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
 biconditionals
 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

Liberal Arts Math 
 Apportionment:
 quota rule and paradoxes
 Hamilton’s method
 Jefferson’s method
 Adam’s method
 HuntingtonHill 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
 nearestneighbor 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:
 dividerchooser
 lonedivider
 lonechooser
 lastdiminisher
 sealed bids
 markers
 Introductory Counting:
 fundamental counting principle
 permutations
 combinations
 Introductory Scheduling:
 Voting:
 voting methods
 fairness criteria
 weighted voting

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
 onetoone
 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

Linear Algebra
**By scheduled sessions/appointment only; no dropin tutoring

 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
 GramSchmidt process
 least squares
 inner product spaces
 Vectors and Vector Spaces:
 vector equations
 subspaces
 null space
 row and column spaces
 bases
 dimension

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

Continuity (definition, intermediate value theorem)
**By scheduled sessions/appointment only; no dropin tutoring

 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

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

Calculus II and III (multivariable)
**By scheduled sessions/appointment only; no dropin tutoring

 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 VectorValued Functions:
 dot product
 cross product
 lines
 curves in space
 differentiation
 integration
 motion in space
 lengths of curves
 curvature
 normal vectors

Discrete Math
**By scheduled sessions/appointment only; no dropin tutoring

 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

Differential Equations
**By scheduled sessions/appointment only; no dropin tutoring

 HigherOrder Differential Equations:
 initialvalue problems
 boundaryvalue problems
 homogeneous equations with constant coefficients
 nonhomogeneous equations
 reduction of order
 undetermined coefficients
 variation of parameters
 CauchyEuler 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
 RungeKutta methods
 multistep methods
 higherorder equations and systems
 secondorder boundary value problems
 Series Solutions of Linear Equations:
 solutions about ordinary points
 solutions about singular points
 Solution of FirstOrder Differential Equations:
 direction fields
 separable equations
 linear equations
 exact equations
 solutions by substitutions
 Riccati equation
 numerical methods
 modeling
 Systems of Linear FirstOrder Differential Equations:
 homogeneous linear systems (distinct, repeated or complex eigenvalues)
 nonhomogeneous linear systems (solved via undetermined coefficients or variation of parameters)
 matrix exponential

Trigonometry
**By scheduled sessions/appointment only; no dropin tutoring

 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
 sumtoproduct formulas
 producttosum 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
 coterminal angles
 reference angles
 unit circle trigonometry
 Trigonometric Identities: common identities, verifying identities
 Vectors:
 rectangular and polar form
 arithmetic
 unit vectors
 angle between vectors

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, oneway 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

Advanced Statistics
**By scheduled sessions/appointment only; no dropin tutoring

 Analysis of Variance:
 variance components
 factorial designs
 complete, incomplete, and randomized block designs
 response surfaces
 splitplot and repeated measures designs
 mixed models
 ANCOVA
 experimental design
 effect sizes
 preplanned comparisons
 posthoc 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
 bivariate transformations
 hierarchical models
 multivariate distributions
 Hypothesis Testing:
 types of error
 most powerful tests
 likelihood ratio tests
 composite hypotheses
 power analysis
 basis of Ttests and Ftests, chisquared tests for goodness of fit or independence
 ftest 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
 MannWhitney
 sign test
 Wilcoxon signedrank
 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:
 leastsquares 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
