. Is this possible in O n time. Where are you comparing the values of ar[i] and ar[j], which is the necessary condition in the given problem statement.
Cause the second number has to be at a later position, there's never a pair for the last position. Thank man!. I've just spent half an hour looking through this and the parent comments above which are given some credit for the idea - it's a really clever solution to the problem, and if you read petreeftime's description above, it covers it pretty well. I found a key to understanding it was to alter the code so that you see the contents of all the relevant variables at each step, and then it became clear how it was working I'm using Python 3.
The first step works out the mod value of the current array element - that's really the only thing that matters - a 3 and a 6 will have the same effect as a 3 and a 3 for a k of 3. The third step adds the current array element to the nums list, which will allow that to be counted towards future possibilities in other steps. Great - just spent half an hour trying to work out how this worked, and now I have I feel like I've achieved something today!
Thanks for the code. Thanks for the explanation petreeftime! Thank you usinha02 for the elegant solution, and thank you petreeftime for an awesome explanation! Although I understood most of it, and this maybe most naive doubt that I have. I wasn't able to understand the following condition:.Q1 FizzBuzz Write a program that prints the numbers in the given range.
Print a new line after each string or number. Next line will have T integers, denoted by N. But follow the rules given in the problem statement. N is an integer. Please read the below instructions carefully. Q2 Sum of Two Numbers. You are given two numbers a and b. Your task is to find the sum of two numbers. Input The first line contains an integer t, denoting the number of test cases.
Next t lines contain two integers, a and b separated by a space. Output For every number a and b, output the sum of two numbers a and b. HackerEarth Questions Asked on 24th June Q Monk and the Magical Candy Bags Our Monk loves candy!
He picks up a bag, eats all the candies in it and drops it on the ground. But as soon as he drops the bag, the number of candies in the bag increases magically! Amazed by the magical spell, Monk can now have a lot more candies! Output : Print the answer to each test case in a new line.
Input Constraint. Each digit is made of a certain number of dashes, as shown in the image below. For instance 1 is made of 2 dashes, 8 is made of 7 dashes and so on. You have to write a function that takes this string message as an input and returns a corresponding value in terms of a number. This number is the count of dashes in the string message. Today is her birthday. Chandu wants to give her some sorted arrays on her birthday. But the shop has only unsorted arrays. But, he doesn't have much time to sort the arrays manually as he is getting late for the birthday party.
Help him, or his girlfriend will kill him. He took three hours to solve it. The teacher got agitated at Chandu and asked you the same question. Can you solve it? Answer Chandu is very fond of strings. Or so he thinks! But, he does not like strings which have same consecutive letters. No one has any idea why it is so. Now, the problem is quite simple. You simply need to perform one operation - if there are two same consecutive letters, delete one of them.
Output: For each test case, print the answer to the given problem. Subscribe to: Posts Atom.Skip to content. Instantly share code, notes, and snippets. Code Revisions 12 Forks 1. Embed What would you like to do? Embed Embed this gist in your website.
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Hence, today I kept all those suggestions in mind while solving a new problem question. The question is such: Given an array S of n integers, find three integers in S such that the sum is closest to a given number, target. Return the sum of the three integers. You may assume that each input would have exactly one solution.
The sum that is closest to the target is 2. It would be great to hear back if I need to make further improvements. Any help will be highly appreciated. Set kMax to k. Define iMin to be i - 1. Start your for loop loop with index at iMin. At the start of each iteration, set k to kMax. When [i][j][k-1] is no longer too high, resume your uppy-downy scheme. Whenever you increment icheck if [i][k-1][k] is too low.
If so, increase i until [i][k-1][k] is no longer too low. Check if [i-1][k-1][k] gives a better match and store it as temp. AFter changing scope like this, check the opposite end of the scope. So if you just reduced kcheck if [i][k-1][k] is too low. Do this until scope is stable. So you can kill off any number that's belowprovided it's not the last number at or below Additionally, once we get toany number greater than that is not the last number at or above is not going to help.
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Judging by the complexity of your method Triplet. A way to accomplish this would be to sort the integers in the method hashCode before calculating the hash. In fact, Triplet. Regardless of the above, you are creating unnecessary List s in Triplet. Here, the explicit creation of an ArrayList from the contents of the List returned by the invocation of Arrays.
The same applies to the process of converting the elements of other to a List. You could even bypass the creation of an intermediate List completely by using a stream:. The easiest way to go about it is probably, just like in the method hashCodeto sort the integers from the triplets as a List and then compare the two List s for equality.
Actually, you could already sort the integer's in the Triplet 's constructor, which would ensure that you only ever have to sort the three integers of a Triplet once. True, this does not preserve the order of the integers, but then, this is not really necessary for the purpose of this program either. There is no need to add the result to a new ArrayList you could just use. You creating some unnecessary objects that still need to be cleaned up by the garbage collector.
Instead of:. The reason why you came up with two different solutions is: Your mind is preset to procedural solutions an premature optimization. The "sum of three" problem only differs in step 1. Yes, this solution might perform awfully for large input arrays but with the given example it is fast enough.
What do we need to change to adopt the previous solution to the "sum of two" solution to the "sum of three" problem? Now we have a similar solution for a similar problem. We could even go further and transform the factory method for the Pairs to be parameterized so that the same solution could be used for all "find combinations with matching sum" problems.
My approach is totally focused on the problem. No optimization or "clever tricks" have been used. That allowed me to easily extend the first approach to a more general version to handle similar problems. Sign up to join this community. The best answers are voted up and rise to the top.
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Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Given an array A of N integers. So there are two triplets 1,2,2 and 2,2,1. Look at the ijk values which are indices. So, there are 12 possibilities of triplets of indices that can have array values as 221.
I tried this but i want to decrease the time complexity :. In this section what I did is ran 3 loops checked all the possibility of possible triplets with given constraints that should be divisible by only one of i, j and k.
All possible combinations of triplets won't be much.
Then iterated our previously created vector with 3 possible i, j, k. All the 3 i, j, k can't be equal because sum is divisible by only one and we have taken care of this in getpossiblenumbers function. But when two of i, j and k are equal take care of counts as I did in 3 cases above. As per the question, there can be duplicate as well as unique values in the array eg.
To get an optimized solution the algorithm is divided into two major parts- unique values, duplicate values. Main Idea Remove the duplicates and keep their counts. Numbers are less than Hence time complexity will reduce a lot.
Learn more. Good triplets sum and divisor Ask Question. Asked 6 months ago. Active 6 months ago. Viewed 3k times. Array values of a triplet i,j,k is A[i], A[j], A[k].
What have you tried so far?
Count Divisors of n in O(n^1/3)
What is the question? Show us what yozu have tried so far and where you got stuck. Used 3 nested for loops, then if else conditions. Your predicate is weird. Active Oldest Votes. Arjun Singh Arjun Singh 3 3 silver badges 8 8 bronze badges. Akhil Manchanda 53 4 4 bronze badges. Akash Swain Akash Swain 27 1 1 bronze badge. Expected output is wrong.
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Tanzania has been a focal point for Gecko on the Move (GOTM) since 2016, particularly in Mto Wa Mbu. Our efforts have primarily centred around Bandari School, where we’ve been training teachers annually in mathematics, emphasising the effective use of manipulatives in teaching. Over the past four years, GOTM has employed a local teacher dedicated to enhancing our impact. This teacher not only supports educators at Bandari but also initiates outreach programs in neighbouring schools.
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Our children develop their knowledge and skills through curriculum planning based on the requirements of the National Curriculum, the White Rose Scheme (this has been temporarily re-organised in Year 2 in order for the full curriculum to be taught before the SAT`s tests) as well as Mastering Number programme. Planning is carefully designed in small steps and through a PVA approach – Practical, Visual then Abstract, with numerous opportunities for children to apply their knowledge to real life situations.
