Mathematics and Art
Haris Aziz -
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. I…
Category > Mathematics
The Power of Graphs
Haris Aziz -
Graphs are mathematical structures that model pairwise relations between objects. They are represented by vertices and edges where the edges may be directed or undirected. Whenever I am working on…
Good Mathematics
Haris Aziz -
Arxiv is where you normally expect preprints of technical papers in mathematics, physics and computer science. However, it was a surprise to run into a general essay on ‘good mathematics’…
Blum’s Advice (part 2)
Haris Aziz -
Manuel Blum has some helpful advice for graduate students starting a PhD. This is a sequel to the previous entry. Blum refers to the joke that ‘a PhD knows more…
Blum’s Advice
Haris Aziz -
Manuel Blum has some unique and helpful advice for graduate students starting a PhD. A lot of the advice applies to anyone, however. Blum advises to not use books like…
Algorithmic Decision Theory
Haris Aziz -
Every two years, DIMACS and LAMSADE (at University Paris Dauphine) organize a workshop on algorithmic decision theory. This year it happened to be in Paris. The workshop was jointly held…
Modeling Systems
Haris Aziz -
“Things should be made as simple as possible – but no simpler.” (Albert Einstein) Mathematical models are abstractions of complex systems. Such systems are used in physical sciences, and also…
Problem Solving & Research: Advice from Descartes
Haris Aziz -
Research in mathematical sciences and computer science is in many ways a matter of problem solving. One tries to use whatever tools one has to get one’s way round a…
How to Write Mathematics
Haris Aziz -
Among mathematical writers, Paul Halmos was unique because of his clear exposition and introduction of clever notations. Halmos, known for his famous autobiography, also wrote an insightful essay on how…
Letters to a Young Mathematician
Haris Aziz -
Explaining the elegance, utility and ubiquity of mathematics to the general public has always been an onerous task for mathematicians. However, if anyone does it well, it is Prof Ian…
