Module FOUD0367: Mathematical Thinking

Department: Foundation Year (Durham)

FOUD0367: Mathematical Thinking

Prerequisites

• None

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide the opportunity for students to engage in logical reasoning using mathematical notations.
• To develop mathematical thinking skills, and the skills of formulation of rigorous mathematical derivations and proofs.
• To develop students' mathematical problem solving skills through the exploration of open ended problems.

Content

• Sets and Functions.
• Mathematical statements, notations and symbols.
• The logical combinators, truth table, logical quantifiers.
• Implications.
• Introduction to proof- definition, theorem and proposition, disprove using counter example.
• Techniques of proof.
• Introduction to Number theory and Problem Solving.

Learning Outcomes

• By the end of the module students will understand:
• Mathematical statement, logical combinators and quantifiers (SSK1).
• Sets and Functions (SSK2).
• Proof and disproof (SSK3).
• The basic concepts of Problem Solving (SSK4).
• Limits and infinity (SSK5).
• Number theory (SSK6).

• By the end of the module students will have acquired the skills to be able to:
• apply mathematical language in a logical reasoning (SSS1),
• apply variety techniques in proof (SSS2) ,
• formulate and write precise mathematical proofs (SSS3).

• By the end of the module students will be able to:
• demonstrate problem solving skills (KS1)
• produce clear and precise explanations of results (KS2).

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
• Much of the learning, understanding and consolidation will take place through the use of structured assignment sheets during seminars, tutorials and students' own time.
• An in class test, developing or consolidating the previous weeks’ work, will be set which will contribute towards final the module mark. This test also performs a formative role enabling students to reflect on their own performance, identify areas of weakness, and practice some of the skills and techniques which will be required in the final test.
• Ability to recall, select and use knowledge and manipulative skills will be tested by tasks set by the tutor on a weekly basis, mid-module invigilated tests and an end of module test.
• In addition to obtaining an overall weighted mark of 50% or above, students must obtain a mark of 50% or above for following element - End of Module Test.
• In class test covers SSK1. SSK2, SSS1, SSS3, KS1, KS2
• End of module test covers SSK1-6, SSS1-3, KS1, KS2
• Assignments cover SSK1-6, SSS1-3, KS1, KS2

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given assignment self testing units on a weekly basis and students will mark them themselves in the Seminar session. This fulfills a formative as well as summative role.

■ 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