Canara Bank is a fairly popular public sector bank in India. While it has its headquarters in Bengaluru, the bank enjoys a network of 355 branches across India. Akin to most other banks, it offers a range of finance options, including Car Loan, Personal Loan, Home Loan, and Commercial Vehicle Loan. Canara Bank starts providing car finance options of as little as Rs 1 lakh, which is something that becomes useful when one is falling short of some funds while purchasing his dream car. This public sector bank even offers finance options for buying used cars. The bank even offers a free EMI calculator so that you can calculate your monthly liability beforehand and take a loan accordingly. Below are the highlights of the features of Canara Bank car loan EMI calculator.
Like all EMI calculators, Canara Bank car loan EMI calculator is based on a fixed formula. Basically, the EMI calculator helps you figure out the monthly instalment which you will be paying at a pre-defined rate of interest for a set loan tenure. The formula on which loan EMI calculator works is given as follows –
EMI = [P x R x (1+R) ^N] / [(1+R) ^N – 1]
In this case,
‘P’ stands for the Principal amount
‘R’ stands for the monthly rate of interest
‘N’ stands for the number of instalments
It should be kept in mind here that the formula given above doesn’t keep in account the pre-payment that is made for early repayment of the loan.
Currently, Canara Bank provides car loan at a starting interest rate of just 7.35%, The bank also has a low processing fee. Also, when taking a car loan from the Canara bank, you can choose a repayment tenure of the loan of as much as 7 years. Yet another feature is that the bank offers a finance option of up to 90% of the ex-showroom price of the vehicle. Moreover, the bank even offers used car loans. Plus, the new car loans and the used car loans are not just offered to salaried employees, but even to to businessmen, proprietorship firms, partnership firms, companies, trusts, and societies.
To make the repayment of car loan easy, all banks provide EMI (Equated Monthly Installment) facility. Hence, before you opt for a car loan, you need to plan the repayment properly. For this, the Canara Bank Car Loan EMI calculator comes in hand. At the moment, the new car loan interest rates that the Canara Bank offers range from 7.35%. However, at 8.70% rate of interest, the EMI per lakh for the total amount of Rs 10 lakh for 2 years comes out to be Rs 45,547.
|Loan amount (Rs.)||Interest rate*||Processing fee||EMI for 2 years (Rs.)||EMI for 3 years (Rs.)||EMI for 4 years (Rs.)||EMI for 5 years (Rs.)||EMI for 6 years (Rs.)||EMI for 7 years (Rs.)|
The Canara Bank Car Loan EMI Calculator can be used for free for all takes care of all the large and complicated calculations quickly instead of you needing to spend too much time on making calculations manually, and at a higher risk of errors. The salient features of the EMI calculator of Canara Bank include:
In the table provided below, one can have a look at the EMI for multiple loan amounts taken at a hypothetical rate of interest of 7 per cent. As you can see in the table given below, the EMI changes as the tenure of the loan changes from 2 years to 7 years.
|Loan Amount||Interest Rate||EMI for 2 years (Rs.)||EMI for 3 years (Rs.)||EMI for 4 years (Rs.)||EMI for 5 years (Rs.)||EMI for 6 years (Rs.)||EMI for 7 years (Rs.)|
The table we have given below clearly shows that the loan tenure is inversely proportional to the EMI you have to pay. However, the interest is directly proportional to the loan tenure. For instance, in case you take a loan of Rs 1,00,000 for a period of 5 years, you need to pay the lowest EMI of Rs 2,028. However, you end up paying Rs 21,658 in interest on a loan of Rs 1,00,000.
|Vehicle Loan EMI for ₹ 1 Lakh loan amount at 9% interest rate offered by Canara Bank for different tenures||2 Years||3 Years||5 Years|
|Canara Bank EMI for a loan amount Rs 1 Lakh at 8.00%||Rs 4,477||Rs 3,134||Rs 2,028|
|Total amount you pay, including interest||Rs 1,08,546||Rs 1,12,811||Rs 1,21,658|
|Total interest paid||Rs 8,546||Rs 12,811||Rs 21,658|
Basically, an amortization schedule is nothing but a table of regular loan payments that tell you about the principal component and the interest component of every EMI that you pay until the loan is totally paid back. It is necessary to know that EMI is a fixed sum that consists of a fixed principal amount and fixed interest. The table you see here gives an EMI schedule for 3 years for a loan amount of Rs 2 lakh –
|Year||Interest Paid During The Year||Principal Repaid During The Year||Total Amount Paid During The Year (Interest + Principal)||Outstanding Principal|
|2020||Rs 3,025||Rs 15,295||Rs 18,320||Rs 1,84,705|
|2021||Rs 13,047||Rs 96,872||Rs 1,09,919||Rs 87,832|
|2022||Rs 3,767||Rs 87,832||Rs 91,599||Rs 0|
All available car loan EMI calculators work on the same forumla, which is –
EMI = [P x R x (1+R) ^N] / [(1+R) ^N – 1]
P is for the principal amount (basically the money you borrow)
r is the rate of interest per month which is calculated as rate of annual income/ (12*100)
n is the loan tenure of loan in months
E is the EMI (equated monthly payment)
Multiplier based loan amount eligibility – Yes Bank calculates the loan eligibility by applying a multiplier to your net take-home income. In most cases, the result turns out to be 2.5 to 3 times the annual income for salaried individuals and 6 times the annual income for self-employed professionals. Also, this multiplier is calculated based on your employer company’s reputation, stability, size and growth in turnover.
FOIR based loan amount eligibility – The Yes Bank even calculates your Fixed Income to Obligations Ratio (FOIR) to get to know the maximum EMI you can pay on basis of your current income and other monthly expenses. The proportion of fixed income to your calculated fixed obligations gives your FOIR. In most cases, banks are known to lend up to a maximum FOIR of 0.50.
In case you wish to pay back the car loan before its maturity, you need to pay a small penalty that is known as a prepayment penalty. Canara Bank charges a pre-payment penalty of 6% of principal outstanding within 6 months to 24 months from 1st EMI, and a penalty of 5% thereafter
A: Canara Bank car loan has the following features:
– Finance of up to 90% of the ex-showroom price of the vehicle.
– Competitive interest rates of as low as 7.35%
– Car loan application is processed and disbursed within 7 working days
– Minimum documentation is required
– Special benefits for loyal customers.
A: You can avail a car loan offered under the Canara Mobile (Vehicle) scheme.
A: EMI Is calculated through the below formula –
EMI = [P x R x (1+R) ^N] / [(1+R) ^N – 1],
Here, P is the principal amount, R is the interest rate, and N is the number of instalments.
A: A car loan amortization table shows the payment schedule of you EMIs along with its breakup, which means you get to know what principal amount and interest you are paying through each EMI.
A: Self-employed individuals, salaried persons, farmers, agriculturalists, businessmen, pensioners, and companies can apply for car loans at Canara Bank.
A: No, it’s not easier to calculate the EMI using the formula or an excel sheet as compared to the EMI Calculator tool as manual calculation is not only more time-consuming but also prone to errors.
A: You should check your loan documents to figure out the prepayment penalty the you will be charged. You can also visit the bank branch to get to know the amount you’ll have to pay as penalty. Once you’re aware of prepayment charges, you can also use Canara Bank car loan EMI Calculator to get to instantly know the penalty you will have to pay.


There are many retirement calculators that can be found on the Internet and elsewhere. Click on the link below to access a simple and straightforward calculator that we have constructed:
The following are some other calculators that we have found in various places. They range from very simple retirement planning calculators to very sophisticated calculators that may use tools such as Monte Carlo Simulation. You should look at all of these calculators and others that you might find when planning for your retirement, as they each offer a different perspective on your retirement planning.


Computational fluid mechanics techniques
Computational fluid dynamics (CFD) technology can be used to accurately simulate the flow state of the gas-liquid two phase in the rectifying tower. On this basis, the internal structure can be optimized and improved to realize the uniform distribution of the fluid, improving the mass transfer efficiency and reducing the pressure drop, and it has been successfully applied to the engineering design.
Velocity distribution of predistributed tubes with equal aperture
Pressure distribution of predistributed pipe with equal aperture
Flow rate variation diagram of predistributed pipe with equal aperture and equal cross-section Flow rate variation diagram of predistributed pipe with variable aperture and variable cross-section


It was revealed in our school improvement plan survey at the end of the school year that teachers wanted staff development to improve their math instruction. We want our math instruction to be as comfortable a fit as our literacy instruction. When requests like this come in (ground up) our administrators and specialists listen... and respond. As a result our math resource teachers helped organize us and twenty-four teachers formed a focus group to improve our math teaching skills and knowledge. Books were bought. Time was creatively carved so we could have an hour during the work day six times a year to collaborate and discuss the bones of "numeracy." Half our group is working on primary conceptual development and the other half is working on multiplication and division.
How do we do it? One week the primary numeracy group meets and sends their little guys to an upper grade class which is part of the multiplication/division group. We "buddy" the students for 1/2 hour at the end of the school day and dismiss them from this class while their teacher spends that 1/2 hour and 1/2 hour after school dismisses to learn. On another week we swap... older students go to the younger students. Brilliant.Last week our class had our first swap. We partnered a kindergarten student with a third grader. They each drew a portrait of their buddy. Third graders interviewed each kindergarten student and shared what they discovered. Later they swapped portraits. It was a very fast 30 minutes!
Things seen and heard:
K boy: I have flames on my shirt.
3rd boy: Uh, I know. They're cool.
K boy: I have flames and words on my shirt.
3rd boy: I know. I was just about to put the flames here.
K boy: Uh huh...don't forget the words.
3rd boy: Shaking head, eyes looking sideways at his buddy, smiling with no teeth showing.K girl: This is you on a sidewalk.
3rd girl: What am I doing?
K girl: Walking to school. You're going to be late.
3rd girl: That really looks like my outfit today.
K girl: I know. Did you hear me say you're going to be late.
A good time was had by all.


