Math

1. Math Trivia

2. Trivia • This game of trivia is a game of knowledge and haste. • teams. • Each round has 5 questions: • 30 seconds given per question • 2 minutes after all questions have been given • Each question is worth 1 point • 4 rounds, chosen from 8 categories.

3. Probability Real Numbers Geometry Nonreal Numbers Algebra Games Calculus Notation

4. Probability • Probability theory is: • Measure theory where the measure of the whole space is 1. • Topology where the area of the whole space is 1. • Operations Research where the objective value is 1. • Not related to any of measure theory, topology, or operations research. • If 10 coins are flipped, what is the probability that 4 are heads and 6 are tails? • A mythical three sided coin satisfies the following probability: The sum of the probability of landing on two of the sides is equal to twice the probability of landing on the third. What is the probability of landing on the third? • Ten people will play the following game: • Each player is given $10 • Each player is privately and simultaneously given the choice: Take an additional $2. If he does so, $1 will be taken away from every other player. • If each player plays his optimal strategy, how much money will everybody take home? • Three balls are randomly drawn from a bowl containing 6 white and 5 black balls. What is the probability that one of the balls is white and the other two are black?

5. Return Probability • Probability theory is: • Measure theory where the measure of the whole space is 1. • Topology where the area of the whole space is 1. • Operations Research where the objective value is 1. • Not related to any of measure theory, topology, or operations research. • If 10 coins are flipped, what is the probability that 4 are heads and 6 are tails? • A mythical three sided coin satisfies the following probability: The sum of the probability of landing on two of the sides is equal to twice the probability of landing on the third. What is the probability of landing on the third? • Ten people will play the following game: • Each player is given $10 • Each player is privately and simultaneously given the choice: Take an additional $2. If he does so, $1 will be taken away from every other player. • If each player plays his optimal strategy, how much money will everybody take home? • Three balls are randomly drawn from a bowl containing 6 white and 5 black balls. What is the probability that one of the balls is white and the other two are black?

7. Geometry • What is the volume equation of a cone? • What is a polynomial with 40 sides called? • What is the name of a picture drawn by repeating a single shape with no overlaps or gaps? • What is the name of a four-sided shape in which all four sides are the same length? • Any planar graph on a plane can be colored with four colors. How many colors does it take to color any planar graph on a torus?

8. Geometry • What is the volume equation of a cone? • What is a polynomial with 40 sides called? Tetracontagon • What is the name of a picture drawn by repeating a single shape with no overlaps or gaps? Tesselation • What is the name of a four-sided shape in which all four sides are the same length? Rhombus • Any planar graph on a plane can be colored with four colors. How many colors does it take to color any planar graph on a torus? 7 Return

10. Algebra • Simplify • Find . • What is the property that says ? • The form “” has a special name. What is it? • What is the fewest number of standard coins that are needed to guarantee that you can sum to any number between and ?

11. Algebra • Simplify • Find . • What is the property that says ? Associative • The form “” has a special name. What is it? Indeterminant • What is the fewest number of standard coins that are needed to guarantee that you can sum to any number between and ? 10 Return

13. Calculus • What is the name of the following theorem: ? • What well known theorem relates a certain line integral to a certain double integral? • A differentiable function: • Is always continuous. • Is always defined for all real numbers. • Has a local maximum. • Satisfies the Lipschitz condition. • What are the two most well-known functions that satisfy ? • Let be the unit circle and be the complex function given by . What is ?

14. Calculus • What is the name of the following theorem: ?The fundamental theorem of calculus, part 1. • What well known theorem relates a certain line integral to a certain double integral? Green’s Theorem • A differentiable function: • Is always continuous. • Is always defined for all real numbers. • Has a local maximum. • Satisfies the Lipschitz condition. • What are the two most well-known functions that satisfy ? and • Let be the unit circle and be the complex function given by . What is ? Return

16. Notation • Give the name of the function given by • Q: What mathematical symbol did math whiz Ferdinand von Lindemann determine to be a transcendental number in 1882? • What well known number does the Greek letter phi stand for? • In the expression of a typical integral such as , what is the “” called? • If you reverse the order of operations (PEMDAS SADMEP), what would evaluate to?