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We aim for every topic to be taught through the PVA approach to maths in all year groups. This means that all the children have to be able to ‘make’ the number, the calculation or shape before moving on to the next stage. We use a range of equipment including real life objects (e.g. straws, buttons, pasta) and then recognise mathematical equipment such as cubes, Numicon, Dienes and number lines. After making, the children will then need to draw a visual representation which could just be their own representation or a drawing of the mathematical equipment such as cubes, Numicon, a part-whole model, a bar model or a number line.Children also have regular practise at writing numbers. They may draw them in a variety of ways – big and small, using a variety of mark making tools.
creative curriculum design and progression
If you were to walk into a maths lesson at garden Suburb Infant School, you would see:
- Teachers demonstrating secure subject knowledge, teaching lessons which are explicitly adapted to be both ambitious and to meet the needs of pupils with Special Educational Needs.
- Teachers asking open questions giving children time to ‘Think, Pair, Share’ and then asking lots of children to answer without putting their hands up
- Children answering in full sentences, confidently explaining their thinking or strategy, using given sentence stems where necessary
- Vocabulary for a lesson on display and teachers referring children back to it frequently throughout the lesson
- Children using hands on resources and then drawing their own visual representations in order to solve calculations and problems
- Children working in mixed ability groups, working independently but also co-operatively as required
- Teachers ensuring that pupils apply mathematical concepts and challenge themselves through the use of problems and ‘real world’ tasks
- A supportive classroom environment where mistakes are shared and seen as only a step to the correct answer, therefore all pupils feel able to ‘have a go’
- A relevant working wall which supports children with their learning and understanding
Click on the documents at the bottom of the page, to see how our Curriculum Intent in Mathematics relates to our whole school Curriculum Intent, as well as our Mathematics Policy.


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- Calculating inbreeding and cumulative selection differentials in the Grootfontein Merino Stud
|Last update: March 23, 2012 10:51:20 AM|
CALCULATING INBREEDING AND CUMULATIVE SELECTION DIFFERENTIALS IN THE GROOTFONTEIN MERINO STUD
G.J. Delport, J.J. Olivier & G.J. Erasmus
The algorithm presented by Quaas (1976) to calculate the inverse of a large numerator relationship matrix automatically supplies inbreeding coefficients. Far less processing time is used than with conventional methods and far bigger data sets can be handled. The method is illustrated on four generations of the Grootfontein Merino Stud. Inbreeding varied from 0 to 25 percent. The same principle, using the same sort of programme is used to calculate cumulative selection differentials. This method is shown to be simple but very effective and makes provision for unequal number of progeny and over lapping generations.
SASAP Congress 1986


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Join us Tuesday June 18th from 6:00-8:30 pm for some free family fun! There will be tattoos, face painting, D.J., raffles and lots of fun! We will have hamburgers and hotdogs, vegetarian meals are available upon request - please email Christine Chute at firstname.lastname@example.org If you are available to help and would like to volunteer, please contact Kerrin Blake at Kerrinblake@gmail.com
Hope to see you at this great event! Flyer attached.
It's not too late to return your sponsorship form! The Math Bee Challenge raffle will be held after April vacation. All pledge sheets and monies will be collected when the students return from April break. Thank you for your support of the Math Bee Challenge and the Hurld School PTO.
Join us on Tuesday, April 2nd at 7:00 pm in the cafeteria, babysitting will be offered. We will be discussing the Backyard Barbeque, Annual planting day and our Math Bee Fundraiser. We look forward to seeing you!
Friday, April 5th will be the all school rally to promote the Math Bee. All pledge sheets were sent home and another copy is attached for your convenience. Let's make this year's Math Bee another great event!
Monday March 25th is our first Family Math Night. This is our official kickoff for the Math Bee, the PTO's only fundraiser of the year! Join us from 6:30-8:00 p.m. in the cafeteria for an evening of family fun playing math-related games. Every student who attends Family Math Night will be entered to win a pair of tickets to a Bruins game! Hope to see you all there.
posted Mar 11, 2013, 3:36 PM by Hurld PTO
updated Apr 1, 2013, 3:08 PM
The Hurld PTO's only fundraiser, Math Bee Challenge, officially kicked off with a successful Family Math Night! Thank you to all that attended. All pledge forms were distributed to children on the 28th and a copy can be found in the Student Backpack section. We encourage all families to participate in our only fundraiser of the year. This fundraiser has been lots of fun for students and teachers as well as being very successful. We are looking forward to another great Bee!
posted Mar 11, 2013, 2:51 PM by Hurld PTO
updated Mar 18, 2013, 2:20 PM
Join us on March 25th from 6:30-8:00 for Family Math Night! Come have some fun with us while we get ready for our Math Bee. Enjoy fun math games and activities for the whole family. All students who participate in this event will be entered in a special drawing!


Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Session Chair: Jan Sykulski Session Chair: Stephane Clenet
4:30pm - 4:50pm
Exact Modal Expansion using Dispersive Quasi Normal Modes (DQNM) of open and periodic nanophotonic structures
Minh Duy Truong2, Guillaume Demésy1, Frédéric Zolla1, André Nicolet1
1Aix-Marseille Université, France; 2CNRS, France
In this paper we present recent developments in our modal expansion technique for electromagnetic structures with highly dispersive media and its application in unbounded geometries. The formulas, based on a simple version of the Keldyˇs theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly non reciprocal. A dispersive benchmark case, a diffraction grating, made of a periodic slit array etched in a free-standing silver membrane, is presented.
4:50pm - 5:10pm
Finite element formulations for systems with high-temperature superconductors and soft ferromagnetic materials
University of Liège, Institut Montefiore B28, Dept. of Electrical Engineering and Computer Science, B-4000 Liège, Belgium
Modelling systems containing high-temperature superconductors and ferromagnetic materials requires to handle their nonlinear constitutive laws. Many numerical methods are possible but not all of them offer reliable results and efficient simulations. In this work, we investigate different finite element formulations (h-conform and b-conform) and linearization techniques. We show that none of the methods is optimal for modelling both materials at the same time and we propose a coupled formulation that exploits the best method for each material. The proposed coupled formulation is shown to be more efficient in all tested situations.
5:10pm - 5:30pm
Diagonal material matrices for arbitrary simplicial meshes for solving Poisson problems with one unknown per element
Fabrizio Bellina, Ruben Specogna
EMCLab, DPIA, Università di Udine, Italy
We present a technique to extend the geometric construction of diagonal material matrices-known also as diagonal discrete Hodge operators-to arbitrary triangular and tetrahedral meshes and arbitrary material parameters.
The proposed material matrices are tailored to enable the use of a complementary-dual formulation for Poisson problems with one unknown per element.
5:30pm - 5:50pm
Implementation of High Order on Surface Radiation Boundary Conditions
Nathan Ida, Nassif Berrabah, Subramania Hariharan
The university of Akron, United States of America
Electromagnetic scattering problems that involve far-ﬁeld radiation patterns and the calculations of total currents induced in a per-fect conductor can be solved using local radiation boundary conditions. These local conditions are often imposed on a domain enclosing the scatterer and the typical ﬁnite element methods are incorporated so that the well-posedness of the modiﬁed problems encompassing the local radiation boundary conditions is preserved. Much effort in recent years has been devoted to attempts to construct higher order far ﬁeld conditions, so that the solution accuracy can be improved. In this work, we avoid extensive computations, and bring the radiation boundary on the scatter’s surface itself. This procedure is known as the On Surface Radiation Boundary Condition (OSRBC). The limitations in the past have been he implementable order of the OSRBC. Regardless, the key feature of the OSRBC to calculate the relevant quantities for engineers is the normal derivative of the solution on the OSRBC. The present work introduces a new method for calculation of the normal derivative of the electric ﬁeld on the surface of a scatterer of known shape. The method is based on a formulation of the boundary conditions through a recursive sequence of differential operators. The numerical implementa-tion of this formulation allows one to extract a relation which is then used to solve for the quantity of interest, such as radar cross-section.
