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In pursuit of Zeta-3 – The World’s Most Mysterious Unsolved Math Problem, by Paul Nahin – a review

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

From Princeton University Press

I have to admit that I felt very skeptical when I started reading this book. In the prologue it is stated that the book is aimed at enthusiastic readers of mathematics with an AP level of high school maths. Then, diving into the book one sees what looks at first sight like a pure maths textbook at graduate level. But Paul Nahin isn’t one to pull a fast one like that, so I read further. In fact, I raced through it, hugely enjoyed it, and in the end agree with Nahin that someone with a US AP level of high school maths, or here in South Africa a confident first year undergraduate could actually understand everything in the book.

The book is not written as a textbook on mathematics, much as it might look like one, but rather it is taking an historical path through the investigations into the mysteries of zeta(3).…

By | April 23rd, 2022|Book reviews, Reviews|3 Comments
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Lecturer/Senior lecturer position available in the UCT department of Maths and Applied Maths

The Department of Maths and Applied Maths at UCT has a position open at the level of lecturer or senior lecturer. The advert can be found here:

SCI_17099_L_SL_MAM

Applications in all areas of Mathematics and Applied Mathematics will be considered.

Minimum requirements include:

For the level of Lecturer:

  • A PhD (at the time of appointment) in Mathematics or Applied Mathematics or related areas.
  • A record of research outputs.
  • Postdoctoral and some teaching experience would be advantageous”

    For the level of Senior Lecturer:

  • A PhD in Mathematics or Applied Mathematics
  • An established track record of published research outputs.
  • Demonstrable teaching experience.
  • A record of postgraduate student supervision.

    Responsibilities include:

  • Teaching and developing undergraduate and postgraduate courses offered by the department of Mathematics and Applied Mathematics.
  • Developing and pursuing an active research program, which includes student supervision.
  • Course convening, departmental and faculty administrative duties.

    The annual remuneration package for 2017, including benefits are:

  • Lecturer R592,451
  • Senior Lecturer R728,442

    To apply, please e-mail the documents listed below in a single pdf file to Ms Vathiswa Mbangi at recruitment04@uct.ac.za

  • –  UCT Application Form (download at http://forms.uct.ac.za/hr201.doc)
  • –  Cover letter, and
  • –  Curriculum Vitae (CV)
  • –  Teaching and Research statement

    An application which does not comply with the above requirements will be regarded as incomplete.

…
By | June 5th, 2017|Advertising, Job advert|0 Comments
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The Mathematics of Secrets – by Joshua Holden, a review

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

From Princeton University Press.

This is an extremely clearly, well-written book covering a lot of ground in the mathematics of cyphers. It starts from the very basics with simple transposition cyphers and goes all the way through to elliptic cyphers, public key cryptography and quantum cryptography. Each section gives detailed examples where you can follow precisely the mathematics of what underlies the encryption. Indeed the mathematics is non-trivial in a fair number of places, but it is always explained well, and I think that anyone with a first year university level of mathematics should be able to understand the bulk of it. I think that if you were to come at this book with a high-school level of mathematics, there would be some aspects which would be pretty hard work, but with some persistence, even those would be understandable, and perhaps the breakthroughs in understanding would feel like a great (though doable) achievement for the maths enthusiast.…

By | November 20th, 2018|Book reviews, Reviews|1 Comment
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If Africa is to develop – Math has to be part of it!

Almost every nation in Africa is inspired by South Africa in terms of economic growth. But wait a minute, is South Africa really up there, well let’s see! In the recent world economic forum Global Information Technology Report of 2015, on mathematics and science education rankings, South Africa emerged as the worst country from the ranking. Refer to Link 0.

Actually, it is indeed astonishing that in the global rankings conducted by OECD every 2 years in the fields of science, reading and mathematics, there isn’t a single representative from Africa.  Is it because the continent is still under developed? well not directly but yes, it has something to do with it. The fact of the matter is that there seems to be a one-to-one correspondence between education (particularly math and science) and economic development as discussed in the OECD findings see: Link 1, Link 2.

 

How clear is this post?
…
By | January 12th, 2016|Uncategorized|1 Comment
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Ten Great Ideas about Chance – By Persi Diaconis & Brian Skyrms, a review

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

http://i1.wp.com/press.princeton.edu/sites/default/files/styles/large/public/covers/9780691174167.png?resize=336%2C480&ssl=1

From Princeton University Press

This book straddles a tricky middle ground, given that it introduces topics from scratch and goes into some very specific details of them in a relatively few pages, before jumping onto the next. On starting to read it, I was skeptical of how this could possible work, but by the end of it I believe that I saw the real utility of a book like this. The audience is quite specific, but for them it will be a gem.

