College

(Algebra)

•  Functions
• Types (linear, quadratic, polynomial, rational, exponential, logarithmic), properties, transformations 
• Equations and Inequalities
• Solving linear, quadratic, absolute value, and rational equations/inequalities
• Systems of Equations
• Solving linear and non-linear systems using substitution, elimination, matrices
• Complex Numbers
• Operations, polar form, De Moivre's theorem
• Sequences and Series
• Arithmetic and geometric sequences, series, binomial theorem
  

(Calculus I)

• Limits and Continuity
• Understanding limits, computing limits, continuity of functions 
• Derivatives 
• Definition, rules (product, quotient, chain), implicit differentiation
• Applications of Derivatives
• Critical points, optimization, motion problems, related rates
• Integrals
• Definite and indefinite integrals, Fundamental Theorem of Calculus, basic integration techniques 
• Applications of Integrals
• Area under a curve, volume of solids of revolution, work, average value
  

(Calculus II) 

• Advanced Integration Techniques 
• Integration by parts, partial fractions, trigonometric integrals, substitution 
• Sequences and Series 
• Convergence tests, power series, Taylor and Maclaurin series
•  Parametric Equations and Polar Coordinates
• Graphing, derivatives, and integrals in polar form
• Applications of Integrals
• Arc length, surface area, center of mass, differential equations 
• Improper Integrals 
• Convergence and evaluation
  

(Statistics I)

• Descriptive Statistics
• Mean, median, mode, standard deviation, variance, histograms 
• Probability Concepts 
• Basic probability, conditional probability, independence, Bayes' theorem
• Distributions
• Binomial, normal, Poisson distributions
• Inferential Statistics
• Sampling, confidence intervals, hypothesis testing (z-tests, t-tests) 
• Correlation and Regression 
• Scatter plots, correlation coefficients, linear regression
  

(Statistics II ) 

• Advanced Inferential Statistics 
• ANOVA, chi-square tests, non-parametric tests
• Regression Analysis
• Multiple regression, logistic regression, model selection 
•  Time Series Analysis 
• Trends, seasonal components, forecasting methods 
•  Multivariate Statistics 
• Factor analysis, cluster analysis, principal component analysis
• Bayesian Statistics
• Prior and posterior distributions, Bayesian inference
  

(Linear Algebra)

• Vectors and Vector Spaces 
• Vector operations, linear combinations, bases, dimension 
• Matrices
• Operations, determinants, inverses, rank, systems of linear equations 
• Eigenvalues and Eigenvectors
• Calculation, diagonalization, applications
• Linear Transformations
• Definition, kernel, image, matrix representation 
• Orthogonality
• Inner product, orthogonal projections, Gram-Schmidt process