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nature of mathematics

Questions and Answers of Nature Of Mathematics

Investigate some of the properties of primes not discussed in the text. Why are primes important to mathematicians? Why are primes important in mathematics? What are some of the important theorems
We mentioned that the Egyptians wrote their fractions as sums of unit fractions. Show that every positive fraction less than 1 can be written as a sum of unit fractions.
The Egyptians had a very elaborate and welldeveloped system for working with fractions. Write a paper on Egyptian fractions.
Form a group using a geoboard. Go to www.mathnature.com for some ideas about writing this paper.
Write a paper or prepare an exhibit illustrating the Pythagorean theorem. SHAPES CLEAR SIZE TOTAL PER METER 11-01 AREA 8,00 Geoboard illustrating the Pythagorean theorem
Write a paper on the symmetries of a cube. Look at Problem 60, Section 5.6 for some ideas about writing this paper.Data from Problem 60Cut out a small square and label it as shown in Figure
What is a Diophantine equation?
Prepare an exhibit on cryptography. Include devices or charts for writing and deciphering codes, coded messages, and illustrations of famous codes from history. For example, codes are found in
Find the decimal representation of each of the given rational numbers. a. 14 b. in 100 c. P ~Im e. / f. g.
Change the terminating decimals to fractional form.a. 0.123b. 56.28c. 0.3479
Given the set A = {-1, 0, 1}. Does this set A have an element that satisfies the inverse property for multiplication?
Is the set N of natural numbers a group for multiplication?
Let us partition the set of natural numbers into two sets, E (even) and O (odd). Consider the operations of addition (+) and multiplication (×) in the set {E, O}. Does the set form a group for
What is the distinguishing characteristic between the rational and irrational numbers?
A segment of length √2 is shown in Figure 5.15. Describe a process you might use to draw a segment of length √3.Figure 5.15 1 4 9 16 25
Explain the identity property.
Explain the inverse property.
What is a group?
What is a field?
Tell whether each number is an element of N (a natural number), Z (an integer), Q (a rational number), Q´ (an irrational number), or R (a real number). You may need to list more than one set for
Tell whether each number is an element of N (a natural number), Z (an integer), Q (a rational number), Q´ (an irrational number), or R (a real number). Since these sets are not all disjoint, you may
Express each of the numbers in Problems 9–12 as a decimal. 1875 mla mlin
Express each of the numbers in Problems 9–12 as a decimal. d. 2/1/
Express each of the numbers in Problems 9–12 as a decimal. b. d.
Express each of the numbers in Problems 9–12 as a decimal. . -14
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.5b. 0.8
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.25b. 0.75
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.45b. 0.234
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.111b. 0.52
Change the terminating decimals in Problems 13–20 to fractional form.a. 98.7b. 0.63
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.24b. 16.45
Change the terminating decimals in Problems 13–20 to fractional form.a. 15.3b. 6.95
Change the terminating decimals in Problems 13–20 to fractional form.a. 0.64b. 6.98
Carry out the operations with decimal forms in Problems 21–26. a. 6.28 - 3.101 c. 1.36 + 0.541 b. d. 6.31 12.62 6.824 + 1.32 -
Carry out the operations with decimal forms in Problems 21–26. a. 4.2 0.921 c. -6.03 X (-4.6) b. 8.23 + (-0.005) d. 5.002 X 9.009
Carry out the operations with decimal forms in Problems 21–26. a. -0.44 x 0.298 c. 3.72 0.3 b. 10.5(6.23) d. (-5.95) (-7.00) -
Carry out the operations with decimal forms in Problems 21–26. a. 13.06 0.02 c. 0.5(6.2 + 3.4) b. 8 = 4.002 d. 0.25(5.03-4.005)
Carry out the operations with decimal forms in Problems 21–26. a. 3.2 X 1.4 +2.8. c. 3.2 1.4 X 2.8 b. 3.2 X (1.4 +2.8) d. (3.2 + 1.4) X 2.8
Carry out the operations with decimal forms in Problems 21–26. a. 5.2 x 2.3 - 4.5 c. 8.2 +2.8 X 23 b. 5.2 2.3 X 4.5 d. 8.2 X 2.8 +23 -
Identify each of the properties illustrated in Problems 27–32.a. 5 + 7 = 7 + 5b. 5 ·1 / 5 = 1
Identify each of the properties illustrated in Problems 27–32.a. 5 · 1 = 1 · 5b. 3(4 + 8) = 3 (4) + 3(8)
Identify each of the properties illustrated in Problems 27–32. a. a + (10 + b) = (a + 10) + b b. a + (10 + b) = (10 + b) + a
Identify each of the properties illustrated in Problems 27–32.a. mustard + catsup = catsup + mustard commutativeb. (red + blue) + yellow = red + (blue + yellow)
Identify each of the properties illustrated in Problems 27–32. 15 + [a + (-a)] = 15 + 0
Identify each of the properties illustrated in Problems 27–32. x2+x-1 x2+x-1 x2-1 x2-1
Find Figure 5.18 shows the cover of a leading mathematics journal. It depicts the symbols for the twelve animals in the Chinese zodiac. (2013, for example, is the year of the snake and 2014 is the
If x is any element in the Chinese zodiac, then x Figure 5.18 shows the cover of a leading mathematics journal. It depicts the symbols for the twelve animals in the Chinese zodiac. (2013, for
