Mathematics for Data Science I

A foundational course covering essential concepts in functions, single-variable calculus, and graph theory to model real-world scenarios.

Mathematics for Data Science I was an essential course that built the abstract reasoning and problem-solving toolkit required for data science. The course progressed logically from foundational concepts like set theory to the practical application of functions, including linear, quadratic, polynomial, exponential, and logarithmic forms. A key part of the course was a rigorous introduction to single-variable calculus, covering limits, derivatives, and integrals, which are crucial for optimization and understanding rates of change. Finally, the course transitioned into discrete mathematics with a comprehensive unit on graph theory, exploring everything from basic traversal algorithms like BFS and DFS to complex shortest path and minimum spanning tree problems.

Instructors

Course Schedule & Topics

The course is structured over 12 weeks, including a final week for revision.

Week Primary Focus Key Topics Covered
1 Set Theory & Functions Number systems, sets and their operations, relations and their types, functions and their types.
2 Coordinate Geometry & Lines Rectangular coordinate system, slope of a line, parallel and perpendicular lines, various representations and general equations of a line, straight-line fit.
3 Quadratic Functions Properties of quadratic functions, finding minima, maxima, vertex, and slope; solving quadratic equations.
4 Polynomials Algebra of polynomials (addition, subtraction, multiplication, division), graphing polynomials including x-intercepts, multiplicities, end behavior, and turning points.
5 Advanced Functions Horizontal and vertical line tests, exponential functions, composite functions, and inverse functions.
6 Logarithmic Functions Properties and graphs of logarithmic functions, solving exponential and logarithmic equations.
7 Limits & Continuity Sequences, limits for sequences and functions of one variable, relationship between limits and continuity.
8 Differentiation Differentiability, computing derivatives, L’Hôpital’s rule, tangents, linear approximation, and finding critical points (local maxima and minima).
9 Integration Computing areas under a curve, the integral of a function of one variable, relationship between derivatives and integrals.
10 Introduction to Graph Theory Graph representation, Breadth-First Search (BFS), Depth-First Search (DFS), Directed Acyclic Graphs (DAGs), and topological sorting.
11 Graph Theory Algorithms Shortest paths (Dijkstra’s, Bellman-Ford, Floyd–Warshall), and Minimum Cost Spanning Trees (Prim’s, Kruskal’s algorithm).
12 Revision Week Comprehensive course review and preparation for the final examination.

Material used