Foundational mathematics for computing, with tutorial component
Chapter 1 : Logic, Relations, Functions, and Graphs
Mathematics relies on absolute certainty. Unlike empirical sciences, which build models based on observation and measurement, mathematics builds structures base…
Chapter 2 : Sequence and Series
In the previous unit, we studied functions that operate on the continuous real number line. We could input any real number, including fractions and irrational d…
Chapter 3 : Matrices and Determinants
Up to this point, we have solved equations involving single variables. We manipulated one number at a time. This scalar approach works perfectly for simple alge…
Chapter 4 : Analytical Geometry
Analytical geometry connects the abstract world of algebra to the visual world of geometry. Instead of drawing shapes with a physical compass and a straightedge…
Chapter 5 : Vector and Vector Space
In the previous units, we worked exclusively with single numbers. A single number can measure temperature, mass, or cost. However, a single number cannot descri…
Chapter 6 : Permutations and Combinations
Mathematics often requires us to determine the size of a set. In the previous units, we counted elements manually or calculated infinite limits. However, comput…