Koo-Guan Choo

Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney.

Postal address:	Dr Koo-Guan Choo School of Mathematics and Statistics F07 University of Sydney NSW 2006 Australia
Office:	Room 614 Carslaw Building
Email:	kooc@maths.usyd.edu.au
Telephone:	+61 2 9351 4221
Department Fax:	+61 2 9351 4534

Higher Degrees:

1964, Nanyang University, Singapore: B.Sc.


1967 University of Ottawa, Ottawa, Canada: MSc.
Thesis: On the dual of a C*-algebra
Supervisor: Professor B.J. Tomiuk

1972 University of British Columbia, Vancouver, Canada:Ph.D.
Thesis: On the Whitehead groups of semi-direct products of free groups
Supervisor: Professor E. Luft

Academic Experience:

1965-1967, Teaching Assistant, University of Ottawa, Ottawa, Canada.

1967-1972, Teaching Assistant, University of British Columbia, Vancouver, Canada.

1972-1974, Postdoctoral Research Teaching Fellow, University of British Columbia, Vancouver, Canada.

1975-1980, Lecturer, University of Sydney, Sydney, Australia.

1981-2005, Senior Lecturer, University of Sydney, Sydney, Australia.

2005-Now, Honorary Senior Lecturer, University of Sydney, Sydney, Australia.

Research interests:

Topics of my research interests:

• Projective class groups, Whitehead groups
• Coherent rings
• Finite topological spaces
• Cardinal numbers
• Non-normal operators on Hilbert spaces
• Various problems on Catalan numbers

Books

The following is the text book for first year Discrete Mathematics course:

• (with D.E.Taylor) Introduction to Discrete Mathematics, (Addison Wesley Longman Australia, First published 1994, Reprinted 1994, 1995, 1996, 1997, 1998), ix + 148 pp.

Lecture Notes

My lecture notes include:

• Complex Analysis (Course notes for second year), 1987.
• Fourier Series (Course notes for second year), 1987.
• Linear Algebra I (Course notes for second year), 1988.
• Hilbert Spaces and Banach Algebras (Course notes for fourth year/postgraduate), 1987-1988.
• Lectures on Topology (Course notes for third year), 1989-1998.
• Lectures on Linear Programming and Inner Product Spaces (Course notes for second year), 1989-1995.
• Lectures on Linear Programming (Course notes for second year), 1996-1997.
• Lecture on Hilbert Spaces, (Notes for MAPass), 1994, 2000.
• Lectures on Metric Spaces (Course notes for third year advanced), 1994-1998
• Lectures on Metric Spaces (Notes for MATH3901 Metric Spaces), 1999-2004
• (with Sandra Britton) Topology (Notes for MATH3001 Topology), 1999-2004.
• (with Sandra Britton) Vector Calculus and Complex Variables (Notes for MATH2001), 1999-2004.
• (edited by J Henderson) Notes on Linear Programming (Notes for MATH2051), 1998-2004.
• (with David Eaasdown) Course Notes for MATH1605 Calculus (Pharmacy), 2002-2004.

Publications

For my publications, click:

Publications

I am a member of the Analysis group.

Teaching

2005

Semester 2

MATH1004 Discrete Mathematics (Normal)

2004

Semester 1

MATH2001 Vector Calculus and Complex Variables

MATH1002 Linear Algebra

Semester 2

MATH1605 Calculus for Pharmacy

2003

Semester 1

MATH2001 Vector Calculus and Complex Variables

MATH1002 Linear Algebra

Semester 2

MATH1605 Calculus for Pharmacy

2002

Semester 1

MATH2001 Vector Calculus and Complex Variables

MATH1002 Linear Algebra

Semester 2

MATH1004 Discrete Mathematics (Normal)

MATH1605 Calculus for Pharmacy

2001

Semester 1

MATH2001 Vector Calculus and Complex Variables

MATH3901 Metric Spaces

Semester 2

MATH1004 Discrete Mathematics (Normal)

Catalan Structures

The number of "balanced" strings of n left and n right brackets is the Catalan number c[n] of order n.

For example, the Catalan number of order 3 is 5. That is, c[n] = 5 and we have 5 balanced strings: ((())) ()(()) (())() (()()) ()()()

The Catalan numbers count many other types of finite structures, such as planar diagrams or smiling faces, hand shaking problem, mountain ranges, balanced paths stacking of dominos, railway wagon problem or 231-avoiding permutations, planted planar trees or rooted plane trees, Murasaki diagrams, standard Young tableaux, stacking of coins, increasing functions, well-parenthesized products, river systems, full binary trees, polygon dissections, sequences with non-negative partial sums, and so on. For want of a better name I shall call them Catalan structures. Here are some examples.

Catalan numbers

Finite Topology

Here are the Hasse diagrams for the nonhomomorphic topologies on sets of 5 and 6 elements:

• Finite topology on five elements
• Finite topology on six elements

Other Interests

My interests include:

• Chinese Paintings
• Chinese Calligraphy
• Reading Chinese History
• Travelling

Memberships

The National University of Singapore Alumni Association (Australia) Inc. (NUSAAI) was formed in 1993.

• Committee Member (1993-1995, 2002, 2004-2006), Assistant Secretary (1996-2000), Vice President (2001, 2003) of NUSAAI (The National University of Singapore Alumni Association (Australia) Inc.)
• Member of Australian Mathematical Society, 1975-now.
• Member of American Mathematical Society, 1967-now.

Stories

I have collected some interesting stories. Here are some of them:

• No standing 1
• No standing 2
• No standing 3
• Beggar 1
• Beggar 2