Welcome to Target Defence Academy here we have detailed syllabus for NDA. NDA written examination is divided into two papers namely Mathematics and General Ability Test (GAT). The boys and girls who are seeking to apply for NDA must begin their preparation for the written exam by following the detailed NDA Syllabus which has been discussed in this article.
Important Information about NDA Exam:
Name of the Exam
National Defence Academy (NDA)
Union Public Service Commission, UPSC.
Frequency Of Exam
Twice in a Year (April & September)
Written Test consisting of Objective Type QuestionsIntelligence & Personality Test (SSB)
Mode of exam
Papers in NDA Exam
MathematicsGeneral Ability Test
Mathematics: 300 MarksGAT: 600 Marks
Total No. of Questions
Mathematics: 120GAT: 150
Mathematics: -0.83GAT: -1.33 marks
2.5 Hours For Each Paper (5 hours total)
Language of Question Paper
English &Hindi English Language paper has to be attempted in English.
After getting to know the NDA Exam Pattern it is important for the candidates to know the Syllabus of NDA Exam. The NDA Syllabus is discussed below.
NDA Maths Syllabus:
The chapters covered for NDA Maths Syllabus are given in the table below.
Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals, and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem, and Logarithms.
Concept of a real-valued function, domain, range, and graph of a function. Composite functions, one-to-one, onto, and inverse functions. The notion of limit, Standard limits, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative-application. Derivatives of sum, product, and quotient of functions, a derivative of a function concerning another function, the derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima
Matrices and Determinants
Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
Integral Calculus and Differential Equations
Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential, and hyperbolic functions. Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications.Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of differential equations, solution of the first order, and first-degree differential equations of various types—examples. Application in problems of growth and decay.
Angles and their measures in degrees and radians. Trigonometric ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties of triangles.
Vectors in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, the addition of vectors, scalar multiplication of a vector, scalar product, or dot product of two vectors. Vector product or cross product of two vectors. Applications—work done by a force and moment of a force and in geometrical problems.
Analytical Geometry Of Two and Three Dimension
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between two lines. Distance of a point from a line. Equation of a circle in standard and a general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. The angle between two lines and the angle between two planes. Equation of a sphere.
Statistics and Probability
Probability: Random experiment, outcomes, and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary, and composite events. Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems. Conditional probability, Bayes’ theorem—simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.
The topic-wise question distribution in Maths
Geometry, Matrices & Determinants
Statistics & Probability
NDA General Ability Test Syllabus:
The General ability test comprises two papers English and General Knowledge. The English paper consists of 200 Marks while the General Knowledge is of 400 Marks.
NDA Syllabus- English
The question paper in English will be designed to test the candidate’s understanding of English. The syllabus covers various aspects like as given below:
No. of Questions
No. of Marks
Ordering of Words in a Sentence
NDA Syllabus- General Knowledge
Check the topic-wise number of questions and marks distribution in the table below.
No. of Questions
No. of Marks
History & Freedom Movement
NDA Syllabus- Physics
NDA Syllabus For Physics
Physical Properties and States of MatterModes of transference of HeatMass, Weight, Volume, Sound waves and their propertiesSimple musical instrumentsRectilinear propagation of LightDensity and Specific GravityReflection and refractionPrinciple of ArchimedesSpherical mirrors and LensesPressure BarometerHuman EyeMotion of objectsNatural and Artificial MagnetsVelocity and AccelerationProperties of a MagnetNewton’s Laws of MotionEarth as a MagnetForce and MomentumStatic and Current ElectricityParallelogram of ForcesConductors and Non-conductorsStability and Equilibrium of bodiesOhm’s LawGravitationSimple Electrical CircuitsElementary ideas of workHeating, Lighting, and Magnetic effects of CurrentPower and EnergyMeasurement of Electrical PowerEffects of HeatPrimary and Secondary CellsMeasurement of Temperature and HeatUse of X-RaysGeneral Principles in the working of Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightning Conductors, Safety Fuses.
NDA Syllabus- Chemistry
NDA Syllabus For Chemistry
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction.Acids, bases and salts.Carbon— different formsPhysical and Chemical ChangesFertilizers—Natural and ArtificialElementsMaterial used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and GunpowderMixtures and CompoundsElementary ideas about the structure of AtomSymbols, Formulae, and simple Chemical EquationAtomic Equivalent and Molecular WeightsLaw of Chemical Combination (excluding problems)ValencyProperties of Air and Water
NDA Syllabus- General Science
NDA Syllabus For General Science
Common Epidemics, their causes, and preventionDifference between the living and non-livingFood—Source of Energy for manBasis of Life—Cells, Protoplasms, and TissuesConstituents of foodGrowth and Reproduction in Plants and AnimalsBalanced DietElementary knowledge of the Human Body and its important organsThe Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists
NDA Syllabus- History, Freedom Movement
NDA Syllabus For History
Forces shaping the modern world;RenaissanceExploration and Discovery;A broad survey of Indian History, with emphasis on Culture and CivilisationFreedom Movement in IndiaFrench Revolution, Industrial Revolution, and Russian RevolutionWar of American Independence,Impact of Science and Technology on SocietyElementary study of Indian Constitution and AdministrationConcept of one WorldElementary knowledge of Five Year Plans of IndiaUnited Nations,Panchsheel,Panchayati Raj, Democracy, Socialism and CommunismRole of India in the present worldCo-operatives and Community DevelopmentBhoodan, Sarvodaya,National Integration and Welfare StateBasic Teachings of Mahatma Gandhi
NDA Syllabus- Geography
NDA Syllabus For Geography
The Earth, its shape and sizeOcean Currents and Tides Atmosphere and its compositionLatitudes and LongitudesTemperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation and PrecipitationConcept of timeTypes of ClimateInternational Date LineMajor Natural Regions of the WorldMovements of Earth and their effectsRegional Geography of IndiaClimate, Natural vegetation. Mineral and Power resources;Location and distribution of agricultural and Industrial activitiesOrigin of Earth. Rocks and their classificationImportant Sea ports and main sea, land, and air routes of IndiaWeathering—Mechanical and Chemical, Earthquakes and VolcanoesMain items of Imports and Exports of India
NDA Syllabus For Current Events
Knowledge of Important events that have happened in India in recent yearsProminent personalities of both Indian and International level, Cultural activities and sports activities, Current important world events.
Intelligence and Personality Test
The SSB procedure consists of two stages. Only those candidates who clear written exam are permitted to appear for SSB round. The details o SSB exam are given below:
NDA SSB Personality Test
Officer Intelligence Rating (OIR)Picture Perception Description Test (PP&DT).


Have you ever wondered how mathematics was used with little to no verbal language? Have you ever wondered why we calculate time the way we do in base 60? Or have you simply even wondered how currency came about? If you answered yes to any of these questions with a spark of interest, then Quite Right: The Story of Mathematics, Measurement, and Money, by Norman Biggs, is the book for you! Through the progression of this book, you will learn many aspects of the history of mathematics, measurement, and money.
Some strong points of this book are the explanations and the amount of content covered. Throughout the book, the reader will be taken through many different mathematical concepts that have been around for centuries and how those concepts played a role in society based on the given region’s culture. Readers will be able to visit places like Egypt and visit people like the Babylonians! This book does use the history of mathematics as a stronghold for the content area, but it also has a lot of solid tie-in material that involve forms of measurement and money.
Some of the weak points of the book have to deal with the disbursement of content and the ability to comprehend certain mathematical topics. As said before, the history of mathematics is the majority of this book, so if one is going in hoping to learn more about measurement or money, it would be best to find a different book. However, if a solid mix in of measurement and money is well enough, then this is an excellent choice! Along with some disbursement issues, the pacing can be odd as well, but can be overlooked quickly with the next upcoming possibly more interesting topic. The recommended mathematical reading level definitely requires some college level mathematics, as the mathematics can go fairly in depth and abstract enough where some deeper mathematical knowledge is required.
All in all, anyone that is looking for some interesting facts about the history of mathematics, measurement, and money, then this is a great read! As long as the reader has a fairly good sense of mathematics, the book will be a pleasant experience to read through. I would say that this book gave me a greater understanding of why mathematics is a thing in society from a theoretical point of view. For a rating, I would give this book a solid 7.5 out of 10.


