The navigability of Mathemafrica isn't ideal, so I have created this post which might guide you to what you are looking for. Here are a number of different categories of post which you might like to take a look at: First year mathematics notes and resources (particularly for the University [...]

By | January 17th, 2018|0 Comments

PDE: Physics, Math and Common Sense. Part I: Conservation Law

Source: CFDIinside blog INTRODUCTION The course of Partial differential equations (PDEs) usually is a tough one. There is a number of factors contributing to this toughness: PDE course combines the knowledge from calculus, algebra, ordinary differential equations (ODEs), complex analysis and functional analysis. Simply put, there is a lot that you need to know about! PDE methods often (or should I say, mostly?) come from physics, but this aspect is not always emphasized and, as a result, the intuition is lost. There is lots of abstraction in the PDE course material: characteristics, generalized functions (distributions), eigenfunctions, convolutions and etc. Many of these concepts actually have simple interpretations, but again, this is not emphasized. PDEs themselves are tough. In contrast to ODEs, there are no general methods for all kinds of PDEs. The field is young and a bit messy. This series of posts aims to demystify PDEs and show some general way of handling PDE problems by combining physical intuition and mathematical methods. I am a strong believer in computational approach to mathematics. If you wish, it also can be called an engineering mathematics. They core idea of it: we must get an answer. With the examples presented here we will go all the way from formulating the problem to getting the solution. This also means that on the top of PDEs we would need to deal with another tough mathematical topic: numerical methods. But lets not to get ahead of ourselves and first find out “why PDE?” or using Shakespearian pun […]

Advice for MAM1000W students from former MAM1000W students – part 5

While I resisted Mam1000W every single day, I even complained about how it isn't useful to myself. Little did I know when it all finally clicked towards the end that even though I wasn't going to be using math in my life directly, the methodology of thinking and applying helps [...]

Advice for MAM1000W students from former MAM1000W students – part 4

In high school, as I believe was the case for many students, there wasn't much incentive to work very hard regularly on math - concepts were easy to grasp first hand in class. That's the kind of attitude I brought towards MAM1000W last year (2017). Unfortunately things didn't turn out as [...]

Advice for MAM1000W students from former MAM1000W students – parts 2 and 3

Part 2: ------- So one thing that really helped me was having a partner in tuts. We would do the tuts as far as we could and we would then try to help one another in the tuts and ask the tutors for help if there was a difference in [...]

Advice for MAM1000W students from former MAM1000W students – part 1

This is the first in a series of posts where I will be putting up the sage words of advice of former MAM1000W. Often, these students struggled their way through the course, before making a breakthrough in their study methods. I hope that maybe it will be easier to listen [...]

Hypatia, The Life and Legend of an Ancient Philosopher – by Edward J. Watts, a review by Henri Laurie

Review written by Henri Laurie. From Oxford University Press This is an important book for anybody interested in the history of mathematics and in the history of women intellectuals. To recap very briefly: Hypatia is well-known as the mathematician/philosopher who was murdered by a Christian mob in 415 [...]

Mathematical Foundations of Quantum Mechanics – By John Von Neumann, edited by Nicholas A Wheeler

NB. I was sent this book as a review copy. From Princeton University Press I have to admit that I was rather embarrassed to encounter this book, as I had never heard of it, and given the topic, and the author, it seemed that it must be one [...]

An Introduction to analysis – By Robert G Gunning, a review

NB. I was sent this book as a review copy. From Princeton University Press While this book is called An Introduction to Analysis, it contains far more than one might expect from a book with such a title. Not only does it include extremely clear introductions to algebra, [...]

Cartesian product

We know we can use binary operations to add two numbers, x and y: $latex x+y, x-y, x \times y, x \div y.$ Furthermore there are other operations such as $latex \sqrt{x}$ or any other root and exponents. Operations can involve other mathematical objects other than numbers, such as sets. $latex def^n$ Given two [...]

By | April 14th, 2018|1 Comment

3. power sets

Recall powers (or exponents) of numbers: $latex 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$ Similarly, sets have the power operation to create new sets. $latex def^n$ If A is a set, then the power set of A is another set denoted as \$latex \mathbb{ P }(A) = \text{ set [...]

By | April 10th, 2018|1 Comment