Module FOUD0367: Mathematical Thinking

Department: Foundation Year (Durham)

FOUD0367: Mathematical Thinking

Pre-requisites

Corequisites

Excluded Combinations

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.