| Basic Math |
- Arithmetic with Decimals, Fractions or Mixed Numbers
- Arithmetic with Whole or Signed Numbers
- Bases, other than base 10
- Basic Problem Solving
- Dimensional Analysis, Units of Measure
- Exponents and Radicals
- Logic:
- Negations
- conjunction
- disjunction
- conditionals
- bi-conditionals
- truth tables
- equivalent statements
- logical arguments
- Order of Operations
- Percentages and Percent Change
- Ration and Proportion
- Reading and Interpreting Charts and Graphs
- Rounding and Estimating
- Scientific Notation
- Sets:
- notation
- operations
- Venn diagrams
- survey problems
- The Real Number System
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| Liberal Arts Math |
- Apportionment:
- quota rule and paradoxes
- Hamilton’s method
- Jefferson’s method
- Adam’s method
- Huntington-Hill method
- Averages:
- mean
- median
- mode
- frequency distributions
- percentile rank
- Basic Probability:
- basic theoretical probability
- experimental probability
- odds
- Brief Survey of Graph Theory:
- introductory Euler and Hamilton circuits and paths
- Fleury’s algorithm
- nearest-neighbor and repetitive nearest neighbor algorithms
- cheapest link algorithm minimal spanning trees
- Kruskal’s algorithm
- Consumer Mathematics:
- simple interest
- compound interest
- ordinary annuities
- mortgages
- amortization
- average daily balance
- Fair Division:
- divider-chooser
- lone-divider
- lone-chooser
- last-diminisher
- sealed bids
- markers
- Introductory Counting:
- fundamental counting principle
- permutations
- combinations
- Introductory Scheduling:
- Voting:
- voting methods
- fairness criteria
- weighted voting
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| Algebra |
- Algebraic Expressions:
- simplifying
- combining like terms
- properties
- exponents
- radicals
- factoring
- Binomial Theorem
- Complex Numbers
- Conic Sections:
- circles
- parabolas
- ellipses
- hyperbolas
- Elementary Sequences and Series:
- terms of sequences
- arithmetic sequences
- geometric sequences and series
- finite series
- Exponentials and Logarithms:
- graphs
- change of base formula
- logarithm rules
- equations
- exponential growth and decay
- logistic equations
- Functions:
- function notation
- domain/range
- intercepts
- properties
- average rate of change
- piecewise defined functions
- graphs
- transformations
- algebra of functions
- inverses
- variation
- applications
- Graphs/Coordinate Systems:
- plotting
- distance formula
- midpoint formula
- domain and range
- symmetry
- intercepts
- one-to-one
- Inequalities:
- linear
- absolute value
- polynomial
- rational
- graphs
- Linear Programming: geometric approach
- Lines:
- slopes
- equations
- graph
- applications
- Matrices:
- matrix algebra
- Gaussian elimination
- inverses
- determinants
- Cramer’s Rule
- Polynomials:
- roots and multiplicities
- graphs
- long and synthetic division
- fundamental theorem of algebra
- Quadratics:
- equations
- vertex
- properties
- applications
- Rational Expressions/Functions:
- asymptotes
- intercepts
- graphs
- partial fractions
- Solving Equations:
- linear
- quadratic
- quadratic in form
- polynomial rational
- radical
- absolute value
- applications
- Systems of Equations:
- systems of linear equations
- systems of nonlinear equations
- Systems of Inequalities:
- systems of linear inequalities
- systems of nonlinear inequalities
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Linear Algebra
**By scheduled sessions/appointment only; no drop-in tutoring
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- Determinants: properties, Cramer’s Rule
- Eigenvalues and Eigenvectors:
- characteristic equation
- diagonalization
- complex eigenvalues
- positive definite matrices
- quadratic forms
- discrete dynamical systems
- Linear Transformations: image, kernel
- Matrices and systems of linear equations:
- solving systems
- row operations
- echelon form
- homogeneous systems
- types of matrices
- rank of a matrix
- Matrix Algebra:
- matrix operations
- inverses
- matrix equations
- Optimization:
- graphical method of linear programming
- simplex method of linear programming
- Orthogonality:
- dot product and inner product spaces
- Orthogonality
- Gram-Schmidt process
- least squares
- inner product spaces
- Vectors and Vector Spaces:
- vector equations
- subspaces
- null space
- row and column spaces
- bases
- dimension
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| Geometry |
- Basic Definitions: points, lines, rays, angles
- Congruent Triangles
- Circles, Polygons, Quadrilaterals
- Coordinate Geometry: midpoint, slope, distance formula
- Perimeters, Areas, Volumes and Applications
- Planes and Parallel Lines
- Similar Figures
- Theorems, Postulates, and Proofs