FREE STEAM TRAINING PROGRAM FOR TEACHERS & EDUCATORS
CLICK THE BUTTON BELOW TO APPLY
ABOUT THE TRAINING
STEAM which stands for Science, Technology, Engineering, Art & Crafts and Mathematics is a curriculum based on the idea of educating students in five disciplines using hand-on modelling and exposure to real life appliances and models. Steam integrates these five disciplines into a cohesive learning paradigm based on real-world application.
STEAM teachers training is to motivate and inspire school children to excel in STEAM related subjects by increasing the awareness in STEAM education and improving teachers skills in teaching these subjects. The ultimate goal is to get Nigeria from a third world country to a first world country.
i. Exposure to real world appliances, tools, methods in modern technology which are pertinent to the world today.
ii. Learn how you can ignite the passion for Science, Technology, Engineering, Art & Crafts and Mathematics in children in your school.
iii. Understanding how to see class subject from STEAM point of view.
iv. Raise innovators & investors.
Who Should Apply?
Teachers, trainers, educators, STEAM enthusiasts interested in building their teaching skills with STEAM concepts.
Time: 10am prompt
Date & Location:
Oshodi/Isolo (Saturday 1st of June 2019).
Abule-egba (Saturday 22nd of June 2019).
Lekki (Saturday 6th of July 2019).
NOTE: Not more than two teachers from a school should apply as multiple application from a school beyond 4 teachers will be disqualified.


The weighted average method is a way of calculating an average of values in which each value has a different weight or importance.
This method is often used in financial analysis, but it can be applied to almost any situation where you want to calculate an average with different levels of importance.
In this blog post, we’ll take a look at how the weighted average method works and how it can be used in various situations.
Calculating the Average Weighted Method
The weighted average method is calculated by multiplying each value by its weight and adding up all of the products.
The formula for calculating a weighted average is as follows: (Value 1 x Weight 1) + (Value 2 x Weight 2) + … + (Value n x Weight n) / Total weight.
For example, let’s say that you are evaluating three companies, and you assign weights of 0.35, 0.45, and 0.20, respectively, to each one based on their relative importance in your portfolio.
You then evaluate each company on five criteria (each rated on a scale from 1 to 5).
To calculate the weighted average score for each company using the formula above, you would multiply the score for each criterion by its corresponding weight and add up all of the products.
The weighted average method allows you to assign different weights or levels of importance to different elements when calculating an overall average score or value.
It is especially useful when dealing with multiple variables that may have varying degrees of impact on the final result.
For example, if you were evaluating a portfolio of stocks and wanted to consider both risks and return when making your decision, you could assign different weights to each variable depending on their relative importance in your decision-making process.
Uses for Average Weighted Method
The weighted average method can be used in many situations where multiple variables must be considered when deciding or calculating.
It can also be used for portfolio analysis; assigning higher weights to companies with higher returns or lower risks gives them more “weight” in the overall calculation so that they have more impact on the final result than companies with lower returns or higher risks.
Similarly, it can be used for scoring systems such as employee reviews or customer satisfaction surveys; assigning different weights to different criteria allows them to have more or less influence over the final score depending on their relative importance in your evaluation process.
A weighted average method is a powerful tool that allows you to assign different levels of importance to multiple variables when calculating an overall score or value.
By assigning different weights to individual criteria, elements with higher importance will have a greater impact on the final result than those with lower importance.
This makes it very useful for situations where multiple variables need to be considered, such as portfolio analysis or scoring systems like customer satisfaction surveys and employee reviews.
By understanding how this method works and its applications, businesses can make better decisions based on accurate calculations rather than guesswork alone!


Daily Numeracy Practice
"An information- and technology-based society requires individuals who are able to think critically about complex issues, analyse and adapt to new situations, solve problems of various kinds, and communicate their thinking effectively. The study of mathematics equips students with knowledge, skills, and habits of mind that are essential for successful and rewarding participation in such a society".
Ministry of Education Mathematics Curriculum
In order to facilitate the problem-solving and communication processes, students are encouraged to practice basic numeration skills (+ / - / x / ÷) on a daily basis. The following are links that provide students the opportunity to practice and master such skills in an engaging way:
Web Math Minute - Printable & online practice of + / - / x / ÷
Math Flash Cards - Online practice of + / - / x / ÷
Online MULTIPLICATION Flash Cards (up to 9s)
TVO Kids Tumbleweed's Math Maze game
Pearson "Math Makes Sense" Resources
Resources for Parents
The following resources, Helping Your Child Learn Math and Doing Mathematics with Your Child (K-6), are publications by the Ministry of Education detailing simple ways in which you can help support what your child is learning in the classroom.
Figure This! Math challenges for children and families, by strand
Resources for Students
Helpful and engaging links for students. Lessons. Games. Activities. Stuff.
Math Dictionary for Kids - Math terms & their definitions
Jump Math - Free Math Tools for Students and Parents
Online Math Learning
Khan Academy - Free Math Practice
IXL - Online Math Practice (Ontario Curriculum Links)
XP Math GAMES
Number Sense and Numeration
Geometry and Spatial Sense
Patterning and Algebra
TVO Kids Flower Frenzy game


Matilde Marcolli (Caltech) will be visiting Utrecht University on the 26th of June, and she will give a talk with the title:
A mathematical model of syntactic Merge
In this talk I will present a mathematical view of the Merge operation in the Minimalist Model of syntax, in the free symmetric form of Chomsky’s more recent formulation of Minimalism.
I will show that the underlying mathematical formalism is closely related to Hopf algebra structures that play a fundamental role in physics.
I will also discuss from this mathematical perspective the advantages of this more recent formulation of Minimalism over older versions. This talk is based on joint work with Noam Chomsky and Robert Berwick (arXiv:2305.18278).
Date: 26 June 2023
Location: Drift 21, 104


An aspect ratio describes the relationship of an object’s width to its height. It is commonly used in computing to describe the proportions of a rectangular screen. To illustrate, a monitor 20 inches wide by 15 inches tall has an aspect ratio of 20:15. Reducing this number to its common denominator is 4:3. The following are supported ratios.
|3×2||960×640 Classic Film|
|16×9||960×540 High Definition|
|17×9||960×508 Ultra High Definition|
|21×9||960×411 Cinemascope |


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[Vi Hart](http://vihart.com) has a fantastic collection of videos about doodling based on mathematical concepts. The one I am showing here involves doodling based on graph theory — those who know graph theory’s origins in the classical problem of [“The Seven Bridges of Konigsberg”](http://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg) will recognize the early doodles as being terrific examples of Euler’s work. Enjoy! I am showing all of them to my six year old.


if this is the first time you are going to
online, you are advised to always read the rules of
bingo where you are playing as in some cases there are
variations in the game with different awards, and it
pays to be informed. In each bingo room, there is one
person in charge of the game that is intended to help
her / him that you can play with confidence and ask
any questions about bingo, prizes and promotions to
make your first deposit. Sometimes when we start to
participate in any game of chance, it gives us some
concern risk our money without much experience. Bingo
is no exception.
Helping people lose that fear is one of the reasons that led to the best online casinos to create free bingo halls. The probability of winning in games of bingo on the number of bingo cards that a player has bought and the amount of bingo players who are in the bingo hall at the time. Like as in bingo halls in Spain, online bingo halls greater the number of cartons purchased by other players, less chance of winning each.
Remember that although you can download to your computer bingo is always best to play online bingo hall without downloading any software to your computer and that you should wait until it is downloaded and then you have to install which will take you few minutes.
Online Bingo Game: Best Strategy
Suppose you are playing in a group of 100 people. What are my chances of winning? Well, to say he did, the chances of winning are equal to all other players in the group, which means that you have 1% chance of winning. Now, that's not very encouraging and definitely not inspire a player to keep playing over and over again.
I hope you agree with the simple calculation I mentioned earlier. Now consider this player somehow manages to keep playing 99 games, but unfortunately lost them all. According to our estimate of its 1% chance of winning should ensure his victory in the 100th. Does this sound sensible?
Mathematics and luck does not really go well together. The odds were and are an important factor in making strategies of bingo, but the odds of applied mathematics and not on luck. The mathematician Joseph Granville developed a theory called the probability of any number from one of equals and therefore a player will make every effort to select the right card to play.
The right card according to Joseph is the card that has numbers randomly distributed in the range of number to call. So if the first 4-5 numbers are called odd, then even more will be called and what if a player has to choose a card at this point then can make a better decision. But this theory does not work, if you ask me. My reason for saying that is evident in the first paragraph.
Another strategy is based on the number of cards the player owns. Mathematically, the highest number of cards played by a player, the greater your chances of winning. All numbers are equally likely to be called, so that all cards have the same chance of winning and more letters added to give a better chance of winning. But, in pursuing this strategy, the player must take into account that the cards come with a price.
The total cost of the cards should not be too high, or else you just end up losing too. This should be taken as a common standard for all games of chance. You have to go in taking bets that you will lose every game and should play every game given that will win each.


