MATHS-1: Mathematics for Data Science 1

Topics covered

• Set theory, relations & functions

  • Number systems
  • Sets and operations
  • Relations and their types
  • Functions and their types

Expected skills: Use set operations and distinguish types of relations and functions.

Topics covered

• Coordinate geometry & straight lines

  • Coordinate system
  • Straight lines
  • Slope
  • Parallel and perpendicular lines
  • Line representations
  • General equations
  • Straight-line fit

Expected skills: Represent lines and use slopes to analyse their geometric relationships.

Topics covered

• Quadratic functions

  • Quadratic functions
  • Maxima and minima
  • Vertex
  • Slope
  • Quadratic equations

Expected skills: Analyse a quadratic function and solve its equation.

Topics covered

• Polynomial algebra

  • Polynomial operations
  • Algorithms
  • Polynomial graphs
  • Roots and multiplicities
  • End behaviour
  • Turning points

Expected skills: Relate polynomial roots and multiplicities to the shape of a graph.

Topics covered

• Functions & exponentials

  • Functions
  • Horizontal and vertical line tests
  • Exponential functions
  • Composite functions
  • Inverse functions

Expected skills: Identify functions, form compositions and reason about inverse and exponential functions.

Topics covered

• Logarithmic functions

  • Properties of logarithms
  • Logarithmic graphs
  • Exponential equations
  • Logarithmic equations

Expected skills: Use logarithm properties to analyse graphs and solve equations.

Topics covered

• Sequences, limits & continuity

  • Sequences
  • Limits of sequences
  • Limits of functions
  • Continuity

Expected skills: Evaluate limits and check continuity of functions.

Topics covered

• Differentiation

  • Derivatives
  • L’Hôpital’s rule
  • Tangents
  • Linear approximations
  • Critical points

Expected skills: Use derivatives to find tangent approximations and critical points.

Topics covered

• Integration

  • Integrals
  • Definite integrals
  • Area computations
  • Relationship between differentiation and integration

Expected skills: Compute definite integrals and connect integration with differentiation and area.

Topics covered

• Graph theory I

  • Graph representations
  • Adjacency lists and matrices
  • BFS and DFS
  • Directed acyclic graphs
  • Algorithmic complexity

Expected skills: Represent graphs and trace breadth-first and depth-first traversals.

Topics covered

• Graph theory II

  • Longest paths
  • Transitive closure
  • Shortest paths
  • Dijkstra and Bellman–Ford
  • Floyd–Warshall
  • Minimum spanning trees
  • Prim and Kruskal

Expected skills: Compare path and spanning-tree algorithms and apply them to a graph.

Topics covered

• Revision & practice

  • Revision of functions, calculus and graph theory
  • Practice problems

Expected skills: Consolidate the course topics and practise selecting suitable methods.