The above formula is known as the “Wallis product,” named after John Wallis, a English mathematician who first recorded it in 1655. Wallis was apparently quite prolific and, among other contributions, is known as the mathematician that introduced the symbol for infinity:
The interest of this blog post, however is the Wallis product. The Wallis product provides a definition for pi, besides the standard definition of the ratio of a circle’s circumference to its diameter:
Pi is typically one of the first “irrational” number learned in school, others being e (2.17182…) and the square root of 2 (1.41421…). “Irrational” simply means the number cannot be written as a simple fraction (like 1/2 or 5/11). This additionally means the number has an infinite number of digits, so you can never write down the exact value.
The Wallis product is an infinite product that shows another way pi can be written and calculated. So why am I bringing up a formula that been around for 361 years? Because recently scientists found the Wallis product in nature. Specifically in the energy levels of a hydrogen atom.
University of Rochester particle physicist Carl Hagen discovered the connection while looking at the error in calculating the energy levels of a hydrogen atom. He said he immediately noticed a pattern and, upon investigation, discovered the pattern matched the Wallis product. What this says as that as energy levels increase, the hydrogen atom model approaches the Bohr model, that of a perfect sphere. Therefore it makes sense that pi makes an appearance.


… the “how high you have to be above the shore to see the Farallons” SRS Challenge to a friend.
You remember the original Challenge about seeing the Farallons. The question there was “can you see the Farallon Islands from the western shoreline of San Francisco?”
There was an interesting observation in that post. It turns out that you can see them from the bluff over the shore, but not when you’re standing on the shore itself.
We figured out that the explanation (ignoring atmospheric refraction effects) was that you have to be some distance above the sand in order to see the islands. The question was really how high do you need to be to see the base of the islands?
I told my friend about the math involved, waved my hands a lot, and drew a few diagrams on a piece of paper. But sometimes, that’s a bit, well… handwavy. What I really wanted was a simple interactive graphic. You know, the kind where you move the slider up and down, and it shows you how far out to sea you can see.
An example of such a widget can be seen at the Physics Classroom Interactive Lens web page. Here’s an example:
|Side-by-side images from Physics Classroom, an interactive lens tool.
If you slide the focus slider (f) and the height slider (H), the image above changes in real-time
to show the relationships between focal length and the height of the original image.
In this widget, when you slide the f and H sliders to the left or right, the paths of the lines change as you wiggle the variable values around.
The Challenge this week is to figure out how to make such a thing to interactively show the relationship between height and visible distance.
This Challenge is really for the teachers out there, who might like to make such a widget to help illustrate and teach a particular point. But I suspect that having the ability to make these little instructive interactables would be a handy sensemaking tool in general.
The REAL Challenge is to find a tool that will help you make such a thing. Once you find that tool, use it to make a simple interactive widget that illustrates this height-over-the-sand to visible-distance relationship.
To get you started, here’s a side-by-side sketch of what such a widget might look like. In the first image, the observer’s eye is 1.7 meters above the beach, which lets the observer see 4.7 km out to the visible horizon.
The interaction is simple: As you drag the red dot up, the value of the “height above the beach” changes. In this image, it’s 100m. You can drag it down to 0, or up to a much higher number. As you drag, the widget updates the “visible distance” number as you drag, and redraws the red line to touch a point on the circle (in this case, one that is 36 km out).
In this next image, I’ve dragged it down a bit. Here it’s just 1.7 meters above the beach, and the red dotted line only goes out 4.7 km. As I drag the dot, the numbers should update, the line to the dot should move up and down, and the line to the point on the circumference of the circle should slide along to show the distance.
NOTE: These are sketches of what the widget might look like. They’re NOT images from a working widget.
The formula connecting these two variables look like this:
distance = 3.7 * (height ^ 0.5)
where height is in meters, and distance is in kilometers. (In the top example, since the height is 100m, the square root of 100 is 10. Hence, 10 * 3.7 = 37 km.)
To start off, see if you can find a toolkit that will let you make a simple widget–that is, one that lets you slide a slider. (Don’t worry about drawing the diagram on your first pass.) Then, once you get that working, try to add in the diagram.
Fair warning: I don’t know how hard this Challenge will be–I haven’t solved it yet (or really started it). On the other hand, this is much more like the SearchResearch Challenges analysts solve in their day-to-day work.
I’ll be fascinated to see what we can come up with.
When you get something working, put it into a web page and post your URL to the comments section. I’ll collect them (along with your comments about how to answer the Challenge) next week.
If it’s going slowly, I’ll give some hints over the next few days (and maybe extend the Challenge for a second week).
As always, let us know what you’re thinking about as you search. What queries did you do? What were your experiences in finding a tool to help build this thing? How did you figure it all out?


Logic will get you from A to B. Imagination will take you everywhere.
More theory …
After last post theoretical questions were open and the time for the writing was out. I will try to answer some of them now =)
First order logic and Unification
First-order logic (FOL) or also called predicate logic has one or more arguments for each predicate and utilizes quantifiers (“for all” and “at least one”). First-order logic is simple but enough to formalize all classic mathematics. A first-order theorem, for example, consists in a set of axioms and sentences that we can reduce from them.
PROLOG is based on FOL and for that, in PROLOG one has the first-order unification algorithm implicit. Unification in logic is nothing more than an algorithmic process to solve systems of symbolic expressions. The solution of an unification problem is like a map of symbolic values for each variable in the system.


Meaning Of Congruent. In geometry, congruent means that one figure is identical to another in shape and size. In mathematics, the definition of congruent angles is “angles that are equal in the measure are known as congruent angles”.
Congruent means same shape and same size. Too often, people's mouth will say one thing but their body language will convey a different message. To be congruent is to be vulnerable.
In Mathematics, The Definition Of Congruent Angles Is “Angles That Are Equal In The Measure Are Known As Congruent Angles”.
The meaning of congruent is congruous. Asa stands for “angle, side, angle” and means that we have two triangles where we know two angles and the included side are equal. What is the meaning of congruent triangles?
It Does Not Matter What Type Of Angle You Have;
Similar to or in agreement with something, so that the two things can both exist or can be…. Congruent angles can be acute, obtuse, exterior, or interior angles. Everyone senses this in others and that is called incongruence.
Congruent Means Same Shape And Same Size.
To be congruent means to be honest and have your nonverbal communication in alignment with your verbal communication. Conflicting, conflictive, incompatible… find the right word. For the pair of triangles in.
His Testimony Was Perfectly Congruent With The Content Retrieved From The Suspect’s Phone.
All of the other measurements of the circles will be identical. Everyone senses this in others and that is called incongruence. To be congruent is to be vulnerable.
The Same Shape And Size, But We Are Allowed To Flip, Slide Or Turn.
When two things are said to be congruent, it means that all of their measurements are identical. Superposable so as to be coincident throughout; It requires the therapist to stay connected at all times, during the counseling process with the client and the impending space.


The Honam Mathematical Journal (abbrev. 'Honam Math. J.') is the journal of the Honam Mathematical Society. It was launched in 1979. One volume is published each year, and each volume consists of four issues (March, June, September, and December).
Aims and Scope
The journal is devoted to the publication of original research papers in pure and applied mathematics. Research topics covered by this journal include algebra, analysis, geometry and topology, probability and statistics, mathematics education, and applied mathematics.


The abacus has had a rich history lasting over two thousand years. Ancient merchants needed a way to count things and make calculations. The Asian abaci are the most well known today, both Chinese and Japanese models still exist. The Japanese model has one row of beads with a separation bar and then four more rows of beads below. This model seems to resonate much more with Western minds than the Chinese model. The Chinese model has two rows above the separation bar and then 5 below. I still can’t wrap my mind around those versions. The abacus can still be seen used to calculate prices in some Asian stores including one in Hong Kong as recent as 2013, it is still taught in a few Asian schools, and can also be a useful tool for blind students of any nationality studying math.
Tim Cranmer was born in Kentucky during the depression where he grew up and became a true pioneer in improving the lives of people in the blind community until he died in 2001. Tim studied math and science and found math cumbersome in braille, so he modified the Japanese abacus by inserting a piece of felt under the beads so they wouldn’t slide around as loosely so numbers wouldn’t be disrupted when he and other blind users touched them. This modified Japanese model is called the modified Cranmer abacus, appearing on the market in 1962, and still available today. Tim Cranmer is also credited with inventing the first braille embosser, and also became vast friends with a teenager as they formed the Frankfort Kentucky ham radio club. The teen was Deane Blazie, who ended up working for Tim as his “Saturday boy” over six years until Deane graduated from college. While hanging out and working for and with Tim, Deane learned a lot about technology, and how Tim did things as a blind man. In the end, this all lead to Deane founding Blazie Engineering where he invented the Braille ‘n Speak, the first PDA like device for the blind, before PDAs of that capability even existed for the sighted. I was fortunate to exchange a few emails with Tim shortly before he died, though I didn’t know that then, when I experimented with a multimeter from RadioShack that could be plugged into a computer through the serial port. Tim did a lot for the blind community, was awarded an honorary PHD late in his life, and was still playing with tech when he died.
When I was in elementary school, a talking calculator with the four basic functions cost $500, so in fourth grade one of my teachers taught me how to use an abacus. Several years later Sharp released a basic talking calculator costing $70, affordable to most people including my parents for Christmas when i was in high school. Calculators were not allowed while taking the ACT test so I took in my abacus. The Procter was convinced it was electronic and took 5 minutes trying to find where the batteries were, they finely gave in and let me use it. The abacus is only a place holder for the person as they do all of the calculations, though more in pieces rather than all at once, while the abacus replaces paper, saving the results along the way.
More recently, I found i could do math in binary on an abacus, and used it on Cisco networking exams. No subnet calculators are yet allowed on those either.
With several computers around me as I write this, I still have an abacus on my desk. It’s still more efficient for me to grab it and add up a few numbers, or save a number than to open up a calculator program and leave where I’m currently working.
I know the abacus hasn’t been updated in decades, but it still gets amazing batter–no, still no batteries. When Allison Sheridan, who records the Nosilla podcast, asked her listeners for examples of old technology listeners were still using I just couldn’t resist.
As I said, the person is still doing all the calculations in their head as the abacus keeps track for them, there are methods that can be learned to help with solving specific situations when doing math on the abacus more efficient making the process much faster than it would be if these steps called secrets weren’t memorized. Here is a nice introduction on how the abacus. Is still an under-valued tool,, along with a comprehensive list of resources on how to learn and teach using one.
I am still grateful to my vision teacher in fourth grade, Marina, who taught me the abacus as it has made math easier for me over the rest of my life. Calculators are great, but if one doesn’t understand what the calculator is doing, they may unknowingly accept wrong answers if numbers are entered incorrectly. I wonder how sighted children might benefit if they also learned at least basic abacus skills in early math classes.
Though very low tech, the abacus is still very useful and, at least for me, will never completely be obsolete.