The book covers a huge range of ideas related to chance, from the underlying mathematics of probability, to the psychology of decision making, the physics of chaos and quantum mechanics, the problems inherent in induction and inference and much more besides.

The book is taken from a long-running course at Stanford which the authors taught for a number of years, and they have tried to condense down the most important aspects of it to a relatively light book.…

By | December 31st, 2017|Uncategorized|1 Comment
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The Probability Lifesaver – by Steven J. Miller, a review

NB. I was sent this book as a review copy. In addition, I lent this book to a student studying statistics, as I thought that it would be more interesting for them to let me know how much they get out of it. This is the review by Singalakha Menziwa, one of our extremely bright first year students.

http://i1.wp.com/press.princeton.edu/sites/default/files/styles/large/public/covers/9780691149547.png?resize=336%2C480&ssl=1

From Princeton University Press

All the tools you need to understand chance, the insight of statistics at base, and more complex levels. Statistics is not just about substituting into the correct formulae but requires understanding of what the numbers mean. Counting rules and Statistical inference were two of the topics I struggled with, especially the logic behind statistical inference, but this book provided great insight and explanations regarding these topics with a step by step procedure and gave enough interesting exercises. Miller’s goal when writing the book was to introduce students to the material through lots of accurately done, in depth worked examples and some fascinating coding for those who want to get more practical, to have a lot of conversations about not just why equations and theorems are true, but why they have the form they do.…

By | October 20th, 2017|Book reviews, Reviews|1 Comment
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A quick argument for why we don’t accept the null hypothesis

Introduction

When doing hypothesis testing, an often-repeated rule is ‘never accept the null hypothesis’. The reason for this is that we aren’t making probability statements about true underlying quantities, rather we are making statements about the observed data, given a hypothesis.

We reject the null hypothesis if the observed data is unlikely to be observed given the null hypothesis. In a sense we are trying to disprove the null hypothesis and the strongest thing we can say about it is that we fail to reject the null hypothesis.

That is because observing data that is not unlikely given that a hypothesis is true does not make that hypothesis true. That is a bit of a mouthful, but basically what we are saying is that if we make some claim about the world and then we see some data that does not disprove this claim, we cannot conclude that the claim is true.…

By | August 28th, 2019|English, Level: Simple, Uncategorized, Undergraduate|0 Comments
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Checking direction fields

I was recently asked about how to spot which direction field corresponds to which differential equation. I hope that by working through a few examples here we will get a reasonable intuition as to how to do this.

Remember that a direction field is a method for getting the general behaviour of a first order differential equation. Given an equation of the form:

 

\frac{dy}{dx}=f(x,y)

 

For any function of x and y, the solution to this differential equation must be some function (or indeed family of functions) where the gradient of the function satisfies the above relationship.

The first such equation that we looked at was the equation:

 

\frac{dy(x)}{dx}=x+y(x).

 

We are trying to find some function, or indeed family of functions y(x) which satisfy this equation. We need to find a function whose derivative (y'(x)) at each point x is equal to the value of the function (ie. y(x)), plus that value of x.…

By | October 11th, 2016|Courses, First year, MAM1000, Undergraduate|1 Comment
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Simpson’s Paradox

Introduction

A key consideration when analysing stratified data is how the behaviour of each category differs and how these differences might influence the overall observations about the data. For example, a data set might be split into one large category that dictates the overall behaviour or there may be a category with statistics that are significantly different from the other categories that skews the overall numbers. These features of the data are important to be aware of and go find to prevent drawing erroneous conclusions from your analysis. Context, the source of the data and a careful analysis of the data can prevent this. Simpson’s paradox is an interesting result of some of these effects.

The Paradox

Simpson’s paradox is observed in statistics when a trend is observed in a number of different groups but it is not observed in the overall data or the opposite trend is observed.

Observing the overall data might therefore lead us to draw a conclusion, but when the data is grouped we might conclude something different.…

By | January 5th, 2020|English, Level: Simple|1 Comment
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Elephant Delta day 1 – Professor Tim Dunne from UCT on The Rasch Model for test outcomes and related item requirements

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Prof Tim Dunne – UCT (photograph taken from the Elephant Delta website)

 

Professor Dunne will be discussing the Rasch model, some information of which can be found here. Quoting from wikipedia:
The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent’s abilities, attitudes or personality traits and (b) the item difficulty.
Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

 

David Andrich pioneer of the Rasch method.…

By | November 23rd, 2015|Conference, Elephant Delta 2015, Uncategorized|0 Comments
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