5:50pm - 6:10pm
Hybrid Kinetic-MHD Simulations of Vacuum Arc Based on Field-Circuit Coupling Method
Feng Chen, Yudong Xu, Zhiyuan Cao, Zhenxing Wang, Lin Yin
Xi'an Jiaotong University, China, People's Republic of
This paper deals with the numerical simulation of vacuum arc based on the field-circuit coupling model. This type of arc is typically found in vacuum interrupters and simulated by the kinetic-MHD hybrid computational model. In the hybrid model, the dynamics of electron is simplified by equating electrons to massless fluids, while the kinetic dynamics of ions is described by equating ions to macroparticles. The hybrid model can illustrate the self-consistent propagation of particles and electromagnetic fields in the vacuum interrupter. Moreover, the coupling model with the external circuit can ensure self-consistent calculation results.


April, 21st 2021
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However, there is also a universal formula for calculating the effective rate. The disadvantage of this formula is that you can get the result only after calculating the interest on the deposit.


As in most scientific and engineering work, analytical studies are required in conjunction with experiments to understand the results of aeronautical research and to predict the characteristics of new aircraft or aeronautical systems. Much of the progress in improving the performance and safety of airplanes relied heavily on analytical work, which in turn depended on the availability and understanding of analytical techniques. This section outlines the status of analytical techniques that I had encountered in my studies and that were generally available to aeronautical researchers at the time I started employment with the NACA in 1940.
Studies of the stability and control of airplanes, my field of specialization, relied almost completely on the application of Sir Isaac Newton's laws of dynamics, which in turn led to the need to solve differential equations. In my college courses in mathematics and physics, Newton's laws of motion were among the first subjects studied, and the various means to apply them in different scientific disciplines occupied most of the subsequent curriculum. Mathematics courses, particularly differential and integral calculus, were presented to students as a general preparation for all the courses. These methods were originally developed largely by Newton to solve his own problems. The present notation for differential and integral calculus was originated by Jacob Liebnitz, a contemporary of Newton. A branch of calculus called differential equations occupied a whole term at MIT. Many of the methods that were taught to solve differential equations, however, applied to special forms of equations that did not occur in connection with airplane stability and control. This subject requires the solution of simultaneous linear differential equations with constant coefficients. The standard mathematics curriculum did not give this subject any special emphasis. As a result, it was left for the professors in the aeronautical courses to emphasize the importance of this particular equation. These professors, in my courses at MIT, were practical engineers without a strong mathematical background. As a result, graduates were provided with only a minimal introduction to the branch of mathematics most useful for their subsequent work. I feel that this situation existed in most of the colleges in the United States at that time, with the result that engineers who wanted to go into this field had to spend a great deal of their time in reviewing work done largely by electrical engineers or by some aeronautical researchers in Europe. Many chose to put their emphasis on other areas with which they were more familiar. The result was undoubtedly a slowing down of progress in this field.
The reason that simultaneous differential equations with constant coefficients arose in  aeronautical stability work may be explained in somewhat more detail as follows. For each variable that describes motion (the degrees of freedom), a differential equation is set up. In the case of longitudinal motion of a rigid airplane, for example, the variables would be vertical displacement, horizontal displacement, and pitch angle. Newton's third law states that force equals mass times acceleration. Thus for each variable, the aerodynamic or gravity forces due to the motion, which may produce forces or moments proportional to the displacement or velocity, are equated to the mass times the acceleration of that variable. Acceleration is represented by the second derivative of the variable with respect to time, velocity the first derivative, and displacement does not involve a derivative. As a result, a differential equation of the second order is written for each degree of freedom, which results in three simultaneous differential equations. These equations, in the usual formulation, are linear for the following reasons.
The airplane is first considered as flying in a trimmed condition. After a disturbance, the forces on the airplane change as a result of the effects of changes in angle of attack or airspeed on the various components of the airplane. These changes are necessarily small in the normal unstalled range of flight. The stall angle, at least on airplanes of WWII vintage or earlier, was usually about 15 degrees, and most disturbances producing forces within the structural capability of the airplane would be much less than this value. Ideal fluid theory shows that within this range, forces vary nearly linearly with angle of attack. The only factor that would change this condition would be the effect of the boundary layer, but the boundary layer on full-scale airplanes designed for efficient flight is so thin that it causes little effect on the forces. Likewise any change in airspeed caused by a disturbance is likely to be small compared to the initial large value of airspeed. Therefore, though the forces vary as the square of the airspeed, the variation in force for a small change in airspeed may be considered to vary almost linearly with the change in airspeed. By comparison with many mechanical systems, the airplane as a whole does not have any coulomb friction tending to hold it in its trimmed condition. Coulomb friction is the force caused by rubbing two solid surfaces over each other, and from an analytical standpoint, is usually considered to be a constant force that is independent of velocity and opposing the motion. The force caused by aerodynamic effects is in marked contrast to that appearing in mechanical systems. This difference results in the validity of linear equations to describe the motion of an airplane, whereas linear equations are usually a poor representation of mechanical systems.
Solution of the system of linear differential equations with constant coefficients can be accomplished by the classical method given in most books on differential equations. These solutions go back to the work of mathematicians in the earliest days of mathematics and were perhaps first summarized in a paper by Leonhard Euler in 1739. This solution is considered elementary from a mathematical standpoint, inasmuch as it involves elementary functions such as exponentials and sine and cosine functions. From the standpoint of the practical engineer using the equipment available when I came to work at Langley, which consisted of slide rules or mechanical calculators, the solution is very time-consuming. Determining the characteristics of the various modes of motion, such as the phugoid oscillation or short-period mode, requires solving for the roots of a fourth-degree algebraic equation. If the effects of a simple autopilot are included, a sixth-degree equation results. This problem can be solved only by trial and error or by methods of successive approximations. Further lengthy calculations are required to determine the constants giving the amplitudes of each mode for known initial conditions.
Aeronautical engineers confronted with these problems made efforts to devise simpler methods for solving for the roots of  equations, as will be described in the subsequent material. At the same time, and usually without the knowledge of aeronautical engineers, electrical engineers had developed different approaches that allowed practical solutions of even more complex systems of linear differential equations. Such solutions were required in the design of electrical circuits, vacuum-tube feedback amplifiers, and transmission lines. One method, first summarized in a book by Hendrik ~ Bode of the Bell Telephone Laboratories, entitled Network Analysis and Feedback Amplifier Design (ref 5.1) exploited the use of sinusoidal forcing functions of various frequencies to the dynamic systems under consideration, from which the stability of the systems could be determined This method was slow to be discovered by the aeronautical engineering profession because of the unfamiliar notation and applications of the electrical engineers. Later, the method was called the frequency-response method and was widely used. A second approach with the general title operational methods was also introduced by the electrical engineers. A British electrical engineer and mathematician named Oliver Heaviside devised a system of operational calculus about 1887. The Heaviside operational calculus was publicized in this country in a book by Vannevar Bush, entitled Operational Circuit Analysis (ref. 5.2) and was introduced to the aeronautical profession by Robert T. Jones in NACA report No. 560, A Simplified Application of the Method of Operators to the Calculation of Disturbed Motions of an Airplane (ref. 5.3). Later, the book by Murray F: Gardner and John L. Barnes, Transients in Linear Systems Studied by the Laplace Transformation (ref. 5.4), described the operational method based on Laplace transforms, which became generally accepted as easier to understand than the Heaviside method. The advantage of operational methods is that solutions for frequently encountered equations and for special inputs such as steps and ramps can be obtained from tabulated precalculated formulas.