C program to find the total number of digits in a number.
Question: The problem of counting the digits in a positive integer or summing those digits can be solved recursively. For example, to count the number of digits think as follows: If the integer is.
There is a pattern in binary representation of the number that can be used to find if number is a multiple of 3. If difference between count of odd set bits (Bits set at odd positions) and even set bits is multiple of 3 then is the number. Example: 23 (00.10111) 1) Get count of all set bits at odd positions (For 23 it’s 3).
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute to sign up. Sign up to join this community. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home; Questions; Tags; Users; Unanswered; 100 using only 5 number of digits. Ask Question Asked 1 year, 6 months ago. Active 1.
C Programming-Write an Efficient Method Check if a Number is Multiple of 3 -If sum of digits in a number is multiple of 3 then number is multiple of 3 e.g.
This is the second part of our article to solve this coding interview question, how to find the sum of digits of an integer number in Java. In the first part, we have solved this problem without using recursion i.e. by using a while loop and in this part, we will solve it by using recursion.It's good to know different approaches to solving the same problem, this will help you to do well on.
That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication.
Find out duplicate number between 1 to N numbers. Find out middle index where sum of both ends are equal. Write a singleton class. Write a program to create deadlock between two threads. Write a program to reverse a string using recursive algorithm. Write a program to reverse a number. Write a program to convert decimal number to binary format.


A C% confidence interval for a population parameter is an interval of numbers such that, if we could generate many different random samples from the population, C% of the samples would contain the true value of the population parameter. A confidence interval provides an interval estimate for a population parameter. To calculate a confidence interval, you must specify the level of confidence, you must have a random sample from the population, and you must know the sampling distribution of the statistic that forms the basis for the confidence interval.
We are interested in estimating the mean of a population, µ. The population has a standard deviation of σ. We have a random sample of N=100 observations from this population. The sample mean,, has a normal distribution with mean µ and standard deviation. The 95% confidence interval for µ is
. We obtain the number 1.96 from a table giving values for a standard normal distribution, using the fact that the probability that a standard normal random variable lies in the interval [ -1.96,1.96 ] is 0.95.
The idea is thatprovides a good estimate of the population parameter μ. A confidence interval provides another estimator of μ that takes into account the variability ofOnce we have calculated a particular confidence interval given an observed sample, we are 95% confident that our interval contains the true value of the population parameter.
In general, for statistics that have a normal distribution, the general formula for a confidence interval is [Statistic - Margin of Error, Statistic + Margin of Error], where Margin of Error = (standard error of the statistic) x (table value). For most cases, we use a t-table to find the appropriate table value for a specified level of significance.
We are interested in estimating the average amount, µ, spent by teenage shoppers at an online music store in a one-month period with 90% confidence. We know that the standard deviation of purchases is $16. We collect a random sample of purchases of 64 teens. The mean value of purchases of these 64 teens is a random variable which has a normal distribution with a mean of µ and standard deviation of $16/8 = $2. In one particular sample, the 64 teens purchased an average of $56 worth of music online. The $56 is the sample average for this particular sample. A different sample of the purchases of 64 teens would have produced a different sample average.
A 90% confidence interval for μ is given by [ $56 - 1.645 x $2, $56 + 1.645 x $2 ] = [ $52.71, $58.29 ]. The number 1.645 is obtained from a standard normal table: the probability that a standard normal random variable is in the interval [ -1.645, 1.645 ] is 90%. We are 90% confident that the population average purchases by teen shoppers is between $52.71 and $58.29.
The best estimate of the population mean is the sample mean, $56. The confidence interval allows us to consider the amount of uncertainty that we have about this estimate. Although our best estimate of μ is $56, we are 90% confident that the value of μ is in the interval [$52,71,$58.29]. This is an estimate that takes into account our uncertainty about our estimation.
In many cases, the formula for a confidence interval is (statistic - TV*SE, statistic + TV*SE), where TV is shorthand for table value and SE is shorthand for the Standard Error of the Statistic. The table value is determined by the sampling distribution of the statistic you are using.
- As our level of confidence increases, the width of the interval increases and the estimate becomes less precise. Specifically, a 90% confidence interval is wider than an 80% confidence interval.
- If we keep the level of confidence the same and if the standard deviation stays the same, an increase in the sample size, N, reduces the width of the confidence interval and the estimate becomes more precise.
- The sample statistic is always contained in the interval. In fact, the sample statistic is in the middle of the confidence interval.
- If we create many different samples, and calculate a confidence interval for each sample, then C% of those samples will contain the true population parameter. 100 - C% of those intervals will NOT contain the true population parameter value.
Why can't I say that there is a 95% probability that the interval contains the population parameter?
This is actually a good question, subject to some debate among statisticians. In most elementary statistics classes, the population parameter is a fixed (but unknown) number. It's not a random variable. Since it's not a random variable, you can't assign probabilities to the values it takes except in a vacuous sense. By "vacuous" sense, I mean the following: suppose the true value of the population mean is 12.4. Then the probability that μ = 12.4 is 1; the probability that μ equals any other value is 0.
In other words, a confidence interval either contains the population parameter (and the probability that it is in the interval is 1.0) or it does not contain the value (and the probability that it is in the interval is 0).
The way to think about confidence intervals is to think about creating many different intervals from many different samples. If we have a 95% CI, then 95% of the intervals calculated from the set of samples will contain the true population parameter and about 5% will not. If we pick ONE sample and calculate ONE interval, we are 95% confident that we got one of the samples that does contain the population parameter.
Many students seem to want to say that a wider interval is more accurate. I think that what they mean is that an interval that has a higher confidence level (and is, thus, wider) is more likely to contain the population parameter. This is another version of interpreting a confidence interval with probability ideas, and is incorrect.


