Overview

Graduate quantitative work assumes fluency with mathematical notation, probability and statistical reasoning. This course reviews the core ideas most often used in later study without attempting to reproduce a full undergraduate mathematics curriculum.

The emphasis is on reconnecting familiar techniques to the questions they are used to answer. Learners revisit functions, derivatives, vectors, matrices, probability, estimation and regression as parts of one analytical language rather than as isolated topics.

The course is intended as preparation. It identifies gaps early, gives learners a common vocabulary and points toward more advanced study in statistics, machine learning, economics and finance.

Learning objectives

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

• read and manipulate common mathematical notation used in quantitative graduate courses;
• use derivatives and simple optimization arguments in applied problems;
• work with vectors, matrices and linear systems;
• interpret probability, expectation, variance and conditional reasoning;
• read basic statistical estimates and regression output critically;
• identify which areas require further preparation before advanced study.

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	Functions and quantitative notation	How are functions, transformations and rates of change used to express analytical relationships?
2	Calculus and optimization	How do derivatives, gradients and constraints support economic and statistical reasoning?
3	Vectors and matrices	How do linear systems, projections and matrix operations organize multivariate problems?
4	Probability	How should uncertainty, conditioning and expectation be represented?
5	Statistics and regression	How are samples used to estimate relationships and quantify uncertainty?
6	Preparation for advanced study	Which concepts recur in later work, and how should learners diagnose remaining gaps?

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.