Primes – the building blocks of all numbers: The dictionary meaning of prime is ‘Of first importance’ or ‘Of the best quality, excellent’ etc. What is so great about prime numbers? A number is said to be a prime if it is divisible only by 1 and itself. 5, for example, is a prime number because it is divisible only by 1 and 5. The number 4 can be divided by 1, 4 AND 2. So it is not a prime number. Numbers that are not primes are said to be composite numbers. The fundamental theorem of Arithmetic states that all numbers are either primes or a product of a unique combination of primes. So in a way the prime numbers are the building blocks for all numbers. Hence the name Prime. Prime numbers have various applications, but perhaps the best reason why Mathematicians study them is that they are extremely basic and mysterious at the same time. It’s amazing how little we know about primes after reflecting on them for thousands of years. Prime numbers were first studied extensively by Greek mathematicians. Euclid, a Greek Mathematician who lived around 300 BC and was known as the Father of Geometry, studied prime numbers in 300 BC. He demonstrated that there are an infinite number of primes. Even after 2000 years his proof stands as an excellent feat of deduction. As of February 2013, the largest known prime number is 257,885,161 − 1, a number which has 17,425,170 digits! Several important results in prime numbers had been proved by the time Euclid’s theorem appeared. Eratosthenes,…
Note: As you begin to insert your responses to the prompts found in this document, please be sure to save it frequently, (and note the location of the file) so as to not lose any of your work. Once completed, you will submit this document to WGU for grading. Instruct What student misconceptions have you encountered related to fraction, decimal, and percentage concepts? How do you help students understand the notion of equivalence among fractions or prepare them for this understanding? One…
206EDU_Final Project_Teaching Interview My teaching philosophy; What makes learning difficult is student’s belief that Math is boring, Math is impossible and Math is irrelevant. Therefore, my teaching philosophy is three fold; Make Math interesting, Make Math possible, Make Math relevant. Questions: Q.1. What grade and subject do you want to teach? (Elementary teachers do not need to discuss ‘subject ') A. I want to teach Grade 6 Mathematics. Q.2. Why do you want to teach this grade level?…
4.3 ANURUPYENA (Ekadhikina Purvena) COROLLARY: Anurupyena (means Proportion) Meaning: By one more than the previous one Anurupyena Sutra is a specific method of division in Vedic Mathematics which shows how to divide numbers when Nikhilam and Paravartya are not applicable. Specific Condition Required: _ As we know the meaning of Anurupyena (as proportion/ratio), we multiply/divide by factor to make divisor closer to larger number (To apply Nikhilam) OR to make closer to smaller number (To apply…
In a polynomial equation, if a number # if (x-#) is a factor of g(x), then # is a zero/root of the polynomial. If the group of three wants to prove that the binomial (x+2) is a factor of the g(x) equation, one option they could explore is using long division with the binomial in the divisor position. Essentially, no one was wrong. Prof. McCory and Ms. Guerra were in the green. 3. Dr. Collier summons you over to his table. He wants to demonstrate the graph of a fourth-degree polynomial function,…
When The Dow Jones Industrial Average was created in 1896, Charles Dow had nothing more than a piece of paper and pencil to mark down all of his calculations. The calculation method that he devised involved an average of 12 different stock pricings then the average would be divided by that same number in order to reveal the industrial average result. This method which was made simple is now the national model for all industrial averages used within the nation’s stock market tallies. Another…
Pythagoras Born: about 569 BC in Samos, Ionia Died: about 475 BC He is named the first mathematician. Pythagoras was born near the Ionian coast of the Mediterranean, in the rich merchant family. After living in Egypt for 22 years and in Babylon for 12 years, he gained deep knowledge in natural and mathematical sciences. He gathered around a group of like-minded people, mostly aristocrats, and created a secret circle. The members of the circle studied various issues of philosophy and mathematics.…
It typically inhabits the lower and middle forest levels but, when hungry, can be found foraging in the canopy for fruit. Generally shy, it tends to avoid contact with humans, and to see one in the wild is a true treat. Like many birds, the Andean cock-of-the-rock exhibits major sexual dimorphism, with the males possessing a prominent crest on their heads that threaten to engulf their faces. This permanent fashionable “hat” is all the rage with the much-drabber females and is used in mating…
Lemma: If p > 3 is prime, then either p = 1 (mod 6) or p = 5 (mod 6). Proof: The residue classes modulo 6 partition Z, so any z in Z satisfies a congruence z = n (mod 6) where n is in {0,1,...,5}. z is divisible by 6 if n = 0, 2 if n = 2, 3 if n = 3, and 2 if n = 4. These cases cover the primes z = 2 and z = 3; if z > 3 is prime, it follows that n = 1 or n = 5, i.e., z = 1 (mod 6) or z = 5 (mod 6). Now suppose there are only finitely many primes congruent to 5 modulo 6, say p_1, ...,…
7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a minimum of 2 complex roots with a maximum of 5 real roots. The…