A third approach for solving these systems of equations was the use of simulators, generally referred to at the time of their development as differential analyzers. Vannevar Bush developed a mechanical differential analyzer at MIT that I saw about 1934 while I was still in high school. This machine took the equations in an integrated form so that the various terms required integration rather than differentiation. The integration was done by devices known as rolling-wheel integrators. The low torque output of these devices was amplified by winch-type electromechanical servos to drive a large array of shafting and gearing that allowed setting in the correct constants from the equations. The whole equipment required a room about 25 by 60 feet. This machine had excellent accuracy and was used by an MIT student to get some of the first solutions for the motion of airplanes with automatic controls. Later, such simulators were made with servodriven potentiometers to enter the constants and electronic operational amplifiers to perform the integrations. These machines had tremendously increased capabilities, but they in turn became obsolete with the development of electronic digital computers.
Although the airplane as a whole can be described accurately by linear differential equations, many of the subsystems, such as control surfaces or autopilots, involve nonlinear components. For example, control surfaces have static friction, and electronic devices often have switches that give a discontinuous output. In general, nonlinear systems include devices in which the output varies in a nonlinear but continuous manner, such as a crank, or in which the output varies discontinuously, such as a bearing with coulomb friction or an on-off switch. Much of the mathematical analysis of nonlinear systems when I was in college had been concerned with the continuous type of nonlinear systems, though solutions were usually available only for systems capable of representation by special types of differential equations. The only method of analysis for discontinuous systems with which I was  familiar was the phase plane method, a graphical method described in the book by Nicolai Minorsky, Introduction to Non Linear Mechanics (ref. 5.5). 1 used this method on problems involving simple types of autopilots. With the eventual development of analog computers, such problems could be solved readily.
A final point that should be appreciated by the reader is the state of computational facilities at the time much of my work at Langley was conducted. Prior to about 1955, the only widely used computers were the slide rule and mechanical calculators such as the Marchant and Frieden that required several seconds to multiply or divide two numbers. To perform lengthy calculations, female employees called computers were employed to calculate results with these machines by following sheets that had the necessary steps listed in tabular form. Such calculation sheets are today called spreadsheets.
In making analytical studies of problems, a very desirable result was a closed-form solution, which means a formula in which numbers can be substituted for any particular case to determine the numerical value of the desired quantity. The determination of these closed-form solutions had been the objective of mathematicians and scientists for many years. In the aeronautical field, for example, Ludwig Prandtl determined the formulas for calculating induced drag of wings, Max Munk derived formulas for moments acting on ellipsoids in steady flow, and Theodore Theodorsen derived formulas for the lift and moments on oscillating wings. The formulas are considered to be in closed form if they give results in terms of known tabulated functions, such as trigonometric functions or Bessel functions. Most of these formulas and their originators became very famous because airplane designers could calculate results accurately for a configuration that at least approximated the one in which they were interested
With the advent of analog computers and later of high-speed digital computers, the need for closed-form solutions was reduced. Most calculations on the digital machines are made by numerical methods. One such method is the step-by-step method in which the response of a system to a disturbance or the trajectory of a vehicle is calculated a small increment at a time. Another numerical method is the Monte Carlo technique, in which many trial solutions are made to find the one with the best answer for the problem. Many problems of structures or fluid mechanics are solved by finite-element methods, in which the equations relating each small element of a large structure or flowfield are solved. These methods involve tremendous amounts of numerical computation, which modern electronic computers can handle in a very short time. Since I had none of these methods in my college education, my facility with such techniques is much less than that of students who grew up in the computer age.
With this background, I will describe some of the analytical studies that I conducted during my early employment at Langley.
Graphical Solution of the Quartic Equation
As pointed out in the introductory section, the solution for the motion of an airplane following a disturbance was very tedious because of the numerical calculations required. One of the problems encountered was solving for the roots of higher degree equations. A fourth-degree equation resulted in the solution for the longitudinal motion of a rigid airplane. For many problems, this equation could be reduced to a second-degree, or quadratic, equation by considering the airspeed constant, a valid assumption if short-period maneuvers were being considered. The lateral equations likewise result in a fourth-degree equation if certain simplifying assumptions are made. These fourth-degree equations, also known as quartics, are called the characteristic equations for the systems, and solving for the roots of these  equations is the first step in calculating the response of an airplane to controls.
Quadratic, cubic, and quartic equations may be written as follows:
High school students of mathematics are familiar with the formula for the solution of a quadratic equation. Formulas also exist for the solution of cubic and quartic equations, though they are considerably more complicated than those for a quadratic. For this reason, graphical methods or methods of successive approximations have been sought for the solution of these equations. In a paper on propeller governors, Herbert K. Weiss presented a set of graphs for the solution of cubic equations in terms of two parameters calculated from the coefficients of the equation (ref. 5.6). Shih-Nge Lin, in appendix I of his MIT thesis, described a method that he developed for a solution of quartic and other higher order equations (ref. 5.7). This procedure is a method of successive approximations that uses repeated long division. This method, though it was considerably quicker than the classical techniques, was still quite time-consuming without considerable practice. I therefore attempted to develop a set of charts for the quartic similar to those of Weiss for the cubic. A brief summary of this method and a sample copy of the charts are presented as appendix IV. These charts were never published. I used them to some extent in my work, but found that the time to solve for the parameters used in the charts and then to return the solution to an expression involving the original variables, required about as much time as Lin's method. This method is presented mainly because it was my only excursion into pure mathematics. With the development of high-speed computers, of course, the engineer no longer has to be concerned with these calculations because readily available computer programs can solve quartic or even much higher degree equations in a fraction of a second. As late as 1962, however, there was still interest in simplified methods for determining the roots of algebraic equations, as shown by a report by James W. Moore and Rufus Oldenburger of which I have an unpublished copy. This report presents a systematized procedure similar to Lin's method and analyses problems of convergence for cases, such as unstable roots, in which convergence of the method may be slow. Oldenburger was a well-known expert on servomechanisms before the subject of automatic control became a favorite subject for control theorists.
The airplane with fixed controls in the unstalled flight regime, fortunately, is beautifully linear. That is, all the aerodynamic forces and moments increase in proportion to the magnitude of the displacement or angular velocity, even down to very small magnitudes of motion. As a result, the measured motion of airplanes had been found to be closely predicted by the theory. Another favorable feature of linear systems is that a given solution is applicable to all magnitudes of motion. An increased initial disturbance simply increases all quantities involved in proportion to the disturbance without changing their time dependence. This condition no longer exists with nonlinear systems, and a separate solution has to be obtained for each magnitude of motion.
Solution of a Nonlinear Problem
The problem of snaking oscillations, discussed in the previous chapter, is an example of a nonlinear problem. The nonlinearity arises because of friction in the rudder control system. The rudder, instead of moving in proportion to the motion of the airplane, sticks until the aerodynamic hinge moments exceed the friction. Then the rudder starts to move under the influence of both the aerodynamic forces and the friction force.
 By the time the snaking motion had been explained, I was familiar with another method to analyze nonlinear systems. Robert T. Jones, while analyzing the stability of some of the first guided missiles developed by the Navy, had devised a technique assuming that the vehicle performs a sinusoidal oscillation. The actual control motion resulting from this sinusoidal motion was then calculated or measured experimentally. He then calculated the response of the system under the assumption that the work done on the vehicle per cycle must be the same as that done by the action of the control, and the angular impulse imparted to the vehicle over a half cycle must equal the change in angular momentum of the vehicle caused by the operation of the control. The work and momentum relations give two equations from which the frequency and amplitude of a constant-amplitude oscillation may be calculated. The expressions for the work and momentum imparted by the control may be shown to be related to the lowest order cosine and sine components of the motion of the control when expressed as a Fourier series. Jones' technique was therefore equivalent to the frequency-response method, which was then generally unknown to aeronautical engineers. It was later found that it had been developed to an extensive degree with different notation by electrical engineers for studying the stability of feedback amplifiers. I was intrigued by this method, because it appeared that the exact form of the control surface motion when subject to static friction would be important. As a result, I attempted to analyze the snaking problem by this method. I first tackled the problem of aileron snaking, a steady oscillation in roll caused by friction in the aileron control system. This problem had never been encountered in practice because of the much larger damping of the roll subsidence mode of an airplane when compared with the damping of the lateral oscillation. A much larger tendency for the controls to float against the relative wind would have been required to produce an aileron oscillation than to produce a rudder oscillation. The problem was easier to formulate, however, because of the simpler equations governing the rolling motion. Even in this case, calculation of the aileron motions subject to the control friction and the aerodynamic moments on the aileron proved to be quite difficult. After working on the problem as a part time activity for several months, I succeeded in obtaining a closed form solution. A typical example of possible steady oscillations for two cases is given in figure 5.1. In the first case, the friction is enough to cause the aileron to stick during part of the cycle; in the second case, the aileron motion is continuous.
