Mastodon
List

Here's some advice on reading mathematics by Harry Markowitz. If you don't know who he is, look here. If you're in EC4024 and you don't know who he is, be afraid.

From his 1959 Efficient Portfolio Selection (fulltext here), pages 37-38.

Mathematics and You

The relationships between securities and portfolios, to be discussed, are mathematical in nature. They follow from definitions of terms and properties of numbers. Like the theorems of geometry, they are subject to precise statement and rigorous definition.

Except for the appendices, this monograph was written to meet the needs of the reader without mathematical training. The writer has attempted to illustrate concepts concretely, to avoid excessively mathematical apparatus in easy stages. Successive chapters build on previously presented concepts, relationships, and apparatus, thus allowing the reader to raise his level of mathematical sophistication gradually.

The non-mathematician cannot expect to skim this monograph as if it were a novel, or skip around in it as if it were a newspaper. The subject progresses step by step. The journey can be completed only if each step is taken in turn. Here are four rules which should aid the reader:

1. Avoid "good" reading habits. Some modern reading methods encourage the reader to grasp phrases in a glance, move steadily forward, never reread a passage, never mull over a detail. Although such practices may be excellent for quickly reading a novel, they are not suited to to comprehension of unfamiliar mathematical material! Rapid reading becomes increasingly out of the question as we introduce more compact notation. A few symbols can represent dozens of words of ordinary English. To attempt to swallow such a concentrated morsel in a single gulp is bound to lead to intellectual indigestion.

2. Pay particular attention to definitions. It is impossible for the reader to understand the significance of a theorem or follow a proof if he does not know the exact meaning of terms. Terms of special significance are in italic type when first introduced.

3. Pay particular attention to theorems. A theorem is a compact, formal statement of an important relationship between concepts. Most of our discussions are directly or indirectly related to some theorem. They explain theorems, prove theorems, illustrate the importance of theorems. If the theorems are understood, their applications to problems of portfolio selection follow as corollaries.

4. Take time to understand proofs. A proof shows that the relationships expressed in a theorem follow from definitions of terms and properties of numbers. A theorem learned by rote will soon loose meaning and slip from memory. Once the reasons for the validity of the theorem are seen, once its proof is understood, once the inevitability and logical necessity of the relationship are comprehended, the theorem becomes like an old friend not easily forgotten, quick to be recognized if met again.

  Posts

1 2 3 154
December 10th, 2019

Using Social Media to Boost your profile

My talk for the social media summit is here. 

November 5th, 2019

Innospace UL talk

Thanks for the invitation to speak, the whole talk is here. 

October 9th, 2019

Understanding the macroeconomy podcast

I really enjoyed my interview with Dr Niall Farrell of the Irish Economics Podcast. You can listen to it here:

September 15th, 2018

Identifying Mechanisms Underlying Peer Effects on Multiplex Networks

New paper with Hang Xiong and Diane Payne just published in JASS: Abstract: We separately identify two mechanisms underlying peer […]

March 24th, 2018

Capital inflows, crisis and recovery in small open economies

Our latest paper, and my first with my Melbourne School of Government affiliation (plus my UL one, of course) is […]

March 7th, 2018

Southern Charm

What's it like working at Australia's number one university, ranked 23rd in the world for social sciences? It's pretty cool, […]

February 7th, 2018

Freedom interview

I did an interview for an app I love using called Freedom. Basically I pay them to block off the […]

December 10th, 2017

Marian Finucane Interview

I did a fairly long interview about the experience of moving to Australia with my family. You can listen here.

November 17th, 2017

Increasing wages for macroeconomic stability

My first piece for the conversation is here. I'm arguing the economy would benefit from wage increases, paid for from […]

November 14th, 2017

Health Workforce Planning Models, Tools and Processes: An Evidence Review

Below is my recorded talk, here are my slides, and the handout for the 4th Global Forum on Human Resources for […]

October 5th, 2017

Aalborg Keynote

My talk from the fourth Nordic Post Keynesian conference is up. The full list of keynotes is here.

October 1st, 2017

AIST Debt and Demography talk

(Apparently Limerick is in the UK now!)

September 7th, 2017

My AIST Keynote: Europe Exposed

In which a camera man faints halfway through--he's OK though, I checked afterwards!

July 22nd, 2017

MacGill Summer School Speech

My speech at the MacGill Summer School is here. Thanks to Joe Muholland for inviting me to speak.

May 25th, 2017

Business Post Articles

All my Sunday Business Post articles (back to 2014/5, when I joined the paper) are available here, behind a paywall, and […]

@barrd on Mastodon