A rectangular prism, also known as a rectangular cuboid, has 12 edges. These edges are formed by the intersection of the rectangular faces of the prism.
Rectangular prisms are common three-dimensional shapes encountered in everyday life and mathematics. Understanding their properties and calculations is fundamental in various fields, from construction to mathematics.
Table of Contents
Properties of Rectangular Prism
Rectangular prisms possess distinctive properties that make them useful in diverse applications. These include volume, surface area, and diagonals.
- Volume: The volume of a rectangular prism refers to the amount of space it occupies. It is calculated by multiplying the length, width, and height of the prism.
- Surface Area: Surface area represents the total area covered by all the faces of the rectangular prism. It includes the area of each individual face.
- Diagonals: Diagonals in a rectangular prism are lines connecting opposite vertices, passing through the center of the prism. Understanding diagonal lengths is crucial in various geometric calculations.
How to Calculate Volume of a Rectangular Prism
Calculating the volume of a rectangular prism involves a straightforward formula:
Volume = Length × Width × Height
For example, if a rectangular prism has a length of 5 units, width of 3 units, and height of 4 units, its volume would be:
Volume = 5 × 3 × 4 = 60 cubic units
How to Calculate Surface Area of a Rectangular Prism
Determining the surface area of a rectangular prism requires summing up the areas of all its faces. The formula for surface area is:
Surface Area = 2lw + 2lh + 2wh
Where l, w, and h represent the length, width, and height of the prism respectively.
Diagonals of a Rectangular Prism
The diagonals of a rectangular prism connect opposite vertices, forming lines within the prism. These diagonals are essential in various geometric calculations, such as determining internal angles and spatial relationships.
Real-world Applications of Rectangular Prisms
Rectangular prisms find extensive use in real-world scenarios, including:
- Architecture: Rectangular prisms serve as building blocks for architectural structures, such as buildings and bridges.
- Packaging: Many packaging materials, like boxes and cartons, are designed in the shape of rectangular prisms for efficient storage and transportation.
- Engineering: In engineering projects, rectangular prisms are utilized in constructing components, machinery, and infrastructure.
Importance of Rectangular Prisms in Mathematics
In mathematics, rectangular prisms hold significant importance:
- Geometry: They are fundamental shapes studied in geometry, helping to understand concepts like volume, surface area, and spatial relationships.
- Algebraic applications: Rectangular prisms are often used as models in algebraic equations, facilitating problem-solving and visualization of mathematical concepts.
FAQs on Rectangular prisms
- What is a rectangular prism?
- A rectangular prism is a three-dimensional shape with six rectangular faces, where each face meets at right angles.
- How do you find the volume of a rectangular prism?
- The volume of a rectangular prism is calculated by multiplying its length, width, and height.
- Why are rectangular prisms important in mathematics?
- Rectangular prisms are significant in mathematics due to their relevance in geometry, algebra, and real-world applications.
- What are some real-world examples of rectangular prisms?
- Examples include buildings, boxes, bookshelves, and shipping containers.
- How are diagonals useful in rectangular prisms?
- Diagonals help determine internal angles, spatial relationships, and other geometric properties of rectangular prisms.
Rectangular prisms are versatile geometric shapes with essential properties and applications in various fields. Understanding their characteristics and calculations is crucial for both practical and theoretical purposes.


Roll over image to zoom
Staedtler - Xcellence math set, 10 pcsSKU: 78085
Staedtler - Xcellence math set, 10 pcs
- Keep everything you need for class or your next design job together with the Staedtler Xcellence math set.
- The 10 pieces of high-quality equipment in this kit are easy to pack up and carry between classes or meetings using the included compact case.
- Short needle safety points on compass and dividers
- Packed in sturdy metal storage case with clear window
- Includes: metal case, 6" Ruler, 45° protractor, 60° protractor, 180° protractor, lettering guide, compass, dividers, pencil, sharpener and eraser
- Number of pieces


The fall semester at SUNY Oneonta begins on Monday and a new academic building is now officially open.
The Fitzelle Hall is the largest academic building on campus to meet tough new standards to make it "green."
A variety of departments including Latino studies, mathematics, computer science, and philosophy call it home.
It takes up 100-thousand square feet and even includes a cafe. It's 30-thousand-feet larger now - but with environmental improvements it uses 20 less energy.
Copyright 2016 Nexstar Broadcasting, Inc. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.


The inquiry,”What could be the domain name in mathematics?”
Is a one among both teachers and students. The reply to this really is both exact straightforward and incredibly sophisticated.
The domain of mathematics is the place. The place where everything begins and finishes.
You will find three ways to define the domain name of mathematics. Step one will be to define it as being https://paragonwef.org/uncategorized/whats-a-chord-in-z/ in the moment as being at the totality of objects and also the thing . The definition would specify it.
Your question would be about all objects that are included within the field of the domain. Today you’ll need to consider a bit about mathematicians will deal with one of these items. Let us use a good instance.
Take a specific object and ask yourself what area it occupies in relation to all other objects. Your answer might be the length of the rod or it might be the length of the cube. Your answer would be the area of the area.
It is important the see here now way they relate with each other and to believe of the objects that are different. In order to do this, you have to analyze the entire picture and consider it from every possible angle. You will have to fill in the blanks by yourself once you have attained this undertaking.
The first point to do when it has to do with the domain would be to make alist of all the stuff that are contained inside of the region. For instance, the smallest sphere are the part of their world. Things that wouldn’t be contained in the checklist would be the sphere’s guts and its centre could be comprised in the list. All these are also called probably the sections of the sphere.
The next thing todo is to figure out which set of properties is contained inside the area of the world wide web. The first set of properties is the sphere’s location and the collection of properties would be the listing of most the things that are included inside the sphere. The set of properties would be the listing of all of the things https://bestresearchpaper.com/ that are contained over the sphere. The set of attributes are the sphere’s section.
Now you will want to look at the things that are contained within the sphere. This will give you a list of all the items that you can actually see. The question, “What is the domain in math?” could also be stated as, “What is the smallest part of the area of the sphere?”
This can be done by looking at the area and multiplying the length of the area with the length of the axis. The length of the axis is the length of the outside of the sphere and the radius of the sphere. The radius is the radius of the sphere divided by the length of the perimeter.
The next step would be to figure out what the things that are contained within the sphere are. This would give you a list of all the things that you can actually see. The question, “What is the domain in math?” could also be stated as, “What is the smallest part of the sphere?”


Homeschool, MFW Homeschool Highlights, My Father's World, My Father's World 1st Grade, My Father's World Kindergarten, Saxon Math 1
I obviously have gotten out of the habit of taking pictures of our homeschool work!
Our oldest (MFW 1st and Saxon Math 1) is currently learning about the fraction 1/4. So for lunch last week, we cut our sandwiches into fourths – three different ways!
We are also FINALLY at the point in the MFW 1st grade curriculum were we have gotten to timeline and Bible reader, and past the worst of the phonics stuff. The phonics portion at the beginning was about to make me poke my eyeballs out. I don’t know why, other than all of the sudden she seemed to start going SOOOO SLOOOOOOOWWWWW and we could never get anything done. But, just in the past week, it’s changed, and I now realize she was just in the brain drain of processing it all, and now that we’re past that hump, she’s off to the races again. Sometimes, I forget that she’s just six and still learning, because she seems to absorb most things so easily.
And since she went to a math camp this summer, she has mastered the dreaded addition and subtraction math facts with ease! Praise the Lord on that one, because I am terribly math challenged, and was struggling on how to help her. Nothing I tried seemed to work. But now, I can hardly keep up. Again.
Our youngest is now four, but we have decided to go ahead and start her on MFW K curriculum, knowing we’d most likely have to really take our time and not push it. Amazingly, she is doing FABULOUS. Her handwriting is terrible, but that is the only thing really she struggles with. I know that that is mostly because of her fine motor skills needing to catch up with her brain, though.
We just finished up the M (Moon) unit with her. This past week, I got into one of my crazy cooking moods, and we made Manicotti for dinner, muffins for breakfast, and surprised the girls with “moon cookies” for dessert. Mommy got to eat all the “oops.”
That’s all I have for this week! I will try to get more on the ball for next week!
Be sure to check out what others are doing in MFW by heading on over to
Oreos wouldn’t last long enough in our house to do the moon phases! 🙂
Well, I did go buy them that morning! I can tell you the rest didn’t last very long afterwards!


In the past, scientists have shown that bees have some surprising math skills. Now, new research shows that bees can even be trained to tell the difference between odd and even numbers. Before this, humans were the only animals known to have this ability.
Bees are smarter than many people think. Through special dances, they can tell each other how far away food is and in what direction. They can count up to four. In recent years, scientists have shown that bees have even greater math abilities than they imagined.
In 2018, researchers in Australia discovered that bees could understand the idea of “zero”. That was a big surprise, since only a few animals, like dolphins, monkeys, and some birds, had shown that they understood zero. Later, the same scientists showed that bees could be trained to add and subtract.
But the idea of odd and even numbers is very different. Even numbers can be split into two equal groups. With odd numbers, one group always has one more item than the other. But except for doing math, it’s not clear how knowing the difference between odds and evens helps humans – much less bees.
Learning odds and evens is a skill that’s usually taught in elementary (primary) school. Often, students are taught to remember that numbers ending in 0, 2, 4, 6, and 8 are even, while numbers ending in 1, 3, 5, 7, and 9 are odd. Until recently, humans were the only animals known to understand this.
To train the bees, scientists in Australia hung up cards with an odd or even number of shapes (like triangles or circles). The cards represented the numbers 1 through 10. Under each card was a small tray with a liquid. If a bee flew to the right card, it would get sugar water. If it chose the wrong card, it got a sour liquid.
The researchers trained one group of bees to choose odd numbers. They trained another group to choose even numbers. They kept training the bees until they got it right 80% of the time.
Then they added a new challenge. They had the bees choose between cards with 11 and 12 shapes on them. The bees had never seen these numbers in their training. Even so, they were able to correctly choose the odd or even number 70% of the time.
The scientists still don’t understand what methods the bees used to get the correct answer.
One reason for this research is that the scientists believe that studying bee brains might help us learn how to build better and faster computers. After all, a bee’s brain is about 86,000 times smaller than a human brain. How does it handle such complicated ideas?
Unless…they’re not so complicated. The scientists built an extremely simple computer system with just five connections called “neurons”. (Your brain has about 86 billion neurons.) Even though this network of neurons was far too small to be considered a “brain”, the scientists were able to train it to tell the difference between even and odd numbers up to 40.
Did You Know…?
Humans seem to prefer even numbers, and have an easier time identifying them. That wasn’t true for the bees. They had an easier time learning to recognize odd numbers.


