Logic and Proof module (MA12002)

University mathematics is built on proof: the ability to explain not just what is true, but why it must be true. In this module, you will learn how mathematicians construct clear, logical arguments with precision. 

You will be introduced to the foundations of mathematical logic, including truth tables and the structure of valid arguments. These ideas help you understand how assumptions lead to conclusions, and how to recognise when an argument is convincing. 

A central part of the module is learning different methods of proof. You will explore direct proof, proof by contradiction, proof by contrapositive, proof by cases, disproof by counterexample, and mathematical induction. These techniques are essential for university-level mathematics, where being able to explain and justify your reasoning is just as important as finding the answer. 

By developing your ability to reason logically and to communicate ideas clearly, this module builds skills that are central to mathematics and valuable in careers where precision, analysis, and effective problem-solving matter. 

What you will learn

In this module, you will: 

• study the foundations of logic and mathematical argument 
• use truth tables to analyse logical statements 
• explore different methods of mathematical proof 
• use counterexamples to disprove false statements 
• study integers, divisibility, prime numbers, and greatest common divisors 
• explore congruences and Diophantine equations

By the end of this module, you will be able to: 

• construct clear and well-structured mathematical proofs 
• choose appropriate proof methods for different problems 
• identify assumptions and follow logical arguments 
• use number theory techniques to solve mathematical problems 
• communicate mathematical reasoning with clarity and precision

Assignments / assessment

• Coursework (40%) 
• Written exam (60%) 

Teaching methods / timetable

You will learn through interactive seminars that introduce key mathematical ideas, methods, and worked examples in a supportive setting. 

Regular guided problem-solving will help you build confidence in choosing methods and applying them to new problems, with opportunities to work both individually and with other students. 

Clear online notes and resources will support your preparation, revision, and independent study, while ongoing feedback from lecturers will help you understand your progress and strengthen your problem-solving skills.