After going through all this work, I concluded that it was hardly worthwhile to attempt a similar solution for the more practical case of the rudder snaking oscillation. The results on the aileron oscillations were never published. Many years later, however, a problem was encountered of control of a missile in which the ailerons were operated by a gyroscope sensing rolling velocity. This problem was exactly equivalent to the problem that I had solved. The only difference was that the hinge moments proportional to rolling velocity were applied to the ailerons by the gyroscope rather than by an aerodynamic floating tendency. It was possible to use my analysis to obtain some design data for the missile. As a result, my analysis was not completely wasted after all.
The frequency-response technique is based on the assumption that although the control motion is nonsinusoidal, the response of the controlled vehicle is very nearly sinusoidal because the relatively large inertia and slow response of the vehicle prevents it from responding appreciably to the higher frequencies in the irregular control motion. This assumption justifies the calculation of the control motion that is based on a sinusoidal vehicle motion. In most discussions of this method, however, the use of the lowest harmonic of the control motion in calculating the vehicle response is not justified on physical grounds. Jones' independent approach, which first based the response of the vehicle on the momentum and work relations over a....
 ....cycle and later showed that these relations gave expressions corresponding to the lowest order harmonic of the control motion, gives a clear physical interpretation of the application of the frequency-response method to nonlinear systems and provides insight into the accuracy of the method for this purpose. In the ensuing years, methods based on the frequency-response method were extensively used at the NACA and elsewhere for design of missile control systems, determination of stability derivatives from flight data (now called parameter identification), and calculation of response to turbulence. The many developments of the method, such as Bode plots, the Nyquist criterion, and root locus techniques gradually became part of the aeronautical engineer's mathematical equipment.
Computation of Lateral Oscillation Characteristics
As pointed out previously, the calculation of the airplane modes of motion prior to the introduction of high-speed computers was a tedious process. The solution for the lateral modes of motion requires the solution of a quartic equation. To simplify the process, approximate procedures were developed. Simple expressions could be found for the characteristics of the spiral mode and the roll subsidence, but accurate calculation of the Dutch roll usually required solution of the complete equations. A graphical method, first developed in 1937 by R. K. Mueller of MIT, proved to be applicable to the Dutch roll mode. Mueller first used the method in developing the world's first electric analog computer, which he used for the calculation of the longitudinal motion of airplanes (ref. 5.8). He discovered, however, that once he had perfected the graphical method, he no longer needed the analog computer. Later the method was discovered independently by K. H. Doetsch and W. J. G. Pinsker, two former German engineers working at the Royal Aircraft Establishment (RAE) after WW II. They called the technique the time vector method and applied it to calculation of the Dutch roll mode. Later, W. O. Breuhaus of the Cornell Aeronautical Laboratory, on a visit to England, learned the method from the RAE engineers and publicized it in the United States (ref. 5.9). Prof. E. E. Larrabee of MIT, on a sabbatical leave at the NACA Langley laboratory, showed how the method could be used to calculate stability derivatives from measured lateral oscillation data (ref. 5.1 0).
The time vector method is based on the fact that in a free oscillation of a linear system, the variables involved always maintain the same ratios of amplitude and the same relative phase angles. The variables can be depicted on a polar vector diagram in which the amplitude of each variable is shown by the length of an arrow and the relative phase angles by the directions of the arrows. In a damped oscillation, the diagram would rotate and shrink, but always maintain the same relative magnitude and angular separation of the vectors. All information about the motion could therefore be obtained by taking a snapshot of the diagram, which showed it at a given instant of time. Fixed relations can also be calculated between displacement, velocity, and acceleration of any quantity based on the frequency and damping of the motion.
The equations of motion involve a series of terms in each equation. In the lateral case, the equations involve roll, yaw, and sideslip. Each term in the equations consists of one of these variables multiplied by a stability derivative which gives the variation of the force or moment with the variable. For example, a typical term might be rolling velocity multiplied by the derivative, variation of rolling moment with rolling velocity. All the rolling moments contributed by the different variables are added up to give the total rolling moment, which must equal the inertia in roll multiplied by the rolling acceleration. This term may be placed on the opposite side of the equation, which results in a sum of terms equal to zero.
 Since the derivatives are constants, each term varies with time in exactly the same way as the variable in that term. A polar vector diagram may therefore be drawn that includes each term in the equation with the tail of each vector coinciding with the head of the previous one. Since the terms add up to zero, the diagram must close. A similar diagram may be drawn for each of the variables: roll, pitch, and yaw.
In using the method, the quantities to be determined are the frequency, the damping, and the ratios of the variables. Usually a value of unity is assigned to one of the variables, such as sideslip, and the ratios of roll to sideslip and yaw to sideslip are to be determined. All other quantities must be known beforehand or estimated. Usually the frequency is estimated first from the simple relation of the frequency of the airplane oscillating with a single degree of freedom in yaw. The damping is assumed to be zero. From these assumptions, initial values of the ratios of the variables may be determined by the closure of the vector diagrams. Then, with these values, more accurate values for the frequency and damping may be determined and these values used in a second attempt. The method is therefore an iterative procedure. Usually the convergence is very rapid and requires only two or three iterations to reach a solution.
The time vector method gained considerable recognition because of the rapidity of solution and because it gave a useful physical picture of the relations between the variables in an oscillation. It occurred to me, however, that the graphical work might be avoided if a similar convergent procedure could be performed analytically. After several trials of different methods, I discovered that the equations could be solved for the ratios of the variables. Therefore, a similar iterative procedure could be set up starting with an assumed value of frequency and a value of damping of zero, to calculate values of the ratios of the variables. I discussed this method with Bernard B. Klawans, an engineer in my branch. He worked out the details of the procedure. As it turned out, with the initial values of frequency and damping, the ratio of roll to yaw could be calculated. Then with this value and the values of frequency and damping, the ratio of sideslip to yaw could be calculated. Finally, with these two ratios, a quadratic equation for the Dutch roll root could be obtained that gave new values for the frequency and damping. Mr. Klawans checked the results for a wide range of variables. The calculations could be carried out readily on a slide rule or mechanical calculator, and the solutions converged very rapidly, usually within two or three iterations. Mr. Klawans published a Technical Note on the results (ref. 5. 11).
I thought this procedure was a worthwhile improvement over the graphical method, but evidently it arrived on the scene too late. In that period, about 1956, analog computers were already available, and some digital computers had been introduced. Soon programs were provided to solve the equations of motion in a matter of seconds. As a result, the approximate procedures that had occupied the efforts of stability and control engineers for many years fell into disuse.


Since I've been looking at a lot of health care data recently, I thought I'd run the US medical care CPI component through the dynamic information equilibrium model (DIEM). It turns out to have roughly the same structure as CPI overall (click to enlarge):
A big difference is that the dynamic equilibrium growth rate is α = 0.035/y, basically a full percentage point above the rate for all items α = 0.025/y. As it's been basically at play since the 50s (at least), medical prices are now twice what prices as a whole have risen in the same period.
