The following is a comprehensive list of high school and college courses in math offered

at Math Academy

High School Level Courses



Addition, subtraction, multiplication, and division; fractions, percents, and decimals; math with multi-digit numbers; operations with negative numbers; factoring integers; greatest common factor; least common multiple; inequalities; scientific notation and significant digits; place value; word problems


Graphing in the x-y plane; lines and rays; midpoint and distance formulas; absolute value; prime factorization of integers; greatest common factors; square roots and radicals; irrational numbers; polynomials and rational expressions; equations; order of operations; factoring polynomials

Algebra I

Use of variables; polynomials and quadratics; exponents; radical expressions; rational expressions; logarithms; graphing in the x-y plane; coordinate pairs; solving linear equations; systems of equations; inequalities; factoring polynomials; point-slope form and slope-intercept form; parallel and perpendicular lines

Algebra II

Simplifying expressions; radical expressions; complex and imaginary numbers; exponential growth and decay; operations with logarithms; quadratic equations and quadratic formula; techniques for factoring polynomials; completing the square; rational equations; matrix properties; function notation; function transformations and graphing; sequences and series; basic trigonometric functions; conic sections; binomial theorem; partial fraction decomposition


Trigonometric functions; inverse trigonometric functions; the unit circle; radians and degrees; trigonometric identities; Pythagorean Theorem; right triangle trigonometry; special right triangles; complementary and supplementary angles; non-right triangle trigonometry; double-angle and half-angle formulas; law of sines and cosines; graphing trigonometric functions; polar and spherical coordinates; Pythagorean identities; Triangle Inequality

Geometry I

Graphing in the Cartesian plane; midpoint and distance formulas; the unit circle; right triangle geometry; trigonometric functions and identities; conic sections; area and perimeter formulas; circles, arc lengths, cords, and radii; finding sides and angles of triangles; relationship between angles of polygons; similar triangles; geometric theorems and proofs; volume and surface area of 3D shapes; Pythagorean Theorem

Geometry II

Geometric proofs; proof techniques and logical symbols; constructions with compass; trigonometric identities; congruence of shapes; similar figures; transformations of shapes and functions; solving right triangles; law of sines and cosines; inscribed and circumscribed shapes; vectors and matrices; polar and spherical coordinates; areas of irregular shapes

3-Dimensional Geometry

Platonic solids; solid geometry; graphing in the x-y-z plane; functions in several variables; graphs and intersections of planes; polyhedra and non-polyhedra; hyperplanes and polytopes; conic sections in 3 dimensions; angles between lines and planes; geodesics; cylindrical and quadratic surfaces; change of coordinates; polar, spherical, and cylindrical coordinates; geometry in higher dimensions

Advanced Euclidean Geometry

Constructions; Hilbert’s axioms; Euclid’s postulates; proof methods and classical logic; conic sections; hyperplanes and lattices; vector geometry; parallel postulate; Triangle Angle Sum Theorem; Pythagorean Theorem; Thales’ Theorem; congruence of segments and angles; congruent and similar triangles

New York State Regents

Test preparation; Algebra I (Common Core), Algebra II (Common Core), Geometry (Common Core), Trigonometry/Algebra II, Physics


Function notation; domain and range; inverse functions; graphing and simplifying rational functions; factoring polynomials and finding zeroes; vertical, horizontal, and slant asymptotes; maxima and minima; limits; tangent lines; curve-sketching; trigonometric and inverse trigonometric functions; matrices and vectors; dot and cross products; sequences and series

AP Calculus

Representation of functions; rate of change; limits at a point; infinite limits; two-sided limits; continuity of functions; criteria for differentiability; first and higher derivatives; derivatives of trigonometric functions; product and quotient rule; chain rule; implicit differentiation; optimization; L’Hospital’s Rule and indeterminate forms; Reimann sums; average value theorem; definite and indefinite integrals; antiderivative techniques; u-substitution; trig substitution; solids of revolution; differential equations; Fundamental Theorem of Calculus; modeling physical and biological systems using calculus; Liebniz notation; parametric functions

AP Statistics

Graphical representations of data; measuring center, spread, and position; bivariate data and scatterplots; categorical data; correlation and least-squares; transforming non-linear data using logarithms and power functions; sampling and experimentation; probability; univariate data; normal distribution; t-distribution; chi-square test; statistical inference; tests of significance; sampling and experimentation; methods of data collection; hypothesis testing; population parameters

Math Competitions/Olympiads

Practice problems for math competitions; math puzzles; customized curriculum to prepare for the competitions


