How to Become a Mathematics Genius

Have you ever heard someone saying: “I can’t do math”? Most likely you’ve said it yourself. Most students have often wondered if there is a specific pill that they need to take to become mathematics genius. If you have ever dreamed of becoming the parents/students’ icon or the talk of the classroom, here are three tips to help you become the mathematics nerd:

First, even if you get stuck in a problem, keep working. Don’t just relax and stare at the problem: think hard. If you are exhausted, come back the following day and try again. Although this may seem uncomfortable, the discomfort stretches the brain to accommodate new abilities.

Second, you must understand that math is sequential. A lot of students feel they can memorize formulas and concepts, or map out the answer before they start. This is not productive. A student should try to understand the concepts behind mathematics. If you understand why and how an equation works, you will remember it easily.

Lastly, learning math is like learning to play musical instruments. You cannot become skilled within few days. To become adept, you must practice for many days. Learning mathematics is also like learning a new language. Start practicing every day and you will be a genius after several months.

References

https://www.toppr.com/bytes/become-mathematics-genius/

https://www.youtube.com/watch?v=uTM5OHfQOUY

Development of Internet

In 1969, a research body in the USA known as Advanced Research Projects Agency (ARPA) set a computer network that connected four universities and was given the name ARPA net. This network is viewed as a forerunner of today’s internet. The aim of the internet was to allow sharing of data and information between computers. The main benefit was that there was fast communication between researchers through electronic mail.

ARPA’s goal was to allow multiple users to send and receive information at the same time. The network used a special data transmission technique known as packet switching which was later adopted for the internet. A computer would send a packet that contained data, destination address information, error detection control information and packet sequencing information.

By 1973, e-mail was the most common service on the internet. It was not until 1979 that the first media company connected to the internet. By 1981, many people had seen the importance of computer networking and the internet. ARPA net formed the backbone on which many organizations started connecting to, hence expanding it. The American military also become a big user of the internet because they would communicate and tap resources available on the net. Next, the American government decided to access the internet for commercial purposes.

By 1987, the internet boasted of 1000 host computers. However, its access was largely limited to the US and some nations in Europe. As the importance of the internet grew, business spent billions of dollars to improve it in order to offer better services to their clients. By 1994, 3 million computers were connected to the internet. Today, the internet has grown and covered the whole world.

References

http://www.livescience.com/20727-internet-history.html

http://www.internetsociety.org/internet/what-internet/history-internet/brief-history-internet

The Relationship Between Computer Science and Mathematics

It is important to note that computers started to operate after advances in mathematics and logics. The computer usually performs processes. But there were some mechanical machines that could do this even before the computer was invented. For instance, Pascal created an adding machine in the early 17th century. The only thing that distinguished computer from other machines is that it could do this with electricity.

Basically, what was needed was formal logic. The inventions of people such as Boole, Pierce, Frege, Russel and Whitehead, Godel and Turing gave the mathematical underpinning to computers, just the same way the inventors of the calculus laid physics foundations.

The mathematical foundation of computers is logic. Other fields like calculus, probability theory, and set theory are mathematical fields that are applied in computers programs but are not very important. But as Russell and Whitehead demonstrated, logic can be a basis for all types of mathematics. That means that although a computer can implement other types of mathematics, the other types cannot run a computer.

Academically, people who take computer science do a lot of Linear Algebra. More practically, a good understanding of mathematical concepts helps students to understand computers. People with a good understanding of mathematical concept easily understand how logic controllers work, how to write better algorithms, and how encryption works.

References

http://www.ww.amc12.org/sites/default/files/pdf/upload_library/22/Ford/DonaldKnuth.pdf

http://web.stonehill.edu/compsci/shai_papers/mathandcs.pdf

Using Repeated Division by 2 to Convert Decimal to Binary

To change binary numbers to decimal numbers, each binary digit should be multiplied by the power of 2 and then add the results. One of the main methods of changing decimal numbers into binary format is repeated division by 2.

When divided by two, any decimal number leaves a reminder of 0 or 1. Consequently, repeated division by 2 results in a string of 0s and 1s which is the binary equal to the decimal number. Suppose you are asked to convert the decimal number B into binary format. When you divide B by 2, you will get a quotient B1 and reminder which has a value of either 0 or 1.

I.e. B = 2 * B1 + r1, where r1 can be either 0 or 1

Next divide the quotient B1 by 2. You will obtain quotient B2 and a new remainder r2.

ie., B1 = 2 * B2 + r2 , where r2 can be either 0 or 1

So that B = 2 (2 * B2 + r2) + r1

= 22B2 + r2 * 21 + r1* 20

Next divide the quotient B2 by 2. The resulting quotient will be B3 and a remainder r3.

i.e., B2 = 2 * B3 + r3

So that B = 2 (2 * (2 * B3 + r3) + r2) + r1

= 22(2 * B3 + r3) + r2 * 21 + r1* 20

= 23 B3 + r3 * 22 + r2 * 21 + r1* 20

Let now convert 2510 into an equivalent binary number.

23/2= 11 reminder 1

11/2=5 reminder 1

5/2= 2 reminder 1

2/2=1 reminder 0

1/2 =0 reminder 1

Now to write the binary equivalent of 2310, read the remainders from the bottom to the top. In our case 2310=101112