Mathematics

Develop deeper mathematical fluency

New algebra, proof-writing and calculus foundations units add worked arguments, varied problems and saved written responses. The full high-school, AP and undergraduate program is still in development.

Ten mathematics courses

Explore in any order. Preparation is guidance, not a navigation lock. Courses share canonical lessons and saved evidence; existing functions and AI-support work remains available below.

• Quantitative reasoning and numerical sense

  Translate fractions, percentages, ratios and units into useful calculations; estimate magnitude and communicate precision without overstating evidence.

• Algebra, functions and mathematical modeling

  Build and solve equations, inequalities and systems, interpret quadratic shape, and use exponential/logarithmic models within a stated domain.

• Geometry and trigonometry

  Use coordinates, similarity, area, volume and angle ratios to construct and check a geometric design with explicit units and domains.

• Probability, uncertainty and expected outcomes

  Count relevant outcomes, distinguish conditional and independent events, update beliefs from base rates and compare random outcomes by expectation and variation.

• Statistics: from samples to qualified conclusions

  Audit observations, describe distributions, reason about sampling and interval estimation, test a prespecified hypothesis and inspect regression without confusing association with causation.

• Linear algebra: directions, systems and approximation

  Use vectors and matrices to model constraints, diagnose solution structure, fit inconsistent observations and interpret preserved directions.

• Calculus: local rates and accumulated change

  Connect limits, derivatives and integrals, use the chain rule and partial derivatives, and justify an optimization claim with its domain and constraints.

• Discrete mathematics: logic, proof and algorithms

  Define finite structures, count outcomes, construct proofs and counterexamples, and analyze graph and algorithm behavior.

• Optimization: feasible choices and competing goals

  Formulate objectives and constraints, solve a small linear program, trace constrained gradient updates and qualify sensitivity and preference claims.

• Numerical methods and dynamical systems

  Approximate roots and integrals with explicit error checks, analyze discrete updates, and distinguish numerical instability from modeled continuous behavior.

Suggested paths, flexible starting points

These routes describe goals, not ability levels. Any learner can change paths, skip familiar topics or choose deeper implementation and mathematical reasoning.

Mathematics for AI: contextual entry points · Applied Mathematics: project investigations

Functions and graphs

Five interactive lessons, followed by a separate transfer assessment. Use tables, graphs and small experiments to interpret rates and compare choices.

Loading local math work…

Course outline: each lesson opens on its own page.

1. Read a graph with its units

   Connect a table, a coordinate pair and a point without being misled by axis scales.

2. Use a function as an input–output rule

   Substitute values, follow the order of operations and check the permitted inputs.

3. Separate a starting value from a rate

   Change slope and intercept independently and calculate a rate from two points.

4. Compare two options at the right scale

   Find where costs match and decide which option is cheaper for an allowed input.

5. Recognize when the rate changes

   Compare equal input steps on a line and a curve without assuming a constant rate.

Skipping preserves your experiments and never awards completion. The course requirement stays five lessons; if all remaining topics are skipped, they are still outstanding.