∑

Mathematics

31 topics

• Elementary K–2 — Early Math

  • Counting, number sense, place value to 100
  • Addition & subtraction within 20
  • Shapes, measurement, time, money basics
  • +1 more topics

• Elementary 3–5 — Arithmetic & Fractions

  • Multiplication & division fluency
  • Fractions, decimals, mixed numbers
  • Area, perimeter, volume of rectangles
  • +1 more topics
  Area rectPerimeter+1

• Middle School 6–8 — Pre-Algebra

  • Ratios, proportions, percents
  • Integers, rational numbers, absolute value
  • Expressions, one- and two-step equations
  • +1 more topics
  PercentSlope+1

• Grade 9 — Algebra I

  Grade 9
  • Variables, expressions, order of operations (PEMDAS)
  • Linear equations & inequalities; systems
  • Functions, slope, lines
  • +2 more topics
  SlopeSlope-intercept+2

• Grade 10 — Geometry

  Grade 10
  • Lines, angles, parallel & perpendicular
  • Triangle congruence & similarity
  • Right-triangle trig (SOH-CAH-TOA)
  • +2 more topics
  PythagoreanDistance+3

• Grade 11 — Algebra II

  Grade 11
  • Polynomial, rational, exponential, log functions
  • Complex numbers, conics
  • Sequences & series
  • +2 more topics
  Vertex formLog rules+4

• Grade 12 — Pre-Calc / Calculus

  Grade 12
  • Trig identities, polar, vectors
  • Limits and continuity
  • Derivatives & rules
  • +2 more topics
  DerivativePower rule+4

• College Freshman — Calculus I & II

  • Limits, derivatives, applications
  • Definite & indefinite integrals
  • Techniques of integration, series
  • +1 more topics
  TaylorIntegration by parts

• College Sophomore — Multivariable & Linear Algebra

  • Partial derivatives, gradient, multiple integrals
  • Vector calculus: divergence, curl, Stokes
  • Matrices, determinants, eigenvalues
  • +1 more topics
  GradientDet 2x2+1

• College Junior — Probability & Statistics

  • Random variables, distributions
  • Expectation, variance, CLT
  • Hypothesis testing, confidence intervals
  • +1 more topics
  ExpectationVariance+1

• College Senior — Real & Abstract Analysis

  • Real analysis: limits, continuity, measure
  • Abstract algebra: groups, rings, fields
  • Topology basics
  • +1 more topics

• Graduate — Master's & PhD Mathematics

  • Functional analysis, PDEs
  • Advanced probability & stochastic processes
  • Numerical methods & optimization
  • +1 more topics

• Discrete Mathematics

  • Foundations of formal logic, truth tables, and propositional calculus
  • Set theory terminology, operations, and Venn diagram representations
  • Counting techniques including permutations and combinations
  • +2 more topics
  P(n, r) = n! / (n - r)!C(n, r) = n! / (r!(n - r)!)+3

• Complex Analysis

  • Holomorphic functions and the Cauchy-Riemann equations
  • Complex integration along paths and Cauchy's Theorem
  • Power series expansions, Taylor and Laurent series
  • +3 more topics
  ux = vy, uy = -vxf(a) = (1/2pi*i) * integral(f(z)/(z-a) dz)+3

• Pre-Algebra — Foundations

  • Master arithmetic operations and the properties of real numbers
  • Simplify expressions using order of operations (PEMDAS)
  • Solve basic linear equations and inequalities with one variable
  • +3 more topics
  a + b = b + aa(b + c) = ab + ac+3

• Partial Differential Equations

  • Classification into elliptic, parabolic, and hyperbolic types
  • Method of Characteristics for first-order linear and quasilinear equations
  • Separation of Variables and Fourier Series for boundary value problems
  • +2 more topics
  u_tt = c^2 * u_xx (Wave Equation)u_t = k * u_xx (Heat Equation)+3

• Real Analysis

  • Rigorous foundations of the real number system and its properties
  • Formal epsilon-delta definitions of limits and continuity
  • Sequences, series, and various modes of convergence
  • +2 more topics
  Axion of CompletenessDefinition of Limit+3

• Linear Algebra

  • Systems of linear equations and Gaussian elimination techniques
  • Vector spaces, subspaces, spanning sets, and linear independence
  • Matrix operations, determinants, and the invertible matrix theorem
  • +3 more topics
  Ax = bdet(A - lambda*I) = 0+4

• Algebra I — Linear Equations & Functions

  • Identify and interpret slopes and y-intercepts in various contexts.
  • Solve and graph linear equations in multiple equivalent forms.
  • Define functions using domain, range, and function notation.
  • +2 more topics
  y = mx + by - y1 = m(x - x1)+3

• Trigonometry — Triangles & Unit Circle

  • Defining sine, cosine, and tangent via right triangle ratios (SOH CAH TOA).
  • Mapping the unit circle to extend functions beyond 90-degree angles.
  • Converting between degrees and radians for circular measurement.
  • +2 more topics
  sin(theta) = opposite / hypotenusecos(theta) = adjacent / hypotenuse+4

• Geometry — Euclidean Plane & Solid

  • Axiomatic foundations of Euclidean geometry and formal proofs
  • Properties of triangles, quadrilaterals, and regular polygons
  • Circle theorems including chords, tangents, and arc lengths
  • +3 more topics
  c^2 = a^2 + b^2Area = (1/2) * base * height+4

• Precalculus — Functions & Analytic Geometry

  • Comprehensive analysis of polynomial, rational, and radical functions.
  • Mastery of exponential and logarithmic properties and equations.
  • Geometric interpretation of conic sections: circles, parabolas, and ellipses.
  • +2 more topics
  f(x) = a(x-h)^2 + klog_b(xy) = log_b(x) + log_b(y)+3

