Module FOUN0491: Mathematical Thinking

Department: Foundation Year [Queen's Campus, Stockton]

FOUN0491: Mathematical Thinking

Prerequisites

• None

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide the opportunity for students to engage in logical reasoning, algorithmic thinking and applications.
• To develop students' mathematical problem solving skills through the exploration of open ended problems.

Content

• Proof by induction
• Sorting algorithms
• Bipartate Graphs and matchings
• Shortest paths in networks (Dijkstra's algorithm)
• Spanning Trees (Prim's and Kruska's algorithm and travelling salesperson problem)
• Minimum tour (postman problem)
• Critical Path Analysis
• Matrices (nxm): addition, subtraction, multiplication, determinant, transpose, inverse, simultaneous equations.

Learning Outcomes

• By the end of the module students will:
• be able to solve a range of predictable problems in Discrete Mathematics
• be able to engage in explicit strategies for beginning, working on and reflecting on mathematical problems
• have an awareness of the basic concepts of Problem Solving

• By the end of the module students will have acquired the skills to be able to:
• apply mathematics to a variety of problems
• use matrices in a number of mathematical situations

• By the end of the module students will be able to:
• apply number in the tackling of numerical problems
• demonstrate problem solving skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures and through discussion in seminars
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Ability to recall, select and use knowledge will be tested by a series of five invigilated open book tests and an end of module invigilated exam
• Problem solving techniques will be tested through two coursework problems and within the end of module invigilated exam

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Weekly exercises.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University