SizzlinShred
Wing · 14 pages

Mathematics, Systems & Languages

Mathematics, Systems and Languages is the wing for learning to think precisely and say it well. It starts with a map of the subject and the grammar of proof, then walks the school sequence of algebra, geometry, trigonometry and calculus, and moves into discrete structures, probability, feedback and dynamics, the vocabulary of systems thinking. Method pages teach how to place yourself honestly, learn a procedure so it lasts, and keep skills alive. A parallel thread treats language as a craft: exact English expression and a reasoned choice of a second language for reading. Every page ends in something a learner can make or check, such as a solved problem, a small program, a diagram or a revised paragraph.

01 Orientation and the Map

  1. Mathematics: Start HereAn orientation to the mathematics wing: why a spine beats a survey, how the trivium frames mathematical work, and which page to read for which need.
  2. A Map of Mathematics: Twenty-Five Areas and What Depends on WhatA guided tour of the branches of mathematics in learning order, with prerequisites and the philosophical and engineering parallels of each.

02 How to Learn Mathematics

  1. Placement, Repair and Retention: Keeping Mathematics AliveHow to place yourself honestly in mathematics, repair only what fails, and keep skills alive with spaced retrieval.
  2. Learning Mathematics: Procedures and the Six AbilitiesA five-step method for learning a procedure so that it lasts, and the six separable abilities that show whether you really understand it.
  3. Proof and Precise Reasoning: From Arguments to TheoremsThe grammar of valid inference: validity and soundness, truth tables, quantifiers, the main proof techniques and counterexamples, framed by the trivium habit of defining, testing and explaining.

03 The School Sequence

  1. Algebra: The Skills That Carry EverythingThe dependency groups of school algebra and the reasons behind each rule, so that errors become diagnosable instead of mysterious.
  2. Geometry, Euclid and TrigonometryThe bridge from classical geometry to trigonometry and precalculus, including a track for studying Euclid and Apollonius by reconstruction.
  3. Calculus and Beyond: Change, Structure and UncertaintyWhat calculus, linear algebra, multivariable calculus, differential equations and statistics each accomplish, with gates a learner can use to check understanding.

04 Structures, Uncertainty and Systems

  1. Discrete Mathematics and Graphs: Counting, Relations and NetworksSets, relations, counting, induction, recurrences, graphs and trees, data modelling, and the discipline of separating an algorithm's result from a proof that it works.
  2. Mathematics for Better DecisionsA tiered curriculum of the practical mathematics that protects you from being fooled by numbers, risk and scale.
  3. Systems Thinking: Feedback, Queues, Information and DynamicsHow to reason about change, feedback and uncertainty in real systems, and where the limits of models lie.
  4. Twelve-Week Arcs and the Capstone Project MethodA 48-week study sequence with end-of-arc deliverables, and a reusable capstone method for a data-and-model project that proves understanding.

05 Language as a Craft

  1. English Expression Mastery: Words, Sentences, Paragraphs and SpeechA twelve-week, three-hours-a-week method for clearer thinking on the page and in speech, with exercises that keep claims honest.
  2. Choosing a Language to Study for Reading: Latin, Greek, French, German and BeyondA text-first framework for choosing which language to learn for philosophy and reading, replacing scoreboard rankings with evidence-aware guidance.