• Ordinary Differential Equations

  • First-order equations: separable, linear, and exact forms
  • Higher-order linear equations with constant coefficients
  • Laplace transforms for solving initial value problems
  • +3 more topics
  dy/dx + P(x)y = Q(x)ay'' + by' + cy = 0+3

• Algebra II — Quadratics, Polynomials, Exponentials

  • Factoring, expanding, and graphing quadratic functions across multiple forms.
  • Analyzing polynomial behavior including end behavior and complex roots.
  • Modeling growth and decay using exponential functions and logarithms.
  • +2 more topics
  x = [-b +/- sqrt(b^2 - 4ac)] / 2ay = a(x - h)^2 + k+3

• Abstract Algebra (Groups, Rings, Fields)

  • Symmetry and structure of groups including subgroups and quotients
  • Homomorphisms, isomorphisms, and the fundamental mapping theorems
  • Ring theory focusing on ideals, integral domains, and polynomials
  • +2 more topics
  G/N = { gN | g in G }a * b = b * a (Commutative Law)+3

• Number Theory

  • Divisibility, prime factorization, and the Euclidean Algorithm.
  • Modular arithmetic and the properties of congruences.
  • Linear Diophantine equations and the Chinese Remainder Theorem.
  • +3 more topics
  a = bq + rgcd(a, b) = ax + by+4

• Topology

  • Point-set topology: open sets, neighborhoods, and bases
  • Continuity and homeomorphism as structural equivalence
  • Compactness, connectedness, and separation axioms
  • +3 more topics
  fcl(A) = A U {limit points of A}+3

• Probability Theory

  • Axiomatic foundations: Sample spaces, events, and Kolmogorov's Three Axioms.
  • Conditional probability, independence, and the application of Bayes' Theorem.
  • Discrete and continuous random variables with their distribution functions.
  • +2 more topics
  P(A|B) = P(B|A)P(A) / P(B)E[X] = sum(x * P(x)) or integral(x * f(x) dx)+3

• Mathematical Statistics

  • Foundations of point estimation including unbiasedness and efficiency
  • Hypothesis testing frameworks and Neyman-Pearson Lemma
  • The construction and interpretation of confidence intervals
  • +3 more topics
  L(theta) = PRODUCT f(xi; theta)MSE(T) = Var(T) + [Bias(T, theta)]^2+3

• Mathematical Logic & Set Theory

  • Propositional and first-order predicate logic foundations
  • Formal proof systems, soundness, and completeness theorems
  • Zermelo-Fraenkel set theory and the Axiom of Choice
  • +2 more topics
  P -> Q <=> ~P v QAx(P(x)) -> ~Ex(~P(x))+3

• Numerical Methods

  • Root-finding algorithms for non-linear equations like Newton-Raphson
  • Linear system solutions using Gaussian elimination and iterative methods
  • Interpolation and curve fitting using polynomials and splines
  • +3 more topics
  x_{n+1} = x_n - f(x_n)/f'(x_n)f'(x) approx [f(x+h) - f(x)] / h+3

⚛

Science

33 topics

• Elementary K–2 — Discover Science

  • Five senses, living vs. nonliving things
  • Weather, seasons, day & night
  • Plants & animals around us
  • +1 more topics

• Elementary 3–5 — Earth & Life Science

  • Life cycles, food chains, ecosystems
  • States of matter; simple forces & motion
  • Solar system, water cycle, weather patterns
  • +1 more topics

• Middle School 6–8 — Integrated Science

  • Cells, body systems, genetics intro
  • Atoms, molecules, chemical reactions intro
  • Plate tectonics, climate, energy resources
  • +1 more topics
  DensitySpeed+1

• Grade 9 — Biology

  Grade 9
  • Cell theory & organelles
  • Photosynthesis & cellular respiration
  • Mitosis & meiosis
  • +2 more topics
  PhotosynthesisRespiration+1

• Grade 10 — Chemistry

  Grade 10
  • Atomic structure, periodic trends
  • Bonding (ionic, covalent, metallic)
  • Stoichiometry, the mole
  • +2 more topics
  MoleIdeal gas+4

• Grade 11 — Physics

  Grade 11
  • Kinematics & Newton's laws
  • Work, energy, power; conservation
  • Momentum, circular motion, gravitation
  • +2 more topics
  KinematicsNewton 2+6

• Grade 12 — Advanced Science

  Grade 12
  • AP Bio: molecular bio, gene regulation
  • AP Chem: thermodynamics, kinetics, electrochem
  • AP Physics: rotation, thermo, modern physics
  • +1 more topics
  GibbsRate law+1

• College Freshman — General Biology & Chemistry

  • Cell biology, genetics, evolution
  • General chemistry: stoichiometry, equilibrium, thermo
  • Lab techniques & scientific writing

• College Sophomore — Organic Chem & Physics

  • Organic chem: functional groups, reactions, mechanisms
  • University physics I & II (mechanics, E&M)
  • Lab reports & data analysis

• College Junior — Biochem, Genetics, Modern Physics

  • Biochemistry: proteins, enzymes, metabolism
  • Molecular genetics, cell signaling
  • Quantum mechanics, special relativity basics

• College Senior — Capstone & Research

  • Senior thesis / capstone research
  • Advanced electives (neuro, astrophysics, etc.)
  • Scientific communication & ethics

• Graduate — Master's & PhD Science

  • Specialized coursework in chosen field
  • Independent research & publication
  • Teaching assistantships
  • +1 more topics

• Astronomy & Astrophysics

  • Stellar evolution from protostars to supernovae and compact remnants
  • Orbital mechanics, Kepler's Laws, and Newton's Universal Gravitation
  • Cosmological expansion, Hubble's Law, and the Big Bang theory
  • +3 more topics
  L = 4 * pi * R^2 * sigma * T^4F = G * M * m / r^2+4

