Finnur LárussonProfessor of Pure Mathematics
Discipline of Mathematical Sciences
tel.: +61 8 8313 3528
My book Lectures
on Real Analysis was published by Cambridge University Press in mid-2012.
Click on the title or the picture of the front cover, and you can have a look inside the book on the CUP website.
The book is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The exposition is brisk and concise, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is intended for second-year undergraduates and for more advanced students who need a foundation in real analysis.
I will be grateful for any comments from readers. Please e-mail me if you find misprints or mistakes in the book.
I welcome enquiries from prospective honours or postgraduate students. Feel free to e-mail me or, if you are in Adelaide, stop by my office.
If you are interested in PhD or MPhil studies in Adelaide, I would be glad to discuss possible thesis topics with you. I mainly work in complex analysis and complex geometry, including pluripotential theory, and applications of abstract homotopy theory to these areas. Start by looking at my papers or read this to get an idea of what sorts of things I do. There are several other people in Adelaide working in related areas. We run an active seminar with talks by locals and visitors.
Recent postgraduate students of mine
Elliot Herrington, PhD 2021, Highly symmetric homogeneous Kobayashi-hyperbolic manifolds
David Bowman, PhD 2016, Holomorphic flexibility properties of spaces of elliptic functions
Alexander Hanysz, PhD 2013, Holomorphic flexibility properties of complements and mapping spaces
Tyson Ritter, PhD 2011, Acyclic embeddings of open Riemann surfaces into elliptic manifolds
Wills Ton Minh Nguyen, MPhil 2023, The closing lemma for Riemann surfaces
Ryan Dye, MPhil 2022, Algebraic Oka theory for curves
Alexander Lai De Oliveira, MPhil 2022, Equivariant Oka theory for Riemann surfaces
Haripriya Sridharan, MPhil 2020, Spaces of holomorphic immersions of open Riemann surfaces into the complex plane
Matthew Ryan, MPhil 2019, The parametric Oka principle for Riemann surfaces
Daniel John, MPhil 2019, Holomorphic immersions of restricted growth from smooth affine algebraic curves into the complex plane
Brett Chenoweth, MPhil 2016, Deformation retractions from spaces of continuous maps onto spaces of holomorphic maps
William Crawford, MPhil 2014, Oka theory of Riemann surfaces