I was curious — was the US an outlier (lol)? I ran the model over a bunch of HICP health data from Eurostat (which the UI is at best silly, at worst pathological) for several countries (Sweden, France, the Netherlands, Switzerland, Germany, the UK, Estonia, Italy, Turkey, Denmark, and Spain). This is definitely a graph you have to click to enlarge:
They're all remarkably similar to each other except France, which came out with an equilibrium rate of α = 0. That could be wrong due to the recent data being in the middle of a non-equilibrium shock — time will tell.
I also compared the dynamic equilibrium to the DIEM model of the CPI (HICP) for all items for each country which produces an interesting plot:
It looks like the US is not much of an outlier on that graph — but that's a bit misleading since the possible inflation rates can't really deviate too much above the diagonal y = x line otherwise headline inflation (i.e. all the components) would rapidly be overtaken by health care price inflation (one of those components). In fact, nearly every time it came out that the health care rate was basically equal to the headline rate. You can see it if we plot the difference versus the headline CPI rate:
Most of the countries are clustered right around zero, with outliers being the US and France. France is an outlier because its health care price inflation has been basically zero for the past decade meaning the difference graphed above is essentially the negative of the inflation rate of about 2%. The US is an outlier in the other direction — by 4 standard deviations if we leave out France and the US in the estimate of the distribution.
If this is correct, the US health care prices rise at nearly a percentage point faster than prices overall, meaning prices are nearly 30% higher today from growth over the period from 1996-2020 (the Eurostat data range) than they would be if those prices grew like any other country's. And these are prices — not income, profits, or consumption.
Here are all the individual graphs. The dashed lines are lines at the dynamic equilibrium rate, but in some of the graphs they appear well off the lines — that's because in some of the cases the different levels add the shocks in different ways (e.g. the 2nd shock is positive but the 3rd shock is negative) so they add or subtract differently for each country. Couple that with the fact that I determine the sign of a shock in the parameter estimation by the sign of the width, not the amplitude but instead of using that sign I set it by hand for the dashed line guides, and well, you see the result — random dashed lines appearing across the graphs (albeit with the right slope). Anyway, click to enlarge.


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Discrete and continuous random variables. Constructing a probability distribution for random variable.
Constructing probability distributions. Probability models example: Probability models. Valid discrete probability distribution examples. Probability with discrete random variable example.
Probability with discrete random variables. Mean expected value of a discrete random variable. Expected value.
Variance and standard deviation of a discrete random variable. Standard deviation of a discrete random variable. Next lesson. Current time: Probability distributions of random variables. Video transcript What I want to discuss a little fr in this video is the idea of a random variable.
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And random variables at Sexy Rotterdam african indian cougars can Looking for quick easy and discrete a little bit confusing because we will want to think of them as traditional variables that you were first exposed to in algebra class. And that's not quite what random variables are. Random variables are really ways to map outcomes of random processes to numbers.
So if you have a random process, like you're flipping a coin or you're rolling dice or you are measuring the rain that might fall tomorrow, so random process, you're really just mapping outcomes of that to numbers. You are quantifying the discrfte.Sexy Women Wants Real Sex Norway
So what's an example of a random variable? Well, let's define one right over here.
So I'm going to define random variable capital X. And they tend to be denoted by capital letters. So random variable capital X, I will define it as-- It is going to be equal to 1 if my fair die rolls heads-- let me write it this way-- if heads.
And it's going to be equal to 0 if tails.
I could have defined this any way I wanted to. This is actually a fairly typical way of defining a random variable, especially for Lolking coin flip. But I could have defined this as And I could have defined this as And this would still be a legitimate random variable.
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It might not be as pure a way of thinking about it as defining 1 as heads and 0 as tails. But that would have been a random variable.
Notice we have taken this random process, flipping a coin, and we've mapped the outcomes of that random process. And we've quantified them.
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We can define another random variable capital Y as equal to, let's say, the sum of rolls of let's say 7 dice. And when we talk about the sum, we're talking about the sum of the let me write Looking for quick easy and discrete the sum of the upward face after rolling 7 dice.
Once again, we are quantifying an outcome for a random process where the random process is rolling these 7 dice and seeing what sides show up on top. And then we are taking those and we're taking the sum and we are defining a random variable in that way.Adult Want Nsa Newton Highlands Massachusetts 2161
So the natural question you might ask is, why are we doing this? What's so useful about defining random variables like this? It will become more apparent as we get a little bit deeper in probability.
But the simple way of thinking about it is as soon as you quantify outcomes, you can start to Looking for quick easy and discrete a little bit more math on the outcomes.
And you can start to use a little bit more fro notation on the outcome. So for example, if you cared about the probability that the sum of the upward faces after rolling seven dice-- if you cared about the probability that that sum is less than or equal to 30, the old way that you would have to have fpr it is the probability that the sum of-- and you would have Looking for quick easy and discrete write all of what I just wrote here-- is less than or equal to You would have had to write that big thing.
And then you would try to figure it out somehow if you had some information. But now we can just write the probability that capital Y is less than or equal to Sex dating in Rexmont It's a little bit cleaner notation. And if someone else cares about the probability that this sum of the upward face after rolling seven dice-- if they say, hey, what's the probability that that's even, instead of having to write all that over, they can say, well, what's the probability that Looking for quick easy and discrete is even?
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Now the one thing that I do want to emphasize is how these Looking for quick easy and discrete different than traditional variables, traditional variables that you see in your algebra class like x plus 5 is equal to 6, usually denoted by lowercase variables. These variables, you can essentially assign foor.
You either can solve for them-- so in this case, x is an unknown.
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You could subtract 5 from both sides and solve for x. Say that x is going to be equal to 1. In this case, you could say, well, x is going to vary.
We can assign a value to x and see how y varies as a function of x. You can either assign a variable, you can assign values to them. quidk
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Or you can solve for them. You could say, hey x is going to be 1 in this case. That's not going to be the case with a random variable. A random variable can take on many, many, many, many, many, many different values with different probabilities.
And it makes much more sense to talk about the probability of a random variable equaling a value, or the probability that it is less than or greater than Looking for quick easy and discrete, or the probability that it has some property. And you see that in either of these cases.
In the next video, eas continue this discussion and we'll talk a little bit about the types of random variables you can have.


Maths is all around us and problem solving is at the heart of the mastery approach. Look for maths problems you can solve together, making connections between what your child has been learning at school and the world around them.
Demonstrating these connections – and representing them in multiple ways – not only supports your child’s understanding and cements their knowledge; it reinforces the relevance of maths in our lives and makes it fun.
- Follow a recipe: work together to find out the quantities needed, ask your child to weigh the ingredients, discuss how you’d halve or double the recipe and discuss the ratio of ingredients.
- Talk about the weather forecast: is today’s temperature higher or lower than yesterday’s? What do the numbers mean?
- Going shopping: talk about the cost of items and how the cost changes if you buy two items instead of one. Let your child count out the coins when paying and discuss the change you get back. Use coins to explore addition, subtraction, multiplication and division.
- Planning an outing: discuss how long it takes to get to the park, and so work out what time you need to leave the house. Encourage your child to work out the best solution based on the time and distances. Discuss what shapes you see when you get there
- Telling the time, discussing the days of the week, talking about money or the coins needed to pay for items, how long things take to cook
- GROWTH MINDSET – Everyone of us can master mathematics given the opportunity.
Ideas for Counting
- Collections of objects – shells, buttons, pretty stones
- Cars on a journey, e.g. how many red cars?
- Animals in a field e.g. sheep, cows
- Stairs up to bed, steps, etc.
- Pages in a storybook
- Counting buttons, shoes, socks as a child gets dressed
- Tidy a cupboard or shelf and count the contents e.g. tins, shoes, etc.
- Counting particular vehicles on a journey e.g. Eddie Stobart lorries, motorbikes, etc.
