Mathematics

The module COMP533 Maths and Statistics for AI and Data Science will cover the following topics:

• DIFFERENTIAL CALCULUS
  • Review of basic calculus: numbers, sets, functions, limits,
  • basic geometry: coordinates, lines, trigonometry
  • Differential calculus: limits, continuity, derivatives, velocity, concavity
  • Optimisation: minima/maxima, gradient descent, second order methods (Newton)
• LINEAR ALGEBRA
  • Basic concepts: vectors, matrices, dot products, matrix product
  • Geometry of matrices and derivatives, linear transformations and partial derivatives
  • Extensions: eigen values and vectors, determinants linear basis and projections, eigen-decomposition & SVD, pseudoinverse.
• Probability Theory
  • Basic probability: events, sample space, frequentist vs Bayesian approach, law of large numbers, conditional probability, independence, Bayes theorem, random variables
  • Probability distributions, probability sampling, random sa mpling, sampling distributions
• Statistics
• Measures of Centre and Variation, Statistical Significance (Confidence intervals) and Tests of Hypothesis
• Errors, Chi-square independence test, Correlation vs causation, Linear Regression
• Descriptive Statistics: Data and Data Presentation: scatter plots, line graphs, bar charts, histograms, box plots

The following material may help you to prepare for this module:

• For an introduction to functions and pre-calculus see

  Centre for Education in Mathematics and Computing: Advanced Functions and Pre-Calculus. University of Waterloo, 2023. https://courseware.cemc.uwaterloo.ca/8 Links to an external site. [accessed 2023-06-19].

• For an introduction to calculus and vectors see

  Centre for Education in Mathematics and Computing: Calculus and Vectors. University of Waterloo, 2023. https://courseware.cemc.uwaterloo.ca/11 Links to an external site. [accessed 2023-06-19].

• For a freely available textbook on logic, proofs, sets, relations, and functions see

  S. Hugtenburg and N. Yorke-Smith: Delftse Foundations of Computation. TU Delft, 2018. https://collection.bccampus.ca/textbooks/delftse-foundations-of-computation-tu-delft-97/ Links to an external site. [accessed 2023-06-19].

• For lecture videos and notes on probability see

  J. Tsitsiklis and P. Jaillet: Introduction to Probability. MIT OpenCourseWare, 2018. https://ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/ Links to an external site. [accessed 2023-06-19].

• For a freely available texbook on statistics see

  D. Lane: Introduction to Statistics. Open Textbook Library, 2003. https://open.umn.edu/opentextbooks/textbooks/459 Links to an external site. [accessed 2023-06-19]

  and the companion website

  D. Lane et al: Online Statistics Education: An Interactive Multimedia Course of Study. https://onlinestatbook.com/2/index.html Links to an external site. [accessed 2023-06-19]

  that also provides videos on the topics covered in the book.