Congratulations to all of the staff, students, parents and governors at The Hamble School for achieving the best set of results ever.
Students at The Hamble School have bucked the national trend by improving their results by over 10% in the headline figure of the percentage of students gaining 5 A*-C including English and maths. This is testament to the whole team at The Hamble School; the embodiment of ‘Achieving Excellence Together’.
- 65% of students achieved an A*-C in English and maths. This is a 14% improvement on the 2015 results.
- 62% of students achieved 5 GCSEs at A*-C grade including English and maths. This is a 14% improvement on the 2015 results. (See graph below. *: A*-C in English and Maths)
- 75% of students achieved an A*-C in English. This is a 24% improvement on the 2015 results and is above the national average.
- 84% of students made expected progress in English. This is a 32% improvement on the 2015 results and is significantly above the national average.
- 73% of students achieved an A*-C in maths. This is a 4% improvement on the 2015 results and is above the national average.
- 68% of students made expected progress in maths. This is in line with the 2015 results and is above the national average.
- A value added best 8 projection improvement of +41.9 to significantly above a 1000 at 1014 exemplifies the success of the students at The Hamble School.
- 2016 Attainment 8 score of 49.25.
- 2016 Progress 8 score of 0.1 compared to -0.31 in 2015.
- 19% of students achieved the English baccalaureate.
- 98.9% of students went into further education or employment.
As a year group the class of 2016 have produced the best results ever. Special mention goes to the following students who achieved fantastic results having made on average four/five levels of progress across the majority of subjects:
- Abigail Robbins: 10A*s
- Hannah Breakwell: 9A*s and 1A.
- Thomas Jobbins: 6A*s and 2As
- Sunny He: 4A*s and 4As
- Alice Fitzgerald: 3A*s and 7As
- Rhianna Hill: 3A*s and 6As
- Ella Boxall: 2A*s and 6As
- Dan Smith: 1A* and 6As
We are very proud of the achievements of our students at The Hamble School.
Levels of Progress
Students are expected to make three levels of progress from Key Stage 2 to Key Stage 4.
|Pupils making three levels of progress in English||67%||55%||84%|
|Pupils making three levels of progress in Maths||63%||69%||68%|
|Pupils making four levels of progress in English||23%||18%||30%|
|Pupils making four levels of progress in Maths||22%||31%||33%|
Value Added Scores
A pupil’s value added score is a comparison of their results at GCSE and equivalent and the average performance of other pupils with a similar ability. The individual pupil scores are added together and averaged to produce the school level VA measure. This number is presented as a number based around 1000. Measures above 1000 represent schools where pupils on average made more progress than similar pupils nationally.
|The Hamble School VA Score||959.7||973.5||1014|
Progress 8 is a new secondary accountability measure (introduced in 2016) aimed at measuring the progress of pupils across a selected set of 8 subjects.
It is a type of value added measure, meaning that pupils’ results are compared to the actual achievements of other pupils with the same prior attainment.
The school’s Progress 8 score is the mean average of its pupils’ Progress 8 scores.
This is therefore calculated by adding each individual pupil’s Progress 8 score, and then dividing this total by the number of pupils.
|The Hamble School Progress 8 Score||-0.31||0.1|
Click here to access information about The Hamble School on the DfE school performance tables website.


Now for those who are not familiar with the concept of binary numbers, please read the following post : decimal to binary conversion.
Now, the method works like this. Just traverse the binary number step by step, starting from 0 to n-1, where n is the most significant bit(MSB) ,
multiply them with 2 with raising powers and add the sum together. E.g to convert 1000(which is binary equivalent of 8), just do the following
1 0 0 0 ==> going from right to left
0 x 2^0 = 0
0 x 2^1 = 0;
0 x 2^2 = 0;
1 x 2^3 = 8;
work. Note : The program works only for 16-bit binary numbers(non-floating) or less. Leave a comment if anything is not clear. You are bound to receive a reply.
// Program to convert binary to its decimal equivalent
int i=0,sum = 0;
// prompts the user to input a 16-bit binary number
std::cout<<" Enter the binary number (16-bit) : ";
while ( i != 16 ) // runs 16 times
sum += (x%10) * pow(2,i);
x = x/10;
std::cout<<"\n The decimal equivalent is : "<<sum;
------ OUTPUT ------
------ Programming Advice and Tips ------
1 : Note : The above program only accepts 16-bit binary numbers as inputs. This limit can be increased by increasing the number of loop executions by
changing the value in the while loop from 16 to say 32. (be sure it is a valid number which is a factor of 2 ).
2 : This program is the most basic method to do this type of conversion. However, there are a number of algorithms to do the same, so just GOOGLE out some
of them. Try it out, there are a variety of programs that do the same conversion in different ways.
Please do comment if you don't understand any part or want to know more or just want to say thanks. I love programming and love to teach my friends. Your suggestions and appreciation will make this blog much better.
2 : Decimal to binart conversion (v2.0) : http://programsplusplus.blogspot.in/2012/04/decimal-to-binary-conversion-program.html


Dealing with statistical information and reasoning under uncertainty
Reasoning on probabilities and proportions
Most statistical problems encountered throughout life require the ability to quantify probabilities based on proportions. Recent findings on the early ontogeny of this ability have been mixed. To address these ambiguous findings, we tested whether 12-month-olds and 3- and 4-years-olds rely on proportions of objects to estimate probabilities of random sampling events using identical methods across age groups and similar methods to previous studies.
Simple heuristics and statistical inferences from populations to samples
Human infants, apes and capuchin monkeys engage in intuitive statistics: they generate predictions from populations of objects to samples based on proportional information. We investigated whether intuitive statistical reasoning is also present in long-tailed macaques (Macaca fascicularis), a catarrhine monkey.
Risky decision making
In this project, we investigate risky decision-making in long-tailed macaques (Macaca fascicularis) in a classic risky choice paradigm: The monkeys can choose between a “safe option” that always yields a medium amount of food and a “risky option” with different possible outcomes. We are particularly interested in whether risky decision making is affected by the level of risk that the monkey encounters and whether it matters who gives out the rewards.
Statistical information from repeated types of events
In this project, we investigated whether long-tailed macaques extract statistical information from repeated types of events to make predictions under uncertainty.
Placì S, Fischer J, Rakoczy H (2020)
Do infants and preschoolers quantify probabilities based on proportions?
Royal Society Open Science 7(9): 191751 - DOI -
Placì S, Padberg M, Rakoczy H, Fischer J (2019)
Long-tailed macaques extract statistical information from repeated types of events to make rational decisions under uncertainty
Scientific Reports 9: 12107 - open access -
Placì S, Eckert J, Rakoczy H, Fischer J (2018)
Long-tailed macaques (Macaca fascicularis) can use simple heuristics but fail at drawing statistical inferences from populations to samples
Royal Society Open Science 5(9): 181025 - DOI -


The Creator and Writer of Steecy
Stavros Klaoudatos when he was 15
Stavros is the creator of steecy.com. He created this website in May 2021. His vision was to create a platform where he could publish many articles for free and help educate people on various topics. He has a passion for Physics, Mathematics, Computer Science, and Economics. He is a Greek male born on 18/03/2005 in Athens. He created steecy when he was 16 years old, which also was the year he published his first book: “Quantum Mechanics for Starters” which can be found on Amazon here. He is the one responsible for the upkeep of the website as well as for the articles written. Furthermore, he has graduated from Stanford’s Coursera course on machine learning with 96.34%. He has published one paper in mathematics and has a GitHub repository filled with completed projects.


To guide students towards greater independence and increased responsibility for their learning.
To develop critical, creative, and reflective thinkers through integrated language arts experiences and to encourage students to be active learners who accept both the challenge and responsibility for their own learning.
Number Systems – operations with rational numbers (positive and negative integers, decimals, and fractions); problem solving and order of operations with rational numbers; equivalent representations of a number; comparing quantities.
Ratios and Proportional Relationships – analyze proportional relationships and use them to solve real-world and mathematical problems; represent ratios in multiple ways; determine if two quantities are in a proportional relationship; identify the constant of proportionality from tables, graphs, and equations; use proportional relationships to solve multistep ratio and percent problems involving simple interest, tax, discounts, gratuities and commissions, fees, and percent of change.
Geometry - identify and draw geometric shapes with given conditions; know the formulas for the area and circumference of a circle and use them to solve problems; use facts about supplementary, complementary, vertical, and adjacent angles to solve for an unknown angle in a figure; solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Expressions and Equations – combine like terms to simplify algebraic expressions; write and solve algebraic equations
Statistics and Probability – collect, organize and interpret data; calculate measures of central tendency; construct an accurate circle graph using a compass and a protractor; use data from a random sample to draw inferences about a population; calculate the probability of simple and compound events.
Performance Tasks – all seventh grade students will complete two performance tasks, in which they will apply their knowledge to real-world scenarios
To enhance student's scientific literacy and to develop the essential inquiry skills needed to investigate complex problems.
Throughout the year, students will integrate quantitative and technical text to analyze and apply content in the classroom. Seventh grade students will further develop inquiry skills by constructing and interpreting data tables and graphs. This will allow students to make evidence-based claims using data and text to support their conclusions
To foster student exploration of the connection between geography and culture.
A central focus of the course will be to examine the key components that are shared by all cultures including the Middle East and Ancient Mesopotamia, the Indian Subcontinent, Sub-Saharan Africa, and the Pre-Columbian Civilizations. To assist our students in reaching this goal, students will be expected to:
- Engage in authentic learning experiences,
- Begin exploration of primary source documents
- Further develop non-fiction literacy skills
- Trace common themes
- Collaborate to examine multiple perspectives
- Utilize digital media to strengthen understanding


Old versionsSee all
A game to help with learning about money. This program uses pictures of actual coins and bank notes in circulation at the time of making the program. It is available in 9 currencies: GB Pounds Sterling, Australian Dollars, Canadian Dollars, US Dollars, Euros, Euros in Dutch, Singapore Dollars, Ringgit Malaysia and New Zealand Dollars. If you would like me to produce a version in a currency not shown then download one of the above to see if it would be useful, first. GB pounds sterling uses 100 pennies = 1 Pound. This decimal system is reasonably standard around the world. Program includes an uninstall facility.


