Game Theory is a branch of mathematics that studies the strategies used by rational agents in competitive situations, where the outcome depends on the choices of all involved parties, often used in economics, politics, and computer science.
In graph theory, what is a bipartite graph?
A A graph with two disjoint sets of vertices
B A graph with cycles
C A graph with no edges
D A graph with a single vertex
A bipartite graph consists of two disjoint sets of vertices where every edge connects a vertex from one set to a vertex from the other set. There are no edges within each set.
What is a Nash equilibrium in Game Theory?
A A situation where one player wins
B A zero sum game
C A strategy where players collaborate
D A stable state where no player benefits from changing strategy
A Nash equilibrium is a concept in Game Theory where no player can improve their payoff by unilaterally changing their strategy, given that the other players’ strategies remain unchanged.
What is the main goal of cryptographic mathematics?
A To simplify mathematical problems
B To create secure communication systems
C To solve linear equations
D To model random events
Cryptographic mathematics focuses on the development of algorithms and protocols that ensure secure communication and data protection, such as encryption and decryption, ensuring privacy and integrity in digital transactions.
What is an Eulerian circuit in a graph?
A A path that visits every edge exactly once
B A cycle that visits every vertex exactly once
C A path that visits every vertex
D A path with no cycles
An Eulerian circuit is a circuit that visits every edge of a graph exactly once and returns to the starting vertex. A graph contains an Eulerian circuit if all its vertices have an even degree.
What is a Hamiltonian cycle in a graph?
A A cycle that includes all vertices exactly once
B A path that covers only odd degree vertices
C A path that does not repeat vertices
D A path that covers all edges
A Hamiltonian cycle is a cycle in a graph that visits every vertex exactly once and returns to the starting vertex. It is a key concept in the study of traveling salesman problems.
What is the purpose of the Diffie Hellman key exchange algorithm?
A To generate random numbers
B To secure online transactions
C To exchange cryptographic keys securely
D To encrypt messages
The Diffie Hellman key exchange algorithm allows two parties to securely exchange cryptographic keys over a public channel without directly sharing the key, ensuring the confidentiality of the communication.
In a graph, what is the degree of a vertex?
A The number of edges incident to it
B The number of vertices it connects to
C The number of paths to it
D The number of vertices in the graph
The degree of a vertex in a graph is the number of edges incident to it, meaning the number of edges that are connected to that vertex. In a directed graph, in degree and out degree can be defined separately.
What is a key feature of an acyclic graph?
A It contains cycles
B It has no edges
C It has no cycles
D It has no cycles
An acyclic graph is a graph that does not contain any cycles. It is often used to represent hierarchical structures, like trees, where there is a one way path from one node to another.
What is the main idea behind randomized algorithms?
A They use random numbers to optimize solutions
B They work only with large data sets
C They use random numbers to optimize solutions
D They guarantee exact solutions
Randomized algorithms use random numbers to influence the process of solving problems, improving efficiency and sometimes providing approximate solutions to problems where deterministic algorithms may be too slow or complex.
What is the concept of modular arithmetic used for?
A Multiplication
B Performing operations on remainders after division
C Solving polynomial equations
D Calculating factorials
Modular arithmetic is a system of arithmetic for integers where numbers “wrap around” after reaching a certain value (the modulus). It is used in cryptography, hashing functions, and number theory.
What is the main purpose of an adjacency matrix in graph theory?
A To calculate graph’s degree
B To represent the graph using edges
C To store information about graph connectivity
D To store the distances between vertices
An adjacency matrix is a square matrix used to represent a graph. The matrix’s elements indicate whether pairs of vertices are adjacent (connected) in the graph. It is especially useful for dense graphs.
What is a complete graph?
A A graph with no edges
B A graph where every pair of vertices is connected
C A graph with exactly one cycle
D A graph with two sets of vertices
A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge. It is denoted as Kₙ, where n is the number of vertices.
What does the principle of optimality in dynamic programming state?
A The problem can be solved by brute force
B The solution to the problem is built from solutions to subproblems
C Subproblems should not be solved independently
D A problem cannot be optimized
The principle of optimality states that the optimal solution to a problem can be constructed efficiently by combining optimal solutions to its subproblems. This is a key concept in dynamic programming.
What does a directed acyclic graph (DAG) help represent in computer science?
A A network of nodes
B Relationships with cycles
C Data flow and dependencies
D Processes with no dependencies
A directed acyclic graph (DAG) is used to represent data flow and dependencies in processes. It is used in various areas, including scheduling tasks, compiling, and representing workflows without cycles.