Final Exam
Who wrote the first complete mathematical work by a woman that is in existence today?
Maria Agnesi
Who wrote the first surviving mathematical text by a woman?
Maria Agnesi
What did Newton call his method of calculus?
Method of fluxions
Which statistical method was formulated by Gauss while he was in prep school?
Method of least squares
For what operation did John Napier use Napier's bones (or Napier's rods)?
Multiplication
Given a point P that is not on line l . According to Playfair's Postulate, how many lines that pass through P are parallel to l ?
One and only one
What are amicable numbers?
Pairs of numbers that are equal to the sum of the proper factors of the other number
According to Pascal, what does Pascal's Wager prove?
Pascal's Wager proves that belief in God is rational
What was the motto on Gauss's unofficial coat of arms?
Pauca sed matura
The following theorem is named for which mathematician? There do not exist non-zero integers, a,b,and c, and n>2 such that aⁿ+bⁿ=cⁿ
Pierre de Fermat
The two men who co-developed probability used different strategies to solve the problem of the points. Which one of the two made a list of all the possible ways that the game could be completed to solve the problem?
Pierre de Fermat
Who was the first mathematician to solve a maximum/minimum problem?
Pierre de Fermat
What are Mersenne primes?
Prime numbers that can be written in the form 2ⁿ-1
What method did Fermat use to solve maximum/minimum problems?
Pseudo-equality method
Which of these statements is NOT equivalent to the Parallel Postulate?
Pythagorean Theorem
Which mathematician is known as the father of modern philosophy?
Rene Descartes
Which mathematician used the letters at the end of the alphabet to represent unknown quantities and the letters at the beginning of the alphabet to represent known quantities or constants?
Rene Descartes
Which two mathematicians co-developed analytic geometry?
Rene Descartes and Pierre de Fermat
What is "syncopated" algebra?
Shorthand way of writing algebraic expressions using abbreviations
If a fair coin is tossed twice, what is the probability of getting two heads?
1/4
What is the base in common logarithms?
10
What is a Mersenne number?
A number that can be written in the form 2ⁿ-1
Which mathematician was the daughter of the British poet, Lord Byron, and wrote about how to program Charles Babbage's Analytical Engine?
Ada Byron King
In which area did Girolamo Cardano make the most significant contributions?
Algebra
What branch of mathematics was introduced in the book, La Geometrie?
Analytic Geometry
Who proved Fermat's Last Theorem?
Andrew Wiles
Who was the first astronomer to put forward the theory that the sun is at the center of the universe?
Aristarchus of Samos
Which book is considered the first book devoted entirely to algebra?
Arithmetica
Why is 6 a perfect number?
Because 6=1+2+3
Which mathematician was the "greatest might have been" in mathematics?
Blaise Pascal
Who were the co-developers of probability?
Blaise Pascal and Pierre de Fermat
Which two mathematicians (in addition to Gauss) finally rejected the Parallel Postulate creating Non-Euclidean Geometry?
Bolyai and Lobachevsky
Who is known as the Prince of Mathematicians?
Carl Friedrich Gauss
What are the three points that lie on an Euler line?
Centroid, Circumcenter, Orthocenter
Which one of the ancient civilizations knew about the triangle that we call "Pascal's Triangle?"
Chinese
Who was the Queen of Sweden when Descartes died?
Christina
Florence NIghtingale's rose diagram was a variant of which of the following graphs?
Circle graph
What information did Gauss add to our understanding of the fundamental theorem of algebra?
Complex solutions occur in conjugate pairs
Which of the following is an application of number theory?
Cryptography
Who is sometimes called the "father of algebra?"
Diophantus
According to Kepler's First Law, what is the shape of planetary orbits around the sun?
Ellipse
Who translated Newton's book, the Principia, into French?
Emilie du Chatelet
Which mathematician whose research was in modern algebra left Nazi Germany to teach at Bryn Mawr College in the United States?
Emmy Noether
What was the title of Girolamo Saccheri's book?
Euclid Freed of Every Flaw
In the Ptolemaic model of the universe, the equant is the center of the epicycle that moves around the earth.
False
The Ptolemaic model of the universe is a heliocentric model
False
True or False: A prime number has only one factor.
False
True or False: Girolamo Saccheri successfully proved Euclid's Fifth Postulate.
False
True or False: Johann Heinrich Lambert successfully proved Euclid's Fifth Postulate.
False
In which country were Descartes and Fermat born?
France
What do we call two numbers that are equal to the sum of the proper divisors of the other number?
Friendly numbers
Who wrote the first book on games of chance titled The Book on Games of Chance?
Girolamo Cardano
Which mathematician is credited with first using the symbol ∫ for the integral?
Gottfried Wilhelm Leibniz
Working independently of Isaac Newton, what other mathematician developed the basics of calculus at just about the same time?