- Keep maths practical and real life
- Money – paying for things, playing shops, purses
- Dishing up dinner – problem solving
- Games (snakes and ladders, dice)
Think about a picture and see what questions you can derive from it to ask your child. For example, using this picture, look how many questions we can ask related to maths:
Mathematics language often uses common words in a new way. For example, ‘difference’, ‘right’, ‘product’, ‘table’.
To support your child’s understanding of mathematical words, ask them to explain the words they’ve been using and what they mean. Find out what new maths vocabulary your child’s teacher is introducing so you can use it at home to complement their learning.
Always encourage your child to explain how they have gone about solving a problem, and work with them to test, prove, explain, reflect and spot patterns. Questioning and prompts can be powerful tools to boost your child’s mathematical thinking: ‘What do you think…?’ ‘Why …?’ ‘What will happen if…?’ ‘What do you notice about…?’ ‘Can you see a pattern between…?’ ‘What if we try…?’
Communicating and discussing maths problems (in a way that others can understand) demonstrates depth of understanding – another fundamental aspect of mastering mathematics.


In most cases, it involves rudimentary arithmetical knowledge. In some circumstances, candidates must also understand some complex mathematical concepts. Financial analyst – Financial analysts are trained to create mathematical models for a variety of institutions, including banks, insurance companies and private businesses. Earning your bachelor’s degree in mathematics is the first step toward a career in this exciting field, and a financial analyst can expect to make an average salary of $85,660 per year. However, most financial professionals only need basic knowledge in algebra and simple rules such as the order of operations to excel in their job.
- With comprehensive financial reporting, automated billing, built-in audit trails, and personalized workspaces, you can unify your business on the Salesforce platform.
- On top of that, they must also understand those concepts to provide better services.
- For example, you can easily and with great precision model a loan amortization schedule.
- Being able to think of money in terms of numbers only is among the most important qualities of an accountant.
- Easily manage your global operations with best-in-class accounting.
Get compliant with the new ASC 606 and IFRS 15 standards, automate calculations, and reduce period-end close for a complete picture of your revenue. The professional associations also provide information on average and potential earnings on their websites (see ‘Where to find more information’, below). On the other hand, Accountants are more focused on understanding plugging numbers into existing formulas and processes. Of course, the salaries firms offer grads vary and it seems the more prestigious the firm, the less need it has to offer an attractive salary package. The median salary, accounting for 50 per cent of those surveyed, was $45,000 – $55,000. Braun gave an example of an unusual field that is in need of an accountant. Accredited by the Association to Advance Collegiate Schools of Business International, the Department of Accounting and Finance offers a stepping stone to in-demand careers.
What Does An Accountant Do? Responsibilities, Skills & Trends
They’re good at helping other people learn.Have you ever tutored a friend in a tough class? Accountants help others learn things — what records to hang on to for tax time, how to record tricky international financial transactions and more.
There is math involved, but I would not consider it to be of any intense difficulty. A lot of accounting majors will have statistics and some toned down level of calculus for social sciences or something as part of the program. To be effective in this role, an accountant must understand the basic functions of a business to accurately analyze and interpret financial data.
CFOs will often take more of an active hand in developing fundraising and finance strategies for an organization. As part of the C-level executive team, a CFO participates in business strategy sessions that will lay the foundations for a company’s long-term growth. Large organizations have a lot of moving parts, and different departments may not always see their place in the grand https://www.bookstime.com/ scheme of things. Internal auditors review all of an organization’s business procedures, while making sure all departments are acting in compliance with the appropriate laws and statutes. After examining financial data within an organization, an internal auditor will make recommendations to improve risk management procedures, internal controls, and governance processes.
Linear algebra, quantum mechanics, and engineering calculations are just a few of the core courses you’ll need to take for this major. Earning a mathematics minor alongside another major provides students several professional benefits, even outside of math-heavy fields. Mathematics courses offer students logic expertise, general problem-solving skills, and an intuition for the world around them—all of which can be applied in any pursuit. Introduction to mathematical statistics – Statistics are among the most commonly used concepts in applied math. An introductory statistics course will teach students the skills they need to make estimates, calculate probability, and study data in real-world situations. Economist – If there’s one thing an economist needs to know, it’s mathematics. Many graduates with a math degree go on to perform market analysis and forecasts, and work with data crucial to the nation’s economy.
Common Job Opportunities For Math Majors
Once someone studies this subject, they can have a clear career path. However, some candidates may hesitate before choosing it due to its connection with numbers. Most people believe that they must know mathematics to study financial accounting. Before discussing that, however, it is crucial to understand what financial accounting is.
Today, accountants and CPAs are performing tasks that require analytical skills at increasing rates, largely due to the proliferation do you have to be good at math for accounting of data across industries. A common misconception is that you have to be good at math to be an accountant.
Is A Ba In Accounting Good?
Those with five or more years of experience can earn as much as $129,250 per year. Professionals in this field need to be able to use advanced accounting software and other computer-based tools to work effectively. Accounting professionals must pay strong attention to detail in order to keep information accurate and organized. With the amount of financial data that must be analyzed, it can be easy to make mistakes; however, simple errors can translate into much larger problems if they’re not caught. Additionally, a certified public accountant is an accountant who has passed the CPA exam and has met state licensing requirements.
That’s because to be an accountant, you have to be comfortable with numbers. Contrary to popular belief, you don’t need to be able to do much math at all to do accounting. Primarily addition and subtraction, with a bit multiplication and division. Problem solving skills, which people that are good in math usually have, are also important to have in accounting when you need to figure out why your out of balance, or off on a check figure.
Quantitative Finance Vs Finance
While accounting is all about numbers, there is really no need for an accounting student to be a math whiz. Let us take a look at the differences between maths and accounting.
The proposal does not change university entry requirements for business and chartered accounting degrees. While math knowledge is critical, most accounting software takes care of it.
Wisdom Comes From Learning, Not Teaching
If Shelbie has a cup of tea, a good book, or a deep conversation, she is a happy camper. With a background in accounting, classical music, and blogging, she believes learning is one of life’s greatest adventures. I love to do accounting so much but people discourage me a lot because I did Geography,Economics and Mathematics in High school.I really love to take accounting as a career. These figures are based on an annual wage for all workers in the accounting field.
Most accountants may neglect them, which can be detrimental to their work. Overall, some of the skills required for financial accounting are below. In most cases, financial accounting requires some fundamental math knowledge.
Accountants must follow lots of rules, principles, tax codes, and regulations governing what data to report and how to report it. While it is okay to be creative in terms of how you set up spreadsheets or develop presentations, “creative accounting” – or making up your own rules – is not. Accounting staff bear serious responsibility not only for an organization’s financial records, but for its overall financial health and security. That means being truthful – sticking with what you know is right and not wavering even when challenged. Cannon said often, students don’t realize that accountants give insight to managers and executives.
Being able to think of money in terms of numbers only is among the most important qualities of an accountant. You need to be somewhat good at math to get an accounting degree , but not necessarily a genius.
Financial Analysts In Investment Banks
This effort has expanded upon the public’s expectations of accurate reporting to go beyond basic honesty. As a result, companies are now expected to report their financial statements to the public in order to paint a complete picture of their current standing and reduce uncertainty in the market. While pursuing your master’s, you’ll explore new frontiers in accounting; you’ll also gain an in-depth understanding of the ethics and leadership principles that are expected of a CPA.
Mathematicians will regularly use formulas and numbers to bring about certain conclusions. There is no pattern to what mathematics equations will be needed, and the subject is a great deal vaguer than what some imagine. You don’t necessarily have to excel at math to be an accountant, but you should be comfortable working with numbers. In fact, 22 percent of accountants surveyed reported that working with numbers was what gave them the most job satisfaction, according to Robert Half. Accounting courses completely cover what you need to know how to do. You won’t need a high degree of math ability, but don’t rely on your spreadsheet or other tools exclusively. Sometimes things are put in wrong and having decent mental math abilities will allow you to catch stuff.