• Oceanography

  • Physical properties of seawater including salinity, density, and light
  • Global ocean circulation patterns, thermohaline flow, and surface currents
  • Marine geology including plate tectonics and deep-sea bathymetry
  • +2 more topics
  Density = Mass / Volume (kg/m^3)P = rho * g * h (Hydrostatic Pressure)+3

• Geology & Earth Science

  • Plate tectonics and the internal structure of the Earth
  • Mineral identification and the rock cycle process
  • Geologic time scales and the fossil record
  • +2 more topics
  Density = Mass / VolumeAge = (1/lambda) * ln(1 + Daughter/Parent)+3

• Meteorology & Atmospheric Science

  • Structure and composition of the Earth's atmosphere
  • Thermodynamics of moisture, cloud formation, and stability
  • Global circulation patterns and large-scale weather systems
  • +3 more topics
  P = rho * R * T (Ideal Gas Law)F = m * a (Newton's Second Law applied to parcels)+4

• Human Anatomy & Physiology

  • Structural organization from chemicals and cells to complex organ systems.
  • Homeostatic regulation through negative and positive feedback loops.
  • The musculoskeletal system's role in support, protection, and locomotion.
  • +3 more topics
  BP = CO x TPR (Blood Pressure = Cardiac Output x Total Peripheral Resistance)CO = HR x SV (Cardiac Output = Heart Rate x Stroke Volume)+3

• Microbiology

  • Structure and function of prokaryotic and eukaryotic microbes
  • Microbial genetics, metabolism, and mechanisms of pathogenesis
  • Environmental roles and industrial applications of microorganisms
  • +2 more topics
  Generation timeExponential growth+3

• Botany

  • Understanding plant structure, function, and life cycles
  • Analysis of photosynthesis and cellular respiration mechanisms
  • Classification and evolution of bryophytes to angiosperms
  • +3 more topics
  PhotosynthesisWater Potential+4

• Zoology

  • Classification and phylogeny of the animal kingdom
  • Comparative anatomy and physiological systems
  • Evolutionary mechanisms and adaptive radiations
  • +3 more topics
  p^2 + 2pq + q^2 = 1 (Hardy-Weinberg Equilibrium)rB > C (Hamilton's Rule for altruism)+3

• Genetics & Genomics

  • DNA structure, replication, and the Central Dogma of molecular biology.
  • Mendelian inheritance patterns and non-Mendelian complex traits.
  • Genomic mapping, sequencing technologies, and bioinformatics tools.
  • +3 more topics
  p^2 + 2pq + q^2 = 1p + q = 1+3

• Biochemistry

  • Molecular basis of life identifying structural and functional biomolecules
  • Enzyme kinetics, catalytic mechanisms, and protein folding dynamics
  • Central metabolic pathways including glycolysis and the citric acid cycle
  • +3 more topics
  pH = pKa + log([A-]/[HA])v = (Vmax * [S]) / (Km + [S])+4

• Organic Chemistry

  • Structure and bonding of carbon-based molecules and functional groups
  • Nomenclature, stereochemistry, and conformational analysis of alkanes
  • Substitution (SN1/SN2) and elimination (E1/E2) reaction mechanisms
  • +3 more topics
  Rate = k[Substrate][Nucleophile] (SN2)Rate = k[Substrate] (SN1/E1)+3

• Neuroscience

  • Neuronal physiology, action potentials, and synaptic transmission
  • Functional neuroanatomy and the organization of the nervous system
  • Sensory and motor systems processing and integration
  • +2 more topics
  V_m = 61 * log10([K_out]/[K_in]) (Nernst Equation for Potassium)g = I / (V - E) (Conductance based on Ohm's Law)+3

• Physical Chemistry

  • Thermodynamics: The study of heat, work, and spontaneous chemical change.
  • Quantum Mechanics: Describing atomic structures and molecular bonding models.
  • Chemical Kinetics: Measuring and predicting rates of chemical reactions.
  • +2 more topics
  PV = nRTDelta G = Delta H - T * Delta S+4

• Analytical Chemistry

  • Mastering precision and accuracy in quantitative chemical measurements
  • Understanding chemical equilibrium, acid-base, and redox titrations
  • Principles of spectroscopic methods and electromagnetic interactions
  • +3 more topics
  pH = pKa + log([A-]/[HA])A = epsilon * b * c+4

• Ecology & Conservation Biology

  • Energy flow through trophic levels and the 10 percent rule
  • Population dynamics, growth models, and carrying capacity
  • Biodiversity metrics and the value of ecosystem services
  • +3 more topics
  dN/dt = rN(1 - N/K)H = -sum(Pi * ln(Pi))+4

• Thermodynamics & Statistical Mechanics

  • Laws of Thermodynamics and the definition of state variables
  • Statistical foundations of entropy through microstate counting
  • Thermodynamic potentials including Gibbs and Helmholtz energy
  • +3 more topics
  dU = TdS - PdV + mu dNS = k * ln(W)+4

• Quantum Mechanics

  • The wave-particle duality and the probabilistic nature of subatomic matter
  • Solutions to the Schrodinger equation for stationary and time-dependent states
  • Quantum operators, observables, and the Heisenberg uncertainty principle
  • +3 more topics
  H(psi) = E(psi)p = h / lambda+4

• Materials Science

  • Atomic bonding and crystal structures in metallic and ceramic solids
  • Mechanical properties including stress-strain behavior and toughness
  • Phase diagrams and the kinetics of phase transformations in alloys
  • +3 more topics
  sigma = F / Aepsilon = delta L / L+4

• Computer Science Fundamentals

  • Fundamental logic gates and binary arithmetic systems
  • Time and space complexity using Big O notation
  • Core data structures including arrays, linked lists, and trees
  • +2 more topics
  2^n (Maximum values represented by n bits)T(n) = O(log n) (Binary search time complexity)+3