Kinematics and the physics of motion; Newton’s laws of motion; position, velocity, acceleration, and jolt; force; free-body diagrams; momentum; work; rotational motion; centripetal and centrifugal force; angular and tangential velocity; angular momentum; torque; elastic and inelastic collisions; kinetic and potential energy; inertia; rotational energy; fluid mechanics; electricity and magnetism; current, voltage, and power; circuit diagrams; Coulomb’s Law; Kirchoff’s Current and Voltage Laws; direct and alternating current; resistance and capacitance; induction; thermodynamics and heat transfer; entropy; thermal energy; waves; diffraction; the Doppler Effect; equations of waves; wavelength, amplitude, and frequency; reflection and refraction; vibrations; light and sound waves; longitudinal waves; polarization; particle physics; subatomic particles; elementary particles; matter and radiation; quantum field theory

AP Computer Science

Java programming language; object-oriented programming; program design; data abstraction and encapsulation; class design and implementation; implementation techniques; procedural abstraction; declaration of variables, constants, and classes; iteration; testing and debugging; finding and correcting errors; number representation in different bases; data structures; lists and arrays; algorithms; traversals, insertions, and deletions; searching and sorting


High School Level Test Prep


High School Admissions Test


Test prep and test taking strategies; algebra and functions; geometry; numbers and operations; data analysis

Mathematics Levels 1 and 2; Physics


Test prep and test taking strategies; pre-algebra; elementary and intermediate algebra; coordinate and plane geometry; trigonometry

Reading Comprehension; Logical Reasoning; Scrambled Paragraphs; Mathematics; Multiple Choice Questions; Various mathematical topics; Basic math; Algebra; Factoring; Substitution; Geometry; Basic Coordinate Graphing; Logic; Word Problems

College-Undergraduate Level Courses

College Algebra

Solving quadratic equations; solving linear equations; factoring polynomials; completing the square; exponents; logarithms; radical expressions; rational expressions; graphing in the x-y plane; midpoint and distance formulas; parallel and perpendicular lines; solving linear equations; systems of equations; inequalities; functions and function notation; function transformation and graphing; matrix properties; basic trigonometric functions; conic sections

Representation of functions; rate of change; limits at a point; infinite limits; two-sided limits; continuity of functions; criteria for differentiability; first and higher derivatives; derivatives of trigonometric functions; product and quotient rule; chain rule; implicit differentiation; optimization; Liebniz notation; Extreme Value Theorem; Mean Value Theorem; inflection points; first and second derivative tests for finding inflection points

L’Hospital’s Rule and indeterminate forms; Reimann sums; average value theorem; definite and indefinite integrals; antiderivative techniques; u-substitution; trig substitution; integration by parts; partial fraction decomposition; solids of revolution; differential equations; Fundamental Theorem of Calculus; modeling physical and biological systems using calculus; differentiation under the integral

Calculus 3

Parametric functions; calculus in polar, spherical, and cylindrical coordinates; multi-variable calculus; partial derivatives; Green’s Theorem; Stokes’ Theorem; vector calculus; dot and cross products; sequences and series; convergence of series; harmonic, geometric series, and power series; Taylor and Maclaurin series; Fourier series; radius of convergence; ratio test; comparison test; alternating series test; root test

Slope fields; separation of variables; Fourier Transforms; Laplace Transforms; Taylor and Maclaurin series; Bessel Functions; general and particular solution to differential equations; damped harmonic motion; oscillation problems; bifurcations; non-homogeneous differential equations; strategies for non-linear differential equations; boundary value problems; dynamical systems; existence and uniqueness; reduction of order method; Cauchy-Euler Equations

Partial Differential Equations

Distribution theory; Fourier transforms; Laplace transforms; Schrodinger equations; Green’s theorem; Euler-Lagrange equations; boundary condition; boundary value problems; Dirichlet problems; heat and wave equations; Maxwell’s equations; Navier-Stokes equations; Poisson’s equation; Green’s function; applications of partial differential equations; numerical methods for finding solutions

Matrix addition and subtraction; matrix multiplication; matrix row operations; matrix inversion; transpose matrices; skew and zsymmetric matrices; determinants; solving systems of equations; Gaussian elimination; reduced row echelon form; rank of a matrix; Cramer’s Rule; minors and cofactors; eigenvalues and eigenvectors; vector spaces; orthogonality; transformation matrices; vector spaces; subspaces; linear span; projection; matrix decompositions

Advanced Statistics: Fundamentals and axioms; combinatorial probability; conditional probability and independence; binomial, poisson and normal distributions; law of large numbers and the central limit theorem and random variables and generating functions.

