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Group Theory in a Nutshell for Physicists, by Tony Zee – A review

I studied group theory for the first time around 15 years ago at the beginning of my PhD. There were six of us in the class, and I found it both a magical, as well as a mysterious subject. We had a great lecturer, but the way that the course was set up, and as a course designed for theoretical physicists, where the tools were more important than the construction of the tools, a lot of ideas were left as mysterious boxes where the right answers were guaranteed so long as the algorithm was correctly followed.

Tony Zee is known for his incredible ability to lead the student on a path from little knowledge, to an intuitive understanding of a topic in a seemingly painless process. His books are not necessarily the most technically rigorous (note that this doesn’t mean that they are wrong, but that the appropriate level of detail is chosen for the new learner such that the overarching ideas aren’t fogged in unnecessarily complication), but they are, in my opinion some of the best texts for taking a learner from nothing, to a working knowledge with which they can perform calculations that I’ve ever come across.…

By | September 11th, 2016|Book reviews, Reviews|1 Comment
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Finding Fibonacci, by Keith Devlin – a review

This book was sent to me by the publisher as a review copy.

I have a terrible admission to make. I came to this book with a paltry knowledge of Fibonacci (Leonardo of Pisa). The knowledge that I thought that I had was quickly shown in fact to be incorrect, so I was largely starting with a blank slate (Fibonacci did not discover the Fibonacci sequence, nor would he be terribly happy to know that in the popular psyche, this is what he is famous for).

In fact, this book is not really about Fibonacci (Devlin has another book about him). This is a book about the writing of a book, and about Devlin’s process of uncovering the history and importance of what Fibonacci had accomplished. It is a book about the research of the history of mathematics, and as such, it is a lovely tale: one of fortuitous moments of discovery, and of frustrations of searching for manuscripts.…

By | April 28th, 2017|Uncategorized|1 Comment
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Visual Differential Geometry and Forms – a mathematical drama in five acts, by Tristan Needham – a review

NB. I was sent this book as a review copy.

From Princeton University Press

Studying physics, some two decades ago at The University of Bristol, I found the majority of what we covered relatively intuitive. Even the arcane world of quantum mechanics, while impossible to truly visualise, is, paradoxically, often relatively simple to calculate, and the objects that you use are directly from the world of complex numbers, differential equations and linear algebra. What stumped me however were tensors. I found it so hard to really picture what was going on with these objects. Vectors were ok, and the metric tensor I could handle, but as soon as you got onto differential forms, all my intuition went out the window. The world of differential geometry, while I could plug and chug, felt like putting together sentences in a foreign language where all I had were rules for using the syntax and grammar, without a deep understanding of what the objects were

This book would have answered all of my prayers back then.…

By | December 11th, 2021|Book reviews, Reviews|0 Comments
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Relativity, The Special and General Theory, 100th anniversary edition – by Albert Einstein

NB. I was sent this book as a review copy.

From Princeton University Press.

In 1917, two years after publishing his work on The General Theory of Relativity, Einstein published a popular science account of both The Special, and General Theories of relativity. It is with some embarrassment that I have to admit that I’d never read this before, despite taking a number of undergraduate and postgraduate courses in relativity. Einstein understood the importance that his results had on our understanding of the universe, but also that the profundity of them could not truly be grasped by the general public, despite the headlines which covered many newspapers around the world on his results, without a popular exposition. 1917 was the publication of the first edition of this explication, but he continued to update them up until 1954. This allowed him to extend the theoretical discussion with the experimental verifications and discoveries which occurred over the next decades, including that of the expanding cosmology, spearheaded by Hubble’s observations.…

By | April 19th, 2019|Book reviews, Reviews|1 Comment
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Life without Mathematics is indescribable

Life without Mathematics is indescribable. When I was still young my parents used to play lotto hoping that out of the blue they can become rich but every time they fail, one day my dad saw the poster of the ‘seer’ claiming that he can give people the perfect combinations of numbers so that they can win. For one year my parents went to him and those combinations failed. We did not know anything about mathematics, but now mathematics has opened not only our eyes but minds…..  The idea of Permutations and combinations, we actually realized that mathematics is not only about passing and getting scores but it is about making life simple and easy for everyone. Because of Mathematics my parents now know the possibilities of arranging 6 numbers out of 1 to 49.

I am a student but already the little that I know has save my family’s expenses and equipped them with the idea of factorials, combinations and permutations.…

By | May 1st, 2015|Uncategorized|3 Comments
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A course in Complex Analysis, by Saeed Zakeri – a review

NB. I was sent this book as a review copy.

