Discrete Math - Central Bureau of Statistics Case Study - Euler Ian and Hamiltonian Circuit - Five Color Theorem - Science and Maths Assignment Help

Assignment Task:

Central Bureau of Statistics Case Study Discrete Math Assignment Help

Scenario I

You have been working as a mathematical analyst for the Central Bureau of Statistics operating in Kathmandu Nepal. The Bureau helps the Nepal government with statistics in order to help in developing public policy planning, collecting and analyzing socioeconomic data and developing methodologies for reliable data collection and implementation is doing various researches on different technological aspects of the country.

With the use of data recorded from various sources, they are using mathematics to determine the fastest routes and time for travelling different corners of the city to free the general public from traffic congestion. With the help of minimum weighted spanning tree, they are trying to use the least amount of pipelines to connect all the terminals of the locality. The Bureau is also determining the best possible ways to add streets to congested areas of cities uses graph theory.

For the storage of data and information, the bureau is using linear algebra for data compression and reduction of noise in data. All the data are stored as huge strings of 1’s and 0’s. For the automation of certain processes, Boolean algebra with various gates is used and simplified to reduce the complexity of circuits. You as a mathematical analyst are required to perform various tasks relating to the discrete structure and perform necessary calculations and provide applicable solutions to the problems given to you.

Learning Outcomes Covered

LO1: Examine set theory and functions applicable to software engineering.

LO2: Analyze mathematical structures of objects using graph theory.

LO3: Investigate solutions to problem situations using the application of Boolean algebra.

LO4: Explore applicable concepts within abstract algebra.

Part 1

With reference to the scenario, prepare a report which examines the set theory and functions applicable to software engineering and analyze mathematical structures of objects using graph theory.

Section 1

• Perform algebraic set operations in a formulated mathematical problem.
• Determine the cardinality of a given bag (multiset).
• Determine the inverse of a function using appropriate mathematical techniques.
• Formulate corresponding proof principles to prove properties about defined sets.

Section 2

• Model contextualized problems using trees, both quantitatively and qualitatively.
• Use Dijkstra's algorithm to find the shortest path spanning tree in a graph.
• Assess whether a Euler Ian and Hamiltonian circuit exists in an undirected graph.
• Construct a proof of the Five Color Theorem. 

Part 2 

Prepare a technical booklet which investigates solutions to problem situations using the application of Boolean algebra and explore applicable concepts within abstract algebra.

Section 1

• Diagram a binary problem in the application of Boolean algebra.
• Produce a truth table and its corresponding Boolean equation from an applicable scenario
• Simplify a Boolean equation using algebraic methods and design a complex system using logic gates.
• Describe the distinguishing characteristics of different binary operations that are performed on the same set.
• Determine the order of a group and the order of subgroup in given examples.
• Validate whether a given set with a binary operation is indeed a group.

Section 2

Prepare a presentation for twenty minutes that explains an application of group theory relevant to your course of study. And write a few paragraphs summarizing the key ideas or concepts you have presented. 

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