Chapter Wise Notes with Examples

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 based on strict logical deduction. We do not accept a mathematical statement as true because it looks correct or works in mo…

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 decimals, and observe a continuous curve on a graph. However, computer science rarely deals with continuous infinity. Com…

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 algebraic problems. However, it fails completely when a system contains hundreds of interacting variables. To handle massive…

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, we define them using exact algebraic equations on a coordinate plane. This allows us to analyze curves with absolute m…

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 describe a physical force or a movement through space. If you tell a graphics engine to move a character by five units, the en…

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, computer science frequently deals with finite but massively large sets. A database might contain millions of possible query co…