Mathematical Reasoning

Overview

The notion of mathematical statements and elementary logic. Mathematical symbols and notation. The language of sets. The concept of mathematical proof, and typical examples. Communicating mathematics to others.

Learning Objectives

By the end of the module, students are expected to be able to: state key mathematical statements and definitions and be familiar with standard mathematical notation and its meaning; describe the role played by mathematical proof and reproduce the proofs of key mathematical statements using the methods of induction, proof by contradiction and direct proof; identify patterns within proofs that can be used in other contexts and use them successfully in the construction of new proofs; use natural language to communicate key mathematical concepts to fellow students in a rigorous way.

Skills

The key skills that will be developed through the module are: problem solving skills, presentation skills and logical thinking skills.
The final module mark is determined by various components: tutorial participation, homework assignments, oral presentations, and a report. As a guideline, one can expect four pieces of written homework, and two oral presentations (the first being a practice run carrying few marks). Details of the assessment scheme will be made available at the start of the semester.

Assessment

None