Symbols
This symbol, written as "∧", represents the logical operation of conjunction.
This type of proof involves assuming the opposite of what you want to prove and deriving a statement that doesn't make sense
What is "proof by contradiction"?
This number can also be written as 9 mod 8?
What is 'one'?
The name of the path that uses every edge of a graph exactly once
What is an Euler path?
Duke University's basketball team has a fierce rivalry with this nearby university, known as the Tar Heels.
What is the University of North Carolina at Chapel Hill?
This symbol, written as "∀", denotes that a property holds for all elements in a particular set.
"For all"
What is the best way to prove that the square root of 2 is irrational?
What is "proof by contradiction"?
Modular arithmetic finds historical use in this ancient civilization's calendar system, known for its highly precise calculations
What is ancient Egypt?
What is the term for the number of edges connected to a vertex in a graph?
What is the degree of a vertex?
This famous Duke University basketball coach led the team to five NCAA championships during his tenure from 1980 to 2006.
Answer: Who is Mike Krzyzewski (Coach K)?
This symbol, written as "¬", is used to denote the negation of a statement.
What is "not"
This type of proof uses a step-by-step logical sequence to show that a statement follows from previously established statements.
What is "direct proof"?
When two numbers give the same remainder when divided by a fixed number, they are said to be this, modulo that number.
What is "congruent"?
This term describes a path that visits each vertex of a graph exactly once.
What is a Hamiltonian path?
This iconic central landmark on Duke's campus, is known for its impressive Gothic architecture.
What is Duke Chapel?
This symbol, written as "∃", is used to indicate the existence of at least one element that satisfies a given property
Question: What is "there exists"?
This type of proof shows that if a statement is true, then another related statement must also be true, often used in conjunction with indirect proofs.
What is "proof by contraposition"?
An algorithm by this ancient Greek mathematician uses modular arithmetic to find the Greatest Common Factor
Who is Euclid?
According to Euler's formula for planar graphs, if V, E, and F represent vertices, edges, and faces respectively, what is the formula?
What is V−E+F=2?
This former U.S. president attended Duke University's School of Law.
Who is Richard Nixon?
This symbol, written as "↔", is used to denote logical equivalence between two statements.
What is "if and only if" or "bi-conditional"?
This proof technique involves proving a base case and then showing that if the statement holds for one case, it holds for the next.
What is "proof by induction"?
Modular arithmetic is extensively used in this branch of mathematics that deals with encryption and decryption techniques that is also a course offered by Duke Pre-College
What is cryptography (or cryptology)?
The seven bridges puzzle was created in this city
What is Königsberg?
Duke University is renowned for its medical school and health system, which bear the name of this tobacco magnate.
Who is James Buchanan Duke?