A mathematical paradox is any statement (or a set of statements) that seems to contradict itself (or each other) while simultaneously seeming completely logical. Paradox (at least mathematical paradox) is only a wrong statement that seems right because of lack of essential logic or information or application of logic to a situation where it is not applicable. There are many paradoxes in mathematics.
The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. Although none of his work survives today, over 40 paradoxes are attributed to him which appeared in a book he wrote as a defense of the philosophies of his teacher Parmenides. Parmenides believed in monism, that reality was a single, constant, unchanging thing that he called 'Being'. In defending this radical belief, Zeno fashioned 40 arguments to show that change (motion) and plurality are impossible.
This is related to Russell's Paradox, which asked if the set of things that don't contain themselves contained itself. By creating self-destructing sets like these, Bertrand Russell and others showed the importance of establishing careful rules when creating sets, which would lay the groundwork for 20th-century mathematics.
The Interesting Number Paradox relies on an imprecise definition of \"interesting,\" making this a somewhat sillier version of some of the other paradoxes, like the heterological paradox, that rely on contradictory self-references.
Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction.
The above results show an essential difference between abstract existence and trainability. Mathematically proving the existence of a good NN is not enough - one must also show that it can be obtained in practice. This paradox is very much related to the work of Alan Turing and Kurt Gödel. About 100 years ago, mathematicians set out to show that mathematics was the ultimate consistent language of the universe. There was a tremendous amount of optimism, similar to the optimism we see in AI today. However, Turing and Gödel turned this optimism on its head: it is impossible to prove whether certain mathematical statements are true or false, and some problems cannot be tackled with algorithms. Much later, the mathematician Steve Smale proposed a list of 18 unsolved mathematical problems for the 21st century. His 18th problem, featured in the title of our paper, concerned the limits of intelligence for both humans and machines. The mathematics of foundations, i.e., figuring out what is and is not possible, is now entering the world of AI.
The fastest human in the world, according to the Ancient Greek legend, was the heroine Atalanta. Although she was a famous huntress who even joined Jason and the Argonauts in the search for the golden fleece, she was renowned for her speed, as no one could defeat her in a fair footrace. But she was also the inspiration for the first of many similar paradoxes put forth by the ancient philosopher Zeno of Elea: about how motion, logically, should be impossible.
It might seem counterintuitive, but pure mathematics alone cannot provide a satisfactory solution to the paradox. The reason is simple: the paradox isn't simply about dividing a finite thing up into an infinite number of parts, but rather about the inherently physical concept of a rate.
The paradox identified by the researchers traces back to two 20th century mathematical giants: Alan Turing and Kurt Gödel. At the beginning of the 20th century, mathematicians attempted to justify mathematics as the ultimate consistent language of science. However, Turing and Gödel showed a paradox at the heart of mathematics: it is impossible to prove whether certain mathematical statements are true or false, and some computational problems cannot be tackled with algorithms. And, whenever a mathematical system is rich enough to describe the arithmetic we learn at school, it cannot prove its own consistency.
\"The paradox first identified by Turing and Gödel has now been brought forward into the world of AI by Smale and others,\" said co-author Dr. Matthew Colbrook from the Department of Applied Mathematics and Theoretical Physics. \"There are fundamental limits inherent in mathematics and, similarly, AI algorithms can't exist for certain problems.\"
\"When 20th-century mathematicians identified different paradoxes, they didn't stop studying mathematics. They just had to find new paths, because they understood the limitations,\" said Colbrook. \"For AI, it may be a case of changing paths or developing new ones to build systems that can solve problems in a trustworthy and transparent way, while understanding their limitations.\"
It's a monumental head-scratcher known as the 'grandfather paradox', but in September last year a physics student Germain Tobar, from the University of Queensland in Australia, said he has worked out how to \"square the numbers\" to make time travel viable without the paradoxes.
The new research smooths out the problem with another hypothesis, that time travel is possible but that time travellers would be restricted in what they did, to stop them creating a paradox. In this model, time travellers have the freedom to do whatever they want, but paradoxes are not possible.
Those two paradoxes are resolved in the same way. We came to a contradiction by assuming that a certain physical object or process exists. Once we abandon this assumption, we are free of the contradiction. These paradoxes show limitations of the physical world: a certain village cannot exist, or the actions of a time traveler are restricted. There are many similar examples of such physical paradoxes, and they are resolved in the same way.
So far we have seen that some paradoxes show us that there are physical objects or processes which cannot exist, while other paradoxes are about language and can be ignored. There is, however, a third class of paradoxes that come from language that cannot be ignored.
Mathematicians (and philosophers too) can use the fact that contradictions are not permitted to prove theorems. This is called reduction to the absurd or proof by contradiction: if you want to prove that a certain statement is true, assume it is false and derive a contradiction. Since there cannot be contradictions, the assumption of falsehood must be incorrect and therefore the original statement is true. Such proofs play a major role in modern mathematics.
Mathematical paradoxes are statements that run counter to one's intuition, sometimes in simple, playful ways, and sometimes in extremely esoteric and profound ways. It should perhaps come as no surprise that a field with as rich a history as mathematics should have many of them. They range from very simple, everyday common-sense issues, to advanced ones at the frontiers of mathematics. That is why this article has so many \"expertise level\" boxes above.
In addition to the seemingly paradoxical existence of non-Lebesgue-measurable sets, there are some more serious paradoxes. Perhaps the most famous is the Banach-Tarski paradox. This says that a sphere in 3 dimensions can be divided into a finite number of subsets (specifically, 5) which, without changing their shapes or sizes, can be reassembled into two spheres, each identical to the original one. This of course violates everything we thought we knew about what \"measure\" is supposed to mean. The way the paradox gets away with this trick is that the sets are not measurable.
Constructivist mathematicians (and some others) generally prefer proofs that do not require AC, on the grounds that such proofs are more \"clean\". However some proofs are significantly cleaner when the AC is assumed, providing elegance and generality for numerous theorems. The remarkable thing about the Axiom of Choice is that both accepting it and rejecting it lead to things that seem like paradoxes. Accepting AC is leads to the Banach-Tarski paradox in measure theory. Rejecting it turns out to break the notion of size in a different way, specifically without AC it isn't possible to prove that if two sets don't have the same number of elements then one of them must have fewer elements.
We could chart these competing ideas but, starting in the late 1920s, Kurt Gödel and subsequent researchers established the futility of seeking meaningful mathematical systems that are devoid of paradoxes. Indeed, one could claim that the power of mathematics is intrinsically tied in with its paradoxes.
Among mathematicians there are at least two tribes: those who seem not to dwell on internal inconsistencies and who are more interested in building new structures or discovering new truths, and those who would look more closely at the connections and contradictions that lie at the foundations of our mathematical methods. We need mathematicians who can be both, aiming to reach beyond existing horizons while still being reflective and critical about the models we use. We should not be paralysed by the paradoxes at the heart of our structures, but recognise that the paradoxes may be a source of power, and clarify and leverage them.
Note: learners who do well in Paradox will have typically taken at least a couple ofcollege-level classes in mathematics or computer science. On the other hand, Paradox doesnot presuppose familiarity with any particular branch of mathematics or computer science.You just need to feel comfortable in a mathematical setting.
Computer processing happens in digital electronic circuits. Theirdesign is based on Boolean expressions and the representation ofinteger numbers in the binary numeral system discovered byGottfried Leibniz (1646 - 1716). Instead of using ten digits as weare used to do in the decimal numeral system, the binary systemrequires only two. The sequence of integers starts with 0, followedby 1. Now there isn't a third digit to be used for 2, and so we mustoccupy another binary position, resulting in 10, followed by 11 (for3), and for 4, written as 100, we need yet another binary position.Arithmetic using this notation is based on extremely simple rules.Instead of having to learn a large number of single-digit sums youonly have to know that 0+0=0, 0+1=1+0=1 and 1+1=0, with 1 as carry.These simple formulæ have direct counterparts in Boolean expressions,and they are easy to represent by logic gates, devices implementingBoolean functions. As a consequence, all of the algorithms andmathematics that can be described with Boolean logic can be constructedusing logic gates. 59ce067264


In Example 2, we used an uncalibrated pipette to pipette a
certain volume three times (three times 10.00 ± 0.023 mL). Suppose that we
now calibrate this pipette. After calibrating, we find that its volume is
9.987 mL, with an error of 0.004 mL. Again, we use this pipette three times. What
is the total error in the final volume of 29.934 mL?