As promised in my last post, I’m going to discuss how to convert any recipe measurements from cups to grams. This will help you tremendously with gluten-free baking. It will free you up in flour substitutions as you can change the ratio of gluten-free flours as long as they add up to the same weight of flour overall.
Example: I have an almond tortilla recipe (to be posted later) that I make that requires both tapioca and arrowroot flour. So if I run short of one, I can substitute the other easily as long as the total weight remains the same. Tapioca and arrowroot have very similar but not identical properties. From experience with this recipe, I know I can make the substitution in a pinch. I could not substitute chickpea flour for tapioca flour. Their properties are very different. This is a very brief example for a much more complex, later discussion.
The missing piece of the puzzle is how do you find out how much each flour weighs. They’re all different densities so one cup of chickpea flour does not weigh the same as one cup of tapioca flour. Sorry it’s not that easy. The manufacturers do help us out though. It’s right on the nutritional facts panel on the package. They provide the serving size in both conventional and metric. That is our baking rosetta stone. 🙂
Here’s where the math comes in. You’ll have to figure out how many servings (according to the package) are needed for your recipe then multiple by the grams listed per serving.
Example: For this package of gluten-free flour mix, one serving is 2 tablespoons. If your recipe calls for 1/2 cup of gluten-free flour, you can look at the downloadable chart below and tell that you need 8 tablespoons which is 4 servings. 4 servings multiplied by 28 grams per serving equals 112 grams. So for this recipe, you know that 1/2 cup of my flour is equivalent to 112 grams.
That’s not so hard! Now you can quickly convert any recipe you have to grams and take advantage of using a scale to measure out your ingredients. You’re one step closer to modifying (and dare I say it, creating) your gluten-free recipes with the confidence of a professional chef!
I have created a handy downloadable chart of measurement equivalents for you. Download Measurement Chart (PDF)
Note: If you buy your flours in bulk, you can still find the cups to grams equivalents. You can use any number of websites that have already figured it out. Traditional Oven is quite popular. They have great variety of flours listed, including all purpose and whole wheat flours—very helpful for converting a conventional recipe over to gluten-free.


By Andrzej Polanski
This textbook offers mathematical versions in bioinformatics and describes organic difficulties that motivate the pc technology instruments used to regulate the big information units concerned. the 1st a part of the ebook covers mathematical and computational equipment, with useful functions offered within the moment half. The mathematical presentation avoids pointless formalism, whereas ultimate transparent and special. The e-book closes with an intensive bibliography, achieving from vintage examine effects to very contemporary findings. This quantity is fitted to a senior undergraduate or graduate path on bioinformatics, with a powerful specialise in mathematical and computing device technological know-how background.
Read Online or Download Bioinformatics PDF
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Often I believe the 2 earlier studies. This ebook isn't very stable as an advent. First learn another e-book corresponding to Setubal and Meidanis, "Introduction to Computational Molecular Biology"; or Krane & Raymer, "Fundamental recommendations of Bioinformatics". those books have extra readable narrative and examples.
This e-book constitutes the refereed complaints of the overseas convention on Mass info research of indications and photographs in medication, Biotechnology and Chemistry, MDA 2006 and 2007, held in Leipzig, Germany. . the subjects contain recommendations and advancements of sign and photo generating systems, item matching and item monitoring in microscopic and video microscopic photos, 1D, 2nd and 3D form research, description and have extraction of texture, constitution and placement, photo segmentation algorithms, parallelization of snapshot research and semantic tagging of pictures from lifestyles technological know-how purposes.
Genomics examine has made major advances in recent times. during this booklet, a group of internationally-renowned researchers percentage the main updated details in a box that has in recent times switched emphasis from gene identity to practical genomics and the characterization of genes and gene items.
This moment variation volumediscusses the innovative improvement of swifter and cheaper DNA sequencing applied sciences from the prior 10 years and specializes in normal applied sciences that may be used by a wide range of plant biologists to handle particular questions of their favourite version structures.
- RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods
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Extra info for Bioinformatics
The statistical test described above is parametric and is called the t-test. Depending on sizes of the groups, variances and other assumptions, diﬀerent variants of the t-test can be constructed. Generally, tests belonging to the t family are used for comparing mean values of normally distributed variables. Other examples of parametric tests are, the ANOVA test for comparing means between multiple groups of measurements and the Bartlett test for homogeneity of variances. 3 Nonparametric Tests In many situations involving analysis of statistical data, the assumption of known distributions of variables cannot be justiﬁed.
This latter property is known as the Markov property. A Markov chain is a Markov process for which X(t, ω) ∈ S, where S is a discrete set. Usually the state space S is a subset of the integers. In other words, a Markov chain exhibits random transitions between discrete states. The theory presented here is focused on the case of a ﬁnite number of states, N , numbered 1, 2, . . , N . Also, we discuss most systematically the case of discrete times 0, 1, 2, . . , k, . .. However, we also add some facts about the case of continuous time.
This serves as an indicator of the dispersion of the random variable around its expected value. The square root of the variance, called the standard deviation and denoted by σ(X) = Var(X) is the scale parameter of the distribution X − E(X). For expectations of functions or moments of random variables to exist, the corresponding series or integrals must be convergent. 15) increases too fast with x, the series or integrals may not converge. Also, if the distribution of a random variable has tails that are too heavy, certain moments of the random variables may not exist; well-known examples are Cauchy or Student t distributions.
Bioinformatics by Andrzej Polanski


Calculus: A Conceptual Approach
|Years of Operation||1983*-1998|
|Sites Offered||CAR, LAN|
From the CTY Summer Catalog (1996):
Calculus is one of the greatest achievements of the human intellect. Students in this course explore the underlying concepts of functions, differential and integral calculus, and differential equations. They develop an understanding of the rules and procedures which too often in a more traditional course are just memorized. Each topic is presented geometrically, numerically, and algebraically. Formal definitions and procedures evolve from the investigation of practical problems and applications. The course is flexibly paced, incorporating independent work, discussion, and supplemental lectures by the instructor.
CTY's Calculus course offers an excellent conceptual foundation for students who intend to continue their study of mathematics. Students have the opportunity to progress through the equivalent of most of the Advanced Placement AB curriculum. Therefore, this course is not recommended for students who plan to take AB Calculus in their home schools. Students who are successful in CTY's Calculus course should take Advanced Placement BC Calculus or a second-semester calculus course at a local college during the school year following CTY.


ARR stands for Annual Recurring Revenue. It is a measure of the amount of revenue that a company can expect to receive on a yearly basis and is typically used as a metric by subscription-based businesses.
How do you calculate ARR?
ARR is calculated by taking the total monthly recurring revenue for a given year and multiplying it by the number of months in that year. For example, if a company has $100,000 in monthly recurring revenue, its ARR would be $1.2 million.
The simple formula would be: Total monthly recurring revenue x 12 (months) = Annual recurring revenue.
Some benefits of tracking ARR include:
- It provides a clear picture of a company's growth
- It can be used to predict future revenue
- It can help identify upselling and cross-selling opportunities


Last week, the CEDEI School teachers attended workshops on various topics in order to keep their knowledge up to date. The trainings addressed pedagogical and educational issues.
One of the topics was "Reading Appreciation," in which the importance of promoting this activity for students was analyzed. Another training session dealt with "Mathematics as a tool to work on concentration, attention, and memory." In this workshop, teachers learned about the many benefits of mathematics. They talked about using Neurolinguistic Programming in different subject areas to remove mental blocks. They practiced neuronal exercises that they can use with students and learned about tools to facilitate learning in mathematics and other areas.
The teachers also attended workshops on topics such as: Assessment, Discipline, Self-realization, Education and Gender, The Didactics of Mathematics, "Brain Gym," and others.


Data Science (DS) is a multidisciplinary field that uses scientific methods, algorithms, and systems to extract knowledge and insights from structured and unstructured data. Data Scientists are the detectives of the data world, responsible for unearthing valuable business insights from raw data. These professionals employ various statistical, machine learning, and data visualization techniques to understand patterns, predict future trends, and inform strategic decision-making. In the data pipeline, data scientists are the final consumers of the data, using the infrastructure built by data engineers and cleaning and further processing done by data analysts.
In today's data-rich environment, the role of a Data Scientist has become increasingly significant. These professionals must have a strong foundation in mathematics and statistics, as well as proficiency in programming languages like Python and R. They often utilize machine learning tools and libraries such as scikit-learn and TensorFlow, and are skilled in data visualization tools like Matplotlib, Seaborn, or Tableau. Additionally, a solid understanding of databases and SQL is crucial. As businesses of all sizes continue to generate massive volumes of data, the need for data scientists to analyze and interpret this data is greater than ever. By unlocking actionable insights from complex datasets, Data Scientists play an invaluable role in guiding business strategies and future growth.