- Triangles: angles, types, measurements
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Continuity (definition, intermediate value theorem)
**By scheduled sessions/appointment only; no drop-in tutoring
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- Derivatives:
- definition
- product and quotient rules
- chain rule
- implicit differentiation
- logarithmic and exponential functions
- Hyperbolic Functions:
- Definitions
- Properties
- Derivatives
- Integrals:
- definition/Riemann sums
- definite and indefinite integrals
- fundamental theorem of calculus
- Integration Techniques:
- antiderivatives
- trigonometric integrals
- substitution
- trigonometric substitution
- by parts
- partial fractions
- approximate integrals
- improper integrals
- Limits:
- definition
- limit theorems
- graphs
- trigonometric limits
- L’Hospital’s Rule
- Parametric Equations
- Polar Coordinates
- Sequences and Series:
- convergence of sequences
- absolute and conditional convergence of series
- common series
- integral test
- comparison tests
- alternating series
- ratio test
- root test
- power series Taylor series
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| Calculus (single variable) |
- Applications of Derivatives:
- rates of change
- marginal cost/revenue/profit
- velocity and acceleration
- analysis of graphs
- mean value theorem
- max/min values
- optimization
- related rates
- Newton’s method
- Applications of Integrals:
- areas between curves
- length of curves
- work
- volume
- surface area
- average value
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Calculus II and III (multivariable)
**By scheduled sessions/appointment only; no drop-in tutoring
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- Functions of Several Variables:
- Planes
- Surfaces
- graphs and level curves
- limits
- continuity
- partial derivatives
- chain rules
- directional derivatives
- gradient
- tangent planes
- linear approximation
- extrema
- Lagrange multipliers
- Multiple Integration:
- iterated integrals
- area in the plane
- volume
- change of variables
- mass
- inertia
- surface area
- Jacobians
- Vector Calculus:
- vector fields
- line integrals
- conservative vector fields
- Green’s theorem
- Divergence
- Curl
- surface integrals
- Stokes’ Theorem
- Vectors and Vector-Valued Functions:
- dot product
- cross product
- lines
- curves in space
- differentiation
- integration
- motion in space
- lengths of curves
- curvature
- normal vectors
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Discrete Math
**By scheduled sessions/appointment only; no drop-in tutoring
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- Boolean Algebra:
- Functions
- logic gates
- minimization of circuits
- Counting:
- pigeonhole principle
- permutations
- combinations
- Discrete Probability: Bayes’ Theorem, expected value
- Functions:
- Injections
- Surjections
- Inverses
- composition
- Graphs:
- Representation
- Isomorphism
- Connectivity
- Euler & Hamiltonian paths
- trees
- Integers and Numbers:
- division algorithm
- primes
- Euclidean algorithm/gcd
- integers mod n
- bases other than 10
- Logic:
- propositional logic
- rules of inference
- equivalences
- qualifiers
- Order Relations:
- partially ordered sets
- lattices
- Boolean algebras
- extreme elements and bounds
- Proofs: methods and strategies
- Relations:
- Representations
- Properties
- linear recurrence relations
- equivalence relations
- Sets:
- set operations
- Venn diagrams
- families of sets
- Sequences and Series: explicitly defined, recursion
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Differential Equations
**By scheduled sessions/appointment only; no drop-in tutoring
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- Higher-Order Differential Equations:
- initial-value problems
- boundary-value problems
- homogeneous equations with constant coefficients
- non-homogeneous equations
- reduction of order
- undetermined coefficients
- variation of parameters
- Cauchy-Euler Equation
- solving systems of linear equations by elimination
- nonlinear differential equations
- modeling
- The Laplace Transform:
- definition of the Laplace transform
- inverse transforms, transforms of derivatives
- translations on the saxis
- translations on the taxis
- derivatives of a transform
- transforms of integrals
- transform of a periodic function
- Dirac delta function
- systems of linear equations
- Numerical Solutions of Ordinary Differential Equations:
- Euler methods and error analysis
- Runge-Kutta methods
- multistep methods
- higher-order equations and systems
- second-order boundary value problems
- Series Solutions of Linear Equations:
- solutions about ordinary points
- solutions about singular points
- Solution of First-Order Differential Equations:
