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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

The short story Paul Bunyan versus the Conveyor Belt (1947) by William Hazlett Upson focuses on a conveyor belt in the shape of a Möbius strip. The story can be found in several books that include
Print out a map of the state you live in that shows the outline of all of the counties. Using at most four colors, color the map so that no two counties that share a common border are the same color.
Using paper, scissors, and tape, perform the construction described in the Recreational Mathematics box. Once you have completed the construction, cut along the dashed line as instructed. Set the
Using at most four colors, color the map of the counties of New Mexico. Do not use the same color for any two counties that share a common border. San Juan Rio Arriba Taos Colfax Union Los Alamos
Using clay (or glazing compound), make a doughnut. Without puncturing or tearing the doughnut, reshape it into a topologically equivalent figure, a cup with a handle.
Go to the website Fantastic Fractals at www.fantastic-fractals.com and study the information about fractals given there. Print color copies of the Mandlebrot set and the Julia set.
(a) Sketch an object of genus 1. (b) Sketch an object of genus 2.
To transfer his two-dimensional tiling known as Symmetry Work 45 to a sphere, M. C. Escher used the spherical geometry of Bernhard Riemann. Write a paper on Escher’s use of geometry to complete
To complete his masterpiece Circle Limit III, M. C. Escher studied a model of hyperbolic geometry called the Poincar? disk. Write a paper on the Poincar? disk and how it was used in Escher?s art.
The definition of the meter has changed several times throughout history. Write a report on the history of the meter, from when it was first named to the present.
Write a report on the development of the metric system in Europe. Indicate which individual people had the most influence in its development.
Do industries located near your school export goods? If so, are they training employees to use and understand the metric system? Contact local industries that export goods and write a report on your
The website www.onlineconversion.com gives 16 units of length used in the U.S. customary system. It also gives their metric equivalent. Determine the metric equivalent of each of the following units
René Descartes is known for his contributions to algebra. Write a paper on his life and his contributions to algebra.
Write a report explaining how the ancient Egyptians used equations. Include in your discussion the forms of the equations used.
Chinese mathematician Foo Ling Awong, who lived during the Pong dynasty, developed a technique, other than trial and error, to factor trinomials of the form ax2 + bx + c, a ≠ 1. Write a paper about
When were exponents first used? Write a paper explaining how exponents were first used and when mathematicians began writing them in the present form.
Italian mathematician Girolamo Cardano (1501–1576) is recognized for his skill in solving equations. Write a paper about his life and his contributions to mathematics, in particular his
The Rhind Papyrus indicates that the early Egyptians used linear equations. Do research and write a paper on the symbols used in linear equations and the use of the linear equations by the early
Find a newspaper or a magazine article that contains the mathematical concept of inequality.(a) From the information in the article write a statement of inequality.(b) Summarize the article and
Ratio and proportion are used in many different ways in everyday life. Submit two articles from newspapers, magazines, or the Internet in which ratios and/or proportions are used. Write a brief
The ancient Greeks are often considered the first true mathematicians. Write a report summarizing the ancient Greeks’ contributions to rational numbers. Include in your report what they learned and
Write a report on the history of π. In your report, indicate when the symbol π was first used and list the first 100 dig-its of π.
Write a report on the history of the development of the irrational numbers.
Explain what deficient numbers and abundant numbers are. Give an example of each type of number.
Write a report on the GIMPS project. Describe the history and development of the project. Include a current update of the project’s findings.
Find an article in a newspaper or magazine that contains scientific notation. Write a paragraph explaining how scientific notation was used. Attach a copy of the article to your report.
The digits 1 through 9 have evolved considerably since they appeared in Fibonacci’s book Liber Abacci. Write a report tracing the history of the evolution of the digits 1 through 9 since
Read the Profiles in Mathematics. Read one of Paulos’s books and write a 500-word report on it.
Write a report on the history of the number 0 in the Hindu–Arabic numeration system.
Obtain data from the U.S. Department of the Treasury and from the U.S. Bureau of the Census Internet websites to calculate the current U.S. national debt per person. Write a report . Include in your
A set of numbers that was not discussed in this chapter is the set of complex numbers. Write a report on complex numbers. Include their relationship to the real numbers.
A topic generally associated with sequences is series.(a) Research series and explain what a series is and how it differs from a sequence. Also write a formal definition of series. Give examples of
Write a report indicating where the golden ratio and golden rectangle have been used in art and architecture. You may wish to include information on art and architecture related to the golden ratio
Write a report on the history and mathematical contributions of Fibonacci.