• Engineering Fundamentals

  • Introduction to fundamental engineering units, dimensions, and standards.
  • Mastery of static equilibrium and force vector decomposition techniques.
  • Analysis of basic electrical circuits using Ohm's and Kirchhoff's laws.
  • +3 more topics
  F = m * aV = I * R+4

• Optics & Photonics

  • Wave-particle duality of light and Maxwell's electromagnetic theory
  • Geometrical optics including reflection, refraction, and lens design
  • Physical optics covering interference, diffraction, and polarization
  • +3 more topics
  n1 sin(theta1) = n2 sin(theta2)f = r / 2+4

✎

English Language Arts

23 topics

• Elementary K–2 — Foundations of Reading

  • Phonics, sight words, blending sounds
  • Reading aloud & shared picture books
  • Capitalization, periods, simple sentences
  • +1 more topics

• Elementary 3–5 — Reading & Writing

  • Chapter books; main idea & details
  • Paragraph structure & 5-paragraph essay
  • Parts of speech, subject-verb agreement
  • +1 more topics

• Middle School 6–8 — Literature & Composition

  • Novels (e.g. The Outsiders, The Giver)
  • Theme, character, plot, point of view
  • Argumentative & informational writing
  • +1 more topics

• Grade 9 — English I

  Grade 9
  • Short stories, poetry, drama (Romeo & Juliet)
  • Grammar: parts of speech, clauses
  • Narrative & expository essays
  • +1 more topics

• Grade 10 — English II (World Lit)

  Grade 10
  • Homer, Greek tragedy, Things Fall Apart
  • Rhetoric: ethos, pathos, logos
  • MLA citation; research basics

• Grade 11 — English III (American Lit)

  Grade 11
  • Puritan → Modernist periods
  • Gatsby, Crucible, Huck Finn
  • Rhetorical analysis; SAT/ACT prep

• Grade 12 — English IV (British/World Lit)

  Grade 12
  • Beowulf, Chaucer, Shakespeare, Romantics
  • College essays & personal statements
  • Literary criticism lenses

• Writing Toolkit

  • Essay: hook + thesis -> body (PEEL) -> conclusion
  • Thesis = topic + claim + reasons
  • Citations: MLA, APA, Chicago

• College Freshman — Composition & Rhetoric

  • ENG 101: academic essay structure
  • Argumentation, evidence, revision
  • Research papers & APA/MLA citation

• College Sophomore — Survey of Literature

  • American, British, or World lit survey
  • Close reading & textual analysis
  • Comparative essays

• College Junior — Literary Theory & Genre

  • Critical theory: formalism, feminism, postcolonial
  • Genre studies (poetry, drama, novel)
  • Author or period seminars

• College Senior — Capstone & Creative Writing

  • Senior thesis or portfolio
  • Advanced creative writing workshops
  • Publishing & professional writing

• Graduate — MA / PhD English

  • Research methods & bibliography
  • Specialized seminars in chosen field
  • Conference papers & journal articles
  • +1 more topics

• American Literature

  • Evolution of Puritanism and the Enlightenment in Colonial texts
  • Rise of American Romanticism, Transcendentalism, and the Gothic
  • Realism, Naturalism, and the shift toward disillusionment
  • +3 more topics
  Puritan Work Ethic + Predestination = Early American IdentityTranscendentalism = Intuition + Nature + Over-Soul+4

• British Literature

  • Old English origins and the transition to Middle English epics
  • Renaissance humanism and the evolution of the Shakespearean sonnet
  • The Romantic movement's reaction to Industrial Revolution logic
  • +3 more topics
  Petrarchan SonnetShakespearean Sonnet+3

• World Literature

  • Evolution of heroic archetypes from Gilgamesh to modern anti-heroes
  • Analysis of post-colonial narratives within the global literary canon
  • Exploration of magical realism and its socio-political foundations
  • +2 more topics
  Epic CycleHegemonic Discourse vs. Subaltern Narrative+2

• Creative Writing

  • Mastering narrative structure and the hero's journey arc.
  • Developing complex characters through internal and external conflict.
  • Crafting sensory-rich settings using showing rather than telling.
  • +2 more topics
  Protagonist + Goal + Obstacle = DramaShow, Don't Tell = Sensory Detail > Abstract Label+1

• Linguistics

  • Investigation of phonology, morphology, and syntax structures
  • Analysis of semantic meaning and pragmatic context in use
  • Exploration of sociolinguistics and language variation
  • +2 more topics
  S -> NP VPNP -> (Det) (Adj) N+3

• Poetry & Prosody

  • Investigation of poetic meter, rhythm, and structural form.
  • Analysis of scansion techniques for English accentual-syllabic verse.
  • Categorization of poetic sound devices and rhyme schemes.
  • +2 more topics
  IambTrochee+4

• Technical & Professional Writing

  • Mastering audience analysis to tailor tone and complexity
  • Writing clear, concise, and action-oriented documentation
  • Designing usable layouts for reports and manuals
  • +3 more topics
  Gunning Fog Index = 0.4 * [(words/sentences) + 100 * (complex words/words)]Passive vs. Active voice+2

• Shakespeare

  • Introduction to Shakespearean sonnets, tragedies, and comedies.
  • Analysis of Early Modern English syntax and iambic pentameter.
  • Historical context of the Elizabethan and Jacobean eras.
  • +3 more topics
  Iambic PentameterShakespearean Sonnet+2

• Rhetoric & Argumentation

  • Mastering the Aristotelian triad: Ethos, Pathos, and Logos
  • Identifying and debunking common logical fallacies
  • Analyzing the structure of the classical Oration
  • +3 more topics
  Ethos + Pathos + Logos = PersuasionClaim + Data + Warrant = Argument+2

