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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 anticipated…by as early as April I had already started playing “catch-up” for I hadn’t been putting in any practice on the staff done in class. Tests were nightmares. With every course demanding its share of my attention, I found myself crying the other day alone in my room, asking myself, “what went wrong?”. Well, the answer was pretty simple – EVERYTHING.

Eventually, I figured a way to potentially get back on my feet – I became a very good friend of my WebAssign voluntary quizzes. In combination with past papers (WHICH I HIGHLY RECOMMEND) and the daily uploaded ‘practice questions and solutions’, I was able to gain back some bit of confidence.

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By Jonathan Shock| May 9th, 2018|Uncategorized|0 Comments

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

Part 2:

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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 opinion.

Another thing that helped studying, going through past papers and tuts were so important.

If I was ever stuck and couldn’t really understand the textbook I would go on YouTube and watch a guy named Professor Leonard. He’s videos are super long but extremely helpful and worth your time.

And last but not least, it’s important that you try your best to work everyday with maths because once you fall behind its difficult to catch up. Even if you do just one problem a day I promise it will help In the future.

and part 3:

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I would suggest to MAM1 students that they should not fall behind the maths syllabus if they have tests in other subjects because it is very difficult to catch it up and requires much more effort than one thinks.…

By Jonathan Shock| May 8th, 2018|Uncategorized|1 Comment

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 to students who have been through the struggle, than the advice of lecturers who seem to know it all (though I promise you, we do not!).

Here is the first:

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As an Actuarial Science student I was aiming for 70% last year. I clearly remember that at orientation I asked some of the older ActSci students at orientation what they had done when they scored below what they needed to. I was so shocked, and a little scared when the group I asked said they never had. I wasn’t worries at this stage though because I thought I’d done well at maths at school, and I’d do well at maths here.…

By Jonathan Shock| May 8th, 2018|Uncategorized|4 Comments

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 CE in Alexandria. She is one of the best-attested woman philosophers in the Greek tradition.

Watts turns this on its head: he tells the story of a life, one of singular achievement, and one in which the manner of death is not the most important part. The picture he paints is of a very remarkable woman, who became the head of her father’s school at a relatively young age and came to dominate the scholarly activity of her city, at the time one of the three most important centres of learning in the Mediterranean.

It is important to realise that although women did study philosophy at the time, and therefore also mathematics, which was seen as preparation for philosophy, very few of them were able to continue well into adulthood.…

By Jonathan Shock| May 6th, 2018|Uncategorized|2 Comments

0.4. Cartesian product

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

$def^n$ Given two sets, A and B, we can define multiplication of these two sets as the Cartesian product. The new set is defined as

$A \times B = \{(a,b): a \in A, b \in B\}$

Before looking at abstract examples, consider this case:

e.g.1. Assume there is a student in a self-catering residence and they want to make food preps for the first four days in the week. They want to know how many possible combinations they can make using fruits (between grapes and apples) and meals (pasta and meatballs, chicken wrap).

To solve this, let $A = \{ \text{ grapes, apples } \} \text{ and } B = \{ \text{pasta and meatballs, chicken wrap} \}$

Then the possible meal options are: (grapes, pasta and meatballs), (grapes, chicken wrap), (apples, pasta and meat balls) and (apples, chicken wrap).

The Cartesian Product of sets A and B would be:

$\text{A x B} = \{( \text{ grapes, pasta and meatballs}), (\text{ grapes, chicken wrap }), (\text{ apples, pasta and meat balls }), (\text{ apples, chicken wrap}) \}$

We can think of the above example in more abstract terms.…

By Yolisa| April 14th, 2018|Uncategorized|3 Comments

0.3. power sets

Recall powers (or exponents) of numbers: $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

Similarly, sets have the power operation to create new sets.

$def^n$ If A is a set, then the power set of A is another set denoted as

$\mathbb{ P }(A) = \text{ set of all subsets of A } = \{ x: x \subseteq A \}$

Recall: A is a subset of B if every element in A is also in B. Furthermore, if A is a finite set with n-elements, then we can find the number of subsets in A by using this formula:

$2^n$

To find the power set of A, we write a list of all the subsets of A first – remembering that:

the empty set is a subset of every set,
and every set is a subset of itself

Let’s look at some examples:

e.g.1. $A = \{1, 2, 3 \}$

Using the formula $2^n$ , we know that there are $2^3 = 8$ possible subsets of A, namely:

$\varnothing, \{1, 2, 3 \}, \{1 \}, \{2 \}, \{3 \}, \{1, 2 \}, \{2, 3 \} \text{ and } \{1, 3 \}$

Hence the power set is the set that contains all the above subsets:

$\mathbb{ P }(A) = \{ \varnothing, \{1, 2, 3 \}, \{1 \}, \{2 \}, \{3 \}, \{1, 2 \}, \{2, 3 \}, \{1, 3 \} \}$

Note: The cardinality (size) of $\mathbb{ P }(A) = 8 = 2^3$ where size of A= 3 elements

e.g.2.

