Pathway 07 · Advanced
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.
- Audience
- Advanced undergraduates, graduate students and independent readers who want to read research-level mathematics critically and efficiently.
- Modules
- 6, in order
- Level
- Advanced
Prerequisites
- At least one of the university-level paths, or equivalent coursework
- Calculus, linear algebra and basic differential equations for reading the book
- Willingness to read slowly with pen and paper
You will be able to
- Restate a definition in quantifier form and produce an example and a non-example
- Identify the hypotheses and conclusion of a stated result and test it on a special case
- Classify statements in a text as definitions, classical results, the author's framework, proposed formulations or computational demonstrations
- Reconstruct a short derivation from a text, marking every step that is not yet justified
- Write a one-page reading note giving the main claim, what it depends on, a verified example and open questions
Modules
Work through these in order.
- 01
Notation and conventions
Find and record a text's conventions before reading its arguments.
- 02
Definitions and statements
Read definitions and results for their exact logical content.
- 03
Following a derivation
Reconstruct arguments line by line and locate the steps that need justification.
- 04
Classifying claims
Separate classical mathematics from an author's framework and proposed formulations, using the RIDA MATH classification.
- 05
Reading the book
A guided reading of the book chapter by chapter, applying the previous modules to its definitions, statements and examples.
- 06
Writing and asking
Turn a reading into a written note and precise questions for discussion.