Gottfried Wilhelm Leibniz
Which mathematician was the highest ranking woman in the U.S. Navy when she died?
Grace Hopper
Who coined the phrase "de-bugging" when she discovered that a moth had gotten into one of the early computers and caused a short in the machine?
Grace Hopper
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch of mathematics?
Graph Theory
Euler gave several proofs of Heron's formula for the area of a triangle with side lengths a,b,and c.: Area = √(s(s−a)(s−b)(s−c)) What is s?
Half the perimeter of the triangle
What was Marin Mersenne's contribution to the development of mathematics?
He hosted regular gatherings of mathematicians who exchanged ideas
Pierre de Fermat readily corresponded with his mathematical colleagues about his ideas and findings related to number theory. He had one "bad habit" that annoyed his colleagues to the point where they threatened not to work with him anymore. What was that "bad habit?"
He often stated problems and theorems but did not solve them himself in order to challenge his colleagues
What was the major contribution of Father Marin Mersenne to the development of mathematics?
He organized regular meetings of scholars that allowed them to share their ideas
Many mathematicians made progress on the proof of the Fundamental Theorem of Algebra. What was Euler's contribution?
He proved the theorem for polynomial equations of degree less than or equal to 6
What was Viete's contribution to the development of the modern symbolism of algebra?
He used letters to represent unknown quantities
With which physical disability was Euler afflicted in his later years?
He was blind
Why is Leonhard Euler known as the most prolific mathematician?
He wrote a massive amount of material during his lifetime, much of which remained unpublished at his death
What is the subject of the Prime Number Theorem?
How many prime numbers are there less than a given positive integer?
What was the problem of the points?
How should the stakes be distributed fairly when a game is stopped early?
Who was the first female mathematician that we have information about?
Hypatia
What does "Cogito ergo sum" mean?
I think therefore I am
What is the difference between an arithmetic sequence and a geometric sequence?
In an arithmetic sequence, consecutive terms have a common difference. In geometric sequences, consecutive terms have a common ratio
Who wrote The Principia?
Isaac Newton
What did Saccheri call the polygon that we know as the Saccheri Quadrilateral?
Isosceles birectangle
What does the Fundamental Theorem of Algebra tell us about the equation x^4+3 =4x?
It has at most four complex solutions
Who is the father of English cryptography?
John Wallis
Who founded the theory of games?
John von Neumann
Which mathematician was unable to obtain a professorship in her native country of Russia or in Germany but did obtain a position in Sweden?
Sofia Kovalevskaya
Which French mathematician corresponded with Carl Friedrich Gauss using the pseudonym, L. LeBlanc?
Sophie Germain
Which French mathematician intervened with the French army to guarantee Gauss's safety during the Napoleonic wars?
Sophie Germain
In which stage of algebraic development did Diophantus make contributions?
Syncopated
Which one of Euclid's postulates is also known as the Parallel Postulate?
The Fifth Postulate
What did Lambert call the difference between the angle-sum of a triangle and 180 degrees?
The defect
According to one of the principles in the Copernican model, what is at the center of the moon's orbit?
The earth
What were the primary contents of the book, Ars Magna?
The solution of cubic and quartic equations
According to Newton, what is a fluxion?
The speed at which a quantity changes
What is true about the sum of the numbers on each row of Pascal's triangle?
The sums are all powers of two
What is the heavenly body that is at the center of the Copernican model of the universe?
The sun
What is true about the base angles of a Saccheri quadrilateral?
They are both right angles
How were Descartes' and Fermat's coordinate systems different from ours today?
They never referred to a vertical axis
Are there any odd perfect numbers?
This remains an unsolved problem
What is the defining characteristic of a Lambert quadrilateral?
Three of the angles are right angles
What is Newton's third law of motion due to gravity?
To every action there is an equal and opposite reaction
Why did John Napier invent logarithms?
To make computation with large numbers less tedious
Isaac Newton was the Lucasian Professor of Mathematics at what university in England?
University of Cambridge
What strategy did Girolamo Cardano use to solve cubic equations?
With a particular substitution, he transformed the cubic equation into a quadratic equation which he did know how to solve
According to the Generalized Binomial Theorem, (1+α)^x = 1 + αx + α(α−1)/2! * x^2 +.... The value of x must be a real number. What is the restriction on α?
abs(α) < 1
Which of the following is known as Euler's identity?
ei^x=cosx + i⋅sinx
What is the restriction on the function, f(x), in the Fundamental Theorem of Calculus?
f(x) must be continuous on [a, b]
What is a chord of a circle?
line segment that intersects a circle in two points
According to Niomachus' conjecture, how many digits did the nth perfect number have?
n
Which number did Euler refer to as "neither nothing, nor greater than nothing, nor less than nothing"?
√-1