Graduate Level Courses

Abstract Algebra

Group theory; abelian groups; cyclic groups and generators; subgroups; simple groups; dihedral groups; finite groups; homomorphisms and isomorphisms; group actions; kernel of a function; Lagrange’s Theorem; ring theory; integral domains; field properties; algebra over a field; field extensions; norms; Gaussian integers; ideals; quaternions; algebraic numbers; polynomial fields; lie algebra; Galois theory

Composite numbers; prime numbers; divisors; Euclid’s algorithm and divisibility; square-free objects; modular arithmetic and congruence; Fermat’s Little Theorem; Euler’s totient function; Chinese Remainder Theorem; quadratic residue; Diophantine equations; prime numbers; Lagrange’s theorem; combinatorical theorem; primality tests; algebraic number theory

Limits of sequences and functions; arithmetic, geometric, and harmonic series; convergence and divergence of series; Cauchy sequence; power series; telescoping series; alternating series; Fourier series; pointwise, uniform, and absolute convergence; tests for convergence; integral test; ratio test; direct comparison test; limit comparison test; root test; alternating series test; Dirichlet’s test; continuity of functions; uniform and absolute continuity; differentiability of functions; derivatives; partial derivatives; integrals and antiderivatives; Fundamental Theorem of Calculus; multiple integrals; differentiating under the integral; Reimann sums; measure theory; compactness; metric spaces; solution of differential equations; change of variables

Analytic functions; complex differentiation and integration; Cauchy integral formula; Laplace transforms; Power series, Taylor series, and Laurent series; residue theory; complex analysis; isometries in the complex plane; conformal mapping; power series; uniform convergence; radius of convergence; poles; zeroes; singularities; branch points; countour integrals; gamma and beta functions; Reimann zeta functions; Reimann surfaces; infinite products; complex dynamics

Topological spaces; uniform and metric spaces; open and closed sets; continuity; bases and subbases; open cover; limit point; Blaire category theorem; compact spaces; connectedness; separation axioms; Kolmogorov, Frechet, and Haudsorff spaces; Banach spaces; Lp spaces; normal space; tensor products; finite products; order theory; homotopy equivalence; algebraic topology; differential topology; topological and differentiable manifolds; polytopes; covering spaces; vector fields; Frobenius Theorem; Lie groups; Stokes’ Theorem; geometric topology; knot theory

Differential Geometry

Curvature; differential geometry of surfaces; first and second fundamental forms; calculus on manifolds; Reimannian manifolds; Finsler manifolds; connections; Levi-Civita connection; tensor analysis; lie groups; bundles and connections; Symplectic geometry; differential topology; critical values; diffeomorphism; character classes; non-Euclidean geometry; geodesics; symmetric spaces; complex manifolds; index theory; homogeneous spaces

Complex manifolds; Reimannian manifolds; geodesics; symmetric spaces; Lie groups; sympletic geometry; conformal geometry; Hodge theory and Fredholm theory; representation theory; projective spaces; non-Euclidean geometry; finite geometry; computational geometry; discrete geometry; algebraic geometry; fractals

Normed vector spaces; Hilbert spaces; Euclidean space; Banach spaces; Lp spaces; duality and separation theory; function spaces; locally convex spaces; Banach-Steinaus theorems; orthonormal basis; uniform boundedness; spectral theory; open mapping theorem; Hausdorff space; operator theory; real and complex algebras; topological vector spaces; wavelets

Iterative methods; rate of convergence; series acceleration; error analysis; interval arithmetic; significant figures; least squares; numerical algorithms; numerical linear algebra; eigenvalues; orthogonalization; approximation formulas; interpolation methods; spline, polynomial, and trigonometric interpolation; linear systems; root-finding algorithms for nonlinear equations; numeric integration and differentiation; numerics for ordinary and partial differential equations; optimization; finite element methods; grids and meshes; Monte Carlo method


Encryption and decryption; cryptanalysis; ciphers; zero knowledge proof; concurrency and protocol security; symmetric-key algorithms; asymmetric-key algorithms; authentication; transport and exchange theory; weak keys; robustness; symmetric algorithms; hash functions; attack models; database security; cryptographic game theory; multivariate cryptography; quantum cryptography; stenography

Graduate Level Test Prep


Quantitative reasoning; arithmetic; algebra; geometry; data analysis; numerical reasoning


Quantitative reasoning; data sufficiency; arithmetic; algebra; geometry; word problems; combinatorics; data analysis

Share This
Hey there! Glad you found us.

Hey there! Glad you found us.

sign up today and get your first 30 minute session free

Great! You will be redirected to our booking page where we are waiting for a simple steps to booking your session. You are almost done!