Can you really calculate the value of a Facebook fan?
A friend of mine had an interview the other day and the interviewer asked “How would you calculate the value of a Facebook fan for our company page?” My friend was puzzled and spewed out some sort of financial equation that he hoped was giving the interviewer what she wanted to hear in order to get the job.
Unfortunately, that’s the problem with social media. It’s not cut and dry. And like any nascent marketing channel, the numbers are hard to calculate. But many social media managers and marketers are forced to come up with some sort of ROI so they can continue to get paid. On top of that, many confuse cost of a campaign with the value of a fan/follower and that’s incorrect. The value of a fan or follower fluctuates over time. You can propose some general hypotheses; however, the value of a fan is different for every company, every fan, and every product.
Although cost and value are connected, they are not the same and they are not mutually exclusive. The value of a fan is ultimately calculated using a person’s purchasing history and referral history. In other words, the value of a fan or follower is actually based on the value of their transactions and actions each month. To quote Olivier Blanchard, “Until a Facebook ‘fan’ has transacted with you (or influenced a transaction), the monetary value of that fan is precisely zero.” And let’s not forget that the cost consists of not only acquisition cost but also the cost to maintain that fan, e.g. your social media person and some incremental IT expenses.
Let’s look at an example campaign run by Company A to generate new Facebook fans. Let’s just say that you figured out that the cost to run the campaign was $5,000 and Company A acquired 1,000 new fans through that campaign. You can do the simple math and deduce that the cost of those fans was $5.00 per fan. Let’s then say that 100 of those fans each buys $1,000 worth of product from Company A over a 6 month period totaling $100,000 in sales. Let’s also say that we have calculated the cost to maintain each fan to be $1 per month. The average revenue per user (ARPU) over this six month period is $100 ($100,000/1,000 users) for these new fans. To calculate the net value of a new fan we subtract the acquisition and maintenance costs from the ARPU:
$100 revenue – $5 acquisition cost – $1 x 6 months maintenance cost = $89 net value/6 months = $14.83/month per fan.
The math on referrals is a bit more complicated, because you have to split the value of any referral purchase between the purchaser and the referrer. In the above example, you can add some percentage of the referred purchases to the revenue portion of the equation to get a more complete picture.
Now, this is simple math and anyone can plug these numbers into the equation to get some sort of value of each fan. Where it gets more complicated is that some would argue that there also should be an arbitrary value assigned to brand awareness. I would argue that brand awareness has value only if that brand awareness directly results in sales. And this is where the real complexity lies. What metrics should you use to factor in the value of brand awareness? Should you use ‘People Talking About Us’ on Facebook and number of brand mentions on Twitter? Sure you could, but those don’t measure sentiment and even if they did, can you attribute them to a particular fan? And even if you find a decent metric, how do you assign a dollar value to those metrics?
The bottom line is that not all fans are created equal. Some fans may buy from you seasonally, some may buy from you annually, some may not buy from you at all but may refer friends, and some may have clicked “like” one time and never returned (95% never return to a company’s Facebook Fan page after liking it so all activity thereafter is dependent on you getting your content into their news feed or their friends’ news feeds).
Does this mean calculating a Facebook fan is a worthless exercise? No, in fact, Facebook fans are valuable, but only when you definitively figure out how you can monetize them through your marketing strategy. By developing campaigns that have a specific call-to-action that turns those fans into buyers is what will bring you the biggest bang for your buck in your Facebook strategy investment.
Photo credit: Geograph.org.uk – Creative Commons.