Is the set of Chinese zodiac elements with the operation of commutative?Figure 5.18 shows the cover of a leading mathematics journal. It depicts the symbols for the twelve animals in the Chinese
Is there an identity element?Figure 5.18 shows the cover of a leading mathematics journal. It depicts the symbols for the twelve animals in the Chinese zodiac. (2013, for example, is the year of the
Check whether each of the sets and operations in Problems 37–45 forms a group. N for +
Check whether each of the sets and operations in Problems 37–45 forms a group. N for
Check whether each of the sets and operations in Problems 37–45 forms a group. W for +
Check whether each of the sets and operations in Problems 37–45 forms a group. W for X
What do we mean by clock arithmetic?
How can the operations of addition and multiplication be defined for a 24-hour clock?
Discuss the meaning of the definition of congruence modulo m.
Define precisely the concept of congruence modulo m.
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 9 + 6 c. 5 X 3 b. 5-7 d. 2 7
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 7 + 10 c. 6 X 7 b. 7-9 d. 1 + 5
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 5 + 7 c. 26 b. 4-8 d. 9 3
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 4 x 8 c. 1 + 12 b. 2 x 3 d. 10 + 6
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 3 X 5-7 b. 7+3 X 2
Perform the indicated operations in Problems 5–10 using arithmetic for a 12-hour clock. a. 5 X 2 11 - b. 5 X 8 +5X4
Which of the statements in Problems 11–16 are true?a. 5 + 8 K ≡ (mod 6)b. 4 + 5 K ≡ (mod 7)
Which of the statements in Problems 11–16 are true? a. 5 = 53, (mod 8) b. 102 1, (mod 2)
Which of the statements in Problems 11–16 are true? a. 472, (mod 5) b. 108 12, (mod 8)
Which of the statements in Problems 11–16 are true? a. 5,670 = 270, (mod 365) b. 2,00139, (mod 73)
Which of the statements in Problems 11–16 are true? a. 2,007 = 0, (mod 2,007) b. 246 150, (mod 6)
Which of the statements in Problems 11–16 are true? a. 126= 1, (mod 7) b. 144 12, (mod 144)
Perform the indicated operations in Problems 17–22. a. 9 + 6, (mod 5) b. 7 11, (mod 12) c. 4 X 3, (mod 5) d. 1 = 2, (mod 5)
Perform the indicated operations in Problems 17–22. a. 5 + 2, (mod 4) b. 2-4, (mod 5) c. 6 X 6, (mod 8) d. 57, (mod 9)
Perform the indicated operations in Problems 17–22. a. 4 + 3, (mod 5) b. 6 12, (mod 8)
Perform the indicated operations in Problems 17–22. = a. 2 3, (mod 7) b. 121 x 47, (mod 121)
Perform the indicated operations in Problems 17–22. a. 7 + 41, (mod 5) b. 45, (mod 11)
Perform the indicated operations in Problems 17–22. a. 62 x 4, (mod 2) b. 712, (mod 13)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. x + 3 = 0, (mod 7) b. 4x 1, (mod 5)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. x + 5 = 2, (mod 9) b. 4x = 1, (mod 6)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. x - 2 =3, (mod 6) b. 3x = 2, (mod 7)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. 5x = 2, (mod 7) b. 7x + 1 = 3, (mod 11)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. x = 1, (mod 4) b. x + 4 = 5, (mod 9)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. x= 1, (mod 5) b. 4 + 6 = x, (mod 13)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. 4k = x, (mod 4) b. 4k + 2 = x, (mod 4)
Solve each equation for x in Problems 23–30. Assume that k is any natural number. a. 2x 13, (mod 7) b. 5x 3x + 70=0, (mod 2) -
Assume that today is Monday (day 2). Determine the day of the week it will be at the end of each of the following periods. (Assume no leap years.)a. 24 daysb. 155 daysc. 365 daysd. 2 years
Assume that today is Friday (day 6). Determine the day of the week it will be at the end of each of the following periods. (Assume no leap years.)a. 30 daysb. 195 daysc. 390 daysd. 3 years
Your doctor tells you to take a certain medication every 8 hours. If you begin at 8:00 a.m., show that you will not have to take the medication between midnight and 7:00 a.m.
Suppose you make six round trips to visit a sick aunt and wish to record your mileage to the nearest mile. You forget the original odometer reading, but you do remember that the units digit has
Suppose you are planning to purchase some rope. You need between 15 and 20 pieces that are 7 inches long and one piece that is 80 inches long. The rope can be purchased in multiples of 12 inches. How
If you know that your aunt in Problem 34 lives somewhere between 10 and 15 miles from your house, how far exactly is her house, given the information in Problem 34?Data from problem 34Suppose you
Is the set {0, 1, 2, 3, 4, 5} a group for addition modulo 6?
Is the set {0, 1, 2, 3, 4, 5, 6} a group for addition modulo 7?
Is the set {0, 1, 2, 3} a group for addition modulo 4?
Is the set {0, 1, 2, 3} a group for multiplication modulo 4?
What is a prime number?
Describe a process for finding a prime factorization.
What is the canonical representation of a number?
What does g.c.f. mean, and what is the procedure for finding the g.c.f. of a set of numbers?
What does l.c.m. mean, and what is the procedure for finding the l.c.m. of a set of numbers?
Compare and contrast finding the g.c.f. and l.c.m. of a set of numbers.
Which of the numbers in Problems 7–10 are prime?a. 59b. 57c. 1 d. 1,997

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