• Literary Theory & Criticism

  • Tracing the evolution from Classical Poetics to Post-structuralism
  • Analyzing the relationship between author, text, and reader
  • Examining power structures, gender, and class through literature
  • +2 more topics
  Sign = Signifier + Signified (Saussure)Hegemony = Consent + Coercion (Gramsci)+3

⚖

History & Social Studies

28 topics

• Elementary K–2 — My Community

  • Family, neighborhood, community helpers
  • Maps of home, school, neighborhood
  • National holidays & symbols
  • +1 more topics

• Elementary 3–5 — US States & Regions

  • Regions of the United States
  • Native peoples & European exploration
  • Colonial America & American Revolution
  • +1 more topics

• Middle School 6–8 — Ancient & US History

  • Ancient civilizations (Egypt, Greece, Rome)
  • Middle Ages & early modern world
  • US founding documents; westward expansion
  • +1 more topics

• Grade 9 — World Geography / History I

  Grade 9
  • Early civilizations & classical world
  • Major religions
  • Medieval Europe & feudalism

• Grade 10 — World History II

  Grade 10
  • Renaissance, Reformation, Sci. Revolution
  • Exploration, Enlightenment, revolutions
  • Industrial Revolution; WWI, WWII; Cold War

• Grade 11 — US History

  Grade 11
  • Colonial America → Constitution (1776–1789)
  • Civil War & Reconstruction (1861–1877)
  • Gilded Age → New Deal → WWII
  • +1 more topics

• Grade 12 — US Gov & Economics

  Grade 12
  • Three branches; Bill of Rights; federalism
  • Landmark cases: Marbury, Brown, Miranda
  • Micro: supply, demand, elasticity
  • +1 more topics
  GDPInflation+2

• College Freshman — Western & World Civ

  • Western civilization survey
  • World history themes & comparative cultures
  • Historiography basics

• College Sophomore — US History Survey

  • Colonial era through Civil War
  • Reconstruction to modern America
  • Primary source analysis

• College Junior — Regional & Thematic Seminars

  • European, Asian, African, Latin American history
  • Topics: race, gender, war, economics
  • Research paper using archives

• College Senior — Capstone Thesis

  • Senior thesis with original research
  • Advanced seminar in chosen subfield
  • Public history / museum studies electives

• Graduate — MA / PhD History

  • Historiography & methodology seminars
  • Language exams; archival research
  • Comprehensive exams
  • +1 more topics

• US History I (Colonial — 1877)

  • Origins of colonial expansion and European-Indigenous interactions.
  • The American Revolution and the drafting of the Constitution.
  • Sectionalism, slavery, and the expansion into the American West.
  • +1 more topics
  Articles of Confederation (1781-1789) < Constitution (1789-Present)Cotton Gin (1793) -> Expansion of Slave Labor+3

• US History II (1877 — Present)

  • Transformation from an agrarian society to an industrial superpower
  • Expansion of civil rights and the evolution of federal authority
  • Transition from isolationism to global leadership in the 20th century
  • +2 more topics
  Industrialization + Urbanization = Progressive Era ReformMass Production + Credit Expansion = Roaring Twenties+3

• Medieval History

  • The transition from Roman antiquity to the Early Middle Ages.
  • Feudalism, manorialism, and the socio-economic structures of Europe.
  • The political and religious influence of the Catholic Church.
  • +2 more topics
  476 CE1066 CE+3

• World History II (1500 — Present)

  • Transformation from late medieval feudalism to global maritime empires
  • The intellectual shifts of the Scientific Revolution and Enlightenment
  • Waves of political revolution and the rise of industrial capitalism
  • +2 more topics
  14531789+4

• Ancient Civilizations

  • Evolution of Mesopotamian city-states and the invention of writing
  • The Nile River's role in Egyptian political and religious stability
  • The Indus Valley's sophisticated urban planning and drainage systems
  • +2 more topics
  Hammurabi's CodeNile Inundation = Agricultural Surplus = Divine Kingship+2

• Modern European History

  • Transformation from absolute monarchy to democratic nation-states
  • Impact of the Industrial Revolution on social and economic structures
  • Rise of competing ideologies: Liberalism, Socialism, and Nationalism
  • +2 more topics
  17891815+4

• World History I (Prehistory — 1500)

  • Origins of humanity and the transition from foraging to agriculture.
  • Development of river valley civilizations in Mesopotamia, Egypt, and Asia.
  • The Golden Ages of classical Greece, Rome, Han China, and Gupta India.
  • +2 more topics
  Agricultural Surplus = Population Growth + Labor SpecializationHammurabi's Code+3

• Asian History

  • Evolution of major civilizations in East, South, and Southeast Asia
  • Rise and fall of the Silk Road and maritime trade networks
  • Impact of Confucianism, Buddhism, and Hinduism on social structures
  • +3 more topics
  Mandate of HeavenMeiji Restoration (1868)+3

• African History

  • Evolutionary origins and early migrations from the African Rift Valley
  • Rise of major empires including Mali, Songhai, Ghana, and Axum
  • Impact of Trans-Saharan and Trans-Atlantic trade networks
  • +2 more topics
  Mali Empire peaked under Mansa Musa c. 1312-1337The Berlin Conference of 1884-1885 partitioned Africa+2

• Latin American History

  • Pre-Columbian civilizations: Aztec, Maya, and Inca structures
  • Colonial period under Spanish and Portuguese imperial rule
  • 19th-century independence movements and state formation
  • +3 more topics
  14941810-1825+3

• Human & Physical Geography

  • Examination of spatial patterns between humans and the natural environment.
  • Analysis of population dynamics, migration, and cultural landscapes.
  • Study of physical systems including climate, landforms, and ecosystems.
  • +3 more topics
  Population Density = Total People / Land AreaRate of Natural Increase = Birth Rate - Death Rate+4