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- Automorphic forms are mathematical functions that exhibit certain symmetries when transformed.
- Automorphic numbers are a specific type of number that retains its form even when transformed.
- Self-conjugate numbers are a type of automorphic number that remains the same when its digits are reversed.
- Imitative numbers are a type of automorphic number that imitates a smaller version of itself at the end of its square.
- Digit squares are a type of number that is the square of a number whose digits are the same as the number itself.
- Perfect digit squares are a special type of digit square that exhibit unique properties.
- Automorphic sequences are a sequence defined by automorphic numbers.
- Perfect digit powers are a fascinating concept related to automorphic numbers.
- Automorphic forms have diverse applications in various branches of mathematics.
What are Automorphic Forms?Automorphic forms are significant in modern mathematics due to their applications in various branches of research. These forms are a type of mathematical function that satisfies certain conditions related to symmetry and transformation. More specifically, an automorphic function is a complex-valued function that remains unchanged after undergoing a specific transformation. Automorphic functions play a crucial role in many areas of mathematics, including number theory, algebraic geometry, and representation theory. They also have significant applications in physics, particularly in the study of string theory and quantum mechanics. One of the most notable applications of automorphic forms is their connection to automorphic numbers. An automorphic number is a number that remains unchanged when its digits are squared and added to the resulting digits. For example, the number 5 is an automorphic number because 5^2 = 25, and the digits in 25 add up to 7. When 7 is squared and added to the resulting digits (49), the result is 5. The connection between automorphic forms and automorphic numbers lies in the fact that automorphic numbers can be expressed as Fourier coefficients of certain automorphic forms. This insight has led to significant advancements in the study of automorphic numbers and their properties.
Understanding AutomorphismAutomorphism, a fundamental concept in abstract algebra, is a symmetry of a mathematical structure that preserves its properties. This concept is related to automorphic numbers, which are numbers that can be transformed into their own square by rearranging their digits. Automorphism is significant in mathematics as it helps us study objects by understanding their symmetries. In the world of automorphic numbers, automorphism plays a crucial role in determining the properties of such numbers. An automorphic sequence is a sequence of numbers where each number is an automorphic number. The sequence can also be defined by an automorphism that maps each number in the sequence to the next number. Automorphisms of this type allow us to generate sequences of automorphic numbers. For example, consider the base-10 automorphic numbers. The automorphism of the single-digit automorphic numbers is constructed by mapping a single-digit number to its square. The automorphism of the two-digit automorphic numbers is constructed by mapping the first and second digits to the last and second to last digits, respectively. This process can be repeated for any number of digits, making it possible to generate larger sequences of automorphic numbers.
“The automorphism of the single-digit automorphic numbers is constructed by mapping a single-digit number to its square.”Automorphism is a powerful tool that allows us to study the properties of automorphic numbers and sequences. By understanding the symmetries of these mathematical structures, we can gain insight into their behavior and explore new avenues of research in the field of automorphic forms.
Exploring Self-Conjugate NumbersA self-conjugate number is a type of automorphic number that remains the same when its digits are reversed. In other words, a self-conjugate number is a number that is a palindrome. For example, 121 and 3443 are both self-conjugate numbers. Self-conjugate numbers have unique properties that distinguish them from other automorphic numbers. For instance, any self-conjugate number that ends with an odd digit can be expressed as the sum of two perfect squares. Additionally, every digit in a self-conjugate number must be either 0, 1, 3, 7, or 8. The first few self-conjugate numbers are:
|Number||Square||Sum of Perfect Squares|
|0||0||0 + 0|
|1||1||1 + 0|
|2||4||4 + 0|
|3||9||9 + 0|
|4||16||16 + 0|
|5||25||25 + 0|
|6||36||36 + 0|
|7||49||49 + 0|
|8||64||64 + 0|
|9||81||81 + 0|
|11||121||100 + 21|
Unveiling Imitative NumbersImitative numbers are a type of automorphic number that shares similarities with its square. An imitative number n is defined as a number whose last d digits are its own square, where d is the number of digits in the number. For instance, the number 376 is an imitative number because it ends with the square of 6, which is the last digit of 376. Imitative numbers have several intriguing properties, including the fact that their digit sum is always divisible by 3. Additionally, every imitative number is also a perfect digit square, making them a subset of that group. However, not all perfect digit squares are imitative numbers.
“Imitative numbers are a fascinating concept within the world of automorphic numbers, possessing unique characteristics that make them a subject of interest for mathematicians.”One example of an imitative number is 5, since 5^2 = 25, and the last digit of 25 is 5. Another example is 376, as mentioned earlier. By studying imitative numbers, mathematicians can gain insights into the properties and patterns of these interesting numbers.
The Fascination of Digit SquaresOne of the captivating concepts within automorphic numbers is the idea of digit squares. Digit squares are numbers that remain unchanged when their square is taken, except for the last digits. For example, the number 25 is a digit square because its square, 625, ends with the same two digits. Similarly, the number 76 is a digit square because its square, 5776, ends with the same two digits. Digit squares can also be expressed in terms of their digits. A digit square is said to be of the form n^2, where n is a natural number, if its last digits match the last digits of n. For example, 25 is of the form 5^2, and 76 is of the form 6^2. Digit squares are closely related to automorphic numbers. In fact, all digit squares are automorphic numbers, but not all automorphic numbers are digit squares. This means that every digit square is a number that is its own automorphic number. For instance, the number 1 is a digit square because its square, 1, ends with the same digit. Therefore, 1 is also an automorphic number. Another example of a digit square is the number 376. When we square this number, the result is 141376, which ends in the same three digits as the original number. Hence, 376 is also an automorphic number. Digit squares hold a great fascination in mathematics due to their unique properties and relationship to automorphic numbers. They have been studied extensively, and many interesting patterns and properties have been discovered.
Examples of Digit Squares
“The study of digit squares is a fascinating area of research, providing insights into the properties and patterns of automorphic numbers.”
Perfect Digit Squares and their PropertiesIn this section, we will explore a fascinating type of automorphic number known as perfect digit squares. These numbers are unique and possess certain characteristics that set them apart from other digit squares. Let’s dive in and explore their properties.
“A perfect digit square is a specific type of digit square, where the square of the number ends with the same digits as the number itself.”For example, the number 5 is a perfect digit square because its square is 25, which ends with the same digit as the original number. Similarly, 6 is a perfect digit square because its square is 36, ending with the same digit as the original number. Perfect digit squares are an essential component of automorphic numbers, and we can see their significance when we compare them to regular digit squares. Unlike perfect digit squares, regular digit squares do not have to end with the same digits as the initial number. For example, 2 is a digit square as its square is 4. However, its square does not end with the same digit as the original number. To better understand the properties of perfect digit squares, let’s examine them more closely in the table below.
|Perfect Digit Squares||Examples|
|Even Perfect Digit Squares||0, 1, 81|
|Odd Perfect Digit Squares||5, 6, 25, 76|
Unraveling Automorphic SequencesIn this section, we will explore automorphic sequences, a sequence that is defined by automorphic numbers. Automorphic sequences have attracted significant attention in mathematics due to their intriguing properties. In an automorphic sequence, each term is obtained by adding one to the previous term’s index. The corresponding automorphic number is obtained by squaring the previous term and comparing it with the last digits of the next term. For example, the first few terms of the automorphic sequence are: 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, … To understand how to derive the corresponding automorphic numbers, consider the third term of the sequence: 5. Its corresponding automorphic number is obtained by squaring the previous term, 1, to get 1. The last digit of the product is compared to the next term, 6, which is the same. Therefore, 5 is an automorphic number. In the same way, the fourth term, 6, corresponds to the automorphic number 6 since the square of the previous term, 2, is 4, and its last digit matches the next term’s last digit. Automorphic sequences have fascinating properties. Firstly, the sequence contains infinitely many automorphic numbers. Secondly, every automorphic number can be found in the sequence. Lastly, the sequence is non-repeating, which means that no term appears more than once. To summarize, automorphic sequences are fascinating sequences that are defined by automorphic numbers. They have unique properties that make them significant in mathematics.
The Power of Perfect Digit PowersPerfect digit powers, a fascinating concept within automorphic numbers, are numbers that can be expressed as a power of their own digits. For instance, 5^1, 6^2, and 7^3 are perfect digit powers. These numbers are also classified as automorphic numbers since they exhibit the property of remaining unchanged when their square is shifted to the right. In other words, the last digit of their square is always the same as the original number. Perfect digit powers are not as common as other types of automorphic numbers, but they have unique properties that make them intriguing objects of study. For example, all perfect digit powers greater than 4 end in 6 or 1. Additionally, only the numbers 1, 5, and 6 can be the base of a perfect digit power.
Examples of Perfect Digit PowersThe following table showcases some perfect digit powers:
Applications of Automorphic FormsAutomorphic forms have a wide range of applications in various fields of mathematics, including number theory, algebraic geometry, mathematical physics, and cryptography. These forms provide a powerful tool for studying complex mathematical systems, making them an essential tool for researchers in many disciplines. One of the most significant applications of automorphic forms is in number theory. These forms provide a mathematical framework for studying the distribution of prime numbers and other important number-theoretic functions. In particular, automorphic forms have been used to prove the Riemann Hypothesis, one of the most famous unsolved problems in mathematics. Automorphic forms are also used extensively in algebraic geometry, which is the study of geometric objects defined by polynomial equations. They play a vital role in understanding the geometry of complex algebraic curves and surfaces, and in studying the arithmetic properties of those objects. Mathematical physics is another field that benefits from the use of automorphic forms. They have been used to study the properties of string theory, a theoretical framework that aims to unify the fundamental forces of nature. Cryptography is yet another area where automorphic forms have applications. In particular, they are used in the creation of secure communication protocols and digital signatures. Automorphic forms provide a way to create public-key cryptographic systems that are resistant to attacks by hackers and other malicious actors.
Example: Elliptic CurvesOne of the most significant applications of automorphic forms is in the study of elliptic curves, which are geometric objects defined by polynomial equations. They have a wide range of applications in modern cryptography, and they form the basis of many public-key encryption systems used in secure communication protocols.
|Number Theory||Proving the Riemann Hypothesis|
|Algebraic Geometry||Studying the geometry of complex algebraic curves and surfaces|
|Mathematical Physics||Understanding the properties of string theory|
|Cryptography||Creation of secure communication protocols and digital signatures|
“Automorphic forms provide a powerful tool for studying complex mathematical systems, making them an essential tool for researchers in many disciplines.”Automorphic forms provide a deep connection between various branches of mathematics, which makes them an essential tool for researchers in many fields. The applications of automorphic forms are broad and far-reaching, and they have the potential to revolutionize modern cryptography, number theory, algebraic geometry, and mathematical physics.
ConclusionIn conclusion, automorphic forms are a fascinating area of mathematics that provide valuable insights into the properties and relationships of numbers. Through our exploration of different types of automorphic numbers, including self-conjugate and imitative numbers, we gained a deeper understanding of their definition and properties. Furthermore, we examined the importance of digit squares, perfect digit squares, automorphic sequences, and perfect digit powers in automorphic forms.
The Significance of Automorphic FormsAutomorphic forms have extensive applications across diverse areas of mathematics, making them a valuable tool for researchers and mathematicians. These applications include number theory, algebraic geometry, and even physics and engineering.
The Future of Automorphic FormsAs we continue to explore the depths of automorphic forms and their properties, we are likely to discover new types of automorphic numbers and applications in other areas of mathematics. The development of new techniques and tools for studying automorphic forms will likely lead to new breakthroughs and discoveries in the field. In conclusion, the world of automorphic forms is vast and multifaceted, providing endless opportunities for exploration and discovery. By understanding these concepts and their significance, we gain a deeper appreciation for the beauty and complexity of mathematics.
What are automorphic forms?
Automorphic forms are mathematical functions that satisfy certain transformation properties under a specific group of transformations. They play a significant role in various areas of mathematics, including number theory and representation theory.
What is automorphism?
Automorphism is a function that preserves certain properties of an object. In the context of automorphic forms, an automorphism is a bijective transformation that preserves the structure and properties of the form.
What are automorphic numbers?
Automorphic numbers are numbers that remain unchanged or are only slightly changed when squared or raised to a specific power. These numbers possess a unique relationship with their digit squares and have interesting properties.
What are self-conjugate numbers?
Self-conjugate numbers are a type of automorphic number that remains unchanged when squared. In other words, the square of a self-conjugate number ends with the same digits as the original number.
What are imitative numbers?
Imitative numbers are another type of automorphic number that exhibits a special property. When raised to specific powers, imitative numbers imitate their own digits in a cyclic manner.
What are digit squares?
Digit squares are numbers that can be expressed as the sum of the squares of their individual digits. These numbers are closely related to automorphic numbers and provide interesting insights into their properties.
What are perfect digit squares?
Perfect digit squares are a special type of digit square where the sum of the squares of the digits equals the original number. These numbers have unique properties and connections to automorphic numbers.
What are automorphic sequences?
Automorphic sequences are sequences defined by a specific pattern of automorphic numbers. Each term in the sequence is an automorphic number, and the sequence follows a predetermined rule or formula.
What are perfect digit powers?
Perfect digit powers are a concept closely related to automorphic numbers. These numbers exhibit a unique property where each digit raised to a certain power equals the original number.
What are the applications of automorphic forms?
Automorphic forms have diverse applications in mathematical research and problem-solving. They are used in areas such as number theory, representation theory, and the study of modular forms. They also have applications in physics and cryptography.


Modern Logic: Since G?del: Decidable and Undecidable Theories
MODERN LOGIC: SINCE GÖDEL: DECIDABLE AND UNDECIDABLE THEORIES
Suppose T is a theory (i.e., a set of sentences) in a formal language L of logic. A decision procedure for T is a mechanical procedure for calculating whether any given sentence of L is a logical consequence of T. We say that T is decidable if it has a decision procedure and undecidable if not. The decision problem for T is to determine whether or not T is decidable. (One can avoid the slightly vague notion of a mechanical procedure by noting that a theory T is decidable if and only if the set of its logical consequences is computable.)
Quantifier elimination and related model-theoretic techniques have yielded proofs that many important first-order theories are decidable. Examples are the theory of addition of integers (Presburger 1930), the theories of real-closed fields and algebraically closed fields (Tarski 1951), the theory of abelian groups (Szmielew 1955), and—if a number-theoretic conjecture of Schanuel is true—the theory of the field of real numbers with exponentiation (Macintyre and Wilkie 1996). The first theory shown to be undecidable was first-order Peano arithmetic; Kurt Gödel proved its undecidability in 1931. Many other undecidable theories are known, but the proofs of undecidability are all based directly or indirectly on Gödel's ideas. In 1970 Yuri V. Matiyasevich (1993) improved Gödel's result by showing that the set of diophantine sentences true in the natural numbers is not computable (a diophantine sentence is one of the form "There are natural numbers m, n, and so on such that E is true," where E is an arithmetical equation using m, n, and so on). Part 3 of "Decidable and Undecidable Theories" of J. Donald Monk (1976) gives many examples.
We say that a formal language L of logic is decidable if the empty theory in L is decidable—in other words, if there is a mechanical test to determine which sentences of L are valid. Gödel's ideas led to a proof that if L is a nontrivial first-order language, for example, with at least one binary relation symbol besides equality, then L is undecidable (Church 1936). Later research extended this result to various important sublanguages of first-order languages. But there are also decidable languages, for example, languages of propositional logic and a number of languages with monadic predicate symbols (e.g., the language of syllogisms). See Egon Börger, Erich Grädel, and Yuri Gurevich (1997) for full information on decidable and undecidable languages. After their book appeared, a new family of decidable languages was discovered, the guarded languages, whose decidability implies the decidability of various modal logics (see Grädel, Hirsch, and Otto 2002).
The decision problem for logical languages is also known as the Entscheidungsproblem. See Paulo Mancosu (1999, §8) on the place of this problem in early twentieth-century thinking about the foundations of mathematics, particularly within the school of David Hilbert.
Börger, Egon, Erich Grädel, and Yuri Gurevich. The Classical Decision Problem. Berlin: Springer, 1997.
Church, Alonzo. "A Note on the Entscheidungsproblem." Journal of Symbolic Logic 1 (1936): 40–41. Correction ibid : 101–102.
Gödel, Kurt. "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I." Monatshefte für Mathematik und Physik 38 (1931): 173–198. Edited and translated in Kurt Gödel. Collected Works Volume I: Publications 1929–1936, ed. Solomon Feferman, et al, pp. 144–195. New York: Oxford University Press, 1986.
Grädel, Erich, Colin Hirsch, and Martin Otto. "Back and Forth between Guarded and Modal Logics." ACM Transactions on Computational Logics 3 (2002): 418–463.
Macintyre, Angus, and Alex Wilkie. "On the Decidability of the Real Exponential Field." Kreiseliana, edited by P. Odifreddi, pp. 441–467. Wellesley, MA: A.K. Peters, 1996.
Mancosu, Paolo. "Between Russell and Hilbert: Behmann on the Foundations of Mathematics." Bulletin of Symbolic Logic 5 (1999): 303–330.
Matiyasevich, Yuri V. Hilbert's Tenth Problem. Cambridge, MA: MIT Press, 1993.
Monk, J. Donald. Mathematical Logic. New York: Springer, 1976.
Presburger, Mojżesz. "Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt." Comptes Rendus du Premier Congrès des Mathématiciens des Pays Slaves, Warszawa 1929. Warsaw (1930): 92–101; supplementarty note ibid : 395.
Szmielew, Wanda. "Elementary Properties of Abelian Groups." Fundamenta Mathematicae 41 (1955): 203–271.
Tarski, Alfred. A Decision Method for Elementary Algebra and Geometry. Berkeley: University of California Press, 1951.
Tarski, Alfred, Andrzej Mostowski, and Raphael M. Robinson. Undecidable Theories. Amsterdam: North-Holland, 1953.
Wilfrid Hodges (2005)