- direction fields
- separable equations
- linear equations
- exact equations
- solutions by substitutions
- Riccati equation
- numerical methods
- modeling
- Systems of Linear First-Order Differential Equations:
- homogeneous linear systems (distinct, repeated or complex eigenvalues)
- nonhomogeneous linear systems (solved via undetermined coefficients or variation of parameters)
- matrix exponential
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Trigonometry
**By scheduled sessions/appointment only; no drop-in tutoring
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- Angles and their Measure:
- degrees minutes seconds
- radians
- linear and angular speed
- arc length
- area of sector
- Area of a Triangle
- Basics of Simple Harmonic Motion
- Complex Numbers:
- polar form
- DeMoivre’s Theorem
- Conic Sections:
- circles
- parabolas
- ellipses
- hyperbolas
- Formulas:
- sum and difference formula
- double angle formula
- half angle formulas
- sum-to-product formulas
- product-to-sum formulas
- Graphs of Trigonometric Functions:
- domain
- range
- amplitude
- period
- phase shift
- curve fitting
- Inverse Trig Functions
- Law of Sines, Law of Cosines
- Polar Coordinates: coordinates, polar equations
- Trigonometric Equations
- Trigonometric Functions:
- basic properties
- right triangle trigonometry
- co-terminal angles
- reference angles
- unit circle trigonometry
- Trigonometric Identities: common identities, verifying identities
- Vectors:
- rectangular and polar form
- arithmetic
- unit vectors
- angle between vectors
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| Statistics |
- Descriptive Statistics:
- measures of central tendency
- measures of dispersion
- graphical data display
- summary statistics
- Inferential Statistics:
- confidential intervals (means, proportions, variance, standard deviation)
- hypothesis testing (z tests, t tests, F tests, chi squared tests, one-way ANOVA)
- sample size estimation
- Process and Quality Control: control charts
- Probability:
- counting
- fundamental principles of probability
- discrete and continuous probability distributions
- normal probabilities
- central limit theorem
- Relationships between Variables:
- linear correlation
- simple linear regression
- Understanding Data:
- variable types
- populations and samples
- sampling techniques
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Advanced Statistics
**By scheduled sessions/appointment only; no drop-in tutoring
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- Analysis of Variance:
- variance components
- factorial designs
- complete, incomplete, and randomized block designs
- response surfaces
- split-plot and repeated measures designs
- mixed models
- ANCOVA
- experimental design
- effect sizes
- preplanned comparisons
- post-hoc tests
- power analysis
- Common Families of Distributions:
- discrete and continuous distributions
- transformations and expectations
- expected values
- moments and moment generating functions
- location and scale families
- inequalities and identities
- joint and marginal distributions
- bi-variate transformations
- hierarchical models
- multivariate distributions
- Hypothesis Testing:
- types of error
- most powerful tests
- likelihood ratio tests
- composite hypotheses
- power analysis
- basis of T-tests and F-tests, chi-squared tests for goodness of fit or independence
- f-test for equality of variance
- Multivariate Statistics:
- multivariate regression
- MANOVA
- dimension reduction techniques (PCA, MDS, factor analysis, canonical correlation, discriminant functions, clustering techniques)
- Nonparametric Statistics:
- Kruskal Wallis
- Mann-Whitney
- sign test
- Wilcoxon signed-rank
- Wilcoxon rank sum test
- spearman rank correlation
- Kendall’s tau
- Bootstrapping
- bayes decision rules
- Probability Theory:
- set theory
- conditional probability and independence theorems
- random variables
- density and mass functions
- point estimation
- interval estimation
- sufficient statistics
- likelihood and likelihood ratio tests
- evaluation estimators
- Regression:
- least-squares and maximum likelihood methods
- statistical inference in regression
- confidence and prediction intervals
- classification problems
- boosting algorithm
- multiple linear regression
- model selection techniques
- model checking
- logistic regression
- nonlinear methods
- dummy variables
- modern regression techniques
- time series
- Sampling Theory and Practice:
- sampling distributions
- types of random samples
- sample design
- sample analysis
- variance estimation
- sampling from the normal distribution
- generating a random sample
- imputation and multiple imputation
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