Computation
Expand (4-3i)(5+51)
35+5i
G. H. Hardy wanted three things for mathematics; however Godel's Second incompleteness theorem proved math is not consistent, and Alan Turing proved math is not decidable. What did Godel's First Incompleteness Theorem prove math was not?
What is complete?
The study of the four basic operations addition, subtraction, multiplication, and division.
What is Arithmetic?
The famous mathematician credited with the invention of graph theory and whose number is the base of the natural logarithm.
Who is Leonard Euler?
The linear operator that returns a function giving the rate of change.
What is the derivative?
Find the Least Common Multiple of 8 and 20
What is 280?
Convert the Roman numeral to decimal: LVII
What is 57?
The study of arithmetic over the integers, prime numbers, and diophantine equations.
What is Number Theory?
The Father of Set Theory who claimed that there are different sizes of infinity.
Who is Georg Cantor?
This symbol is typically used to represent the sum of terms following a predictable pattern.
What is a sigma?
Find the zeros of the polynomial:
2x3 - x2 - 7x + 6
x = -2, 1, 3/2
There are several properties of number systems we take for granted; commutativity, associativity, and distributivity. All of these laws still apply to complex numbers, but which property of numbers is lost to quaternions?
What is Commutativity?
The study of how variables change in relation to others and solving these change equations.
What is Differential Equations?
This man wrote the most influential book on geometry ever written and introduced deductive reasoning.
Who is Euclid?
Typically thought of as linear transformation, these operators are represented by arrays and act on vectors.
What is a Matrix?
Compute the matrix multiplication AB
A: 1st row 2 & 3, 2nd row 6 & 4
B: 1st row 1 & 2, 2nd row 3 & 5
1st row: 11 & 19
2nd row: 18 & 32
Graph theory was invented to solve this problem involving traversing every bridge in the Russian city now known as Kaliningrad.
What is the Konigsberg Bridge Problem?
The study of abstract algebraic structures such as groups, rings, fields, and vector spaces. This is the framework used in modern physics and alternate number systems.
What is abstract algebra?
Revered 19th-century mathematician who left his mark on every field of math he touched. A child savant who helped his father with his taxes and devised a formula for a laborious task given by his teacher at age 7. Most noted for his work on the Fundamental Theorem of Algebra, non-euclidean geometry, complex analysis and topology.
Who is Gauss?
Shorthand used to signify two numbers have the same remainder when divided by the same number.
In more technical terms, it signifies that two numbers are in the same equivalency class mod n.
Congruency
For some constant k the polynomial p(x) = 3x2 + kx + 117 has the property that p(1) = p(10). Evaluate p(20).
p(20) = 657
How many colors are required to color any map such that no two borders share the same color?
What is 4?
The study of systems whose outcome is heavily dependent on the initial conditions.
What is Chaos Theory?
This Hungarian man was one of the most prolific mathematicians of the 20th century, traveling around the nation to work with others on many subjects, mainly in discrete math. He worked with so many other mathematicians, that almost everyone who has written a paper has a number associated with how connected with this man they are (Grisham's is 6).
Who is Paul Erdos?
Symbol used to take the product of a predictable sequence of numbers.
Pi (the product operator)