Learn
Learning pathways with real structure.
Each pathway states who it is for, what you should know first, what you will be able to do, and the modules in order — then links to the explainers, labs, research, and book sections that support it.
- 01Foundation
University Foundations
The algebra, functions, trigonometry and exponential reasoning that university calculus assumes from the first lecture. It ends with an informal but careful introduction to limits, so the first formal course starts on solid ground.
5 modules · Algebra and equations · Functions and graphs · Exponentials and logarithms …
Open pathway - 02University
University Calculus
Single-variable and multivariable calculus as taught across Calculus I–III: limits, derivatives, integrals, series, partial derivatives and multiple integrals. The emphasis is on knowing why each technique applies, not only how to run it.
6 modules · Limits and continuity · Differentiation and its uses · Integration …
Open pathway - 03University
Differential Equations
Ordinary differential equations from first-order equations through linear constant-coefficient equations, systems and Laplace transform methods, ending with initial and boundary value problems. Every method is paired with a way to check its answer.
6 modules · First-order equations · Linear equations with constant coefficients · Nonhomogeneous equations …
Open pathway - 04Advanced
Transform Methods
The Laplace, Fourier and Mellin transforms, their operational rules and convolution, studied both as computational tools and as related constructions. The final module connects this classical material to the operator-based framework of chapters 2 and 3 of the book.
6 modules · Laplace transform foundations · Operational rules and inversion · The Fourier transform …
Open pathway - 05University
Linear Algebra and Matrices
Vector spaces, linear maps, matrices and eigen-structure, including spaces of functions and the matrix of differentiation. The path ends with the Matrix Boundary Method described in chapter 5 of the book.
6 modules · Vectors, systems and elimination · Vector spaces, bases and dimension · Linear maps and their matrices …
Open pathway - 06Advanced
Complex Variables and Root Geometry
Complex numbers, polar form, roots of polynomials and rational functions, with attention to where roots lie and what that location implies. The later modules connect this to the angular–hyperbolic representation in chapter 3 of the book and the trigonometric and hyperbolic root representation in chapter 4.
6 modules · Complex numbers and the plane · Exponential form and roots · Polynomials and their roots …
Open pathway - 07Advanced
Research Reading
How to read mathematical research and technical books, including the RIDA MATH book itself: notation, definitions, claims and the status of each statement. The path is practiced on real text, with a written reading note as the product of each unit.
6 modules · Notation and conventions · Definitions and statements · Following a derivation …
Open pathway
How to use a pathway
Self-study or guided — the structure is the same.
- 01
Check prerequisites
Each pathway lists what it assumes. Gaps point to an earlier pathway.
- 02
Work the modules in order
Modules build on each other; the topics list is a checklist, not a syllabus to skim.
- 03
Test intuition in the lab
Linked Math Lab instruments let you check behaviour numerically before proving it.
- 04
Verify the outcomes
Outcomes are stated so you can test yourself. If one fails, return to its module.
Study skills
Practical guides for every pathway.
- How to Read a Mathematical DefinitionA practical method for reading definitions: parse the quantifiers, separate standing conditions from the claim, build examples and non-examples, probe edge cases, and write the negation. Worked on the ε–δ limit and on linear independence.
- How to Structure a Problem-Solving AttemptFive phases (understand, plan, execute, check, reflect) shown on one complete example, the initial value problem y′ − 3y = cos 2x with y(0) = 0, plus what to write down when you are stuck.
- How to Verify a Mathematical ResultSix independent ways to test an answer (substitution, special cases, limiting behavior, sign and dimension checks, numerical spot checks, and a second method), applied to an antiderivative and a Laplace transform pair, with a clear line between evidence and proof.
- How to Read Technical NotationA working guide to the notation of university analysis: derivative operators, integrals with bounds and parameters, transform notation, matrices and indices, summation, and the conventions that trip readers up, with a glossary table.
- How to Ask a Precise Mathematical QuestionHow to turn "I'm stuck" into a question that can be answered quickly: context, what you tried, where it breaks, a minimal example, and clear notation. Includes before-and-after examples and how to bring a question to a session or the community.