3 edition of An Introduction to the Differential and the Integral Calculus found in the catalog.
by Percival & co.
Written in English
Calculus and Ordinary Differential Equations ().pdf writen by David Pearson: Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals. The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy Kovalevsky theorem.
Part of Z-Library project. The world's largest ebook library. New post "Full-text search for articles, highlighting downloaded books, view pdf in a browser and download history correction" in our blog. #N#Thomas' Calculus. George B. Thomas, Joel R. Hass, Christopher Heil, Maurice D. Weir. Language: english. File: PDF, MB. Cengage Learning. Download N piskunov differential and integral calculus pdf book pdf free download link or read online here in PDF. Read online N piskunov differential and integral calculus pdf book pdf free download link book now. All books are in clear copy here, and all files are secure so don't worry about it.
Elements of the differential and integral calculus. This is an amazing book related to differential and integral provides crystal clear explanations, is very consistent and goes gently deeply into each topic. Author(s): William Anthony Granville, Percey F Smith and William Raymond Longley. Integral calculus is an important part of calculus, as important as differential calculus. In differential calculus we study the relationship between two quantities, let’s say between distance and time. For this relationship we usually use the rate of change between two variables. In integral calculus, however, we take the inverse process of.
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This is a reproduction of a book published before This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections,Author: F.
Glanville Taylor. Piskunov's textbook is the best pedagogical introduction to calculus with applications. Their weakest points are in its chapters related to differential calculus in several variables.
Probably the reason for this deficiency is that linear algebra was not an accepted subject in the technical curriculum at the time this book was written/5(7).
The book also has a tone that is unusual today: Courant speaks to us the way a dignified, open-hearted professor speaks to an intelligent student. No rambling pretensions; just to-the-point, good mathematics.
This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this by: The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math.
Introduction to Calculus (Differential and Integral Calculus) In mathematics, calculus is a branch that is all about the assessment of numbers that varies in a one-liner way. This branch of mathematics deals with continuous change.
An introduction to the differential and integral calculus; with an appendix, illustrative of the theory of curves and other subjects. This is an amazing book related to differential and integral provides crystal clear explanations, is very consistent and goes gently deeply into each topic.
Author(s): William Anthony Granville, Percey F Smith and William Raymond Longley. INTRODUCTION TO DIFFERENTIAL AND INTEGRAL CALCULUS (EXCLUDING TRIGONOMETRIC FUNCTIONS) (A) DIFFERENTIAL CALCULUS 8.A.1 INTRODUCTION.
Differentiation is one of the most important fundamental operations in calculus. Its theory primarily depends on the idea of limit and continuity of Size: 1MB.
Introduction to Calculus (Differential and Integral Calculus) Calculus is a branch of mathematics that deals with derivatives and integrals of functions. Read more about types and applications of calculus in real life at BYJU'S. Diﬀerential calculus is about describing in a precise fashion the ways in which related quantities change.
To proceed with this booklet you will need to be familiar with the concept of the slope (also called the gradient) of a straight line. You may need to revise this concept before Introduction to differential calculus File Size: KB. An Introduction To The Study Of The Elements Of The Differential And Integral Calculus An Introduction To The Study Of The Elements Of The Differential And Integral Calculus Elements of the Differential and Integral Calculus.
AN INTRODUCTION TO ANALYSIS INTEGRAL CALCULUS. Due to Covid 19 virus issue, we are unable to deliver the books with in lockdown period. Introduction to Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.
I used this book in an Honors Calculus course decades ago, and it's still a useful reference. Unlike most calculus books, this is one from which you can learn real mathematics by self-study.
It is not only solid on calculational techniques, but is also an introduction to real analysis, and to good mathematical reasoning and proof technique.
Introduction xxvii Acknowledgments xxix 1 From Arithmetic to Algebra (What must you know to learn Calculus?)1 Introduction 1 The Set of Whole Numbers 1 The Set of Integers 1 The Set of Rational Numbers 1 The Set of Irrational Numbers 2 The Set of Real Numbers 2 Even and Odd Numbers 3 Factors 3 Prime and.
Further, Courant's treatment introduces the differential and integral calculus simultaneously, emphasizing the central point of the calculus, namely, the connection between definite integral, indefinite integral, and derivative. Exposition exhibits the close connection between analysis and its applications, /5(5).
This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and Brand: Vieweg+Teubner Verlag. In general, Differential Calculus providesa method for calculating “the rate of change” of the value of the variable quantity.
On the other hand, Integral Calculus provides methods for calculating the total effect of such changes, under the. Richard Courant Differential & Integral Calculus Vol I Blackie & Son 2nd ed.
The book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science and engineering, no matter whether he is a student of a university or.
Calculus has two basic applications: differential calculus and integral calculus. The simplest introduction to differential calculus involves an explicit series of numbers.
Given the series (42, 43, 3, 18, 34), the differential of this series would be (1,15, 16). The paper is poor, you can piksunov several paper qualities throughout the book.
Differential And Integral Calculus – N – Free Download PDF. And an objective reference to the busy professional that aims to go straight to the point. The Length of an Arc and Its Derivative 2. Sorrybut the links it did not work with me at allplease help If u.Integral Calculus is the branch of calculus where we study about integrals and their properties.
Integration is a very important concept which is the inverse process of differentiation. Both the integral calculus and the differential calculus are related to each other by the fundamental theorem of this article, let us discuss what is integral calculus, why is it used for. Integral Calculus for Beginners; With an Introduction to the Study of Differential Equations book.
Read reviews from world’s largest community for reader /5(16).


I was talking with one of my colleagues about how we can improve problem solving skills within our students to encourage higher-order thinking skills. In the past, I've shared with him Dan Meyer's 3 Acts and he was as amazed as I was. Together, we've been working on creating problems for algebra1, 2, and geometry that are set up for this process, and he shared with me a video similar to this one that he showed his students. It's a simple video; there's nothing fancy about the way its made and there is no narration, but the possibilities are endless in the way its interpreted. He used it to illustrate scientific notation. My first thought was to ask the question, 'How many Earth's fit inside Betelguese? How many suns fit inside VY Canis Majoris?' You could relate it to similarity, 3-dimensional space, fractions, or a hundred other topics. Regardless of how I end up using it, I plan on removing the diameters from the video so that my students can do some research to find the information that they think they need to answer their questions.
This video further illustrates to me how many questions can be generated from any picture or video. The phrase 'a picture is worth a thousand words' has become more real. I now try to look at my everyday surroundings from a mathematical perspective. I always tell my students that if math didn't exist, nothing else would either, but they always blow me off. Now I'm beginning to gather solid, concrete examples that they can see. I think the way I'm going to approach it from now on is show my students these examples so we can explore them as a class, and then use them to illustrate that math truly is everywhere. If I can get them to believe this, them I'm one step closer to getting them to appreciate everything that happens around them at any given moment.
So, what are your thoughts? What questions come to mind when you see this video?


