Algebra & Precalculus
The foundation curriculum that prepares you for any university-level math course — calculus, linear algebra, discrete math, statistics. Builds symbolic fluency from variables and equations through functions, polynomials, exponentials, trigonometry, and the proof and set-theory groundwork that modern mathematics rests on.
1 pillars1 courses15 concepts
What you'll learn
Main Path
The mandatory throughline of this roadmap.
Algebra & Precalculus(15 concepts)
- What Algebra Actually Is
- Linear and Quadratic Equations
- Inequalities and Absolute Value
- Functions: The Central Object
- Polynomials and Factoring
- Exponentials and Logarithms
- Trigonometry: Angles and the Unit Circle
- The Six Trigonometric Functions
- Trigonometric Identities
- Coordinates, Lines, and Conic Sections
- Sequences and Series
- Mathematical Notation and Proof
- Set Theory Basics
- Logic and Quantifiers
- Where Algebra Goes — Abstract Structures
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History
A working understanding of human history — from the first hominids to the global world we live in now. The trunk walks the throughline most people never got: how civilizations actually emerge, why empires rise and fall, and how the modern world was made. Clusters dive into the cities, classical mind, slave trade, revolutions, world wars, and how historians actually do their job.
Mathematics
A working understanding of mathematics — the universal language scientists, engineers, and quants use to describe the world. The trunk gives you the throughline from how mathematicians think to how math models reality; clusters dive into proof, trig, calculus mechanics, advanced linear algebra, number theory and cryptography, probability, stochastic processes, and the foundational limits of math itself.
Databases
A complete curriculum on databases — from the relational model and ACID through PostgreSQL internals, production operations, modeling patterns, and the modern data ecosystem (NoSQL, distributed SQL, warehouses, streaming, vectors). Built for working engineers who want database knowledge that survives any system they touch.
~360h
Environmental Science
A rigorous curriculum on the Earth as a coupled system — its biogeochemical cycles, ecosystems, climate, pollution pathways, and the sustainability and policy frontier. Built for working professionals who already had a weak intro environmental class and want a complete, mechanistic mental model: how the carbon cycle actually works, why climate models project what they do, where pollutants travel, and which interventions move planetary boundaries. Every course pairs scientific mechanism with a real-world implication so the learner can reason about environmental decisions, not just recite definitions.
~320h
Economics
A working understanding of how economies actually behave — how scarcity drives choice, how markets allocate resources (and fail to), how money and policy steer the macroeconomy, and how trade, behavior, and institutions shape long-run prosperity. The trunk gives you the throughline a literate citizen needs; clusters dive into elasticity, market failures, consumer/producer theory, monetary and fiscal policy, trade policy, behavioral finance, and economic history.
History
A sweeping journey through human civilization from the earliest societies to the modern world. This curriculum explores the forces that shaped empires, revolutions, and cultural transformations across every inhabited continent. Students will develop the analytical skills to interpret primary sources, recognize historical patterns, and understand how the past continues to shape contemporary politics, economics, and culture.
~320h
Frequently asked questions
What does the Algebra & Precalculus roadmap cover?
1 courses broken into 15 bite-size concepts, each taught as an interactive lesson with quizzes and spaced review.
Do I need prior experience to start?
No. The roadmap starts from fundamentals and builds in prerequisite order — each concept unlocks the next, so you're never thrown into material you haven't been prepared for. If you already know the basics, a placement check skips you ahead.
Is the Algebra & Precalculus roadmap free?
You can sign up free and start learning immediately. Mochivia's premium subscription unlocks unlimited daily lessons and the full roadmap depth.
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