Modular arithmetic

3. Focus Students: Description of Student A: Abby Prior Learning Abby’s prior knowledge of multiplication of fractions is limited because this is not introduced until the 4th grade. The student was able to get the first two problems on the pre-assessment correct which asked the students to find the missing value that would make the equation true when multiplying. The student does not understand the concept of unit fractions or the relationships between multiplying fractions and repeated…

Data Type Description and example use **You must provide an example of what each data type could be used for** String A data type used in programmings such as an integer and floating point unit, but is used to represent text rather than numbers. • I bought 3 CD’s which were from 3 different artists. It shows that I bought it from 3 different people. • If (Option 1==Option 2) If the values are the same, then it is true. If they are different, then it is false. • Usernames are an example of…

to 5. Thus, we have 11. But since there are only 7 days in a week we need to subtract 7 from 11. Thus, we have 4. Hence, the desired answer is Thursday. Situations similar to examples 7-1 to 7-4 can be represented mathematically using modular arithmetic or arithmetic modulo n. Definition 7-1: Two integers a and b are said to be congruent modulo n, where n is a natural number, if (a-b)/n is an integer. In this case, we write a≡b mod…

existence of infinity as axiomatic. However, the axiom of infinity cannot be a mere logical law. We can imagine a self-consistent universe containing only finitely many objects (we can even imagine one with numbers that add and multiply, as in modular arithmetic); we cannot imagine a self-consistent universe that violates a genuine logical law, such as (p and q) implies p. We know that an infinity of objects exists, not through mere logic, but because we can imagine the infinite process of…

which m = (11 - 1)(13 - 1) = 10 x 12 = 120. Find a number not divisible by m, such as 7, the first public number. The second public number is derived from multiplying the two initial numbers, 11 x 13 = 143. The private number is formed using modular arithmetic with the first public number to find d, where 7d = 1 mod 120. So the private number is 103. These three numbers are then used as the codes to encode and decode the messages, much like the codes sent out through the enigma machine during…

Anxiety in the Classroom Stress is caused by many different factors such as troubling thoughts, tragic events, or other hardships. Contrary to belief, adults are not the only ones who can experience high levels of stress. Children and teens from all ages can experience stress as well. On many occasions, children and teens feel pressured due to academic expectations imposed on them. Although, occasional stress is inevitable, constant stress can lead to anxiety. Therefore, on many occasions the…

怀䢀埔r Piece #2 (1976) by Sol LeWitt, viewed at The University of Akron, at Collection of the Akron Art Museum, on September 16, 2014, is a great example of the artist’s work. Although his artwork ranges from wall drawings to these types of structures, and even sculptures, this object viewed at the museum represents the diverse works of art that were presented at his time period in an accordingly fashion. The theory that Sol LeWitt worked off of in the creation of his objects was, but is not…

memory. This computer still made a larger impact because numerous invention is still used today, they include, “a binary system of arithmetic, separate memory and computing functions, regenerative memory, parallel processing, electronic amplifiers as on-off switches, circuits for logical addition and subtraction, clocked control of electronic operations, and a modular design” (www.ece.iastate.com). This computer led to a controversy over the ABC. This was because J. Presper Eckert and John…