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By Yolisa| April 10th, 2018|Uncategorized|1 Comment

https://giphy.com/gifs/infinite-boxes-vG1Dgq3JRXLMc

Consider a set $A = \{2, 3, 7\} \text{ and } B = \{2, 3, 4, 5, 6, 7\}.$ Note that every element in set A is also found in set B, however, the reverse is not true (B contains elements 4, 5 and 6 which are not in A)

Consider another case, $A = \{2n: n \in \mathbb{ N }\} = \{ 0, 2, 4, 6, ... \} \text { and } B = \mathbb{Z} = \{ ..., -2, -1, 0, 1, 2, ... \}.$ Again, we can see that every element in set A is also found in set B and similarly, everything in B cannot be found in set A. B contains negative and odd integers, which are not in A.

To describe this phenomena, mathematicians defined subsets:

$def^n$ Suppose A and B are sets. If every element in A is an element of B, then A is a subset of B and we denote this as $A \subseteq B$

If B is not a subset of A, as in the above cases, then there exists at least one element, say $x \in B \text{ such that } x \notin A. \text{ We denote this as } B \subsetneq A$

e.g.1. $\{2, 3, 5, 7, ... \} \subseteq \mathbb{ N }$ but $\{\frac{1}{3}, 2, 5, 7, ... \} \subsetneq \mathbb{ N }$ since $\frac{1}{3} \in \mathbb{ Q }$

e.g.2. $\mathbb { N } \subseteq \mathbb { Z } \subseteq \mathbb{ Q } \subseteq \mathbb{ R }$

e.g.3. $(\mathbb{ R } \times \mathbb{ N }) \subseteq (\mathbb{ R } \times \mathbb{ R })$ since $(\mathbb{ R } \times \mathbb{ N }) = \{(x, y): x \in \mathbb{ R }, y \in \mathbb{ N }\}$ and $( \mathbb{ R } \times \mathbb{ R }) = \{ (x, y): x \in \mathbb{ R }, y \in \mathbb{ R } \}$ Hint: look at what sets y is in

Every set is a subset of itself :

e.g.1.

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By Yolisa| April 10th, 2018|Uncategorized|2 Comments

Reverse Mathematics – By John Stillwell, a review

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

From Princeton University Press

I’m not sure I’ve read a mathematics book which was so hard to review, not because of the quality of the book (which is superb), but because the way of thinking is in some senses so different to the way we normally think about mathematics. This, indeed, is also the book’s best feature. This book gets you thinking about mathematics in ways which I have never explored before, and which have definitely given me a new, and I think, improved perspective on formal mathematics.

In general in mathematics we start with a set of assumptions (axioms), and explore the consequences of them. Within Euclidean geometry we start with ideas about lines, and points, and circles, and then see what other theorems can be proved from these. Within set theory too, we start with a set of ideas about equalities of sets, existence, pairings, unions etc which we hold to be true and then see what can be said of other properties of sets, which are not straightforwardly stated in the axioms.…

By Jonathan Shock| March 18th, 2018|Uncategorized|2 Comments

Singalakha’s guide to plotting rational functions

To sketch the graph of a function $k(x)=\frac{f(x)}{g(x)}$ :

Find the intercepts:
1. X-intercepts, set y=0 (there can be multiple)
2. Y-intercept, set x=0 (there can be only one)
Factorise the numerator and denominator if possible:
1. Sign table: determine where the function is negative and where it is positive
Find the Vertical asymptotes:
1. This occur if the function in the denominator is equal to zero, i.e $g(x) = 0$ , AND that in the numerator must not be zero, i.e $f(x)\ne 0$ .
Find any Horizontal asymptote:
1. If the degree of the function in the numerator, i.e $f(x)$ , is less than the degree of the function in the denominator, i.e $g(x)$ , then the horizontal asymptote is the line $y = 0$ .
2. If the degree of the function in the numerator, i.e $f(x)$ , is equal to the degree of the function in the denominator, i.e $g(x)$ , say for example, the degree of $f(x)$ and $g(x)$ is $n$ for some non-negative $n$ element of integers, then there is a horizontal asymptote.

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By Jonathan Shock| March 15th, 2018|Uncategorized|1 Comment

My vlogging channel

Hi all, I’m not sure if it counts as vlogging, or making maths videos regularly fits into a slightly more niche category, but anyway, I wanted to advertise some videos that I’ve been putting up recently. I’m doing this in an attempt to find a different communication channel with my first year maths class, and so far the videos are getting reasonable feedback. I have a long way to go in terms of making them slick, and I goof up from time to time, but it’s an interesting experience. If you have specific questions that you would like me to discuss in a video. Let me know.

In this video I talk about a method for solving inequalities involving absolute values:

How clear is this post?

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By Jonathan Shock| March 13th, 2018|Uncategorized|2 Comments

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