17. Notation • Give the name of the function given by Floor Function • Q: What mathematical symbol did math whiz Ferdinand von Lindemann determine to be a transcendental number in 1882? • What well known number does the Greek letter phi stand for? The golden ratio • In the expression of a typical integral such as , what is the “” called? A differential • If you reverse the order of operations (PEMDAS SADMEP), what would evaluate to? Return

19. Games • In the game of roulette, the roulette wheel has 18 red numbers, 18 black numbers, and 2 green numbers. A Each red number has an 18:1 payout. If Alice places $1 on a red number, what is the expected return? • In a standard deck of 52 playing cards, two cards are drawn. What is the probability that the second card is an ace? • A game is to be played among three people: A number between 1 and 100 is chosen at random and hidden. Each person must then choose a number, whoever is closed wins. What number should the first player choose? • If two players play perfect games of tic-tac-toe, who will win? • The first player • The second player • Neither • Four people must walk across a bridge at night, but they only have one flashlight (which is required to navigate the bridge). A can cross in 1 minute, B in 2 minutes, C in 5 minutes, D in 10 minutes. Only two people may cross at once. Using an optimal strategy, how long does it take for all four to cross?

20. Games • In the game of roulette, the roulette wheel has 18 red numbers, 18 black numbers, and 2 green numbers. A Each red number has an 18:1 payout. If Alice places $1 on a red number, what is the expected return? • In a standard deck of 52 playing cards, two cards are drawn. What is the probability that the second card is an ace? • A game is to be played among three people: A number between 1 and 100 is chosen at random and hidden. Each person must then choose a number, whoever is closed wins. What number should the first player choose? 25 or 75. • If two players play perfect games of tic-tac-toe, who will win? • The first player • The second player • Neither • Four people must walk across a bridge at night, but they only have one flashlight (which is required to navigate the bridge). A can cross in 1 minute, B in 2 minutes, C in 5 minutes, D in 10 minutes. Only two people may cross at once. Using an optimal strategy, how long does it take for all four to cross? 17 minutes Return

22. Nonreal Numbers • In nonstandard analysis what is the term used for numbers greater than 0 but less than any positive real number? • What conjecture says that there are no cardinals satisfying ? • What is the name for the set ? • In the ordinal numbers every number has a successor . In the surreal numbers every number also has a corresponding . What is called? • In complex analysis it is common to map the plane to the punctured sphere, or vise versa. What is the term for this mapping?

23. Nonreal Numbers • In nonstandard analysis what is the term used for numbers greater than 0 but less than any positive real number? Infinitesimal • What conjecture says that there are no cardinals satisfying ? continuum hypothesis • What is the name for the set ? Gaussian Integers • In the ordinal numbers every number has a successor . In the surreal numbers every number also has a corresponding . What is called? Predecessor • In complex analysis it is common to map the plane to the punctured sphere, or vise versa. What is the term for this mapping? Stereographic Projection. Return

25. Real Numbers • What number, a one followed by 100 zeros, was first used by nine-year-old Milton Sirotta in 1940? • What is the 2 digit number whose cube root is the square root of the sum of its digits? • , where . • What number made the 1980 Guinness Book of World Records for the largest number used in a serious mathematical proof? (Hint: this number is often cited as the largest number used in a proof. While it once was, other larger numbers now old that title.) • Which is the largest: , , or ? Return

26. Real Numbers • What number, a one followed by 100 zeros, was first used by nine-year-old Milton Sirotta in 1940? Googol • What is the 2 digit number whose cube root is the square root of the sum of its digits? 27 • , where . • What number made the 1980 Guinness Book of World Records for the largest number used in a serious mathematical proof? (Hint: this number is often cited as the largest number used in a proof. While it once was, other larger numbers now old that title.) Graham’s Number • Which is the largest:, , or ? Return

28. Reference Information • Created in 2013 by Dr. Jeffrey Beyerl for use in the math club at the University of Central Arkansas • This is just a PowerPoint with internal hyperlinks, but of course like anything you download from the internet: use at your own risk.