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

• Set notation and Boolean Algebra
• Mathematical statements, notations and symbols.
• The logical combinators, truth table, logical quantifiers
• Implication
• Introduction to proof- definition, theorem and proposition, disprove using counter example
• Techniques of proof including direct proof, proof by induction, proof by contradiction, axiomatic proof
• How to solve a problem
• Limits and infinity
• Number theory

Learning Outcomes

• By the end of the module students will understand:
• Mathematical statement, logical combinators and quantifiers (SSK1).
• Set notation and Boolean Algebra (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 worksheets during seminarts, tutorials and students' own time.
• In class tests, developing or consolidating the previous weeks’ work will be set which will contribute towards final the module mark. These tests also perform 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 exam.
• 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 exam.
• In addition to obtaining an overall weighted mark of 50% or above, students must obtain a mark of 50% or above for following element/s - Test 1, Test 2 and the final exam.
• Test 1 covers SSK1. SSK2, SSS1, SSS3, KS1, KS2
• Test 2 covers SSK3, SSK4, SSS2, SSS3, KS1, KS2
• Examination covers SSK1-6, SSS1-3, KS1, KS2
• Portfolio covers SSK1-6, SSS1-3, KS1, KS2

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given self testing units on a weekly basis. The module has variety form of assessment; portfolio tasks with a rapid marking turnaround fulfill 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