When two panes of glass are placed face to face, four interior reflective surfaces exist, labeled 1, 2, 3, and 4. If light is not reflected, it has just one path through the glass (see the figure
Find three physical objects whose dimensions are very close to a golden rectangle.(a) List the objects and record the dimensions.(b) Compute the ratios of their lengths to their widths.(c) Find the
In this section, we discussed the numeration systems of Egypt, China, and Greece. Choose one of these countries and write a paper that includes the following.(a) State the current numerals used in
Make up your own additive system of numeration and indicate the symbols and rules used to represent numbers. Using your system of numeration, write (a) Your age.(b) The year you were born.
One method used by computers to perform subtraction is the “end around carry method.” Do research and write a report explaining, with specific examples, how a computer performs subtraction by
Throughout history, various societies have used different bases for their numeration systems. Groups of people in North and South America, Africa, and Australia all used a variety of numeration
Write a report on how computers use the binary (base 2), octal (base 8), and hexadecimal (base 16) numeration systems.
Write a report on the use of the duodecimal (base 12) system of numeration. You may wish to contact the Dozenal Society for more information.
(a) Make up your own base 20 positional-value numeration system. Indicate the 20 numerals you will use to represent the 20 numbers less than the base.(b) Write 523 and 5293 in your base 20 numeration
The Arabic numeration system currently in use is a base 10 positional-value system, which uses different symbols than the Hindu–Arabic numeration system. Write the symbols used in the Arabic system
Investigate and write a report on the development of the Hindu–Arabic system of numeration. Start with the earliest records of this system in India.
Create your own place-value system. Write 2017 in your system.
Write a paper explaining why the duplation and mediation method works.
In addition to Napier’s rods, John Napier is credited with making other important contributions to mathematics. Write a report on John Napier and his contributions to mathematics.
The study of logic often involves the use of the letters p and q to represent statements. Re-search the use of the letters p and q in the study of logic. Also include a brief description of the
Write a report on the life and accomplishments of George Boole, who was an important contributor to the development of logic. In your report, indicate how his work eventually led to the development
Obtain a legal document such as a will or rental agreement and copy one page of the document. Circle every connective used. Then list the number of times each connective appeared. Be sure to include
(a) Make up three simple statements and label them p, q, and r. Then write compound statements to represent. (p ∨ q) ∧ r and p ∨ (q ∧ r).(b) Do you think that the statements for (p ∨ q) ∧
Do research and write a report on the life and achievements of Augustus De Morgan. Indicate in your report his contributions to sets and logic.
If Zeus could do anything, could he build a wall that he could not jump over? Explain your answer.
Read one of Lewis Carroll’s books and write a report on how he used logic in the book. Give at least five specific examples.
Do research and write a report on fuzzy logic.
Select an advertisement from the Internet, a newspaper, or a magazine that makes or implies a conditional statement. Analyze the advertisement to determine whether the consequent necessarily follows
In an appliance or device that uses fuzzy logic, a change in one condition causes a change in a second condition. For example, in a camera, if the brightness increases, the lens aperture
Find examples of valid (or invalid) arguments in printed matter such as newspaper or magazine articles. Explain why the arguments are valid (or invalid).
Show how logic is used in advertising. Discuss several advertisements and show how logic is used to persuade the reader.
Do research and write a report on each of the following.(a) The relationship between negation in logic and complement in set theory .(b) The relationship between conjunction in logic and intersection
Digital computers use gates that work like switches to perform calculations. Information is fed into the gates and information leaves the gates, according to the type of gate. The three basic gates
Leonhard Euler is considered one of the greatest mathematicians of all time. Do research and write a report on Euler’s life. Include information on his contributions to sets and to logic. Also
Design two circuits that each involve switches labeled p, q, r, and s that appear to be different but are actually equivalent circuits.
Use the U.S. Bureau of Labor Statistics website to create a Venn diagram illustrating the 10 fastest growing occupations for college graduates, based on employment in 2012 and the estimated
George Cantor is recognized as the founder and a leader in the development of set theory. Do research and write a paper on his life and his contributions to set theory and to the field of
Write a short paragraph explaining why the universal set and the empty set are necessary in the study of sets.
Describe three sets of which you are a member.