• Sociology

  • Evolution of social structures from traditional to modern eras
  • Analysis of power dynamics, social stratification, and inequality
  • Examination of the relationship between individuals and institutions
  • +3 more topics
  Social Action = (Motivations + Values) / Social ContextMechanical Solidarity vs. Organic Solidarity+4

• International Relations

  • State sovereignty and the Westphalian system's origins in 1648
  • Realism, Liberalism, and Constructivism as primary analytical lenses
  • The role of international organizations like the UN and NATO
  • +3 more topics
  Power = Resources * Strategy * WillSecurity Dilemma+2

• Cultural Anthropology

  • Definition and history of cultural anthropology as a global social science
  • Analysis of kinship, social structures, and systems of power within groups
  • The application of ethnographic fieldwork and participant observation methods
  • +2 more topics
  Culture = Learned + Shared + Symbolic + Integrated + DynamicRelativism vs. Ethnocentrism+2

• Political Science

  • Evolution of state sovereignty and legitimate authority
  • Analysis of classical and modern political ideologies
  • Comparative examination of global governance structures
  • +3 more topics
  P = M + D - A (Klitgaard's Corruption Formula)Hegemonic Stability Theory+2

• Philosophy

  • Evolution of Western thought from Pre-Socratic origins to modernism
  • Analysis of metaphysics, epistemology, ethics, and political theory
  • Critical examination of the Socratic method and logical frameworks
  • +3 more topics
  Law of IdentityLaw of Non-Contradiction+4

🗣

Foreign Language

4 topics

• Year 1 — Foundations (Spanish)

  Grade 9
  • Alphabet, pronunciation, numbers
  • Greetings, family, weather
  • Present tense regular verbs (-ar, -er, -ir)
  • +1 more topics
  HablarComer+1

• Year 2 — Building Fluency

  Grade 10
  • Preterite & imperfect past tenses
  • Reflexive verbs; object pronouns
  • Comparisons, superlatives

• Year 3 — Advanced Grammar

  Grade 11
  • Future & conditional tenses
  • Subjunctive (present & past)
  • Complex sentences, relative pronouns

• Year 4 — AP / Advanced

  Grade 12
  • AP themes: global challenges, identity, beauty
  • Essays, oral presentations, debate
  • Authentic literature (Borges, García Márquez)

✦

Electives

29 topics

• Computer Science

  • Binary, hex, data representation
  • Algorithms: sequencing, selection, iteration
  • AP CSA: Java classes, inheritance, recursion
  • +1 more topics
  Big-O

• Economics & Personal Finance

  • Scarcity, opportunity cost
  • Supply/demand graphs
  • Banking, credit, taxes, retirement (401k/IRA)
  • +1 more topics

• Visual Art

  • Elements: line, shape, value, color, texture
  • Principles: balance, contrast, rhythm, unity
  • Color theory & color wheel
  • +1 more topics

• Music

  • Notation, time & key signatures
  • Major/minor scales; circle of fifths
  • Intervals, chords, harmony

• Health & PE

  • Nutrition, MyPlate, macros
  • Cardio, strength, flexibility
  • Mental health & first aid (age-appropriate, non-clinical)

• Psychology (AP)

  • History & approaches; research methods
  • Biological bases of behavior; sensation & perception
  • Learning, memory, cognition
  • +2 more topics

• Speech & Debate

  • Argumentation: claim, warrant, evidence
  • Public speaking: delivery, pacing, eye contact
  • Lincoln-Douglas & policy debate basics
  • +1 more topics

• Journalism

  • Inverted pyramid; the 5 Ws + H
  • Interviewing & sourcing; on/off record
  • Press ethics: accuracy, attribution, corrections
  • +1 more topics

• Drama / Theater

  • Stage directions, blocking, projection
  • Script analysis, character motivation
  • Genres: tragedy, comedy, modern realism

• Civics & Citizenship

  • Voting rights & elections
  • Federal, state, local government roles
  • Civic participation; jury duty; public records

• Marketing

  • Analyzing consumer behavior to drive strategic brand value.
  • The 4 Ps: Product, Price, Place, and Promotion frameworks.
  • Market segmentation, targeting, and competitive positioning.
  • +3 more topics
  Customer Lifetime Value (CLV) = (ARPU * Margin) / ChurnReturn on Investment (ROI) = (Net Profit / Total Cost) * 100+3

• Financial & Managerial Accounting

  • Distinguishing between external reporting and internal decision-making.
  • Mastery of the four primary financial statements and GAAP principles.
  • Analysis of product costing, CVP analysis, and overhead allocation.
  • +3 more topics
  Assets = Liabilities + EquityNet Income = Revenue - Expenses+4

• Business Fundamentals

  • Foundations of business ownership, organizational structures, and legal entities.
  • Core financial statements, budgeting basics, and accounting principles.
  • Marketing strategies, consumer behavior, and brand positioning fundamentals.
  • +2 more topics
  Accounting EquationNet Income+3

• Entrepreneurship

  • Identifying market gaps and validating business opportunities
  • Developing lean business models and value propositions
  • Financial modeling, unit economics, and funding strategies
  • +3 more topics
  CAC = Total Marketing Costs / Number of New CustomersLTV = Average Order Value * Frequency * Lifespan+3

• Personal & Corporate Finance

  • Mastering time value of money for personal and firm decisions
  • Analyzing capital budgeting and investment appraisal techniques
  • Understanding capital structure, leverage, and the cost of capital
  • +3 more topics
  FV = PV * (1 + r)^nWACC = (E/V * Re) + (D/V * Rd * (1 - T))+4

• Robotics & Mechatronics

  • Design and modeling of multi-degree-of-freedom robotic systems
  • Integration of microcontrollers, sensors, and actuator feedback
  • Kinematics and dynamics for precise position and velocity control
  • +3 more topics
  V = I * R (Ohm's Law for circuit analysis)Tau = J * alpha (Torque equals inertia times angular acceleration)+4