Marston Conder is a Professor of Mathematics at the University of Auckland, and a Co-Director (with Vaughan Jones) of the NZ Institute of Mathematics & its Applications (NZIMA).
His research interests are in algebra, geometry and combinatorics, and especially the application of combinatorial and computational group theory to the analysis and construction of discrete objects with maximum symmetry. He has published about 90 papers in international journals and refereed conference proceedings.
After a Masters degree at the University of Waikato, Professor Conder obtained a DPhil degree from the University of Oxford, where he won the Senior Mathematical Prize and Johnson Prize in 1980.
He held a postdoctoral fellowship at the University of Otago in 1981, followed by a Royal Society (UK) Research Fellowship at the University of Tuebingen (Germany) in 1982, and a Fellowship from the Alexander von Humboldt Foundation in 1987. He has held other visiting positions at Fribourg (Switzerland), Madrid, Oxford, Singapore, St Andrews (UK), Sydney and Waterloo (Canada).
He was President of the NZ Mathematical Society from 1993 to 1995, co-founder and initial convenor of the NZ Mathematical and Information Sciences Council (now a standing committee of the RSNZ) in 1994, and is a co-founding Director of the NZ Mathematics Research Institute. He participated as a lead expert in the MoRST Review of New Zealand's Scientific Knowledge Base in 1996, and was a member of the TEAC Research Working Group (2000-2001). At the University of Auckland he was Head of the Department of Mathematics from 1996 to 1998, and served a term as Deputy Vice-Chancellor (Research) from 1999 to 2001.
He is a member of the Editorial Board of the NZ Journal of Mathematics and served as a member of the Marsden Fund Council (and convenor of its Mathematical & Information Sciences panel) from 2001 to 2005. In 2002 he chaired a Working Group for the NZ Ministry of Education, to design a Performance Based Research Fund (PBRF) for tertiary education institutions in NZ. He is currently President-Elect of the Academy of the Royal Society of New Zealand (and will take up the President's position at the end of 2006).
He won a Prince & Princess of Wales Science Award in 1989, the NZ Mathematical Society's Research Award for 1993, a Claude McCarthy Fellowship in 1995, a Hood Fellowship for 2005, and 3-year Marsden Fund grants in 1995, 1998, 2001 and 2004. He was elected a Fellow of the Royal Society of NZ in 1998, and awarded a DSc by the University of Oxford in 1999.
Vaughan Jones is a Professor of Mathematics at the University of California at Berkeley and Distinguished Alumni Professor of the University of Auckland, and a Co-Director (with Marston Conder) of the NZ Institute of Mathematics & its Applications (NZIMA).
Vaughan Jones was born and educated in New Zealand, at St Peter's School (Cambridge), Auckland Grammar School, and the University of Auckland, where he graduated MSc with First Class Honours in 1973.
He was awarded a Swiss Government Scholarship and an FWW Rhodes Memorial Scholarship, which enabled him to study for his doctorate at the University of Geneva. In 1979 he was awarded the degree of Docteures Sciences (Mathematique) and the following year the Vacheron Constantin Prize for his doctoral thesis.
He spent his first postdoctoral year as ER Hedrick Assistant Professor of Mathematics at the University of California at Los Angeles (UCLA), and from 1981 worked at the University of Pennsylvania as Assistant and then Associate Professor, before being appointed as Professor of Mathematics at the University of California at Berkeley in 1985.
During the 1980s his research focussed on von Neumann algebras, and in the course of this work he discovered a new polynomial invariant for knots which led to surprising connections between apparently quite different areas of mathematics.
Vaughan Jones was awarded a Fields Medal at the 1990 International Congress in Kyoto (Japan) for his remarkable and beautiful mathematical achievements. The Fields Medal is awarded every four years, and is regarded as the euqivalent of a Nobel Prize. (Some say that Nobel's wife had an affair with a mathematician and that this is the reason why there is no Nobel Prize for Mathematics.) Vaughan Jones is the only New Zealander ever to have won this prestigious award, and it is believed also that he is the only winner from the Southern Hemisphere.
Since then he has gone on to receive numerous awards and honours, for example:
He has published in research in leading international scientific journals, and has been invited to lecture at numerous international conferences, including the following:
He has also served as editor or associate editor of several international journals, including the Transactions of the American Mathematical Society, the Pacific Journal of Mathematics, the New Zealand Journal of Mathematics, Reviews in Mathematical Physics, and the Journal of Mathematical Chemistry.
In addition, he has been a member of the Scientific Advisory Boards of several leading mathematical institutes around the world, including < li> the Fields Institute for Mathematics (Canada)
Although based at the University of California, since 1992 he has returned to New Zealand at least once each year (in his role as Distinguished Alumni Professor at the University of Auckland) and he continues to engage with and stimulate the mathematical sciences community in NZ.
He is principal founder and (now) Director of the NZ Mathematics Research Institute, which is a virtual institute (without premises) established in the 1990s to promote and foster mathematical research of the highest quality in NZ. Since 1994 the NZMRI has run summer research workshops in various parts of NZ on mathematical themes of current importance, at which students and senior researchers can interact and learn from each other and from overeseas experts who are invited to give courses of lectures.
Vaughan Jones has been instrumental in attracting some of the world's best mathematicians to NZ, and the success of these workshops is largely attributable to his vision and energy in setting up the NZMRI. His own style of working is informal, encouraging the free and open interchange of ideas, and this has rubbed off on many others. His efforts have made it possible for graduate students to gain first-hand knowledge of developments at the leading edge of their discipline, here in NZ.
This activity is now set to expand and be enhanced through the newly formed NZ Institute of Mathematics and its Applications, one of the five Centres of Research Excellence selected in 2002 for special funding from the Government. Vaughan Jones will be co-Director of this Institute and head its International Scientific Advisory Board, and continue to make invaluable contributions to scientific research and postgraduate education in his home country.
For further details, see also here and here.
Return to NZIMA Homepage
Last updated on 27 October 2006 by firstname.lastname@example.org


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The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^.devotions for dating divorced couples remarrying..
IM Commentary The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.
$$ If we evaluate this expression on a calculator, we get a value of approximately 19,035 years since the plant has died.
$$ Time in this equation is measured in years from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms (a microgram is one millionth of a gram). Along with hydrogen, nitrogen, oxygen, phosphorus, and sulfur, carbon is a building block of biochemical molecules ranging from fats, proteins, and carbohydrates to active substances such as hormones.
$$ Solving for $c$ gives $$ c = \frac $$ which is approximately equal to $0.


You can find an overview of academic publications, working papers and conference participations on the page of the team.
Currently the research of the Chair of Statistics focuses on developing estimation and inference for semi- and nonparametric regression methods. The main focus lies on kernel and spline estimation of (conditional) moments, quantiles, distributions, et cetera. Besides fundamental research such as the design of semi- and nonparametric forecasting methods for (high dimensional) panel data we work on many aspects of applied statistics. At the moment we especially deal with digital and regional economy, psychology, market and manufacturing research, real-estate- and labor markets.
Semi- and nonparametric regression methods: kernels, splines, quantiles
Panel Forecasting methods
Applied statistics: Regional-, real estate- und labor market economics, demographics, market research
Econometric and statistical theory


JODO GYAN– MATHS WITH MANIPULATIVES
Maths workshop on ‘Mathematical Tools for Meaningful Pedagogical Practices’ organised by Jodo Gyan The objective of the workshop was to change abstract mathematical learning to concrete learning. As the children learn better with what they touch, feel and observe, hands on experience was emphasized upon. Illuminating pedagogical ways to teach Mathematics at the Primary level were the resource team using Jodo Gyanmaterial Beads, Ragnometry, Blocks, Dice etc. The teachers were encouraged to use various new ways to teach Math like juggling of numbers for addition and subtraction using fractions kit , digit cards game, beads for counting, half and skip counting, games for multiplication, taming the table, jodo straws game for 2 D and 3 D geometry, decimals and many more.
The workshop was not only educative but thought provoking. It provided the teachers an insight into innovative teaching methodologies and led them to introspect and adopt the new and better ways to reach out to the children. They were asked to adopt methods to teach the students in ways that not only enhance their learning but enable them to retain the concepts forever. The traditional way of rote learning was advised to be replaced by teaching by experimenting, to suit the changing times and abide by the need of the hour.


