Math History
Who discovered the idea of infinity? The symbol?
The greeks, to describe the infinite number of digits in irrational numbers. Wallis created the symbol in 1655
In a fair game of chance, a player spins a square spinner labelled 1,2,5,8. The player wins the number of dollars corresponding to the number on the spinner. What is the gain of the player each round if the cost to play is $5.
-$1
Show that f(x)=2x is continuous using an epsilon-delta proof
Good luck
What is the biological relevance of the Hill equation?
Specifically, describing cooperative binding of hemoglobin molecule. Can be generalized to describe enzyme kinetics
Reduce the following big O notation: O[ax^7+3x^3+sin(x)]
O[x^7]
When did Godel create his incompleteness axioms, and what is there general significance?
1931
Who is responsible for the method of least squares used in linear regression?
Gauss
Write out the three major steps in proving the First Isomorphism Theorem. Write the major steps in using the First Isomorphism Theorem.
Proving:
Well-defined (why?), Homomorphism, Bijectivity
Using:
Correct kernel, Correct image, Map being used actually is a homomorphism
What do mathematicians see when it snows?
the Koch snowflake
You roll a fair die 5 times. What is the probability of seeing a "full house" in the sense of seeing three rolls of one type, and two rolls of another type?
25/648
What group was so worried about the irrational number, the square root of 2 not being able to be expressed as a ratio of two number that they kept it a secret?
The School of Pythagoras
What interesting sequence is well known for describing many natural phenomena?
hint: golden ratio
Fibonacci
What is the Heine Borel Theorem
closed and bounded iff compact
What is the approximate increase in the Earth's population per day?
2 million
Simplify O[cos(x)]
O[1]
In what year was the Mobius strip discovered?
1858
When are Poisson distributions used?
:)
Give an example of a set which does not have a defined division algorithm
Polynomials over a ring that is not a field
What mathematical phenomenon is demonstrated in the butterfly effect?
Chaos
What is a homogenous equation and why is it beneficial in algebraic geometry?
Invariant under representative choice for classes in the projective plane
Who was the first to calculate the diameter of the earth using a rod stuck in the ground and the rule of three?
Eratothenes
What is the coolest area of stats?
Sports stats
When do sets have minimums?
Well ordered sets
ex: natural numbers
What shape is commonly found in beehives?
Hexagons
How can you turn a polynomial ring into a field?
Consider the field of fractions