Explore Mathematics
Mathematics examines rigorous reasoning about structures, quantities and change. This subject guide introduces the questions, methods and practical work that help learners understand the field before choosing a formal course of study.
A strong starting point is to connect calculus with linear algebra. The first develops a foundation for reasoning; the second provides a setting in which to test ideas. Keep a learning journal that records assumptions, sources and questions that remain unresolved.
Four areas to investigate
Calculus
Connect calculus to the study of rigorous reasoning about structures, quantities and change. Compare an introductory explanation with a worked example, then describe where the approach is useful and where it may fail.
Linear algebra
Connect linear algebra to the study of rigorous reasoning about structures, quantities and change. Compare an introductory explanation with a worked example, then describe where the approach is useful and where it may fail.
Proof methods
Connect proof methods to the study of rigorous reasoning about structures, quantities and change. Compare an introductory explanation with a worked example, then describe where the approach is useful and where it may fail.
Differential equations
Connect differential equations to the study of rigorous reasoning about structures, quantities and change. Compare an introductory explanation with a worked example, then describe where the approach is useful and where it may fail.
Learn through inquiry
Develop and compare mathematical models of a changing population.
Begin with a question narrow enough to investigate. Decide what evidence would support an answer, document the method and explain what further work would be needed.