Computational Beauty of Nature, by Gary Flake, is a very nicely written walk through topics related to chaos and complexity, including fractals, chaos, artificial life, adaptive systems, and neural networks. This is THE one book for folks who want to dive into these topics one level deeper than the popular science books. Each chapter has references to the primary source books and articles, if you want to pursue the topics in greater depth.
The book's website has a set of Java applets and C programs to run the simulations -- for example, you can play with the parameters of L-System fractals to simulate different kinds of plant shapes. The source code is available to download and play with.
Flake does a lovely job of explaining the math and modeling concepts, in a manner that is comprehensible to those of us without extensive math backgrounds. Sometimes his one-page intros go a bit fast for me, but it's easy enough to hit Google, find a relevant tutorial, then go back and finish the chapter. I needed to do this for the sections on matrix math and circuit design -- this is a very pleasurable way to learn.Posted by alevin at August 3, 2002 12:00 AM


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Note: These rankings do not currently include STAAR math scores for grades 3-8!
School Year: 2014-2015
The Texas Education Agency will not be releasing math scores until September, 2015. SchoolDigger will revise the rankings when these scores are made available.
For more information, see the Texas Education Agency announcement.
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A data-driven factual answer engine, not a website indexing search engine. Crunches data on a wide range of topics, with particular strength in science, technology and math computations.
Math & technology
This website features games that teach math, science, and cognitive skills.
This website introduces basic computer programming concepts; change the code and see the results!
This website contains fun math games, brainteasers, manipulatives, and lessons and quizzes that teach addition, subtraction, multiplication, division, and fractions.
This website has tons of fun games to help you practice your math skills.
This website is full of fun math games that are organized by grade level and by topic.


Today we spent our morning at the Flynn watching a show about the Abenaki. It was an interesting show, but a little too long for the average 9 year old. Shows at the Flynn typically last an hour, this show lasted two hours. Despite the extended stay at the Flynn, student behavior was exceptional. In fact since last Wednesday, students have really turned it around and behavior has been great.
We just starting working on fractions. We will be learning to identify fractions, compare fractions, order them, and find fractions of wholes. For example 3/5 of 60 =36
Students have been working on writing short stories. They did a great job of being creative, but need to work on the conventions of writing (proper capitalization, usage, punctuation, and spelling).
The beginning of the year until New Year’s break is on literary elements; plot, setting, character, conflict, and theme. After Thanksgiving we will be reading some Greek Myths.
We just started using Hot Wheels to learn about energy, force and motion. We’ve talked a little bit about friction. Potential energy and kinetic energy are next on the list.
I’ve tried to put pictures of students on my twitter account. I’m not sure if my blog emails you when I update my twitter account, but if you haven’t done so in awhile, look at the pictures on my twitter account: JosephCheney151
If you haven’t already done so, please go to the MBS website and sign up for a conference time. Additionally, if you have any questions/issues you want to discuss please send me an email and I’ll have a response ready for you at your conference.
You can email me any time at: firstname.lastname@example.org


When an individual invests, they don't merely earn interest on their principal balance when they use compound interest. Even their interest is compounded. When they apply their earned interest to their principal balance, they earn even more interest, compounding their profits.At different periods, interest can be compounded-that is, added back into the principal. Interest, for example, can be compounded annually, monthly, daily, or even indefinitely. The faster the main balance grows, the more frequently interest is compounded. While investing, a person might not be aware of what would be their final amount at the end of their investment tenure. In such a situation, a compound interest calculator online can be of great assistance.
Advantages of Availing Compound Interest
- Compound interest accelerates the growth of an investor's money by allowing them to earn interest on interest.
- The longer the investing period, the greater the potential for higher profits.
- Make frequent contributions to an existing investment to increase the compounding potential.
- The more compounding periods an investor has, the better their returns will be. Monthly compounding can earn more than annual compounding.
Compound Interest Calculator OnlineIf an individual plans to apply for a term deposit, it is advisable to use a compound interest calculator online. This will help them figure out how much compound interest they will earn on their investment, such as a Fixed Deposit (FD). A compound interest calculator is an online application that allows an investor to compute compound interest. Compound interest can be calculated for a variety of durations and interest payout frequency, including daily, monthly, quarterly, half-yearly, and yearly. Using a compound interest calculator online, an individual can learn about the power of compound interest and how it may help them grow their investment.
How Does Compound Interest Formula Calculator?The compound interest formula calculator shows an individual how their money can grow by compounding interest. Compound interest can be calculated using annual, quarterly, daily, or continuous compounding on investment, 401K, or savings account.
The Compound Interest Formula Calculator OnlineIn order to calculate interest and principal, this compound calculator uses the formula of compound interest. Given the other known variables, it utilizes the same procedure to solve for principal, rate, or time. This formula can also be used to create an Excel compound interest calculator.
- A = Amount owed (principal + interest)
- n = is the number of compounding periods per time unit
- P = stands for principal amount.
- R = is the annual nominal interest rate expressed as a percentage.
- I = Interest rate
- r = R/100
- r = is the decimal representation of the interest rate of the annual nominal amount.
- In = is the natural logarithm, which is utilized in the calculations following.
- t = time in decimal years; for example, 6 months is 0.5 years.


Course Selections for Fall 2019
Please complete this form so that we can know more about your choices and can register you for courses for Fall 2018. Please note that without completing the Financial Responsibility Form (FRS) we will not be able to start your registration. Also, please complete the Math Placement Test and score 10 or higher on the third section or we will not be able to secure your math course. Complete this course selection form by June 1st so that we can help register you for the June 26 & 27 Summer Orientation.


Hipparchus shows us how to describe the position of any point on Earth with two numbers… and explains the stereographic projection: how to draw a map of the world.
Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension… and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces!
Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy! Transforming the plane, deforming images, creating fractal images…
Proof: “Doing mathematics means , above all, proving what one claims.”
Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning the stereographic projection.


The aim of the course is to develop a broad basic understanding of the geosciences. You will learn about the different subfields, understand their goals and methods, and develop your own area of specialization.
Geoscientists have always solved societal or economic problems in conjunction with other professionals; therefore, an understanding of other geoscience sub-disciplines and related STEM subjects is important.
The workload is measured in credit points (LP or CP = Credit Points in the ECTS system). 1 LP corresponds to about 25 to 30 hours of study. Full-time students take courses of approximately 30 LP per semester. In many semesters this corresponds to 5 modules of 6 LP each or a weekly working time of about 29 - 35 hours. The actual workload can vary considerably, depending on interest and aptitude.
A new version will go into effect in WS 2019/2020. Here are the orders in comparison. There you can also find the overview below in PDF_format.
We only teach the new modules, but have equivalence lists to the old ones. For already students, of course, the study regulations under which you had enrolled here still apply !
|Semester||Required modules||Elective modules|
|1 (WS)||Total: 30 LP
|2 (SS)||Total: 23 LP
Total: 7 LP (one of the two modules must be loaded)
|3 (WS)||Total: 18 LP
||Total: 12 LP
|4 (SS)||Total: 15 LP
||Total: 12-18 LP
|5 (WS)||none||Total: 30 LP
|6 (WS)||Total: 30 LP
SS - Summer semester
WS - winter semester
V - Lecture
S - seminar
Ü - exercise
P - practical course
GÜ - field exercise
Ex - excursion
T - days
Prior to the start of the program, a pre-course in mathematics is offered as part of the introductory study days de and is recommended for all newly enrolled students. For students who want to choose geophysics as a specialization, the participation in the more intensive pre-course "Mathematics for Physicists" is recommended. This will lead seamlessly into the course "Mathematical Methods in Physics I" (elective module for geophysics-oriented students in the 3rd semester).
Basic mathematics and physics modules can be taken either with materials science students or with those in mathematics and physics. The former are more applied and emphasize calculations of facts and similar tasks. Courses for mathematicians and physicists also include proofs and derivations.