• Artificial Intelligence & Machine Learning

  • Foundations of supervised and unsupervised learning algorithms.
  • Mathematical principles behind neural networks and deep learning.
  • Optimization techniques including gradient descent and backpropagation.
  • +3 more topics
  Loss Function (MSE)Perceptron Output+4

• Cybersecurity

  • Foundational principles of the CIA Triad: Confidentiality, Integrity, Availability
  • Network security protocols, firewall architectures, and intrusion detection
  • Symmetric and asymmetric cryptographic systems including RSA and AES
  • +3 more topics
  RSA EncryptionRSA Decryption+4

• Web Development

  • Mastering the core stack: Structure with HTML, styling with CSS, and logic with JavaScript.
  • Responsive design principles and cross-browser compatibility for modern web access.
  • Front-end frameworks and back-end integration via RESTful APIs and JSON data.
  • +2 more topics
  Box ModelSpecificity+3

• Mobile App Development

  • Architectural patterns including MVC, MVVM, and BLoC for state management
  • Cross-platform versus native development paradigms: Flutter, React Native, Swift
  • Mobile user interface design principles and responsive layout constraints
  • +3 more topics
  Responsiveness = Input Latency < 100msPhysical Pixels = Logic Pixels * Device Pixel Ratio+3

• Data Science & Analytics

  • Foundations of exploratory data analysis and statistical inference
  • Supervised learning techniques including regression and classification
  • Unsupervised approaches for clustering and dimensionality reduction
  • +3 more topics
  MSE = (1/n) * sum((y_i - y_hat_i)^2)P(A|B) = [P(B|A) * P(A)] / P(B)+3

• Game Design & Development

  • Core mechanics, dynamics, and aesthetics framework (MDA).
  • Game loop construction and player feedback systems.
  • level design principles and environmental storytelling.
  • +3 more topics
  Expected Value (EV) = Sum(Probability * Outcome)Downtime = (Total Turn Time) * (Players - 1)+3

• Graphic Design

  • Mastering the fundamental elements and principles of visual design
  • Developing proficiency in typography, color theory, and layout
  • Applying technical skills in industry-standard digital software
  • +2 more topics
  Golden RatioRule of Thirds+3

• Film Studies

  • The evolution of cinematic grammar from silent films to digital media
  • Formalist and realist approaches to film theory and mise-en-scene
  • Genre conventions, iconography, and the evolution of narrative structure
  • +3 more topics
  A + B = C (Kuleshov EffectAspect Ratio = Image Width / Image Height+3

• Culinary Arts & Nutrition

  • Mastering fundamental knife skills and professional heat transfer methods
  • Analyzing macro and micronutrient profiles in recipe development
  • Understanding the chemical reactions of the Maillard effect and caramelization
  • +3 more topics
  Energy BalanceBakery Percentage+3

• Photography

  • Mastering the exposure triangle: aperture, shutter speed, and ISO
  • Understanding focal length, depth of field, and lens selection
  • Applying the rule of thirds and advanced framing techniques
  • +3 more topics
  Exposure Value (EV) = log2(N^2 / t)N = f-number (Aperture)+3

• Agricultural Science

  • Evolution of agricultural practices from subsistence to high-tech industrial models
  • Principles of soil health including nutrient cycling and physical composition
  • Biological foundations of plant physiology and animal husbandry systems
  • +3 more topics
  PhotosynthesisSoil Texture+4

• Environmental Studies & Sustainability

  • Understanding planetary boundaries and ecosystem services in the Anthropocene.
  • Analyzing renewable energy systems and the transition to a circular economy.
  • Evaluating policy frameworks for climate mitigation and social equity.
  • +3 more topics
  I = P * A * T (Impact = Population * Affluence * Technology)Energy Return on Investment (EROI) = Energy Delivered / Energy Required+4

• Physical Education & Sports Science

  • Anatomy and physiology basics for sports performance.
  • Biotmechanics of human movement and technique analysis.
  • Principles of sports psychology and mental training.
  • +3 more topics
  Work = Force x DisplacementPower = (Force x Distance) / Time+4

★

Advanced Placement (AP) Tracks

22 topics

• AP Calculus AB / BC

  • Limits, continuity, derivatives, integrals
  • BC adds: series, parametric, polar, vectors
  MVTTaylor

• AP Statistics

  • Exploring data; sampling & experiments
  • Probability, random variables, distributions
  • Inference: confidence intervals, hypothesis tests
  z-scoreSE mean

• AP World / European History

  • Periodization & global comparison
  • DBQ and LEQ essay structures

• AP English Language & Composition

  • Rhetorical analysis, synthesis, argument essays
  • SOAPSTone; rhetorical appeals

• AP Computer Science Principles

  • Algorithms, abstraction, data, internet, impact
  • Create Performance Task

• AP Biology

  • Big Idea 1 — Evolution: natural selection, phylogeny, speciation
  • Big Idea 2 — Energetics: enzymes, cellular respiration, photosynthesis
  • Big Idea 3 — Information: DNA replication, gene expression, regulation
  • +2 more topics
  Hardy-WeinbergChi-square+2

• AP Chemistry

  • Atomic structure, periodicity, bonding (VSEPR, hybridization)
  • Stoichiometry, gases, solutions, intermolecular forces
  • Kinetics: rate laws, mechanisms, activation energy
  • +3 more topics
  Ideal gasArrhenius+3

• AP Physics 1: Algebra-Based

  • Kinematics in 1D and 2D; projectile motion
  • Newton's laws, friction, free-body diagrams
  • Work, energy, power; conservation of energy
  • +3 more topics
  KinematicsNewton 2+4

