Overview

Many technical selection problems test reasoning more than memorized mathematics. This course trains learners to translate compact questions into equations, inequalities, estimates and logical constraints.

The course uses short problems involving ratios, probability, functions, data interpretation and modelling. The goal is to build speed without sacrificing the discipline of stating assumptions.

The material also serves as preparation for technical-track assessments used within the Gordon and SIAI ecosystem.

Learning objectives

By the end of the course, learners should be able to:

• translate verbal conditions into mathematical relationships;
• estimate quantities and check orders of magnitude;
• reason with ratios, rates and conditional probabilities;
• interpret small tables and charts accurately;
• identify hidden assumptions in quantitative questions;
• explain a solution clearly enough that another reader can audit it.

Intended participants and prerequisites

Course structure

The course is organised into six units. Each unit combines concise explanation, worked examples and short analytical exercises.

Unit	Subject	Principal questions
1	Translation	How can verbal conditions be turned into equations and constraints?
2	Rates and ratios	How should quantities with different units and scales be compared?
3	Probability	How do base rates and conditional information change an answer?
4	Estimation	How can approximate answers be built from limited information?
5	Data interpretation	What conclusions are and are not supported by a small dataset or chart?
6	Timed reasoning	How can speed improve without losing transparency and error checking?

Teaching and assessment

Teaching is delivered through concise lectures, technical notes, worked examples and guided exercises. AI-supported interaction may be used to explain concepts, generate additional practice and challenge a learner's reasoning, but assessment remains based on the learner's demonstrated understanding.

Component	Purpose	Weight
Short exercises	Check understanding of the principal concepts	40%
Applied investigation	Use the course framework on a new problem or dataset	30%
Final assessment	Integrated reasoning across the course	30%

A certificate of completion is issued only when the required assessments have been completed at the stated standard. Participation alone does not constitute completion.

Faculty

Materials and technical requirements

Learning environment

Learners need a current web browser and access to the Gordon learning platform. Where a course uses code, spreadsheets, datasets or external readings, the relevant requirements are identified inside the unit.

Course materials

Required readings, datasets and practice materials are identified within each unit. Public courses are designed so that required core materials can be accessed without a separate tuition charge.