Science, Technology, Engineering and Mathematics are integrated across the curriculum, with a view to inspiring and encouraging pupils to develop their enthusiasm and skill in these areas. Through STEM, pupils also develop their teamwork, independence, reasoning and critical and creative thinking.
Our emphasis on STEM reflects our commitment to empower our pupils with the skills to succeed and adapt to an increasingly complex, changing, technological world. We believe that STEM subjects are critical in developing in our future generation, the innovation necessary to sustain their environment and economy.
Many of our alumni pupils have been inspired by their specialist teachers, school workshops and visits, go on to excel in STEM subjects at senior school and beyond and even to embark on STEM based careers in their future; attributing their passion for these subjects to the foundation that they received at St John’s Priory School.


Math Email Helpline
Christian Liberty has an email helpline to assist our CLASS Plan, Family Plan, and Individual Course Plan students who are taking a math course for seventh grade and above. This service is designed as an opportunity for parent and student to work together in framing questions for our math specialists in the event that they have a question about a problem or an example in one of our math textbooks at this level.
Keep in mind that this is a helpline and not a tutorial service. Therefore, this service is not designed to teach your student math. It is still the responsibility of the parent to teach. We are available to help when you and your student have made your best attempts to understand a problem or example in the math homework, and you just cannot seem to get unstuck.
When you, the parent-teacher, have done all that you can to assist your student, yet still find you are not able to help him get past a particular obstacle to his understanding, then it is time to help your student to properly frame a question for our math helpline. Our response to your question will be in the form of a PDF file attachment to an email message. If you do not already have Adobe Acrobat Reader, you will be given the opportunity to download a free copy when you attempt to open and read your PDF attachment.
An email to the helpline should contain the following elements:
• Your student’s full name
• Your student’s ID Number
• The name of the course
• The appropriate lesson number and/or page number in the textbook
• The particular problem(s) or examples(s) causing the difficulty
• What attempts have been made to understand the problem(s) or example(s)
• What attempts have been made to solve the problem(s) and the results of your attempts
Below we display two examples of helpline requests. The first one lacks sufficient information about either the student or the student’s particular difficulty to enable us to offer the kind of help she needs. Such requests usually require a return email from CLASS asking for the necessary specific information that should have been supplied in the original email.
The second one is an example of a properly formed request for help. In this situation, we can readily identify the student and her difficulty and provide immediate direction.
This service provides help for homework and practice test problems. Therefore, it is only available for assistance with the textbook exercises, as well as any corresponding publisher tests that are suggested for extra practice. This service is not available for assistance with any problems on the required CLASS exams.
We thank you in advance for your cooperation. We trust that this service will enhance the education of those students who are assigned a math course through CLASS.
The Math Email Helpline is available for those enrolled with CLASS. To obtain the email address (password required), Click Here.


Now showing items 1-2 of 2
Optimal Actuator Design for Nonlinear Systems
(University of Waterloo, 2019-09-24)
For systems modeled by partial differential equations (PDE's), the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator ...
Optimal Controller and Actuator Design for Nonlinear Parabolic Systems
Many physical systems are modeled by nonlinear parabolic differential equations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, the existence of a concurrent optimal controller and actuator design is ...


Home > Math Riddles
Math Riddles - Hard Math Riddles and Puzzles
Looking for tricky hard math riddles? Math puzzles and riddles are the best way to have fun and exercise your brain at the same time. Hard math riddles are prove to grow your brain power and make you more intelligent - both for children and adults.
That's why playing math games and logic riddles has become so popular among young and old people. You can enjoy free hard math riddles during your free time every day - at home or at work.
Here you can find top math games, puzzles and riddles that you can play and download for free. Simply click on each riddle to open it in a new window and have fun playing it!
Top 3 Ideas to Use Math Riddles
So how can you use free hard math puzzles and riddles? You'll be surprised how many ideas you can come up with to enjoy these mind games. Here are some quick and easy ideas to help you get started.
Riddle Idea #1: Solve Them in Your Free Time
Having a boring day at work? Or maybe you are tired of working too much today. How about a math riddle or a brain teaser to make you forget everything else and laugh and have fun for a while?
Simply check out the many awesome free riddles on this site and enjoy your time - whether you are in the office, at home, or school.
Riddle Idea #2: Share Math Riddles with Your Friends
Solving a mystery puzzles is sometimes more fun in a group than alone. So why not share these tricky math puzzles and riddles with your friends to enjoy them more together?
Riddle Idea #3: Play Puzzles in a Party to Have Fun
Sometimes the best way to add more fun and excitement to a party is throwing in some funny math puzzles and mind games. Soon people will be competing together to see who can guess the correct answer faster and win.
You'll have a blast! So simply choose some of your favorite riddles here and share them in the party you're going to attend, and everyone will be impressed by your awesome idea.
More Hard Funny Riddles and Puzzles:
Enjoyed the funny riddles and free puzzles above? Then you can find and download more free funny tricky riddles below. Simply choose the topic you are most interested in, and you will find a list of top riddles about it.
Also feel free to send these free riddles to your friends. They will have a great time playing these puzzles and mind games and will thank you.


Time: 9:30 – 10:30, 5 lectures from from Monday 14 to Friday 18 July.
Location: VIASM Lecture Hall C2.
Lecturer: Prof. Vu Ha Van (Yale University)
Big Data has been a main focus of science in the last ten years, and will be in the next several decades.
Data is usually given in a (huge) matrix form. (For instance, a 1GB digital picture is a matrix with one billion entries). The problem is to process and obtain information from these huge and often noisy matrices. Quickly and Accurately! This leads to a vast collection of new mathematical challenges.
In these lectures, we aim to cover some of the key mathematical tools that appear very useful in data analysis. These include both classical and new results in high dimensional geometry, random matrix theory, functional analysis, and probability. Most of these results are of independent interest, and in fact have been studied for a long time for entirely different, more theoretical, purposes.
We are going to discuss several applications, the main one will be the community detection problem. How to partition a large group of people into smaller communities such that people in the same community behave roughly the same way.
This is also my personal answer to the popular question: How useful is modern mathematics?
Deadline for registration: 10/7/2014.
Filed under: Workshop & Course |


Ways To Score Well In Class 12 Maths
Maths is a subject that never loses its relevance. It comes in handy even after one’s study life is over. So, one must learn it thoroughly when they are at school. The mathematical concepts and the knowledge can also help people to solve some problems which are really complex. When one is talking about class 12 maths problems then they are quite tough and complicated just like a higher class maths problem should be. One has to understand the concepts well so that one can solve them without a doubt.
Be it chapter 2 maths class 12 or any other chapters, the students must practice it regularly when they are preparing for the final board examination. The higher math skills always involve visual attention, cognitive tasks, and decision-making processes. Solving maths problems at this stage is not only to score well in exams but it is also beneficial because the student’s brains are sharpened because of it.
Table of Contents
Practice all the chapters
Higher-class mathematics chapters (both class 11 and 12) come with plenty of formulas and calculations. Hence one has to practice them daily so that they look simplified. A maths textbook mostly includes Permutation Combinations, 3 Dimensional Geometry, Mathematical Reasoning, and many more. All of these chapters have a set of questions each and the students must solve each of them so that they can get a clear idea of the chapter. Sometimes they can find it difficult to solve a few very complex problems. One can clear their doubts by asking their school teachers. Sometimes the NCERT solution books can also be of major help here. This is because; they come with all the solved answers from the textbook of class 12 maths.
NCERT solutions are helpful
They are quite helpful because these books have all the detailed answers to the maths problems. Not only that, the answers come with all the explanations and if needed illustrations and diagrams as well. Hence, it becomes much easier for the students to understand them and prepare better for the exam. These solution books can always guarantee success for the students and with the solutions; the children get a mental development as well. Class 12 maths examination means it is a CBSE board examination and so one has to score well in order to impact their overall score. If one knows how to prepare, the scoring becomes easier.
How to score well in maths examination?
Well, if one wants to score well in maths in the board examination then they must follow the class 12 maths ncert book for better understanding and practice. Other tips that one must indulge into:
One must start preparing the checklist much before the examination dates. Here, the form that is needed to be followed is that one has to divide maths subjects into respective chapters. Then one has to start focusing on the topics where they are confident and also practice all the questions that are based on these chapters. Once they are done, one should start focusing on the chapters in which they are weak. Here, one must make notes and start solving the questions which are available. It is also necessary to keep a check on the weekly progress.
Studying daily can help one to finish the syllabus right on time. Once that is done then half of the game is already played. It is also very necessary to complete all the homework and assignments given to them – right on time. It is always advised to start with the easy chapters and then move to a difficult one. This can help the students to build up their confidence steadily.
Solve Sample Papers
When it comes to maths practice, this is a crucial part of it. One can solve the sample papers so that they are in good practice before the board examination. It is also a must to solve the previous year’s boar examination paper because one will get an idea of the marking scheme and question patterns of the paper.
Read the Question Paper
Before one starts solving it, one should go through the question paper thoroughly. When one is doing that they should check all the questions given and choose the ones which they can solve easily. One should solve those questions first because they are confident about them and then progress to the tougher ones. One can follow this to get good marks.
One can also rely much on the Infinity Learn blogs when the students are preparing for the board examination and maths subject. Practicing daily as mentioned above is the key to getting good marks. But one should also keep in mind that taking breaks in-between studies are really important. It gives the mind a break and they can concentrate even better.
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