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Enter the length in kilometers below to get the value converted to meters. km2âcm2 1 km2 = 10000000000 cm2 km2âmm2 1 km2 = 1000000000000 mm2 km2âum2 1 km2 = 1.0E+18 um2 km2ânm2 1 km2 = 1.0E+24 nm2 km2âha 1 km2 = 100 ha km2âPlaza 1 km2 = 156.25 Plaza km2âin2 1 km2 = 1550003100 in2 km2âft2 1 km2 = 10763910.416667 ft2 km2âyd2 1 km2 = 1195990.046296 yd2 km2âmi2 1 mi2 = 2.5899881103464 km2 miles per second (mps) SI is also the preferred system of measure in academia and in education. One kilometer is equal to 1,000 meters, which are defined as the distance light travels in a vacuum in a 1 / 299,792,458 second time interval. kilometers in meters conversion factor? The answer is: 1 km equals 1,000.00 m. 1,000.00 m is converted to 1 of what? I didnât invent this technique, and Iâd love to give proper credit, but I honestly donât know where I learned this. 1 km/h is like a very slow walking speed. Rulers are available in imperial, metric, or combination with both values, so make sure you get the correct type for your needs. 1 m este egal cu 1,0936 yarzi, sau 39,370 inch. To convert meters to km, multiply the meter value by 0.001 or divide by 1000. 1 Meter (m) is equal to 0.001 kilometer (km). 14 km(s) / 0.001 = 14000 m(s) Rounded â¦ This is the calculated area of the rectangle, which this tool determines by multiplying together the length and width measurements. 1.2 cm 2: 1.2 x 10 2 cm 2: You can view more details on each measurement unit: km^2 or m^2 The SI derived unit for area is the square meter. Switch units Starting unit. We have 54 * 5 = 270. Conversion base : 1 min/km = 16.666666666667 mps. Square kilometre (International spelling as used by the International Bureau of Weights and Measures) or square kilometer (American spelling), symbol km2, is a multiple of the square metre, the SI unit of area or surface area. Meters. m = km * 1000. Task: Convert 4.5 kilometers to meters (show work) Formula: km x 1,000 = m Calculations: 4.5 km x 1,000 = 4,500 m Result: 4.5 km is equal to 4,500 m Conversion Table For quick reference purposes, below is a conversion table that you can use to convert from km to meters. Metri. meters? kilometers to Q.2:- Fill in the blanks by suitable conversion of units: (a) 1 kg m 2 s â2 = â¦.g cm 2 s â2 (b) 1 m =â¦.. ly (c) 3.0 m s â2 =â¦. Note that rounding errors may occur, so always check the results. The ancient Parisian toise (fathom) was slightly shorter than 2 m and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was exactly 1 â 2 toise. 1 Kilometer (km) is equal to 1000 meters (m). Kilometer. Square kilometre (International spelling as used by the International Bureau of Weights and Measures) or square kilometer (American spelling), symbol km 2, is a multiple of the square metre, the SI unit of area or surface area.. 1 km 2 is equal to: . This can take up to 20-30 seconds. Need a ruler? 2020-11-07 12:23:12 (UTC) | 61.519°N 149.916°W | 40.3 km depth Try our free downloadable and printable rulers, which include both imperial and metric measurements. To convert km/hr into m/sec, multiply the number by 5 and then divide it by 18. systems (based around metres, kilograms and seconds) the metre is used to help derive other units of measurement such as the newton, for force. m = km _____ 0.0010000. How many m^2 in 1 km^2? meters. 1 m to km = 0.001 km. Conversion base : 1 km 2 = 1000000 m 2. To see how many meters is 1KG of filament, look under the 1KG spool column. meters = 1/2 × 1000 = 500. Note that rounding errors may occur, so always check the results. The Russian verst was 1.0668 km. Answer A. kilometers by 1000 (the conversion factor). Kilometer per Liter Fuel Efficiency Calculator, Liter to Km Fuel Efficiency Conversion Keep reading to learn more about each unit of measure. s â1 "). 1 0. km h â2 (d) G= 6.67 × 10 â11 N m 2 (kg) â2 =â¦. The source will explain more and has an online converter for further endeavors with the metric system. What is the Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf. you would multiply both sides by 2 so 1 times 2 equals to 2 km and 1000m times 2 would equal to 2000 m which is choice A. One hour walking at 1 m/s moves you 3.6 km. We assume you are converting between square metre and square kilometre. Popular Speed Unit Conversions. An ellipse is the generalized form of a circle, and is a curve in a plane where the sum of the distances from any point on the curve to each of its two focal points is constant, as shown in the figure below, where P is any point on the ellipse, and F 1 and F 2 are the two foci.  One meter is equal to 100 centimeters or 39.37 inches. One kilometer is equal to 1,000 meters, which are defined as the distance light travels in a vacuum in a 1/299,792,458 second time interval.. by 5/18 . kilometer = meter * 0.001. kilometer = meter / 1000. How to transform 1 km 2 = 1000000 m 2. square kilometer . The meters unit number 1,000.00 m converts to 1 km, one kilometer. How long is 2 kilometers? You can view more details on each measurement unit: m^2 or km^2 The SI derived unit for area is the square meter. 1 km = 1000m 1 h = 3600 s So 1km /h = 1000/3600 = 5/18 = 0.28 m/sec If you want to change km/h to m/s simply multiply the given no. meters, just multiply the quantity in Example: Highway speed is around 100 km/h. A kilometer is among the most widely used metric units of distance and length, including the countries traditionally using the Imperial system units. 1.2 kilometers equal 0.7456454307 miles (1.2km = 0.7456454307mi). For example, to convert 100 m to km, multiply 100 by 0.001, that makes 0.1 km is 100m . One kilometer is equal to 1,000 meters, which are defined as the distance light travels in a vacuum in a 1 / 299,792,458 second time interval. To convert any value in kilometers to meters, just multiply the value in kilometers by the conversion factor 1000.So, 2.6 kilometers times 1000 is equal to 2600 meters. The value will â¦ 26: How many cm 2 are there in a piece of paper 3.0 m by 0.40 m? 1.2 km, 120,600 cm, 1,220,000 mm, 120 meters ...â in ð Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions. meters are in kilometers to meters per second (mps) kilometers per second (kps) kilometers per hour (kph) meters per minute (m/min) imperial units. CONVERT : between other length measuring units - complete list.. How many meters are in 1 kilometer? Converting 1.2 mi to km is easy. transformare din DINUNITATEA în ÎNUNITATEA. 1 Meter = 0.001 Kilometer. kilometer = meter * 0.001. kilometer = meter / 1000. To convert any value in meters to kilometers, just multiply the value in meters by the conversion factor 0.001. Source(s): Longtime college math teacher. a kilometer into meters per second to miles per hour. 3.2 earthquake - Cubitán de Dolores, 1.2 km east of Cubitan de Dolores, Oaxaca, Mexico, on 2020-11-30 03:08:31 (Hora de México) Please wait while we search through millions of records. Please visit all length units conversion to convert all length units. If something is 1 cm long, then it's 1/100 of a meter long. The meters unit number 1,000.00 m converts to 1 km, one kilometer. 1 km = 1000 m. The symbol is "km". 1 Kilometer = 1000 Meters. 1 km = 1000 m. To convert 2.1 kilometers into meters we have to multiply 2.1 by the conversion factor in order to get the length amount from kilometers to meters. One kilometer is equal to 1000 meters. Find an answer to your question âWhich measure is the largest? is metade kilometer in meters? 10 m to km = 0.01 km. according to the most recent 2019 definition. Definition: A kilometer (symbol: km) is a unit of length in the International System of Units (SI). What is a Kilometer? We assume you are converting between square kilometre and square metre. All In One Unit Converter But cm^-1 is "per cm" and m^-1 is "per m." If something occurs only once "per cm" then it would occur 100 times in a meter. The answer is: 1 km equals 1,000.00 m. 1,000.00 m is converted to 1 of what? PromÄna kilometrÅ¯ za hodinu na metry za sekundu, km/h na m/s. Please, choose a physical quantity, two units, then type a value in any of the boxes above. Years ago it was a basic unit in formerly used CGS (centimeter-gram-second) unit system, but in modern times the role of basic unit of length is played by meter. Koeficientem pÅemÄny je 0.277777777778; tedy 1 kilometr za hodinu = 0.277777777778 metru za sekundu, kilometr za hodinu na metr za sekundu Metri. 1.9 kilometers equal 1.1806052653 miles (1.9km = 1.1806052653mi). Kilo means 1000 and km is kilometer. This means we know how many meters in a kilogram of PLA 1.75mm to be 335.3 meters. What is a Meter? The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to â¦ In the metric system, "kilo" is the prefix for 10 3. Anonymous. Mag. 1 km egal cu 0,6214 mile.1 km egal cu 0,6214 mile. The acceleration value 1 m/s2 (meter per second squared) in words is "one m/s2 (meter per second squared)". Converting 1.2 km to mi is easy. The metre is a unit of length in the metric system, and is the base unit of length in the International System of Units (SI). 2 km = 2 x 1000 m = 2000 m. So. 2.55x10-1 km: 2.55 km: None of the previous answers: 25: What is the volume in milliliters of an object that has a volume of 2.5x10 4 mm 3: 4.0 mL: 2.5 mL: 2.5x10 1 mL: 2.5x10 4 mL: None of the previous answers. 14 km(s) * 1000 = 14000 m(s) By division. For example, to convert 100 m to km, multiply 100 by 0.001, that makes 0.1 km is 100m . You can easily calculate average speed having time and distance (given in different units of lenght e.g. To calculate a value in Din 1983, un metru este definit oficial ca lungimea drumului parcurs de luminÄ în vid într-un interval de timp de 1/299.792.458 dintr-o secundÄ. The meter, or metre, is the SI base unit for length in the metric system. meters to kilometers formula. Or if you're wondering how many grams in a meter is 1,000 Grams / 335 Meters = 2.98 grams per meter. meters to kilometers formula. For example, to calculate how many meters is 2 km, multiply 2 by 1000, that makes 2000m is 2 km. In most of the world, it is the most common unit for measuring distance between places. Meter. A kilometer, or kilometre, is a unit of length equal to 1,000 meters, or about 0.621 miles. 2.1 ml Depth 9.6 km Time 2020-12-11 10:30:14 UTC Contributed by NN 1 ; View Nearby Seismicity Time Range ± Three Weeks Search Radius 250.0 km Magnitude Range â¥ 1.0 ANSS Comcat ; For More Information. How far is 2 kilometers in meters? Switch units Starting unit. miles, yards, meters, kilometers, inches etc.) Meters can be abbreviated as m; for example, 1 meter can be written as 1 m. We recommend using a ruler or tape measure for measuring length, which can be found at a local retailer or home center.