Techniques for building and interpreting mathematical models of real-world phenomena in and across multiple disciplines, including linear algebra, discrete mathematics, probability, and calculus, with an emphasis on applications in data science and data engineering.
Create and interpret models involving linear functions.
Calculate correlation coefficients and least squares lines.
Interpret the meanings of correlation coefficients and least squares lines.
Solve systems of linear equations using the Echelon and Gauss-Jordan methods.
Manipulate matrices using addition, subtraction and multiplication.
Calculate and apply the inverse of matrices.
Apply Cramer’s Rule to systems of linear equations.
Apply linear programming to real-world problems.
Define and understand the meaning and applications of slack variables and the pivot.
Solve maximization and minimization problems using the simplex tableau and method.
Calculate probabilities and conditional probabilities of different events.
Apply the basic concepts of probability to real-world situations.
Apply Bayes’ Theorem to find probabilities.
Apply permutations and combinations to real-world problems.
Solve probability problems using counting principles.
Calculate expected values using probability distributions.
Create graphs to model real world problems.
Represent graphs using incidence matrices.
Construct Euler and Hamilton paths and circuits.
Solve shortest-path problems.
Recognize properties of trees.
Calculate limits of various types of functions.
Explain the difference between continuous and discontinuous functions and its implications.
Calculate the rates of changes of functions over specified intervals.
Calculate derivatives of exponential and logarithmic functions, products, quotients, sums and differences.
Apply the chain rule to calculate derivatives of composite functions.
Create and interpret the graphs of derivatives.
Identify increasing and decreasing intervals for functions.
Apply the definition of a derivative to interpret characteristics of graphs of functions.
Use higher derivatives to define concavity and inflection points in graphs.
Apply derivatives to real-world problems.
Calculate antiderivatives.
Calculate integrals of exponential and logarithmic functions, products, quotients, sums, and differences.
Apply integration by substitution and integration by parts.
Interpret the relationship between integrals and the area under a curve.
Apply the Fundamental Theorem of Calculus to real- world problems.
Evaluate functions of several variables.
Solve applications involving partial derivatives.
Identify relative extrema and saddle points.
Use Lagrange multipliers to optimize functions subject to constraints.