From Princeton University Press

This is a no-nonsense, clearly written graduate level textbook on complex analysis, and while it is written for a graduate audience, I think that the way it is laid out, with clear examples throughout, a keen undergraduate with a background in analysis and topology. As such it is far more approachable than many other books on complex analysis and I would say that it would be perfectly suited for physics students wanting to go into areas like quantum field theory, particularly string theorists where the sections on conformal metrics and the modular group would be very helpful.

One thing to look out for in a book like this is the clarity of the proofs, and the number of intermediate lines which are included, and in this case I think that there is just the right amount to make everything easy to follow, but not overwhelming the material.…

By | April 23rd, 2022|Book reviews, Reviews|0 Comments
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Tales of Impossibility – The 2000 year quest to solve the mathematical problems of antiquity, by David S. Richeson – a review

NB I was sent this book as a review copy.

From Princeton University Press.

Four impossible puzzles, all described in detail during the height of classical Greek Mathematics. All simple to define and yet so tempting that it has taken not only the brain power of many, many thousands of mathematicians (amateur and professional alike), but also two millennia to show that however hard you may try, these puzzles are just not possible. The puzzles are:

  • Squaring the circle: With only a compass and a straight edge, draw a square with the same area as that of a given circle.
  • Doubling the cube: With only a compass and a straight edge, draw the edge of a cube with volume twice that of a cube whose edge is given.
  • Constructing regular polygons: Given a compass and a straight edge, construct a regular n-gon in a given circle for n\ge 3.
  • Trisecting an angle: Given a compass and a straight edge, and a given angle, construct an angle that is one third of the original.
…
By | February 9th, 2020|Uncategorized|1 Comment
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So simple a beginning – How four physical principles shape our living world, by Raghuveer Parthasarathy – a review

NB. I was sent this book as a review copy.

From Princeton University Press

 

When a review on the back of a book says “Hands down the most beautiful book I’ve ever read.” my skeptical antennae go into action. This was either going to be absolutely brilliant, or sorely disappointing. Thankfully it is absolutely the former. Parthasarathy takes the reader on an insightful and intuitive journey through the world of biophysics, letting us see how physical laws lead to the wonder of biology at all scales of the organism (and beyond, though he only hints at this). I have read a fair number of books about genetics, but this gave without a doubt the most in-depth view as to what is really going on at the molecular level, about how randomness plays a crucial role, at the level of proteins moving around, at the level of lipid bilayers coallescing, and at the level of gene expression.…

By | June 5th, 2024|Book reviews, Reviews|1 Comment
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Elephant Delta Day 3 – Shirley Wagner-Welsh from Nelson Mandela Metropolitan University on An Investigation into the Effect of Mathematics Self-Efficacy and Mathematics Anxiety on Mathematics Performance

At Nelson Mandela Metropolitan University Very diverse socio-economic circumstances, mostly non-native English speakers. 23 Different languages on campus.

Why this study? There has been a large issue of poor performance and lack of engagement in mathematics.

What can we do about this?

Possible issues:

  • Topics are introduced at a fast pace
  • Students may not have the necessary prerequisites
  • Independent learning is required

Two other issues:

Mathematics self-efficacy:

Self-efficacy is people’s judgements of their capabilities to organise and execute courses of action required to attain designated types of performance (Bandura 1986).

Mathematics self-efficacy affects performance.

This can tell us why students sometimes don’t put in the necessary effort. If a student DOES have a high level of mathematical self-efficacy they tend to work longer on problems.

There does seem to be a link between mathematics self-efficacy and gender: Higher in males (grade 10-12 and pre-service teachers – Malpass, O’Neil and Hocenar: Self‐regulation, goal orientation, self‐efficacy, worry, and high‐stakes math achievement for mathematically gifted high school students) – in another study this was not found.…

By | November 26th, 2015|Conference, Elephant Delta 2015, Uncategorized|0 Comments
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The Wisdom of the Crowds

This content comes primarily from the notes of Mark Herbster (contributed to by Massi Pontil and John Shawe-Taylor) of University College London.

Introduction

The Wisdom of the Crowds, or majority rule and related ideas tend to come up pretty often. Democracy is based (partly) on the majority of people being able to make the correct decision, often you might make decisions in a group of friends based on what the most people want, and it is logical to take into account popular opinion when reasoning on issues where you have imperfect information. On the other hand, of course, there is the Argumentum ad Populum fallacy which states that a popular belief isn’t necessarily true.

This is idea appears also in Applied Machine Learning – ensemble methods such as Random Forests, Gradient Boosted Models (especially XGBoost) and stacking of Neural Networks have resulted in overall more powerful models. This is especially notable in Kaggle competitions, where it is almost always an ensemble model (combination of models) that achieves the best score.…

By | November 15th, 2019|Uncategorized|0 Comments
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A project initiated at the AIMS-IMAGINARY workshop, November 2014, Cape Town | All Rights Reserved
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