• AP Physics 2: Algebra-Based

  • Fluid statics and dynamics (pressure, buoyancy, continuity, Bernoulli)
  • Thermodynamics: kinetic theory, laws, PV diagrams, heat engines
  • Electrostatics: Coulomb's law, electric field, potential, capacitors
  • +3 more topics
  Bernoulli1st Law+4

• AP Physics C: Mechanics (Calculus-Based)

  • Kinematics with calculus; vector analysis of motion
  • Newton's laws with variable forces; drag and integration
  • Work-energy theorem via line integrals; conservative forces
  • +3 more topics
  v = dx/dt; a = dv/dt; x = ∫ v dtF = m a = m dv/dt; Impulse = ∫ F dt+3

• AP Physics C: Electricity & Magnetism (Calculus-Based)

  • Electrostatics: Coulomb's law, Gauss's law, electric potential
  • Conductors, capacitors, dielectrics; energy in fields
  • DC circuits: RC transients via differential equations
  • +3 more topics
  GaussPotential+4

• AP Environmental Science (APES)

  • Earth systems: geology, atmosphere, hydrology, biogeochemical cycles
  • Ecosystems: biomes, energy flow, trophic levels, biodiversity
  • Populations: human demography, growth models, carrying capacity
  • +3 more topics
  Population growthDoubling time+2

• AP United States History

  • Pre-Columbian societies and the Impact of European exploration
  • Colonial development and the Revolutionary era (1754-1783)
  • Sectionalism, the Civil War, and Reconstruction (1844-1877)
  • +2 more topics
  MercantilismMissouri Compromise (1820)+3

• AP European History

  • Transformation of Europe from late Middle Ages through the present
  • Evolution of political power from absolutism to modern democracy
  • Impact of the Renaissance, Reformation, and Scientific Revolution
  • +2 more topics
  RenaissanceReformation+3

• AP Macroeconomics

  • Measurement of economic performance via GDP, inflation, and unemployment.
  • Aggregate demand and supply models for short and long-run equilibrium.
  • The financial sector, money supply, and Federal Reserve monetary policy.
  • +2 more topics
  GDP = C + I + G + (X - M)CPI = (Cost of Market Basket / Cost in Base Year) * 100+4

• AP Microeconomics

  • Scarcity, choice, and opportunity costs in decision making
  • Supply and demand mechanics and market equilibrium
  • Production costs, revenues, and firm profit maximization
  • +2 more topics
  Total Utility = Sum of Marginal UtilitiesElasticity = % Change in Quantity / % Change in Price+4

• AP US Government & Politics

  • Foundational documents including Declaration and Constitution
  • Structure and functions of the three branches of government
  • Civil liberties and civil rights through SCOTUS precedents
  • +2 more topics
  Pluralist DemocracyElite Democracy+3

• AP Psychology

  • Scientific foundations of psychology and research methodology
  • Biological bases of behavior, sensation, and perception
  • Cognitive psychology including learning, memory, and intelligence
  • +3 more topics
  MeanStandard Deviation+4

• AP Human Geography

  • Analyze spatial patterns and human-environment interactions.
  • Examine population dynamics, migration, and demographic shifts.
  • Explore cultural landscapes and the diffusion of ideas/languages.
  • +2 more topics
  Doubling Time (Rule of 70) = 70 / r (percentage growth rate)Rate of Natural Increase (RNI) = (CBR - CDR) / 10+3

• AP Comparative Government & Politics

  • Comparison of six diverse political systems: UK, China, Russia, Iran, Mexico, Nigeria
  • Analysis of power, authority, and the legitimacy of regimes over time
  • Examination of political institutions and executive-legislative relations
  • +2 more topics
  Plurality SystemProportional Representation (PR)+3

• AP Spanish Language & Culture

  • Mastery of the six thematic units including Global Challenges and Families.
  • Development of interpretive, interpersonal, and presentational communication.
  • Deep dive into cultural products, practices, and perspectives in Spanish.
  • +2 more topics
  Persuasive Essay = Source 1 (Article) + Source 2 (Chart) + Source 3 (Audio)Cultural Comparison = Community A (Target) vs. Community B (Home)+2

• AP Chinese Language & Culture

  • Develop advanced interpersonal, interpretive, and presentational communication
  • Master the three modes of communication in diverse cultural contexts
  • Gain deep insights into Chinese history, traditions, and societal changes
  • +3 more topics
  Interpersonal + Interpretive + Presentational = Proficiency5 Cs+1

🌐

Additional World Languages

4 topics

• French — Survey (Years 1–4)

  • Pronunciation, articles, gender & number
  • Present, passé composé, imparfait, futur, conditionnel
  • Subjonctif; AP themes & Francophone literature

• German — Survey

  • Cases (Nom/Akk/Dat/Gen); strong vs weak verbs
  • Word order; modal verbs; Perfekt & Präteritum

• Mandarin Chinese — Survey

  • Pinyin & 4 tones; radicals & stroke order
  • Measure words; topic-comment structure
  • HSK 1–4 vocabulary themes

• Latin — Survey

  • Five declensions; four conjugations
  • Caesar, Vergil; derivative study

🎓

Study Skills & College Prep

4 topics

• Effective Study Methods

  • Spaced repetition; active recall; Feynman technique
  • Cornell notes; Pomodoro time-blocking
  • Reading strategies: SQ3R

• SAT / ACT Preparation

  • Section structure & timing
  • Reading: evidence-based questions
  • Math: no-calc strategies; grid-ins
  • +1 more topics

• College Applications

  • Common App, Coalition, UC application
  • Personal statement & supplemental essays
  • Letters of recommendation; FAFSA basics

• Digital Literacy & Online Safety

  • Evaluating sources; lateral reading
  • Privacy, passwords, two-factor auth
  • Responsible AI use & academic integrity