Communication, interpersonal, analytical and computer skills are actually more important than math in accounting. While accountants do need to be competent in math, they also need to have basic computer skills, strong analytical abilities, good interpersonal skills and a talent for effective communication. Most of the work done in financial accounting concerns using accounting standards. For example, they relate to the IFRS or the GAAP, relevant in various areas.


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Download Mathematical Foundation of Computer Science Notes Pdf. We provide bloccocverbnerbe.ml Mathematical Foundation of Computer Science study materials to. MATHEMATICAL FOUNDATIONS. OF COMPUTER SCIENCE. II B. Tech I semester (JNTUK-R16). Mr. bloccocverbnerbe.mlH. Assistant Professor. DEPARTMENT. Mathematical Foundations of Computer Science 40th International Alex Bredariol Grilo, Iordanis Kerenidis, Jamie Sikora. Pages PDF.
Mathematics underpins all of these endeavors in computer science. We use graphs to model complex problems, and exploit their mathematical properties to solve them.
Mathematical Foundations of Computer Science
As We use recursion to break down seemingly insurmountable problems into smaller and more manageable problems. We use topology, linear algebra, and geometry in 3D graphics.
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There are two variants of the model, one where the adversary needs to pick the modification rule in advance and one where the adversary can select the modification rule after observing the realized uncorrupted input.
For both settings we derive efficient near optimal policy runs in polynomial time.
Computer Science Books :
Our efficient algorithms are based on methodologies for developing local computation algorithms. We also consider a learning setting where the predictor receives a set of uncorrupted inputs and their classification. The predictor needs to select a hypothesis, from a known set of hypotheses, and is tested on inputs which the adversary corrupts.
We show how to utilize an ERM oracle to derive a near optimal predictor strategy, namely, picking a hypothesis that minimizes the error on the corrupted test inputs.
An overview Abstract: Most fixed point models commonly used in computer science share the same equational properties. We provide several complete axiomatic descriptions of these properties using equations or quasi-equations. Some of the fixed point models have an additional structure such as an additive structure.
We show that it is often possible to describe the interaction between the basic fixed point structure and the additional structure by a finite number of equations. If the authors believe that more details are essential to substantiate the main claims, they may include a clearly marked appendix that will be read at the discretion of the program committee.
Simultaneous submissions of papers to any other conference with published proceedings or submitting previously published papers is not allowed. Only electronic submissions in the PDF format are accepted. Submissions will be by the EasyChair conference system.
By submitting a paper the authors acknowledge that in case of acceptance at least one of the authors will attend the conference and present the paper. A paper is eligible for the best student paper award if all of its authors are full-time students at the time of submission.
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This must be indicated in the submission process. We study the hardness of finding short reset words. It is known that the exact version of the problem, i. This is essentially tight since a simple O n -approximation algorithm exists.
However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it inefficient. Therefore, we suggest to study the parameterized complexity of maximization problems with respect to the size of the optimal solutions to their minimization versions. Our main contribution is a parameterized approximation algorithm for MMVC, including its weighted variant.
We also give conditional lower bounds for the running times of algorithms for MMVC and its weighted variant.We provide several complete axiomatic descriptions of these properties using equations or quasi-equations. We study the hardness of finding short reset words. Large chunks of what's currently being explored is in relation to problems that we may or may not be able to solve using machines we're not even sure can, in principle, be built, and on that level "computer science" assumes spherical cows in a frictionless vacuum.
In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming. RL uses ordinary first order logic assertions to support local reasoning and also the hiding of invariants on encapsulated state, in ways suited to verification using SMT solvers.
Algorithms and the Mathematical Foundations of Computer Science
However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it inefficient. Other Updates Course slides: The Course Overview will be updated after class each day with the slides presented in lecture, as well as any handouts released.
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Counting in 2s, 3s, 5s and 10s Task Cards
get link This set of counting task cards is fully aligned to the Year 2 National Curriculum 2014 Maths objective:
follow link Pupils should be taught to:
-count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
Included are 48 task cards, three to a page, complete with answer grids. There are 12 cards for each counting step; 2s, 3s, 5s and 10s. Pupils will count on in multiples of the particular number, filling in the missing numbers. When counting in tens, pupils will count on and back in tens from any 2-digit number.
Cards 1-12 counting on across multiples of 2
Cards 13-24 counting on across multiples of 3
Cards 25-36 counting on across multiples of 5
Cards 37-48 skip counting on and back in jumps of 10
Simply print, laminate and cut up the task cards. Pupils may write their answers using a whiteboard pen directly onto laminated cards or they can record their answers on the response sheet.


Dora Saves the Crystal Kingdom is an educational game for children that gives them the opportunity to use their imagination while also learning valuable reading and math skills.
Styled by Big Fish Games after the popular preschool and kindergarten television phenomenon Dora the Explorer, Dora Saves the Crystal Kingdom invites children to solve problems in seven different interactive games. The games test essential learning skills such as reading, math, language, problem solving and creativity, as well as entertain children along the way.
In Dora Saves the Crystal Kingdom, Dora is joined by her friends Allie and Boots on her adventure to Crystal Kingdom where they all get instruction through games on such topics as shapes, colors, counting, matching, patterns and music, just to name a few. In addition, Dora Saves the Crystal Kingdom also helps teach children basic Spanish, a definite benefit in today's increasingly multicultural world.
Dora Saves the Crystal Kingdom is a family friendly educational game that children of preschool and kindergarten age will be delighted to play.


So I got a disk array and I want to know what sort of IOps workload it can support.
Articles like IOps? provide a pretty standard formula I have seen before, but only answers the question “Given a required workload IOps for an application, how big does the array need to be to support it?” This equation is
Array IOPS = (Workload IOPS * Read Workload Percent) + (Workload IOPS * Write Workload Percent * RAID IO Penalty)
However, sometimes you want to answer the opposite question “Given a total number of IOps for an array, how much workload IOps can it support?”
The answer is really just to solve for Workload IOPS in the above equation. To save you the math,
Workload IOPS = Array IOPS / (Read Workload Percent + Write Workload Percent * RAID IO Penalty)
This could have been pretty handy a couple of years ago when I was trying to build a private cloud, to help me understand how much workload the arrays we used would support – and therefore figure out how many virtual machines we could run.


The game is for kids aged 3 and up. There are small pieces, which seems to be the criteria for ages under 3. (I'm here to tell you that wanting to put everything in your mouth doesn't always stop at 3, but I digress).
It's very reasonably priced and actually quite a lot of fun. The game is simple enough for kids to grasp quickly, yet interesting enough to keep everyone involved until the end. There's no reading required, once the kids learn what the cards all mean (which didn't take long at all).
I find it to be enjoyable to play, which is good because I've played it several times a day since we got it.
I highly recommend this game for young children. It teaches them basic math skills, taking turns and how to win and lose well. And best of all, it's fun to play! :)


I wanted to quickly elaborate on the Fibonacci sequence and why it relates to trading as many people do not understand the link.
The Fibonacci sequence is relevant because it relates directly to the “golden mean”. The golden mean is a fractional curve that tapers based on the Fibonacci sequence and can be found in all organised systems. All living things are organised systems as well as many inanimate structures.
You can find the golden mean everywhere around you, from the aspect ratio of an A4 page to the curve of a shell, the length of your arm or the position of your nose on your face. By implementing Fibonacci sequences on a leaf we will be able to tell where the next stress point is and if it has enough impetus to to continue on it’s tangent or will it run out of steam.
With that simplified explanation behind us it might help to understand how this can be used on trading exchanges.
No matter what commodity is being traded on the exchanges… People are the ones doing the trading. People are living creatures and in a collective they behave as an organised system.
The Fibonacci bands represent the impetus of the collective and can therefore be used to predict stress points.
It also helps that it is part of the academic curriculum which adds another level of predictability to the mix.