Students who learn the required subjects in a hands-on learning format and with gamified, engaging elements perform better. It is exactly because of these reasons that coding and programming appear to be a phenomenal way to deliver math knowledge to students. Imagine teaching fractions, derivatives, or simple equations in a normal classroom and using the same whiteboard your parents use, and now compare it to teaching the same content while your students are coding their very own app, or when they are programming a LEGO Mindstorms EV3.
Virtual robots and cyber robotics are an amazing way to teach STEM and maths, it can help close the gender gap in STEM education, it can show some traditional math haters that this subject can be learned and applied in a different way, and it can help them understand that mathematics is way wider than what the math teacher we had explained back in the day. This is true. Coding, at the bottom line, is math. In order to write a line of code that works well, and that is completely bug-free, coders need to strengthen their algorithmic thinking and computational thinking.
And what are these two ways of thinking in their deepest essence: Math. At the end of the day, if you want your students to learn a great programming language for kids, their mathematical thinking should be performing well enough for them to succeed.
The good news is: Your students can strengthen their mathematical thinking the opposite way around. Their function, which relied on the discrete logarithm problem, led to the Diffie—Hellman public-key exchange protocol that is still in use today. Surprisingly, it was later revealed that Ellis, Cocks, and Williamson discovered the same method while working for the British secret service years before.
Subsequently, ElGamal showed how to build on the Diffie—Hellman key exchange to develop an asymmetric encryption system. Mathematicians have explored other ideas for asymmetric encryption. Though some improvements have been made, many of the original ideas from the 70s are still in use. One of the most influential modifications of the original Diffie—Hellman protocols came from Koblitz and Miller in the mids, who showed how to use elliptic curves in asymmetric cryptography.
Interestingly, elliptic curves not only help to build efficient cryptosystems but are also of great use to the cryptanalyst. Lenstra showed in the mids how the algebraic structure on these curves can be exploited to recover quite large factors from products of prime numbers, which helps to crack RSA encryption.
In the 90s, quantum computing prominently entered the cryptographic stage: Shor showed that a quantum computer can efficiently solve the discrete logarithm problem and can also efficiently decompose large integers into its prime factors. Both problems fall into the category of the so-called Abelian hidden subgroup problem—a type of mathematical problem that is well-suited to quantum computing.
Luckily for anyone who ever uses the Internet, nobody has managed to build an effective quantum computer yet. The Iwo Jima landing, for example, was directed entirely by Navajo code. View the discussion thread. Math course offers insight into creating and solving secret messages. By Matt Gray.
At their simplest, they are used by kids passing notes in class and at their most complex, by governments carrying out military operations. Secret codes In this video, Dr. Yossi Elran explains about the connection between mathematical operators and two kinds of secret codes.
View transcript. What about operators on letters? Operators on letters, really change the letters, and make something that is legible - illegible! This is a nice way of thinking about secret codes. What are secret codes?
There are many, many kinds of secret codes. However, I want to give you just a small taste of two kinds of secret codes, and they differ in the way that we operate on or manipulate the letters.
One kind of an encryption is called substitution - substitution cipher. In a substitution cipher you substitute every letter in the plaintext with another letter. Each letter with the letter after it. It can be made more difficult by shifting each letter 3 or 17 forwards or backwards or even just randomly associating each letter with another letter or another number, and this is just an archetype of substitution ciphers. Another kind of operation is called transposition.
In transposition, you take a sentence and transpose it, mix it up. And this is the way we scrambled them, we just wrote them inside a 5 by 5 table and then we wrote it in the rows and drew out the numbers in the columns.
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