The two Venn diagrams in the right column illustrate what happens when colors are added or subtracted. Do research in an art text, an encyclopedia, the Internet, or another source, and write a report
Do research to explain how it can be shown that the real numbers do not have cardinal number X0.
Do research to explain how Cantor proved that the set of rational numbers has cardinal number X0.
Puzzles Many fun and interesting puzzle books and magazines are available. Using his chapter and puzzle books as a guide, construct five of your own puzzles and present them to your instructor.
Identify three ways that you use estimation in your daily life. Discuss each of them briefly and give examples.
Develop a monthly budget by estimating your monthly income and your monthly output. Your monthly income should equal your monthly output.
(a) About how much water does your household use per day? Use the following data to estimate your house-hold?s daily water usage. (b) Determine from your water department (or company) your
Try to retrace the figure without lifting your pencil from the paper or retracing a line. It can be done, but you need to begin at certain locations.?
Estimate the answer. Estimate the distance from your wrist to your elbow and estimate the length of your foot. Which do you think is greater? With the help of a friend, measure both lengths to
Two friends, Tiffany and Ana, are planning a skiing vacation in the Rockies. They plan to purchase round-trip airline tickets from Atlanta, Georgia, to Denver, Colorado. They will fly into Denver on
Make a shopping list of 20 items you use regularly that can be purchased at a supermarket. Beside each item write down what you estimate to be its price. Add these price guesses to estimate the total
Estimate how fast you can walk 60 ft. Then mark off a distance of 60 ft and use a watch with a second hand to time yourself walking it. Determine the accuracy of your estimate.
When a jury decides whether or not a defendant is guilty, do the jurors collectively use primarily inductive reasoning, deductive reasoning, or an equal amount of each? Write a brief report
Estimate the ratio of your height to your waist size. Then have a friend measure your height and waist size. Determine the stated ratio and check the accuracy of your estimate.
(a) Using newspapers, the Internet, magazines, and other sources, provide examples of conclusions arrived at by inductive reasoning. (b) Explain how inductive reasoning was used in arriving at
Estimate the number of pennies that will fill a 3-ounce (oz) paper cup. Then actually fill a 3-oz paper cup with pennies, counting them to determine the accuracy of your estimate.
Fill a glass with water and estimate the water’s temperature. Then use a thermometer to measure the temperature and check your estimate.
Estimate the number of times your phone will ring in 1 minute if unanswered. Have a classmate phone you so that you can count the rings and thus test your estimate.
In a bag, place objects that you believe have a total weight of 10 lb. Weigh the bag to determine the accuracy of your estimate.
Construct a set of five pieces of data with a mean, median, mode, and midrange of 6 and a standard deviation of 0.
Determine each hotel’s apportionment using Hamilton’s method.When appropriate round quotas to the nearest hundredth.A large hotel chain needs to apportion 25 new staff members among three hotels
Irvine Valley College is hiring a new director of counseling and advisement. The hiring committee ranks the four candidates, Alvarez (A), Brown (B), Singleton (S), and Yu (Y), according to the
Fill in the blank with an appropriate word, phrase, or symbol(s).If a candidate receives a majority of first-place votes in an election, that candidate should be declared the winner. This criterion
The Sailing Club of Lakeport is holding an election to choose the club president. The 42 votes were cast as follows: Comstock, 20 votes; Owens, 15 votes; and Glazer, 7 votes.(a) Using the plurality
Fill in the blank with an appropriate word, phrase, or symbol(s).The total population under consideration divided by the number of items to be allocated is called the standard ______.
Fill in the blank with an appropriate word, phrase, or symbol(s).When each group’s population is divided by the standard divisor, a standard _________ is obtained.
Suppose that a police department has 210 new officers to apportion among six precincts. The department plans to apportion the officers based on the number of crimes committed during the previous year
Suppose that a country with a population of 10,000,000 has 250 legislative seats to be apportioned among four states, where each state has a different population. Determine a population for each
In 1970, the first United States census was taken. The following table shows the population of the 15 states at that time. One hundred five seats in the United States House of Representatives were to
Determine each shift’s apportionment using Webster’s method. (Some divisors between 12 and 12.05 will work.)When appropriate round quotas to the nearest hundredth.A hospital has 200 nurses to be
Determine each shift’s apportionment using Jefferson’s method. (Divisors do not have to be whole numbers.)When appropriate round quotas to the nearest hundredth.A hospital has 200 nurses to be

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