UNSW Math

2026-03-09
notes

these are my notes on some courses I have taken at UNSW / have not taken.

primarily this page serves as a place for me to jot down the prescribed texts for the different courses:

math2801

Introduction to Mathematical Statistics

math2901 ATTACH

  • All of Statistics, by Wasserman
  • Mathematical Statistics & Data Analysis by Rice
  • A first look at rigorous probability theory, by Rosenthal

math3371 - Numerical Linear Algebra ATTACH

  • Peter J. Olver and Chehrzad Shakiban, Applied Linear Algebra, Second Edition, Springer 2018.

(Digital copy P 512.5/244)

  • Lloyd N. Trefethen and David Bau, Numerical Linear Algebra, SIAM Publications, 1997. (Hard

copy, Library Level 4, P512.5/128 A)

math5825 - measure, integration and probability ATTACH

  • G.B. Folland, Real Analysis, Wiley 1984.
  • W. Rudin, Real and complex analysis. McGraw-Hill, 1987.
  • P. Billingsley, Probability and Measure, P519.1/492
  • P.R. Halmos, Measure theory, P517.52/24
  • W. Rudin, Functional analysis. McGraw-Hill, 1991.
  • H.L. Royden, Real Analysis, McMillan, 1978.
  • J.L. Doob, Measure theory, P517.52/171
  • A.N. Kolmogorov and S.V. Fomin, Introductory Real Analysis, Dover, 1975.
WeeksTopic
1Problems of the Riemann integral. Lebesgue’s “problem of measure” in Rd
2Abstract measure theory - σ-algebras, measurable sets, measures, outer measures, Lebesgue measure and its properties, completion of measures.
3Measurable functions, approximation by simple functions
4Lebesgue integral, Monotone Convergence Theorem, Dominated Convergence Theorem, co-incidence of Lebesgue and Riemann integral for Riemann integrable functions
5Probabilistic language. Random variables, expectation
7Lp spaces
8Signed measures, Hahn decomposition theorem, Jordan decompositions, absolute continuity of measures, Lebesgue decomposition, Radon–Nikodym Theorem, Radon–Nikodym derivatives, chain rule
9Weak convergence of measures. Convergence in measure
10Conditional expectations. Martingales. Martingale Convergence Theorems

comp6713 - natural language processing ATTACH

okay sorry - I guess there are a couple cs courses in here too:

I’ve decided not to take this course because it will cost me 7.6K AUD, which is something that I thought much less about in my under-grad.

math5975 - introduction to stochastic analysis ATTACH

  • S. Shreve, Stochastic Calculus for Finance II, Continuous Time Models, Springer 2004.
  • Ioannis Karatzas and Stephen Shreve: Brownian Motion and Stochastic Calculus. Springer, Berlin Heidelberg New York, 1988.
  • Bernt Oksendal : Stochastic Differential Equations: An Introduction with Applications (Universitext), 6 edition, Springer, Berlin Heidelberg New York,

$4,980. (for international students it is $7,470!)

math5905 - Statistical Inference ATTACH

  • Casella, G. and Berger, R. Statistical Inference. Second Edition, Brooks/Cole (2001). This is the recommended textbook.
  • Young, G. and Smith, R. Essentials of Statistical Inference. Cambridge University Press (2005).
  • A.W. van der Vaart. Asymptotic Statistics. Cambridge University Press (1998).
  • Wasserman, L., All of Nonparametric Statistics. Springer (2006).
  • DasGupta, A. Asymptotic Theory of Statistics and Probability. Springer (2008).

a core course for the Stats Masters. allegedly helpful for Time Series. 5k for the course (as is seeming more and more normal); the hecs kids pay 10 times less.

this course will be expensive for me, because naturally I will be interested in purchasing as many of the textbooks as I can to both supplement my own study / know where to look for the rest of my lifetime.

math5835 - advanced stochastic processes ATTACH

this course seems largely like a formality. I already have the math3901 notes printed so I can reference those as necessary.

  • Foundations of Modern Probability, by Olav Kallenberg (any edition)
  • A Course in Probability, by Kai Lai Chung (third edition)
  • Stochastic Processes: From Applications to Theory, by Pierre Del Moral and Spiridon Penev

math5960 - Bayesian Inference and Computation ATTACH

  • Bayesian Data Analysis (second edition), A Gelman, J Carlin, H Stern and D Rubin, Chapman and Hall http://www.stat.columbia.edu/~gelman/book/
  • Bayes and Empirical Bayes Methods for Data Analysis (second edition), B.P.Carlin and T.A.Louis, Chapman and Hall
  • Markov Chain Monte Carlo - Stochastic simulation for Bayesian inference, D. Gammerman, Chapman and Hall
  • Bayesian Inference, 2nd Edition, Vol 2B of “Kendall’s Advanced Theory of Statistics,” A. O’Hagan and J. J. Forster (2004), Arnold, London

comp9418 - advanced machine learning ATTACH

Prescribed Book:

  • Modeling and Reasoning with Bayesian Networks. Adnan Darwiche. Cambridge. 2009

Recommended Resources:

  • Probabilistic Graphical Models: Principles and Techniques. Daphne Koller and Nir Friedman. MIT Press. 2009
  • Probabilistic Graphical Models: Principles and Applications. Luis Enrique Sucar. Springer. 2015.
  • Bayesian Reasoning and Machine Learning. David Barber. Cambridge University Press. 2012.
  • Machine Learning: A Probabilistic Perspective. Kevin P. Murphy. MIT Press. 2012.
  • Pattern recognition and machine learning. Christopher M. Bishop. Springer, 2006.